just do part 1 end of chapter ” Questions and problems”
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FINC 614 Intro to Finance
Homework Packet I
Group Name: _________________
Member 1 Name:
Member 2 Name:
Member 3 Name:
Member 4 Name:
Member 5 Name:
Please answer the following questions as detailed and completely as possible. Good luck!
PART 1 End of Chapter “Questions and Problems”
For the following questions you’ll need to review the problems at the back of each chapter and ensure you are using the required textbook edition per the syllabus. You can use the provided excel resources templates under the “Resources” folder on Sakai to aid in your calculations. Make sure you show your work by copying and pasting from your excel file underneath each of the Chapter questions below in order to receive full credit. A correct answer without the accompanying back-up will only receive partial credit.
A)
Chapter 2
a. # 18 Net Income and OCF answer parts (a) (b) and (c)
B) Chapter 3
a. # 2 Calculating Profitability Ratios
b. # 8 DuPont Identity
C) Chapter 4
a. # 13 Calculating Growth Rates and Future Values
b. # 14 Calculating Rates of Return
c. # 17 Calculating Present Values
D) Chapter 5
a. # 2 Present Value and Multiple Cash Flows
b. # 28 Discounted Cash Flow Analysis
c. # 30 Calculating Annuities Due
E) Chapter 6
a. # 3 Bond Prices
b. # 8 Coupon Rates
c. # 19 Interest Rate Risk
F) Chapter 7
a. # 1 Stock Value
b. # 22 Stock Valuation
c. # 27 Stock Valuation and PE
PART 2 Starbucks & Peer Ratio Analysis
During lecture, we had several breakout sessions whereas we analyzed Starbucks’ Balance Sheet, Income Statement, and Financial Ratios. Using the Ratios downloaded, you’ll select your own “Peer Group” of companies in order to formulate a financial analysis and answer the following questions below.
A) What companies did you consider for your Peer Group? Which companies did you finally select?
B) Why did you select those companies and not others?
C) Using a chart table, compare the most recent year’s ratios between Starbucks ratios to its competitor companies (the ones you selected for your Peer Group). A list of required ratios and a template chart are included in the excel resource, but include the following: Liquidity (Quick, Current, Debt-Equity); Asset Management (Asset Turnover, Receivables Turnover, Inventory Turnover); Profitability (ROA, ROE, ROI, EBITDA, Tax Rate); and Per Share (Cash Flow per Share).
D) Based on your findings, where do you see Starbucks’ outperforming its competitors? Underperforming? What led you to these conclusions?
PART 3 Starbucks & Peer Stock Valuation
A) Using the Peer Group from above, prepare a chart table comparing Starbucks’ Price using a Benchmark method.
B) Calculate the Current Value of the companies (price per share x shares outstanding)
C) What do you believe is the appropriate PE and predicted EPS for the companies? Why did you select these PE and EPS numbers?
D) Calculate the Future Value of the companies based on (C) above.
E) Based on your findings would you purchase Starbucks shares? Why or why not?
|
|
| 2 |
>Ins.
| Input boxes in tan |
| Output boxes in yellow |
| Given data in blue |
| Calculations in red |
| Answers in green |
| NOTE: Some functions used in these spreadsheets may require that |
| the “Analysis ToolPak” or “Solver Add
|
|
|
| – |
in” be installed in Excel.
| To install these, click on “Tools|Add-Ins” and select “Analysis ToolPak” |
| and “Solver Add-In.” |
2-#
|
| 1 |
8 |
| Chapter 2 |
|
| Question 1 |
8
|
|
|
|
|
|
|
|
|
|
|
|
|
| Input area: |
|
|
| Sales |
|
| Costs |
of goods sold
|
| Administrative and selling expenses |
|
| Depreciation expense |
|
| Interest expense |
| Tax rate |
|
|
|
|
|
|
|
|
|
|
|
|
|
| Output area: |
| Income Statement |
Sales
| $
| –
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
| 0 |
Costs –
Administrative and selling expenses –
Depreciation expense – 0
| EBIT |
| $ – |
Interest expense –
| EBT |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
| $ – 0 |
| Taxes |
0
| a) |
| Net income |
$ – 0
| b) |
Operating cash flow |
$ – 0
| c) |
Net income was negative because of the tax deductibility and |
| interest expense. However, the actual cash flow from operations |
| was positive because depreciation is a non-cash expense and |
| interest is a financing, not an operating, expense. |
|
|
| 3 |
-#2
|
| Chapter 3 |
|
| Question 2 |
Input area:
Sales
| Total assets |
| Total debt |
|
| Profit margin |
Output area:
Net income $ –
| Return on assets |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
| ERROR:#DIV/0! |
| Total equity |
$ – 0
|
| Return on equity |
ERROR:#DIV/0!
3-#8
Chapter 3
|
| Question 8 |
Input area:
Profit margin
| Total asset turnover |
Return on equity
Output area:
| Equity multiplier |
ERROR:#DIV/0!
| Debt/equity ratio |
ERROR:#DIV/0!
|
| 4 |
-#13
|
|
| Chapter 4 |
| Question 13 |
Input area: Output area:
|
|
|
|
| Present value |
|
|
|
|
| Year |
s
|
|
| Interest rate |
|
|
| Future value |
ERROR:#DIV/0!
Present value Years Interest rate Future value
$ – 0 ERROR:#DIV/0! ERROR:#DIV/0!
4-#14
Chapter 4
| Question 14 |
Input area: Output area:
Present value Years Interest rate Future value
ERROR:#DIV/0!
4-#1
| 7 |
Chapter 4
| Question 17 |
Output area: Input area:
Present value Years Interest rate Future value
$ – 0
| 5 |
-#2
|
|
| Chapter 5 |
Question 2
Input area:
| Payment for X |
| # of years for X |
| Payment for Y |
| # of years for Y |
|
|
| Discount rate |
Discount rate
Output area:
|
| PV at
|
| 0% |
|
| Value of X |
$0.00 |
|
| Value of Y |
$ – 0
PV at 0%
Value of X $ – 0
Value of Y $ – 0
5-#28
Chapter 5
| Question 28 |
Input area:
Output area:
Discount rate
Year
| Cash flow |
1
2
3
4
| Present value |
$ – 0
5-#30
Chapter 5
|
| Question 3 |
0
Input area:
| Loan amount |
| Loan length (months) |
| APR on loan |
Output area:
| Annuity payment |
|
|
|
|
|
|
|
|
|
|
|
|
|
| ERROR:#NUM! |
| 6 |
-#3
|
|
| Chapter 6 |
Question 3
Input area:
|
|
| Coupon rate |
|
|
| Settlement date |
|
| 1/1/00 |
|
|
| Maturity date |
|
| Yield to maturity |
|
| Coupons per year |
1
| Face value (% of par) |
|
|
| 10 |
0
| Par value ($) |
Output area:
|
| Price |
ERROR:#NUM!
6-#8
Chapter 6
Question 8
Input area:
| Years to maturity |
Yield to maturity
| Bond price |
Coupons per year
Output area:
| Present value of final payment |
ERROR:#DIV/0!
| Present value of coupon payments |
ERROR:#DIV/0!
| Coupon payment |
ERROR:#DIV/0!
| Coupon rate |
ERROR:#DIV/0!
6-#1
| 9 |
Chapter 6
| Question 19 |
Input area:
|
| Bond Bill |
:
Coupon rate
Settlement date 1/1/00
Maturity date
| 1/1/05 |
|
| Redemption (% of par) |
100
|
| # of coupons per year |
2
|
| Bond Ted |
:
Coupon rate
| 0.0% |
Settlement date 1/1/00
Maturity date
Redemption (% of par) 100
# of coupons per year 2
| Change in interest rate |
|
| 2% |
Output area:
| Price of Bond Bill |
| $ 905.29 |
| Price of Bond Ted |
ERROR:#NUM!
| % change in Bond Bill |
-9.4
|
| 7% |
| % change in Bond Ted |
ERROR:#NUM!
| All else same, the longer the maturity |
| of a bond, the ________ is its price sensitivity |
input if greater or lesser for blank space |
| to changes in interest rates. |
Bond Bill
|
| YTM |
Price
0%
| $ 1,000.00 |
|
| 1% |
$ 951.35 |
2% $ 905.29
|
| 3% |
$ 861.67 |
|
| 4% |
$ 820.35 |
|
| 5% |
$ 781.20 |
|
| 6% |
$ 744.09 |
7%
| $ 708.92 |
|
| 8% |
$ 675.56 |
|
| 9% |
$ 643.93 |
|
| 10% |
$ 613.91 |
Bond Ted
YTM
0% ERROR:#NUM!
1% ERROR:#NUM!
2% ERROR:#NUM!
3% ERROR:#NUM!
4% ERROR:#NUM!
5% ERROR:#NUM!
6% ERROR:#NUM!
7% ERROR:#NUM!
8% ERROR:#NUM!
9% ERROR:#NUM!
10% ERROR:#NUM!
YTM and
Bond Price
Bond Bill 0 0.01 0.02 0.03 0.04 0.05 0.06 7.0000000000000007E-2 0.08 0.09 0.1 1290 1233.5298846588714 1179.9547860833316 1129.1105837259636 1080.8432650561801 1035.0082557238843 991.46979716322426 950.10036806453297 910.78014642709434 873.39650916623805 837.84356648711889 Bond Ted 2450.0000000000014 2059.4268723921059 1744.7262330909948 1489.9956330299
15 |
1 1282.8124530428677 1113.4492467221712 974.2702359929923 859.2662927762741 763.69596921664038 683.80787554334461 616.62556532839983
Yield to Maturity
Bond Price
7-#1
|
|
| Chapter 7 |
Question 1
Input area:
|
|
| Dividend |
paid
| Dividend growth rate |
|
| Required return |
|
|
| Year for price |
0
Year for price 3
Year for price 15
Output area:
| Price at Year 0 |
ERROR:#DIV/0!
| Price at
|
| Year 3 |
ERROR:#DIV/0!
| Price at
|
| Year 1 |
5
ERROR:#DIV/0!
7-#22
Chapter 7
| Question 22 |
Input area:
Dividend
|
|
|
| $ 6.30 |
| Initial dividend growth rate |
| Years at growth rate |
| Final dividend growth rate |
Required return
| Today’s closing price |
$ 145.39 |
Output area:
|
| Stock price |
at year
– ERROR:#DIV/0!
Year Dividend Present value
1 $ 6.30 $ 6.30
2 $ – 0 $ – 0
3 $ – 0 $ – 0
4 $ – 0 $ – 0
5 $ – 0 $ – 0
6 $ – 0 $ – 0
7 $ – 0 $ – 0
8 $ – 0 $ – 0
9 $ – 0 $ – 0
10 $ – 0 $ – 0
| Stock price today |
$ 6.30
7-#27
Chapter 7
| Question 27 |
| Input Area: |
Year 1
|
| Year 2 |
Year 3
| Year 4 |
Stock price
| EPS |
| Earnings growth rate |
| Output Area: |
Year 1 Year 2 Year 3 Year 4
| PE ratio |
ERROR:#DIV/0! ERROR:#DIV/0! ERROR:#DIV/0! ERROR:#DIV/0!
| Average PE |
ERROR:#DIV/0!
| Next year’s EPS |
$ – 0
| Target stock price next year |
ERROR:#DIV/0!
2. SBUX
| STARBUCKS & PEER RATIOS |
|
| Starbucks |
| Company 1: |
| Company 2: |
| Company 3: |
| Liquidity |
| Quick Ratio |
| Current Ratio |
| Debt to Equity |
| Asset Management |
| Total Asset Turnover |
| Receivables Turnover |
| Inventory Turnover |
| Profitability |
| ROA % |
| ROE % |
| ROI |
| EBITDA Margin % |
| Tax Rate % |
| Per Share |
| Cash Flow per Share |
3. SBUX
| STARBUCKS VALUATION USING MULTIPLES |
Starbucks Company 1: Company 2: Company 3:
| Benchmark PE ratio X EPS |
| PE Ratio |
| EPS Ratio |
|
|
|
| Price per share |
0 0 0 0
| Benchmark price – sales ratio x Sales per share (Optional) |
Price per share
| Sales ratio |
| Sales per share |
Price per share 0 0 0 0
| Current Valuation |
Price per share
| Shares outstanding |
|
| Value |
0 0 0 0
| Future Valuation |
| PE Ratio (Appropriate) |
| EPS (Predicted) |
Value 0 0 0 0
Essentials of
Corporate Finance
ros13952_fm_i-xxxvi.indd 1 1/4/19 12:19 PM
The McGraw-Hill Education Series in Finance, Insurance, and Real Estate
FINANCIAL MANAGEMENT
Block, Hirt, and Danielsen
Foundations of Financial Management
Seventeenth Edition
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Thirteenth Edition
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ros13952_fm_i-xxxvi.indd 2 1/4/19 12:19 PM
Stephen A. Ross
Randolph W. Westerfield
University of Southern California
Bradford D. Jordan
University of Kentucky
Essentials of
Corporate Finance
Tenth Edition
ros13952_fm_i-xxxvi.indd 3 1/4/19 12:19 PM
ESSENTIALS OF CORPORATE FINANCE, TENTH EDITION
Published by McGraw-Hill Education, 2 Penn Plaza, New York, NY 10121. Copyright © 2020 by McGraw-Hill
Education. All rights reserved. Printed in the United States of America. Previous editions © 2017, 2014, and
2011. No part of this publication may be reproduced or distributed in any form or by any means, or stored in
a database or retrieval system, without the prior written consent of McGraw-Hill Education, including, but not
limited to, in any network or other electronic storage or transmission, or broadcast for distance learning.
Some ancillaries, including electronic and print components, may not be available to customers outside the
United States.
This book is printed on acid-free paper.
1 2 3 4 5 6 7 8 9 0 LWI 21 20 19
ISBN 978-1-260-01395-5
MHID 1-260-01395-2
Portfolio Manager: Charles Synovec
Product Developers: Michele Janicek, Jennifer Upton
Marketing Manager: Trina Maurer
Content Project Managers: Daryl Horrocks, Jill Eccher, Jamie Koch
Buyer: Sandy Ludovissy
Design: Matt Diamond
Content Licensing Specialist: Melissa Homer
Cover Image: ©vladitto/Shutterstock
Compositor: MPS Limited
All credits appearing on page or at the end of the book are considered to be an extension of the copyright page.
Library of Congress Cataloging-in-Publication Data
Ross, Stephen A., author. | Westerfield, Randolph W., author. |
Jordan, Bradford D., author.
Essentials of corporate finance / Stephen A. Ross, Massachusetts
Institute of Technology, Randolph W. Westerfield, University of Southern
California, Bradford D. Jordan, University of Kentucky.
Tenth edition. | New York, NY : McGraw-Hill Education, [2020] |
Includes index.
LCCN 2018056010 | ISBN 9781260013955 (student edition : alk. paper)
LCSH: Corporations—Finance.
LCC HG4026 .R676 2020 | DDC 658.15—dc23
LC record available at https://lccn.loc.gov/2018056010
The Internet addresses listed in the text were accurate at the time of publication. The inclusion of a website does
not indicate an endorsement by the authors or McGraw-Hill Education, and McGraw-Hill Education does not
guarantee the accuracy of the information presented at these sites.
mheducation.com/highered
ros13952_fm_i-xxxvi.indd 4 1/4/19 12:19 PM
v
About the Authors
Stephen A. Ross
Stephen A. Ross was the Franco Modigliani Professor of Finance and Economics at the Sloan
School of Management, Massachusetts Institute of Technology. One of the most widely published
authors in finance and economics, Professor Ross was widely recognized for his work in develop-
ing the Arbitrage Pricing Theory and his substantial contributions to the discipline through his
research in signaling, agency theory, option pricing, and the theory of the term structure of interest
rates, among other topics. A past president of the American Finance Association, he also served
as an associate editor of several academic and practitioner journals. He was a trustee of CalTech.
He died suddenly in March 2017.
Randolph W. Westerfield
Marshall School of Business, University of Southern California
Randolph W. Westerfield is Dean Emeritus of the University of Southern California’s Marshall
School of Business and is the Charles B. Thornton Professor of Finance Emeritus. Professor West-
erfield came to USC from the Wharton School, University of Pennsylvania, where he was the chair-
man of the finance department and member of the finance faculty for 20 years. He is a member of
the Board of Trustees of Oak Tree Capital Mutual Funds. His areas of expertise include corporate
financial policy, investment management, and stock market price behavior.
Bradford D. Jordan
Gatton College of Business and Economics, University of Kentucky
Bradford D. Jordan is Professor of Finance and holder of the duPont Endowed Chair in Banking
and Financial Services. He has a long-standing interest in both applied and theoretical issues in
corporate finance and has extensive experience teaching all levels of corporate finance and finan-
cial management policy. Professor Jordan has published numerous articles on issues such as cost of
capital, capital structure, and the behavior of security prices. He is a past president of the Southern
Finance Association and is coauthor of Fundamentals of Investments: Valuation and Management,
8th edition, a leading investments text, also published by McGraw-Hill Education.
ros13952_fm_i-xxxvi.indd 5 1/4/19 12:19 PM
vi
From the Authors
W hen we first wrote Essentials of Corporate Finance, we thought there might be a small niche for a briefer book that really focused on what students with widely varying
backgrounds and interests needed to carry away from an introductory finance course. We
were wrong. There was a huge niche! What we learned is that our text closely matches the
needs of instructors and faculty at hundreds of schools across the country. As a result, the
growth we have experienced through the first nine editions of Essentials has far exceeded
anything we thought possible.
With the tenth edition of Essentials of Corporate Finance, we have continued to refine our
focus on our target audience, which is the undergraduate student taking a core course in busi-
ness or corporate finance. This can be a tough course to teach. One reason is that the class is
usually required of all business students, so it is not uncommon for a majority of the students
to be nonfinance majors. In fact, this may be the only finance course many of them will ever
have. With this in mind, our goal in Essentials is to convey the most important concepts and
principles at a level that is approachable for the widest possible audience.
To achieve our goal, we have worked to distill the subject down to its bare essentials
(hence, the name of this book), while retaining a decidedly modern approach to finance. We
always have maintained that the subject of corporate finance can be viewed as the workings of
a few very powerful intuitions. We also think that understanding the “why” is just as important,
if not more so, than understanding the “how”—especially in an introductory course. Based on
the gratifying market feedback we have received from our previous editions, as well as from our
other text, Fundamentals of Corporate Finance (now in its twelfth edition), many of you agree.
By design, this book is not encyclopedic. As the table of contents indicates, we have a total
of 18 chapters. Chapter length is about 30 pages, so the text is aimed squarely at a single-term
course, and most of the book can be realistically covered in a typical semester or quarter. Writ-
ing a book for a one-term course necessarily means some picking and choosing, with regard
to both topics and depth of coverage. Throughout, we strike a balance by introducing and
covering the essentials (there’s that word again!) while leaving some more specialized topics
to follow-up courses.
The other things we always have stressed, and have continued to improve with this edition,
are readability and pedagogy. Essentials is written in a relaxed, conversational style that invites
the students to join in the learning process rather than being a passive information absorber.
We have found that this approach dramatically increases students’ willingness to read and
learn on their own. Between larger and larger class sizes and the ever-growing demands on
faculty time, we think this is an essential (!) feature for a text in an introductory course.
Throughout the development of this book, we have continued to take a hard look at what
is truly relevant and useful. In doing so, we have worked to downplay purely theoretical issues
and minimize the use of extensive and elaborate calculations to illustrate points that are either
intuitively obvious or of limited practical use.
As a result of this process, three basic themes emerge as our central focus in writing
Essentials of Corporate Finance:
ros13952_fm_i-xxxvi.indd 6 1/4/19 12:19 PM
vii
An Emphasis on Intuition We always try to separate and explain the principles at work
on a commonsense, intuitive level before launching into any specifics. The underlying ideas
are discussed first in very general terms and then by way of examples that illustrate in more
concrete terms how a financial manager might proceed in a given situation.
A Unified Valuation Approach We treat net present value (NPV) as the basic concept
underlying corporate finance. Many texts stop well short of consistently integrating this
important principle. The most basic and important notion, that NPV represents the excess
of market value over cost, often is lost in an overly mechanical approach that emphasizes
computation at the expense of comprehension. In contrast, every subject we cover is firmly
rooted in valuation, and care is taken throughout to explain how particular decisions have
valuation effects.
A Managerial Focus Students shouldn’t lose sight of the fact that financial management
concerns management. We emphasize the role of the financial manager as decision maker,
and we stress the need for managerial input and judgment. We consciously avoid “black box”
approaches to finance, and, where appropriate, the approximate, pragmatic nature of finan-
cial analysis is made explicit, possible pitfalls are described, and limitations are discussed.
Today, as we prepare once again to enter the market, our goal is to stick with and build on
the principles that have brought us this far. However, based on an enormous amount of feed-
back we have received from you and your colleagues, we have made this edition and its package
even more flexible than previous editions. We offer flexibility in coverage and pedagogy by pro-
viding a wide variety of features in the book to help students learn about corporate finance. We
also provide flexibility in package options by offering the most extensive collection of teaching,
learning, and technology aids of any corporate finance text. Whether you use just the textbook,
or the book in conjunction with other products, we believe you will find a combination with
this edition that will meet your needs.
Randolph W. Westerfield
Bradford D. Jordan
ros13952_fm_i-xxxvi.indd 7 1/4/19 12:19 PM
viii
Organization of the Text
W e designed Essentials of Corporate Finance to be as flexible and modular as possible. There are a total of nine parts, and, in broad terms, the instructor is free to decide the
particular sequence. Further, within each part, the first chapter generally contains an over-
view and survey. Thus, when time is limited, subsequent chapters can be omitted. Finally,
the sections placed early in each chapter are generally the most important, and later sections
frequently can be omitted without loss of continuity. For these reasons, the instructor has
great control over the topics covered, the sequence in which they are covered, and the depth
of coverage.
Just to get an idea of the breadth of coverage in the tenth edition of Essentials, the fol-
lowing grid presents for each chapter some of the most significant new features, as well as a
few selected chapter highlights. Of course, in every chapter, figures, opening vignettes, boxed
features, and in-chapter illustrations and examples using real companies have been thoroughly
updated as well. In addition, the end-of-chapter material has been completely revised.
Chapters Selected Topics Benefits to Users
PART ONE Overview of Financial Management
Chapter 1 New opener discussing Uber
Updated Finance Matters box on corporate
ethics
Describes ethical issues in the context of mortgage fraud,
offshoring, and tax havens.
Updated information on executive and
celebrity compensation
Highlights important developments regarding the very
current question of appropriate executive compensation.
Updated Work the Web box on stock
quotes
Goal of the firm and agency problems Stresses value creation as the most fundamental aspect of
management and describes agency issues that can arise.
Ethics, financial management, and
executive compensation
Brings in real-world issues concerning conflicts of interest
and current controversies surrounding ethical conduct and
management pay.
New proxy fight example involving Trian
Partners and Procter & Gamble
New takeover battle discussion involving
Verizon and Yahoo!
PART TWO Understanding Financial Statements and Cash Flow
Chapter 2 New opener discussing the Tax Cuts and
Jobs Act of 2017
Cash flow vs. earnings Clearly defines cash flow and spells out the differences
between cash flow and earnings.
Market values vs. book values Emphasizes the relevance of market values over book values.
New discussion of corporate taxes in light
of the TCJA
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ix
Chapters Selected Topics Benefits to Users
Chapter 3 Additional explanation of alternative
formulas for sustainable and internal growth
rates
Expanded explanation of growth rate formulas clears up
a common misunderstanding about these formulas and
the circumstances under which alternative formulas are
correct.
Updated opener on PE ratios
Updated examples on Amazon vs. Alibaba
Updated Work the Web box on financial
ratios
Discusses how to find and analyze profitability ratios.
Updated Finance Matters box on financial
ratios
Describes how to interpret ratios.
PART THREE Valuation of Future Cash Flows
Chapter 4 First of two chapters on time value of
money
Relatively short chapter introduces just the basic ideas
on time value of money to get students started on this
traditionally difficult topic.
Updated Finance Matters box on
collectibles
Chapter 5 Second of two chapters on time value of
money
Covers more advanced time value topics with numerous
examples, calculator tips, and Excel spreadsheet exhibits.
Contains many real-world examples.
Updated opener on professional athletes’
salaries
Provides a real-world example of why it’s important to
properly understand how to value costs incurred today
versus future cash inflows.
Updated Finance Matters box on lotteries
Updated Finance Matters box on student
loans
PART FOUR Valuing Stocks and Bonds
Chapter 6 New opener on negative interest on various
sovereign bonds
Discusses the importance of interest rates and how they
relate to bonds.
Bond valuation Thorough coverage of bond price/yield concepts.
Updated bond features example using
Sprint issue
Interest rates and inflation Highly intuitive discussion of inflation, the Fisher effect, and
the term structure of interest rates.
Updated “fallen angels” example using
Teva Pharmaceuticals issue
“Clean” vs. “dirty” bond prices and accrued
interest
Clears up the pricing of bonds between coupon
payment dates and also bond market quoting
conventions.
Updated Treasury quotes exhibit and
discussion
Updated historic interest rates figure
FINRA’s TRACE system and transparency in
the corporate bond market
Up-to-date discussion of new developments in fixed
income with regard to price, volume, and transactions
reporting.
“Make-whole” call provisions Up-to-date discussion of relatively new type of call provision
that has become very common.
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Chapters Selected Topics Benefits to Users
Chapter 7 Stock valuation Thorough coverage of constant and nonconstant growth models.
Updated opener on difference in dividend
payouts
Updated discussion of the NYSE, including
its acquisition by ICE and rising role of
technology of the floor
Up-to-date description of major stock market operations.
Updated Finance Matters box on the
OTCBB and the Pink Sheets markets
PART FIVE Capital Budgeting
Chapter 8 Updated opener on GE’s “Ecomagination”
program
Illustrates the growing importance of “green” business.
First of two chapters on capital budgeting Relatively short chapter introduces key ideas on an intuitive
level to help students with this traditionally difficult topic.
NPV, IRR, MIRR, payback, discounted
payback, and accounting rate of return
Consistent, balanced examination of advantages and
disadvantages of various criteria.
Chapter 9 Project cash flow Thorough coverage of project cash flows and the relevant
numbers for a project analysis.
New opener on project failures and successes Shows the importance of properly evaluating net present value.
New discussion of bonus depreciation
Scenario and sensitivity “what-if” analyses Illustrates how to actually apply and interpret these tools in a
project analysis.
PART SIX Risk and Return
Chapter 10 Updated opener on stock market
performance
Discusses the relationship between risk and return as it
relates to personal investing.
Capital market history Extensive coverage of historical returns, volatilities, and risk
premiums.
Market efficiency Efficient markets hypothesis discussed along with common
misconceptions.
Geometric vs. arithmetic returns Discusses calculation and interpretation of geometric returns.
Clarifies common misconceptions regarding appropriate use
of arithmetic vs. geometric average returns.
Updated Finance Matters box on
professional fund management and
performance
Chapter 11 Diversification, systematic, and
unsystematic risk
Illustrates basics of risk and return in a straightforward
fashion.
Updated opener on stock price reactions to
announcements
Updated beta coefficients exhibit and
associated discussion
Develops the security market line with an intuitive approach
that bypasses much of the usual portfolio theory and
statistics.
New discussion of alpha
PART SEVEN Long-Term Financing
Chapter 12 Cost of capital estimation Intuitive development of the WACC and a complete, web-
based illustration of cost of capital for a real company.
Updated WACC calculations for Eastman
Geometric vs. arithmetic growth rates Both approaches are used in practice. Clears up issues
surrounding growth rate estimates.
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xi
Chapters Selected Topics Benefits to Users
Updated section on company valuation with
the WACC
Explores the difference between valuing a project and
valuing a company.
Chapter 13 Basics of financial leverage Illustrates effect of leverage on risk and return.
Optimal capital structure Describes the basic trade-offs leading to an optimal capital
structure.
New chapter opener on Tax Cuts and Jobs Act
New discussion of the effects of the TCJA
on corporate taxes
Financial distress and bankruptcy Briefly surveys the bankruptcy process.
Chapter 14 Updated opener with Apple dividend
announcement
Raises questions about why raising dividends and
repurchasing stock would please investors.
Updated figures on aggregate dividends,
stock repurchases, and proportion of firms
paying dividends
Brings students the latest thinking and evidence on dividend
policy.
Dividends and dividend policy Describes dividend payments and the factors favoring higher
and lower payout policies. Includes recent survey results on
setting dividend policy.
Updated examples and Finance Matters
box covering buyback activity
Explores the reasons that buybacks are gaining in popularity
now, following the recent recession.
Chapter 15 IPO valuation Extensive, up-to-date discussion of IPOs, including the
1999–2000 period and the recent Alibaba IPO.
Dutch auctions Explains uniform price (“Dutch”) auctions using Google IPO
as an example.
New subsection on crowdfunding Discusses the JOBS Act and crowdfunding.
New subsection on initial coin offerings
New discussion of direct listing
Updated tables and figures on IPO initial
returns and number of offerings
PART EIGHT Short-Term Financial Management
Chapter 16 Operating and cash cycles Stresses the importance of cash flow timing.
Short-term financial planning Illustrates the creation of cash budgets and the potential
need for financing.
Updated Finance Matters box discussing
operating and cash cycles
Explores how comparing the cash cycles of companies can
reveal whether a company is performing well.
Chapter 17 Cash collection and disbursement Examination of systems used by firms to handle cash inflows
and outflows.
Credit management Analysis of credit policy and implementation.
Inventory management Brief overview of important inventory concepts.
PART NINE Topics in Business Finance
Chapter 18 New opener on corporate cash held in
international accounts
Raises questions about how currency appreciation affects
the broader economy.
Foreign exchange Covers essentials of exchange rates and their determination.
International capital budgeting Shows how to adapt the basic DCF approach to handle
exchange rates.
Updated discussion of exchange rates and
political risk
Discusses hedging and issues surrounding sovereign risk.
New discussion of the Tax Cuts and Jobs
Act
Discusses how U.S. legislation changes the way that
corporations manage their profits to minimize taxes.
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xii
Learning Solutions
I n addition to illustrating relevant concepts and presenting up-to-date coverage, Essentials of Corporate Finance strives to present the material in a way that makes it engaging and
easy to understand. To meet the varied needs of the intended audience, Essentials of Corpo-
rate Finance is rich in valuable learning tools and support.
Each feature can be categorized by the benefit to the student:
■ Real financial decisions
■ Application tools
■ Study aids
! CHAPTER-OPENING VIGNETTES
Each chapter begins with a contemporary real-world event to
introduce students to chapter concepts.
” FINANCE MATTERS BOXES
Most chapters include at least one Finance
Matters box, which takes a chapter issue and
shows how it is being used right now in every-
day financial decision making.
Exotic Bonds
Bonds come in many flavors. The unusual types are called “exotics” and can range from the fairly simple to the truly
esoteric. Take the case of mortgage-backed securities
(MBSs). MBSs are a type of securitized financial instrument.
In securitization, cash flows from financial assets are pooled
together into securities, and the securities are sold to inves-
tors. With an MBS, banks or mortgage brokers who originate
mortgages sell the mortgages to a trust. The trust pools the
mortgages and sells bonds to investors. Bondholders re-
ceive payments based on the mortgage payments made by
homeowners. During 2008, problems with MBSs skyrock-
eted due to the precipitous drop in real estate values and
the sharply increased default rates on the underlying
mortgages.
The reverse convertible is a relatively new type of
structured note. One type generally offers a high coupon
rate, but the redemption at maturity can be paid in cash at
par value or paid in shares of stock. For example, one recent
General Motors (GM) reverse convertible had a coupon rate
of 16 percent, which is a very high coupon rate in today’s in-
terest rate environment. However, at maturity, if GM’s stock
declined sufficiently, bondholders would receive a fixed
number of GM shares that were worth less than par value.
So, while the income portion of the bond return would be
high, the potential loss in par value easily could erode the
extra return.
CAT bonds are issued to cover insurance companies
against natural catastrophes. The type of natural catastro-
phe is outlined in the bond. For example, about 30 percent
of all CAT bonds protect against a North Atlantic hurricane.
The way these issues are structured is that the borrowers
can suspend payment temporarily (or even permanently) if
they have significant hurricane-related losses. These CAT
bonds may seem like pretty risky investments, but, to date,
only five have not been paid in full. Because of Hurricane
Katrina, CAT bondholders lost $190 million. CAT bondhold-
ers also lost $300 million due to the 2011 tsunami in Japan.
During 2011, two other CAT bond issues, each worth $100
million, were triggered due to an unusually active tornado
season, and a CAT bond was triggered due to the 2017
earthquake in Mexico. This bond was issued on August 4th
and the earthquake occurred on September 7th.
Perhaps the most unusual bond (and certainly the most
ghoulish) is the “death bond.” Companies such as Stone
Street Financial purchase life insurance policies from indi-
viduals who are expected to die within the next 10 years.
They then sell bonds that are paid off from the life insurance
proceeds received when the policyholders die. The return on
the bonds to investors depends on how long the policyhold-
ers live. A major risk is that if medical treatment advances
quickly, it will raise the life expectancy of the policyholders,
thereby decreasing the return to the bondholder.
FINANCE MATTERS
Generally, when you make an investment, you expect that you will get back more money in the future than you invested today.
But in December 2017, this wasn’t the case for many bond investors.
The yield on a 5-year German government bond was about negative
.20 percent, and the yields on 2-year and 5-year Japanese govern-
ment bonds were negative .14 percent and negative .09 percent, re-
spectively. In fact, in 2016, the amount of debt worldwide that had a
negative yield reached a record $13.4 trillion! And negative yields
were not restricted to government bonds, as at one point the yield on
a bond issued by chocolate maker Nestlé was negative as well.
So what happened? Central banks were in a race to the bot-
tom, lowering interest rates in an attempt to improve their domestic
economies.
This chapter takes what we have learned about the time value
of money and shows how it can be used to value one of the most
common of all financial assets, a bond. It then discusses bond fea-
Interest Rates and
Bond Valuation6
LEARNING OBJECTIVES
After studying this chapter, you should
be able to:
LO 1 Identify important bond features
and types of bonds.
LO 2 Describe bond values and why
they fluctuate.
LO 3 Discuss bond ratings and what
they mean.
LO 4 Evaluate the impact of inflation on
interest rates.
LO 5 Explain the term structure of
interest rates and the determinants
of bond yields.
PART FOUR Valuing Stocks and Bonds
REAL FINANCIAL DECISIONS
We have included two key features that help students
connect chapter concepts to how decision makers
use this material in the real world.
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xiii
! WORK THE WEB
These in-chapter boxes show students how to
research financial issues using the web and how
to use the information they find to make business
decisions. All the Work the Web boxes also include
interactive follow-up questions and exercises.
! CHAPTER CASES
Located at the end of most chapters, these cases focus on
hypothetical company situations that embody corporate
finance topics. Each case presents a new scenario, data, and
a dilemma. Several questions at the end of each case require
students to analyze and focus on all of the material they
learned from the chapters in that part. These are great for
homework or in-class exercises and discussions!
Most of the information is self-explanatory. The Price and Yield columns show the price and yield
to maturity of the issues based on their most recent sales. If you need more information about a
particular issue, clicking on it will give you more details such as coupon dates and call dates.
QUESTIONS
1. Go to this website and find the last bond shown in the accompanying table. When was
this bond issued? What was the size of the bond issue? What were the yield to maturity
and price when the bond was issued?
2. When you search for Chevron bonds (CVX), you will find bonds for several companies
listed. Why do you think Chevron has bonds issued with different corporate names?
W R K T H E W E B
Bond quotes have become more available with the rise of the web. One site where you can find current bond prices (from TRACE) is finra-markets.morningstar.com/BondCenter. We went to
the site and entered “AZO” for AutoZone, the well-known auto parts company. We found a total of
10 bond issues outstanding. Here you see the information we pulled up.
EXPLANATORY WEB LINKS ►
These web links are provided in the margins of the text.
They are specifically selected to accompany text material
and provide students and instructors with a quick way to
check for additional information using the internet.
Bond Price Reporting
In 2002, transparency in the corporate bond market began to improve dramatically. Under
new regulations, corporate bond dealers are now required to report trade information
through what is known as the Trade Reporting and Compliance Engine (TRACE). A nearby
Work the Web box shows how to get TRACE prices.
As we mentioned before, the U.S. Treasury market is the largest securities market in the
world. As with bond markets in general, it is an OTC market, so there is limited transpar
ency. However, unlike the situation with bond markets in general, trading in Treasury issues,
particularly recently issued ones, is very heavy. Each day, representative prices for outstand-
ing Treasury issues are reported.
Figure 6.3 shows a portion of the daily Treasury note and bond listings from The Wall Street
Journal online. The only difference between a Treasury note and a Treasury bond is that notes
have 10 years or less to maturity at the time of issuance. The entry that begins “5/15/2030” is
highlighted. Reading from left to right, the “5/15/2030” tells us that the bond’s maturity is May
15, 2030. The 6.250 is the bond’s coupon rate. Treasury bonds all make semiannual payments
To learn more about
TRACE, visit www.finra
.org.
To purchase newly issued
corporate bonds, go to
www.incapital.com.
204 P A R T 4 Valuing Stocks and Bonds
Although Chris is aware of the bond features, he is
uncertain as to the costs and benefits of some features,
so he isn’t clear on how each feature would affect the
coupon rate of the bond issue. You are Renata’s assis-
tant, and she has asked you to prepare a memo to Chris
describing the effect of each of the following bond fea-
tures on the coupon rate of the bond. She also would like
you to list any advantages or disadvantages of each
feature.
Mark Sexton and Todd Story, the owners of S&S Air, have decided to expand their operations. They in-
structed their newly hired financial analyst, Chris Guthrie,
to enlist an underwriter to help sell $20 million in new
10-year bonds to finance construction. Chris has entered
into discussions with Renata Harper, an underwriter from
the firm of Crowe & Mallard, about which bond features
S&S Air should consider and what coupon rate the issue
will likely have.
CHAPTER CASE
Financing S&S Air’s Expansion Plans with a Bond Issue
1. The security of the bond—that is, whether the
bond has collateral.
2. The seniority of the bond.
3. The presence of a sinking fund.
4. A call provision with specified call dates and call
prices.
5. A deferred call accompanying the preceding call
provision.
6. A make-whole call provision.
7. Any positive covenants. Also, discuss several
possible positive covenants S&S Air might
consider.
8. Any negative covenants. Also, discuss several
possible negative covenants S&S Air might
consider.
9. A conversion feature (note that S&S Air is not a
publicly traded company).
10. A floating rate coupon.
Q U E S T I O N S
APPLICATION TOOLS
Because there is more than one way to solve prob-
lems in corporate finance, we include many sections
that encourage students to learn or brush up on dif-
ferent problem-solving methods, including financial
calculator and Excel spreadsheet skills.
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xiv
WHAT’S ON THE WEB? ►
These end-of-chapter activities show
students how to use and learn from the
vast amount of financial resources
available on the internet.
EXCEL MASTER ICONS ►
Topics covered in the comprehensive
Excel Master supplement (found in
Connect) are indicated by an icon in the
margin.
SPREADSHEET STRATEGIES ►
The unique Spreadsheet Strategies feature
is also in a self-contained section, showing
students how to set up spreadsheets to solve
problems—a vital part of every business
student’s education.
6.1 Bond Quotes You can find current bond prices at finra-markets.morningstar.com/
BondCenter. You want to find the bond prices and yields for bonds issued by Pfizer. Enter
the ticker symbol “PFE” to do a search. What is the shortest-maturity bond issued by
Pfizer that is outstanding? What is the longest-maturity bond? What is the credit rating for
Pfizer’s bonds? Do all of the bonds have the same credit rating? Why do you think this is?
6.2 Yield Curves You can find information regarding the most current bond yields at
money.cnn.com. Go there and graph the yield curve for U.S. Treasury bonds. What is
WHAT’S ON
THE WEB?
BONDS AND BOND VALUATION
When a corporation (or government) wishes to borrow money from the public on a long-
term basis, it usually does so by issuing, or selling, debt securities that are generically called
bonds. In this section, we describe the various features of corporate bonds and some of the
terminology associated with bonds. We then discuss the cash flows associated with a bond
and how bonds can be valued using our discounted cash flow procedure.
6.1
coverage online
Excel
Master
HOW TO CALCULATE BOND PRICES AND YIELDS USING A
SPREADSHEET
Like financial calculators, most spreadsheets have fairly elaborate routines available for calculating
bond values and yields; many of these routines involve details that we have not discussed. However,
setting up a simple spreadsheet to calculate prices or yields is straightforward, as our next two
spreadsheets show:
SPREADSHEET
STRATEGIES
A B C D E F G H
1
2 Using a spreadsheet to calculate bond yields
3
4 Suppose we have a bond with 22 years to maturity, a coupon rate of 8 percent, and a price of
5 $960.17. If the bond makes semiannual payments, what is its yield to maturity?
6
7 Settlement date: 1/1/00
8 Maturity date: 1/1/22
9 Annual coupon rate: .08
10 Bond price (% of par): 96.017
11 Face value (% of par): 100
12 Coupons per year: 2
13 Yield to maturity: .084
14
$ CALCULATOR HINTS
Calculator Hints is a self-contained section
occurring in various chapters that first
introduces students to calculator basics and
then illustrates how to solve problems with
the calculator. Appendix D goes into more
detailed instructions by solving problems with
two specific calculators.
$ EXCEL SIMULATIONS
Indicated by an Excel icon next to
applicable end-of-chapter ques-
tions and problems, Excel simulation
exercises are available for selected
problems in Connect. For even
more spreadsheet practice, check
out Excel Master, also available in
Connect.
HOW TO CALCULATE BOND PRICES AND YIELDS USING A FINANCIAL
CALCULATOR
Many financial calculators have fairly sophisticated built-in bond valuation routines. However, these vary
quite a lot in implementation, and not all financial calculators have them. As a result, we will illustrate a
simple way to handle bond problems that will work on just about any financial calculator.
To begin, of course, we first remember to clear out the calculator! Next, for Example 6.3, we have
two bonds to consider, both with 12 years to maturity. The first one sells for $935.08 and has a 10 per-
cent coupon rate. To find its yield, we can do the following:
Enter 12 100 −935.08 1,000
I/ Y
Solve for 11
Notice that here we have entered both a future value of $1,000, representing the bond’s face value,
and a payment of 10 percent of $1,000, or $100, per year, representing the bond’s annual coupon.
Also notice that we have a negative sign on the bond’s price, which we have entered as the present
value.
For the second bond, we now know that the relevant yield is 11 percent. It has a 12 percent coupon
CALCULATOR
HINTS
INTERMEDIATE (Questions 18–33)
18. Bond Price Movements. Bond X is a premium bond making semiannual
payments. The bond has a coupon rate of 7.5 percent, a YTM of 6 percent,
and 13 years to maturity. Bond Y is a discount bond making semiannual
payments. This bond has a coupon rate of 6 percent, a YTM of 7.5 percent,
and also 13 years to maturity. What are the prices of these bonds today
assuming both bonds have a $1,000 par value? If interest rates remain
unchanged, what do you expect the prices of these bonds to be in one year?
In three years? In eight years? In 12 years? In 13 years? What’s going on
here? Illustrate your answers by graphing bond prices versus time to maturity.
19. Interest Rate Risk. Both Bond Bill and Bond Ted have 5.8 percent coupons,
make semiannual payments, and are priced at par value. Bond Bill has 5
years to maturity, whereas Bond Ted has 25 years to maturity. If interest
rates suddenly rise by 2 percent, what is the percentage change in the price
LO 2
LO 2
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xv
! LEARNING OBJECTIVES
Each chapter begins with a number of learning objectives that
are key to the student’s understanding of the chapter. Learn-
ing objectives also are linked to end-of-chapter problems and
test bank questions.
CRITICAL THINKING QUESTIONS ►
Every chapter ends with a set of critical thinking
questions that challenge the students to apply the
concepts they learned in the chapter to new situations.
! PEDAGOGICAL USE OF COLOR
We continue to use a full-color palette in Essen-
tials not only to make the text more inviting, but,
more important, as a functional element to help
students follow the discussion. In almost every
chapter, color plays an important, largely self-
evident role.
$ CONCEPT QUESTIONS
Chapter sections are intentionally kept short to promote a
step-by-step, building-block approach to learning. Each sec-
tion is then followed by a series of short concept questions
that highlight the key ideas just presented. Students use these
questions to make sure they can identify and understand the
most important concepts as they read.
What do professional athletes Alex Avila, Yu Darvish, and Jimmy Garoppolo have in common? All three signed big
contracts in 2018. The contract values were reported as $8.25 mil
lion, $126 million, and $137.5 million, respectively. That’s definitely
major league money, but, even so, reported numbers like these can
be misleading. For example, in January 2018, Avila signed with the
Arizona Diamondbacks. His contract called for a salary of $4 million
in 2018 and $4.25 million for 2019. Not bad, especially for someone
who makes a living using the “tools of ignorance” ( jock jargon for a
catcher’s equipment).
A closer look at the numbers shows that Alex, Yu, and Jimmy
did pretty well, but nothing like the quoted figures. Using Yu’s
contract as an example, although the value was reported to be
5
LEARNING OBJECTIVES
After studying this chapter, you should
be able to:
LO 1 Determine the future value and
present value of investments with
multiple cash flows.
LO 2 Calculate loan payments, and find
the interest rate on a loan.
LO 3 Describe how loans are amortized
or paid off.
LO 4 Explain how interest rates are
quoted (and misquoted).
CRITICAL THINKING AND CONCEPTS REVIEW
LO 2 14.1 Dividend Policy Irrelevance. How is it possible that dividends are so
important, but, at the same time, dividend policy is irrelevant?
LO 4 14.2 Stock Repurchases. What is the impact of a stock repurchase on a
company’s debt ratio? Does this suggest another use for excess cash?
LO 1 14.3 Life Cycle Theory of Dividends. Explain the life cycle theory of dividend
payments. How does it explain corporate dividend payments that are seen
in the stock market?
LO 1 14.4 Dividend Chronology. On Friday, December 8, Hometown Power Co.’s
board of directors declares a dividend of 75 cents per share payable on
Wednesday, January 17, to shareholders of record as of Wednesday, January
3. When is the ex-dividend date? If a shareholder buys stock before that
date, who gets the dividends on those shares, the buyer or the seller?
LO 1 14.5 Alternative Dividends. Some corporations, like one British company that
offers its large shareholders free crematorium use, pay dividends in kind
(i.e., offer their services to shareholders at below-market cost). Should
mutual funds invest in stocks that pay these dividends in kind? (The
fundholders do not receive these services.)
14.6 Dividends and Stock Price. If increases in dividends tend to be followed
Thursday,
January
15
Declaration
date
Wednesday,
January
28
Ex-dividend
date
Friday,
January
30
Record
date
Monday,
February
16
Payment
date
1. Declaration date: The board of directors declares a payment of dividends.
2. Ex-dividend date: A share of stock goes ex dividend on the date the seller
is entitled to keep the dividend; under NYSE rules, shares are traded ex
dividend on and after the second business day before the record date.
3. Record date: The declared dividends are distributable to those who are
shareholders of record as of this specific date.
4. Payment date: The dividend checks are mailed to shareholders of record.
Example of the
procedure for
dividend payment
FIGURE 14.1
CONCEPT QUESTIONS
6.1a What are the cash flows associated with a bond?
6.1b What is the general expression for the value of a bond?
6.1c Is it true that the only risk associated with owning a bond is that the issuer will not
make all the payments? Explain.
STUDY AIDS
We want students to get the most from this book
and this course, and we realize that students have
different learning styles and study needs. We there-
fore present a number of study features to appeal to
a wide range of students.
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xvi
$ NUMBERED EXAMPLES
Separate numbered and titled examples are extensively
integrated into the chapters. These examples provide detailed
applications and illustrations of the text material in a step-by-
step format. Each example is completely self-contained so that
students don’t have to search for additional information. Based
on our classroom testing, these examples are among the most
useful learning aids because they provide both detail and
explanation.
EXAMPLE 11.4 Portfolio Variance and Standard Deviation
In Example 11.3, what are the standard deviations on the two portfolios? To answer, we first have to
calculate the portfolio returns in the two states. We will work with the second portfolio, which has
50 percent in Stock A and 25 percent in each of Stocks B and C. The relevant calculations can be
summarized as follows:
State of
Economy
Probability
of State
Returns
Stock A Stock B Stock C
Boom .40 10% 15% 20%
Bust .60 8 4 0
SUMMARY TABLES ►
These tables succinctly restate key principles,
results, and equations. They appear whenever
it is useful to emphasize and summarize a
group of related concepts.
I. Internal growth rate
Internal growth rate = ROA × b ___________ 1 − ROA × b
where
ROA = Return on assets = Net income/Total assets
b = Plowback (retention) ratio
= Addition to retained earnings/Net income
= 1 – Dividend payout ratio
The internal growth rate is the maximum growth rate that can be achieved with no external
financing of any kind.
II. Sustainable growth rate
Sustainable growth rate = ROE × b ___________ 1 − ROE × b
where
ROE = Return on equity = Net income/Total equity
b = Plowback (retention) ratio
= Addition to retained earnings/Net income
= 1 – Dividend payout ratio
The sustainable growth rate is the maximum growth rate that can be achieved with no
external equity financing while maintaining a constant debt-equity ratio.
Summary of internal
and sustainable
growth rates
TABLE 3.9
$ KEY TERMS
These are printed in blue the first time they
appear and are defined within the text and
in the margin.
RATIO ANALYSIS
Another way of avoiding the problems involved in comparing companies of different sizes is
to calculate and compare financial ratios. Such ratios are ways of comparing and investigat-
ing the relationships between different pieces of financial information. We cover some of
the more common ratios next, but there are many others that we don’t touch on.
One problem with ratios is that different people and different sources frequently don’t
compute them in exactly the same way, and this leads to much confusion. The specific defi-
nitions we use here may or may not be the same as ones you have seen or will see elsewhere.
If you are ever using ratios as a tool for analysis, you should be careful to document how you
3.2
coverage online
Excel
Master
financial ratios
Relationships determined
from a firm’s financial
information and used for
KEY EQUATIONS ►
These are called out in the text and iden-
tified by equation numbers. Appendix B
shows the key equations by chapter.
$ HIGHLIGHTED PHRASES
Throughout the text, important ideas are presented separately
and printed in boxes to indicate their importance to the students.
Maximize the market value of the existing owners’ equity.
Total Debt Ratio The total debt ratio takes into account all debts of all maturities to all
creditors. It can be defined in several ways, the easiest of which is:
Total debt ratio =
Total assets – Total equity
__________________ Total assets [3.4]
=
$3,630 – 2,625
______________ $3,630 = .28 times
In this case, an analyst might say that Prufrock uses 28 percent debt.1 Whether this is high
or low or whether it even makes any difference depends on whether or not capital structure
matters, a subject we discuss in a later chapter.
Prufrock has $.28 in debt for every $1 in total assets. Therefore, there is $.72 in equity
(= $1 − .28) for every $.28 in debt. With this in mind, we can define two useful variations
on the total debt ratio, the debt-equity ratio and the equity multiplier:
Debt-equity ratio = Total debt/Total equity [3.5]
= $.28/$!.72 = .!38 times
Equity multiplier = Total assets / Total equity [3.6]
= $1 / $.72 = 1.38 times
The fact that the equity multiplier is 1 plus the debt-equity ratio is not a coincidence:
Equity multiplier = Total assets / Total equity = $1 / $.72 = 1.38 times
= (Total equity + Total debt)/ Total equity
= 1 + Debt-equity ratio = 1.38 times
The thing to notice here is that given any one of these three ratios, you can immediately
calculate the other two, so they all say exactly the same thing.
Times Interest Earned Another common measure of long-term solvency is the times
interest earned (TIE) ratio. Once again, there are several possible (and common) definitions,
but we’ll stick with the most traditional:
Times interest earned ratio = EBIT _______ Interest [3.7]
= $741 _____ $141 = 5.26 times
As the name suggests, this ratio measures how well a company has its interest obligations
covered, and it is often called the interest coverage ratio. For Prufrock, the interest bill is
covered 5.26 times over.
ros13952_fm_i-xxxvi.indd 16 1/4/19 12:19 PM
xvii
CHAPTER SUMMARY AND CONCLUSIONS ”
These paragraphs review the chapter’s key points and provide closure to the chapter.
SUMMARY AND CONCLUSIONS
This chapter has described how to go about putting together a discounted cash flow analysis
and evaluating the results. In it, we covered:
1. The identification of relevant project cash flows. We discussed project cash flows and
described how to handle some issues that often come up, including sunk costs,
opportunity costs, financing costs, net working capital, and erosion.
2. Preparing and using pro forma, or projected, financial statements. We showed how
pro forma financial statement information is useful in coming up with projected cash
flows.
3. The use of scenario and sensitivity analysis. These tools are widely used to evaluate
the impact of assumptions made about future cash flows and NPV estimates.
$ CHAPTER REVIEW AND
SELF-TEST PROBLEMS
Review and self-test problems appear
after the chapter summaries. Detailed
answers to the self-test problems im-
mediately follow. These questions
and answers allow students to test
their abilities in solving key problems
related to the content of the chapter.
These problems are mapped to similar
problems in the end-of-chapter mate-
rial. The aim is to help students work
through difficult problems using the
authors’ work as an example.
CHAPTER REVIEW AND SELF-TEST PROBLEMS
9.1 Calculating Operating Cash Flow. Mater Pasta, Inc., has projected a sales
volume of $1,432 for the second year of a proposed expansion project. Costs
normally run 70 percent of sales, or about $1,002 in this case. The depreciation
expense will be $80, and the tax rate is 22 percent. What is the operating cash
flow? (See Problem 9.)
9.2 Scenario Analysis. A project under consideration costs $500,000, has a five-year
life, and has no salvage value. Depreciation is straight-line to zero. The required
return is 15 percent, and the tax rate is 21 percent. Sales are projected at 400
units per year. Price per unit is $3,000, variable cost per unit is $1,900, and fixed
costs are $250,000 per year. No net working capital is required.
Suppose you think the unit sales, price, variable cost, and fixed cost projections
are accurate to within 5 percent. What are the upper and lower bounds for these pro-
jections? What is the base-case NPV? What are the best- and worst-case scenario
NPVs? (See Problem 21.)
END-OF-CHAPTER QUESTIONS
AND PROBLEMS ►
We have found that many students learn better
when they have plenty of opportunity to practice.
We therefore provide extensive end-of-chapter
questions and problems linked to Learning
Objectives. The questions and problems are
generally separated into three levels—Basic,
Intermediate, and Challenge. All problems are
fully annotated so that students and instructors
can readily identify particular types. Throughout
the text, we have worked to supply interesting
problems that illustrate real-world applications
of chapter material. Answers to selected end-of-
chapter problems appear in Appendix C.
QUESTIONS AND PROBLEMS
BASIC (Questions 1–22)
1. Calculating Payback. What is the payback period for the following set of
cash flows?
Year Cash Flow
0 −$7,800
1 3,100
2 3,200
3 2,200
4 1,400
2. Calculating Payback. An investment project provides cash inflows of $865
per year for eight years. What is the project payback period if the initial cost
is $3,100? What if the initial cost is $4,300? What if it is $7,900?
3. Calculating Payback. Stenson, Inc., imposes a payback cutoff of three years
for its international investment projects. If the company has the following
two projects available, should it accept either of them?
LO 1
LO 1
LO 1
Select problems are available in McGraw-Hill Connect. Please see the pack-
aging options section of the preface for more information.
ros13952_fm_i-xxxvi.indd 17 1/4/19 12:19 PM
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xx
T his edition of Essentials has more options than ever in terms of the textbook, instructor supplements, student supplements, and multimedia products. Mix and match to create
a package that is perfect for your course!
Assurance of Learning Ready
Assurance of learning is an important element of many accreditation standards. Essentials of
Corporate Finance, tenth edition, is designed specifically to support your assurance of learn-
ing initiatives. Each chapter in the book begins with a list of numbered learning objectives that
appear throughout the end-of-chapter problems and exercises. Every test bank question also is
linked to one of these objectives, in addition to level of difficulty, topic area, Bloom’s Taxonomy
level, and AACSB skill area. Connect, McGraw-Hill’s online homework solution, and EZ
Test, McGraw-Hill’s easy-to-use test bank software, can search the test bank by these and other
categories, providing an engine for targeted Assurance of Learning analysis and assessment.
AACSB Statement
McGraw-Hill Education is a proud corporate member of AACSB International. Under-
standing the importance and value of AACSB Accreditation, Essentials of Corporate Fi-
nance, tenth edition, has sought to recognize the curricula guidelines detailed in the AACSB
standards for business accreditation by connecting selected questions in the test bank to the
general knowledge and skill guidelines found in the AACSB standards.
The statements contained in Essentials of Corporate Finance, tenth edition, are provided
only as a guide for the users of this text. The AACSB leaves content coverage and assessment
within the purview of individual schools, the mission of the school, and the faculty. While
Essentials of Corporate Finance, tenth edition, and the teaching package make no claim of
any specific AACSB qualification or evaluation, we have, within the test bank, labeled se-
lected questions according to the six general knowledge and skills areas.
McGraw-Hill Customer Care Contact Information
At McGraw-Hill, we understand that getting the most from new technology can be chal-
lenging. That’s why our services don’t stop after you purchase our products. You can e-mail
our Product Specialists 24 hours a day to get product training online. Or you can search
our knowledge bank of Frequently Asked Questions on our support website. For Customer
Support, call 800-331-5094, or visit mpss.mhhe.com. One of our Technical Support Analysts
will be able to assist you in a timely fashion.
Instructor Supplements
■ Instructor’s Manual (IM)
Prepared by LaDoris Baugh, Athens State University
A great place to find new lecture ideas! This annotated outline for each chapter
includes Lecture Tips, Real-World Tips, Ethics Notes, suggested PowerPoint slides,
and, when appropriate, a video synopsis.
Comprehensive Teaching
and Learning Package
ros13952_fm_i-xxxvi.indd 20 1/4/19 12:19 PM
xxi
■ Solutions Manual (SM)
Prepared by Joseph Smolira, Belmont University, Bradford D. Jordan, University of
Kentucky
The Essentials Solutions Manual provides detailed solutions to the extensive end-
of-chapter material, including concept review questions, quantitative problems, and
cases. Select chapters also contain calculator solutions.
■ Test Bank
Prepared by Joseph Hegger, University of Missouri
Great format for a better testing process! All questions closely link with the text
material, listing section number, Learning Objective, Bloom’s Taxonomy Question
Type, and AACSB topic when applicable. Each chapter covers a breadth of topics
and types of questions, including questions that test the understanding of the key
terms; questions patterned after the learning objectives, concept questions, chapter-
opening vignettes, boxes, and highlighted phrases; multiple-choice and true/false
problems patterned after the end-of-chapter questions, in basic, intermediate, and
challenge levels; and essay questions to test problem-solving skills and more advanced
understanding of concepts. Each chapter also includes new problems that pick up
questions directly from the end-of-chapter material and converts them into parallel
test bank questions. For your reference, each test bank question in this part is linked
with its corresponding question in the end-of-chapter section.
■ PowerPoint Presentation System
Prepared by LaDoris Baugh, Athens State University
Customize our content for your course! This presentation has been thoroughly revised
to include more lecture-oriented slides, as well as exhibits and examples both from the
book and from outside sources. Applicable slides have web links that take you directly
to specific internet sites or spreadsheet links to show an example in Excel. You also
can go to the Notes Page function for more tips in presenting the slides. Additional
PowerPoint slides work through example problems for instructors to show in class. If
you already have PowerPoint installed on your computer, you have the ability to edit,
print, or rearrange the complete presentation to meet your specific needs.
■ Computerized Test Bank
TestGen is a complete, state-of-the-art generator and editing application software that
allows instructors to quickly and easily select test items from McGraw-Hill’s test bank
content. The instructors then can organize, edit, and customize questions and answers
to rapidly generate tests for paper or online administration. Questions can include
stylized text, symbols, graphics, and equations that are inserted directly into questions
using built-in mathematical templates. TestGen’s random generator provides the option
to display different text or calculated number values each time questions are used. With
both quick-and-simple test creation and flexible and robust editing tools, TestGen is a
complete test generator system for today’s educators.
■ Excel Simulations
Expanded for this edition! With 180 Excel simulation questions now included in Connect,
McGraw-Hill’s Ross series is the unparalleled leader in offering students the opportunity
to practice using the Excel functions they will use throughout their careers in finance.
■ Corporate Finance Videos
New for this edition, brief and engaging conceptual videos (and accompanying questions)
help students to master the building blocks of the Corporate Finance course.
ros13952_fm_i-xxxvi.indd 21 1/4/19 12:19 PM
xxii
Student Supplements
■ Excel Resources
A great resource for those seeking additional practice, students can access Excel
template problems and the Excel Master tutorial designed by Brad Jordan and Joe
Smolira.
■ Narrated Lecture Videos
Updated for this edition, the Narrated Lecture Videos provide real-world examples
accompanied by step-by-step instructions and explanations for solving problems
presented in the chapter. The Concept Checks from the text also are integrated into
the slides to reinforce the key topics in the chapter. Designed specifically to appeal to
different learning styles, the videos provide a visual and audio explanation of topics
and problems.
Teaching Support
Along with having access to all of the same material your students can view through Con-
nect, you also have password-protected access to the Instructor’s Manual, solutions to
end-of-chapter problems and cases, Instructor’s Excel Master, PowerPoint, Excel template
solutions, video clips, and video projects and questions.
ros13952_fm_i-xxxvi.indd 22 1/4/19 12:19 PM
xxiii
C learly, our greatest debt is to our many colleagues (and their students) around the world who, like us, wanted to try an alternative to what they were using and made the
switch to our text. Our plan for developing and improving Essentials, tenth edition, revolved
around the detailed feedback we received from many of our colleagues over the years who
had an interest in the book and regularly teach the introductory course. These dedicated
scholars and teachers to whom we are very grateful are:
Vaughn S. Armstrong, Utah Valley University
Juan Avendano, Augsburg College
R. Brian Balyeat, Xavier University
John Barkoulas, Georgia Southern University
Laura Beal, University of Nebraska at Omaha
Stephen G. Buell, Lehigh University
Manfen Chen, University of Southern Indiana
Su-Jane Chen, Metropolitan University College of Denver
Ingyu Chiou, Eastern Illinois University
Paul Chiou, Northeastern University
Brandon Cline, Mississippi State University
Susan Coleman, University of Hartford
Bruce A. Costa, University of Montana
Maria E. de Boyrie, New Mexico State University
David Dineen, Seton Hall University
Alan Eastman, Indiana University of Pennsylvania
David Eckmann, University of Miami
Dan Ervin, Salisbury University
Jocelyn Evans, College of Charleston
Ramon T. Franklin, Clemson University
Sharon H. Garrison, University of Arizona
Victoria Geyfman, Bloomsburg University of Pennsylvania
Kimberly R. Goodwin, University of Southern Mississippi
Michael Gunderson, Purdue University
Karen L. Hamilton, Lasell College
Mahfuzul Haque, Indiana State University
John J. Harrington Jr., Seton Hall University
John Hatem, Georgia Southern University
Rodrigo Hernandez, Radford University
Keith Jakob, University of Montana
Abu Jalal, Suffolk University
Acknowledgments
ros13952_fm_i-xxxvi.indd 23 1/4/19 12:19 PM
xxiv
Marlin Jensen, Auburn University
Samuel Kyle Jones, Stephen F. Austin State University
Douglas Jordan, Sonoma State University
Ashok K. Kapoor, Augsburg College
Howard Keen, Temple University
Marvin Keene, Coastal Carolina University
James D. Keys, Florida International University
Ladd Kochman, Kennesaw State University
Denise Letterman, Robert Morris University–Pittsburgh, PA
Seongyeon (Sonya) Lim, DePaul University
Alethea Lindsay, Grambling State University
Qingfeng “Wilson” Liu, James Madison University
Angelo Luciano, Columbia College–Chicago
Suzan Murphy, University of Tennessee
Ohanes Paskelian, University of Houston Downtown
Milena Petrova, Syracuse University
Ted Pilger, Southern Illinois University–Carbondale
Alexandros P. Prezas, Suffolk University
Charles Reback, University of South Carolina Upstate
Thomas A. Rhee, California State University–Long Beach
Jong C. Rhim, University of Southern Indiana
Clarence C. Rose, Radford University
Camelia S. Rotaru, St. Edward’s University
Andrew Saporoschenko, St. Louis University
Michael J. Seiler, Old Dominion University
Roger Severns, Minnesota State University–Mankato
Gowri Shankar, University of Washington–Bothell
Luke Sparvero, SUNY–Oswego
Carolyn Spencer, Dowling College
Andrew Spieler, Hofstra University
Glenn Tanner, Texas State University
John Thornton, Kent State University
Hiep Tran, California State University–Sacramento
Cathyann Tully, Kean University
James A. Turner, Weber State University
John B. White, United States Coast Guard Academy
Susan White, University of Maryland
Fred Yeager, Saint Louis University
Tarek Saad Zaher, Indiana State University
We owe a special debt to our colleagues for their dedicated work on the many supple-
ments that accompany this text: LaDoris Baugh, for her development of the Instructor’s
Manual and PowerPoint slides, and Joseph Hegger, for his extensive revision and improve-
ment of the Test Bank.
ros13952_fm_i-xxxvi.indd 24 1/4/19 12:19 PM
xxv
We also thank Joseph C. Smolira, Belmont University, for his work on this edition. Joe
worked closely with us to develop the solutions manual, along with many of the vignettes
and real-world examples we have added to this edition.
Steve Hailey and Emily Bello did outstanding work on this edition of Essentials. To
them fell the unenviable task of technical proofreading, and, in particular, careful checking
of each and every calculation throughout the text.
Finally, in every phase of this project, we have been privileged to have the complete
and unwavering support of a great organization, McGraw-Hill Education. We especially
thank the MHE sales organization. The suggestions they provided, their professionalism in
assisting potential adopters, and their service to current adopters have been a major factor
in our success.
We are deeply grateful to the select group of professionals who served as our devel-
opment team on this edition: Chuck Synovec, Director; Jennifer Upton, Senior Product
Developer; Trina Maurer, Senior Marketing Manager; Jill Eccher and Jamie Koch, Content
Project Managers; Matt Diamond, Senior Designer; and Michele Janicek, Lead Product
Developer. Others at McGraw-Hill, too numerous to list here, have improved the book in
countless ways.
Throughout the development of this edition, we have taken great care to discover and
eliminate errors. Our goal is to provide the best textbook available on the subject. To ensure
that future editions are error-free, we will gladly offer $10 per arithmetic error to the first
individual reporting it as a modest token of our appreciation. More than this, we would
like to hear from instructors and students alike. Please send your comments to Dr. Brad
Jordan, c/o Editorial—Finance, McGraw-Hill Education, 120 S. Riverside Drive, 12th Floor,
Chicago, IL 60606.
Randolph W. Westerfield
Bradford D. Jordan
ros13952_fm_i-xxxvi.indd 25 1/4/19 12:19 PM
xxvi
PART ONE OVERVIEW OF FINANCIAL MANAGEMENT
1 Introduction to Financial Management 1
PART TWO UNDERSTANDING FINANCIAL STATEMENTS AND CASH FLOW
2 Financial Statements, Taxes, and Cash Flow 22
3 Working with Financial Statements 50
PART THREE VALUATION OF FUTURE CASH FLOWS
4 Introduction to Valuation: The Time Value of Money 97
5 Discounted Cash Flow Valuation 122
PART FOUR VALUING STOCKS AND BONDS
6 Interest Rates and Bond Valuation 165
7 Equity Markets and Stock Valuation 205
PART FIVE CAPITAL BUDGETING
8 Net Present Value and Other Investment Criteria 237
9 Making Capital Investment Decisions 275
PART SIX RISK AND RETURN
10 Some Lessons from Capital Market History 310
11 Risk and Return 350
PART SEVEN LONG-TERM FINANCING
12 Cost of Capital 389
13 Leverage and Capital Structure 424
14 Dividends and Dividend Policy 457
15 Raising Capital 487
PART EIGHT SHORT-TERM FINANCIAL MANAGEMENT
16 Short-Term Financial Planning 521
17 Working Capital Management 553
PART NINE TOPICS IN BUSINESS FINANCE
18 International Aspects of Financial Management 589
APPENDICES
A Mathematical Tables 616
B Key Equations 624
C Answers to Selected End-of-Chapter Problems 627
D Using the HP-10B and TI BA II Plus Financial Calculators 631
Brief Contents
ros13952_fm_i-xxxvi.indd 26 1/4/19 12:19 PM
xxvii
Contents
PART ONE OVERVIEW OF FINANCIAL MANAGEMENT
1 Introduction to Financial
Management 1
1.1 Finance: A Quick Look 2
The Four Basic Areas 2
Corporate Finance 2
Investments 2
Financial Institutions 3
International Finance 3
Why Study Finance? 3
Marketing and Finance 3
Accounting and Finance 3
Management and Finance 4
You and Finance 4
1.2 Business Finance and the Financial Manager 4
What Is Business Finance? 4
The Financial Manager 5
Financial Management Decisions 5
Capital Budgeting 6
Capital Structure 6
Working Capital Management 6
Conclusion 6
1.3 Forms of Business Organization 7
Sole Proprietorship 7
Partnership 7
Corporation 8
A Corporation by Another Name . . . 9
1.4 The Goal of Financial Management 9
Profit Maximization 9
The Goal of Financial Management in a Corporation 10
A More General Financial Management Goal 10
Sarbanes-Oxley Act 11
1.5 The Agency Problem and Control of
the Corporation 12
Agency Relationships 12
Management Goals 12
Do Managers Act in the Stockholders’ Interests? 13
Managerial Compensation 13
Control of the Firm 13
Conclusion 14
Stakeholders 15
1.6 Financial Markets and the Corporation 15
Cash Flows to and from the Firm 15
Primary versus Secondary Markets 15
Primary Markets 16
Secondary Markets 16
Summary and Conclusions 18
Critical Thinking and Concepts Review 18
What’s on the Web? 20
CHAPTER CASE: The McGee Cake Company 21
PART TWO UNDERSTANDING FINANCIAL STATEMENTS AND CASH FLOW
2 Financial Statements, Taxes,
and Cash Flow 22
2.1 The Balance Sheet 23
Assets: The Left-Hand Side 23
Liabilities and Owners’ Equity: The Right-Hand Side 23
Net Working Capital 24
Liquidity 25
Debt versus Equity 25
Market Value versus Book Value 26
2.2 The Income Statement 27
GAAP and the Income Statement 28
Noncash Items 28
Time and Costs 29
Earnings Management 30
2.3 Taxes 31
Corporate Tax Rates 31
Average versus Marginal Tax Rates 32
2.4 Cash Flow 33
Cash Flow from Assets 34
Operating Cash Flow 34
Capital Spending 35
Change in Net Working Capital 35
Conclusion 35
A Note on “Free” Cash Flow 36
Cash Flow to Creditors and Stockholders 36
Cash Flow to Creditors 36
Cash Flow to Stockholders 36
Conclusion 37
An Example: Cash Flows for Dole Cola 37
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xxviii C O N T E N T S
Operating Cash Flow 37
Net Capital Spending 38
Change in NWC and Cash Flow from Assets 38
Cash Flow to Creditors and Stockholders 38
Summary and Conclusions 39
Chapter Review and Self-Test Problem 40
Answer to Chapter Review and Self-Test Problem 41
Critical Thinking and Concepts Review 42
Questions and Problems 43
What’s on the Web? 47
Excel Master It! Problem 48
CHAPTER CASE: Cash Flows and Financial Statements at
Sunset Boards, Inc. 49
3 Working with Financial Statements 50
3.1 Standardized Financial Statements 51
Common-Size Balance Sheets 52
Common-Size Income Statements 53
3.2 Ratio Analysis 54
Short-Term Solvency, or Liquidity, Measures 55
Current Ratio 55
Quick (or Acid-Test) Ratio 56
Cash Ratio 56
Long-Term Solvency Measures 57
Total Debt Ratio 57
Times Interest Earned 57
Cash Coverage 58
Asset Management, or Turnover, Measures 58
Inventory Turnover and Days’ Sales in Inventory 58
Receivables Turnover and Days’ Sales in Receivables 59
Total Asset Turnover 60
Profitability Measures 60
Profit Margin 61
Return on Assets 61
Return on Equity 61
Market Value Measures 61
Price-Earnings Ratio 62
Price-Sales Ratio 62
Market-to-Book Ratio 62
Enterprise Value-EBITDA Ratio 62
3.3 The DUPont Identity 64
An Expanded DuPont Analysis 66
3.4 Internal and Sustainable Growth 68
Dividend Payout and Earnings Retention 68
ROA, ROE, and Growth 69
The Internal Growth Rate 69
The Sustainable Growth Rate 69
Determinants of Growth 70
A Note on Sustainable Growth Rate Calculations 72
3.5 Using Financial Statement Information 72
Why Evaluate Financial Statements? 72
Internal Uses 73
External Uses 73
Choosing a Benchmark 73
Time-Trend Analysis 73
Peer Group Analysis 73
Problems with Financial Statement Analysis 79
Summary and Conclusions 80
Chapter Review and Self-Test Problems 81
Answers to Chapter Review and Self-Test Problems 83
Critical Thinking and Concepts Review 84
Questions and Problems 85
What’s on the Web? 93
Excel Master It! Problem 94
CHAPTER CASE: Ratios and Financial Planning
at S&S Air, Inc. 95
PART THREE VALUATION OF FUTURE CASH FLOWS
4 Introduction to Valuation: The Time
Value of Money 97
4.1 Future Value and Compounding 98
Investing for a Single Period 98
Investing for More Than One Period 98
4.2 Present Value and Discounting 104
The Single-Period Case 105
Present Values for Multiple Periods 105
4.3 More on Present and Future Values 108
Present versus Future Value 108
Determining the Discount Rate 109
Finding the Number of Periods 112
Summary and Conclusions 115
Chapter Review and Self-Test Problems 116
Answers to Chapter Review and Self-Test Problems 116
Critical Thinking and Concepts Review 117
Questions and Problems 118
What’s on the Web? 121
Excel Master It! Problem 121
5 Discounted Cash Flow Valuation 122
5.1 Future and Present Values of Multiple Cash Flows 123
Future Value with Multiple Cash Flows 123
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C O N T E N T S xxix
Present Value with Multiple Cash Flows 126
A Note on Cash Flow Timing 130
5.2 Valuing Level Cash Flows: Annuities and Perpetuities 131
Present Value for Annuity Cash Flows 132
Annuity Tables 133
Finding the Payment 134
Finding the Rate 136
Future Value for Annuities 137
A Note on Annuities Due 137
Perpetuities 138
5.3 Comparing Rates: The Effect of Compounding Periods 140
Effective Annual Rates and Compounding 140
Calculating and Comparing Effective Annual Rates 141
EARs and APRs 142
EARs, APRs, Financial Calculators, and Spreadsheets 144
5.4 Loan Types and Loan Amortization 145
Pure Discount Loans 145
Interest-Only Loans 145
Amortized Loans 146
Summary and Conclusions 150
Chapter Review and Self-Test Problems 151
Answers to Chapter Review and Self-Test Problems 152
Critical Thinking and Concepts Review 154
Questions and Problems 154
What’s on the Web? 162
Excel Master It! Problem 163
CHAPTER CASE: S&S Air’s Mortgage 164
PART FOUR VALUING STOCKS AND BONDS
6 Interest Rates and Bond
Valuation 165
6.1 Bonds and Bond Valuation 166
Bond Features and Prices 166
Bond Values and Yields 166
Interest Rate Risk 169
Finding the Yield to Maturity: More Trial and Error 171
6.2 More on Bond Features 175
Is It Debt or Equity? 176
Long-Term Debt: The Basics 176
The Indenture 177
Terms of a Bond 178
Security 178
Seniority 179
Repayment 179
The Call Provision 179
Protective Covenants 180
6.3 Bond Ratings 180
6.4 Some Different Types of Bonds 182
Government Bonds 182
Zero Coupon Bonds 183
Floating-Rate Bonds 184
Other Types of Bonds 185
6.5 Bond Markets 186
How Bonds Are Bought and Sold 186
Bond Price Reporting 188
A Note on Bond Price Quotes 188
6.6 Inflation and Interest Rates 190
Real versus Nominal Rates 190
The Fisher Effect 190
6.7 Determinants of Bond Yields 192
The Term Structure of Interest Rates 192
Bond Yields and the Yield Curve: Putting It All Together 193
Conclusion 195
Summary and Conclusions 196
Chapter Review and Self-Test Problems 196
Answers to Chapter Review and Self-Test Problems 197
Critical Thinking and Concepts Review 197
Questions and Problems 199
What’s on the Web? 203
Excel Master It! Problem 203
CHAPTER CASE: Financing S&S Air’s Expansion Plans with
a Bond Issue 204
7 Equity Markets and Stock
Valuation 205
7.1 Common Stock Valuation 206
Cash Flows 206
Some Special Cases 207
Zero Growth 208
Constant Growth 208
Nonconstant Growth 211
Components of the Required Return 213
Stock Valuation Using Comparables, or Comps 214
7.2 Some Features of Common and Preferred Stock 216
Common Stock Features 216
Shareholder Rights 216
Proxy Voting 217
Classes of Stock 217
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xxx C O N T E N T S
Other Rights 218
Dividends 218
Preferred Stock Features 219
Stated Value 219
Cumulative and Noncumulative Dividends 219
Is Preferred Stock Really Debt? 219
7.3 The Stock Markets 220
Dealers and Brokers 220
Organization of the NYSE 221
Members 221
Operations 222
Floor Activity 222
NASDAQ Operations 223
ECNs 224
Stock Market Reporting 227
Summary and Conclusions 228
Chapter Review and Self-Test Problems 228
Answers to Chapter Review and Self-Test Problems 229
Critical Thinking and Concepts Review 229
Questions and Problems 230
What’s on the Web? 235
Excel Master It! Problem 235
CHAPTER CASE: Stock Valuation at Ragan, Inc. 236
PART FIVE CAPITAL BUDGETING
8 Net Present Value and Other
Investment Criteria 237
8.1 Net Present Value 238
The Basic Idea 238
Estimating Net Present Value 239
8.2 The Payback Rule 242
Defining the Rule 242
Analyzing the Rule 244
Redeeming Qualities of the Rule 244
Summary of the Rule 245
8.3 The Average Accounting Return 246
8.4 The Internal Rate of Return 248
Problems with the IRR 251
Nonconventional Cash Flows 251
Mutually Exclusive Investments 253
Redeeming Qualities of the IRR 255
The Modified Internal Rate of Return (MIRR) 256
Method 1: The Discounting Approach 256
Method 2: The Reinvestment Approach 256
Method 3: The Combination Approach 256
MIRR or IRR: Which Is Better? 257
8.5 The Profitability Index 257
8.6 The Practice of Capital Budgeting 258
Summary and Conclusions 261
Chapter Review and Self-Test Problems 262
Answers to Chapter Review and Self-Test Problems 262
Critical Thinking and Concepts Review 263
Questions and Problems 266
What’s on the Web? 272
Excel Master It! Problem 272
CHAPTER CASE: Bullock Gold Mining 274
9 Making Capital Investment
Decisions 275
9.1 Project Cash Flows: A First Look 276
Relevant Cash Flows 276
The Stand-Alone Principle 276
9.2 Incremental Cash Flows 277
Sunk Costs 277
Opportunity Costs 277
Side Effects 278
Net Working Capital 278
Financing Costs 278
Other Issues 279
9.3 Pro Forma Financial Statements and
Project Cash Flows 279
Getting Started: Pro Forma Financial Statements 279
Project Cash Flows 280
Project Operating Cash Flow 280
Project Net Working Capital and
Capital Spending 281
Projected Total Cash Flow and Value 281
The Tax Shield Approach 282
9.4 More on Project Cash Flow 283
A Closer Look at Net Working Capital 283
Depreciation 284
Modified ACRS (MACRS) Depreciation 285
Bonus Depreciation 286
Book Value versus Market Value 286
An Example: The Majestic Mulch
and Compost Company (MMCC) 287
Operating Cash Flows 288
Changes in NWC 288
Capital Spending 289
Total Cash Flow and Value 289
Conclusion 291
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C O N T E N T S xxxi
9.5 Evaluating NPV Estimates 291
The Basic Problem 291
Forecasting Risk 292
Sources of Value 293
9.6 Scenario and Other What-If Analyses 293
Getting Started 293
Scenario Analysis 294
Sensitivity Analysis 296
9.7 Additional Considerations in Capital Budgeting 297
Managerial Options and Capital Budgeting 297
Contingency Planning 297
Strategic Options 299
Conclusion 299
Capital Rationing 299
Soft Rationing 299
Hard Rationing 300
Summary and Conclusions 300
Chapter Review and Self-Test Problems 301
Answers to Chapter Review and Self-Test Problems 302
Critical Thinking and Concepts Review 302
Questions and Problems 304
Excel Master It! Problem 308
CHAPTER CASE: Conch Republic Electronics 309
PART SIX RISK AND RETURN
10 Some Lessons from Capital Market
History 310
10.1 Returns 311
Dollar Returns 311
Percentage Returns 313
10.2 The Historical Record 315
A First Look 316
A Closer Look 316
10.3 Average Returns: The First Lesson 321
Calculating Average Returns 321
Average Returns: The Historical Record 321
Risk Premiums 321
The First Lesson 322
10.4 The Variability of Returns: The Second Lesson 323
Frequency Distributions and Variability 323
The Historical Variance and Standard Deviation 323
The Historical Record 326
Normal Distribution 327
The Second Lesson 328
2008: The Bear Growled and Investors Howled 329
Using Capital Market History 330
More on the Stock Market Risk Premium 332
10.5 More on Average Returns 334
Arithmetic versus Geometric Averages 334
Calculating Geometric Average Returns 334
Arithmetic Average Return or Geometric Average Return? 336
10.6 Capital Market Efficiency 337
Price Behavior in an Efficient Market 337
The Efficient Markets Hypothesis 338
Some Common Misconceptions about the EMH 339
The Forms of Market Efficiency 340
Summary and Conclusions 341
Chapter Review and Self-Test Problems 341
Answers to Chapter Review and Self-Test Problems 342
Critical Thinking and Concepts Review 342
Questions and Problems 343
What’s on the Web? 347
Excel Master It! Problem 347
CHAPTER CASE: A Job at S&S Air 348
11 Risk and Return 350
11.1 Expected Returns and Variances 351
Expected Return 351
Calculating the Variance 353
11.2 Portfolios 355
Portfolio Weights 355
Portfolio Expected Returns 355
Portfolio Variance 357
11.3 Announcements, Surprises,
and Expected Returns 358
Expected and Unexpected Returns 358
Announcements and News 359
11.4 Risk: Systematic and Unsystematic 360
Systematic and Unsystematic Risk 361
Systematic and Unsystematic Components of Return 361
11.5 Diversification and Portfolio Risk 362
The Effect of Diversification: Another Lesson
from Market History 362
The Principle of Diversification 363
Diversification and Unsystematic Risk 364
Diversification and Systematic Risk 364
11.6 Systematic Risk and Beta 365
The Systematic Risk Principle 365
Measuring Systematic Risk 365
Portfolio Betas 368
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xxxii C O N T E N T S
11.7 The Security Market Line 369
Beta and the Risk Premium 369
The Reward-to-Risk Ratio 370
The Basic Argument 371
The Fundamental Result 372
The Security Market Line 374
Market Portfolios 374
The Capital Asset Pricing Model 374
11.8 The SML and the Cost of Capital: A Preview 376
The Basic Idea 376
The Cost of Capital 377
Summary and Conclusions 377
Chapter Review and Self-Test Problems 378
Answers to Chapter Review and Self-Test Problems 379
Critical Thinking and Concepts Review 380
Questions and Problems 382
What’s on the Web? 386
Excel Master It! Problem 386
CHAPTER CASE: The Beta for FLIR Systems 388
PART SEVEN LONG-TERM FINANCING
12 Cost of Capital 389
12.1 The Cost of Capital: Some Preliminaries 390
Required Return versus Cost of Capital 390
Financial Policy and Cost of Capital 391
12.2 The Cost of Equity 392
The Dividend Growth Model Approach 392
Implementing the Approach 392
Estimating g 392
Advantages and Disadvantages of the Approach 393
The SML Approach 394
Implementing the Approach 394
Advantages and Disadvantages of the Approach 395
12.3 The Costs of Debt and Preferred Stock 395
The Cost of Debt 396
The Cost of Preferred Stock 396
12.4 The Weighted Average Cost of Capital 397
The Capital Structure Weights 397
Taxes and the Weighted Average Cost of Capital 398
Solving the Warehouse Problem and Similar Capital Budgeting
Problems 400
Calculating the WACC for Eastman Chemical 401
Eastman’s Cost of Equity 403
Eastman’s Cost of Debt 404
Eastman’s WACC 407
12.5 Divisional and Project Costs of Capital 407
The SML and the WACC 408
Divisional Cost of Capital 409
The Pure Play Approach 409
The Subjective Approach 410
12.6 Company Valuation with the WACC 411
Summary and Conclusions 414
Chapter Review and Self-Test Problems 414
Answers to Chapter Review and Self-Test Problems 414
Critical Thinking and Concepts Review 415
Questions and Problems 416
What’s on the Web? 422
Excel Master It! Problem 422
CHAPTER CASE: Cost of Capital for Layton Motors 423
13 Leverage and Capital Structure 424
13.1 The Capital Structure Question 425
13.2 The Effect of Financial Leverage 426
The Impact of Financial Leverage 426
Financial Leverage, EPS, and ROE: An Example 426
EPS versus EBIT 427
Corporate Borrowing and Homemade Leverage 429
13.3 Capital Structure and the Cost of Equity Capital 431
M&M Proposition I: The Pie Model 431
The Cost of Equity and Financial Leverage: M&M Proposition II 431
Business and Financial Risk 433
13.4 Corporate Taxes and Capital Structure 434
The Interest Tax Shield 434
Taxes and M&M Proposition I 435
Conclusion 435
13.5 Bankruptcy Costs 437
Direct Bankruptcy Costs 437
Indirect Bankruptcy Costs 437
13.6 Optimal Capital Structure 438
The Static Theory of Capital Structure 438
Optimal Capital Structure and the Cost of Capital 439
Capital Structure: Some Managerial Recommendations 441
Taxes 441
Financial Distress 441
13.7 Observed Capital Structures 442
13.8 A Quick Look at the Bankruptcy Process 444
Liquidation and Reorganization 444
Bankruptcy Liquidation 444
Bankruptcy Reorganization 445
Financial Management and the Bankruptcy Process 446
Agreements to Avoid Bankruptcy 448
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C O N T E N T S xxxiii
Summary and Conclusions 449
Chapter Review and Self-Test Problems 449
Answers to Chapter Review and Self-Test Problems 450
Critical Thinking and Concepts Review 450
Questions and Problems 451
What’s on the Web? 455
Excel Master It! Problem 455
CHAPTER CASE: Stephenson Real Estate
Recapitalization 456
14 Dividends and Dividend Policy 457
14.1 Cash Dividends and Dividend Payment 458
Cash Dividends 458
Standard Method of Cash Dividend Payment 459
Dividend Payment: A Chronology 459
More on the Ex-Dividend Date 460
14.2 Does Dividend Policy Matter? 462
An Illustration of the Irrelevance of
Dividend Policy 462
Current Policy: Dividends Set Equal to
Cash Flow 462
Alternative Policy: Initial Dividend Greater Than
Cash Flow 462
A Test 463
Some Real-World Factors Favoring a Low Payout 463
Taxes 463
Flotation Costs 464
Dividend Restrictions 464
Some Real-World Factors Favoring a High Payout 464
Desire for Current Income 464
Tax and Legal Benefits from High Dividends 465
Clientele Effects: A Resolution of Real-World Factors? 466
14.3 Stock Repurchases: An Alternative to
Cash Dividends 466
Cash Dividends versus Repurchase 468
Real-World Considerations in a Repurchase 469
Share Repurchase and EPS 470
14.4 What We Know and Do Not Know about Dividend and
Payout Policies 471
Dividends and Dividend Payers 471
Corporations Smooth Dividends 474
Putting It All Together 474
Some Survey Evidence on Dividends 476
14.5 Stock Dividends and Stock Splits 477
Value of Stock Splits and Stock Dividends 478
The Benchmark Case 478
Popular Trading Range 478
Reverse Splits 478
Summary and Conclusions 479
Chapter Review and Self-Test Problem 480
Answer to Chapter Review and Self-Test Problem 481
Critical Thinking and Concepts Review 481
Questions and Problems 482
What’s on the Web? 485
CHAPTER CASE: Electronic Timing, Inc. 486
15 Raising Capital 487
15.1 The Financing Life Cycle of a Firm: Early-Stage Financing
and Venture Capital 488
Venture Capital 488
Some Venture Capital Realities 489
Choosing a Venture Capitalist 489
Conclusion 490
15.2 Selling Securities to the Public: The Basic Procedure 490
Crowdfunding 491
Initial Coin Offerings 493
15.3 Alternative Issue Methods 493
15.4 Underwriters 495
Choosing an Underwriter 495
Types of Underwriting 495
Firm Commitment Underwriting 495
Best Efforts Underwriting 496
Dutch Auction Underwriting 496
The Green Shoe Provision 497
The Aftermarket 497
Lockup Agreements 497
The Quiet Period 498
Direct Listing 498
15.5 IPOs and Underpricing 498
Evidence on Underpricing 499
IPO Underpricing: The 1999–2000 Experience 500
The Partial Adjustment Phenomenon 504
Why Does Underpricing Exist? 505
15.6 New Equity Sales and the Value of the Firm 507
15.7 The Cost of Issuing Securities 507
15.8 Issuing Long-Term Debt 512
15.9 Shelf Registration 513
Summary and Conclusions 514
Chapter Review and Self-Test Problem 515
Answer to Chapter Review and Self-Test Problem 515
Critical Thinking and Concepts Review 515
Questions and Problems 518
What’s on the Web? 519
CHAPTER CASE: S&S Air Goes Public 520
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xxxiv C O N T E N T S
PART EIGHT SHORT-TERM FINANCIAL MANAGEMENT
16 Short-Term Financial Planning 521
16.1 Tracing Cash and Net Working Capital 522
16.2 The Operating Cycle and the Cash Cycle 524
Defining the Operating and Cash Cycles 524
The Operating Cycle 524
The Cash Cycle 525
The Operating Cycle and the Firm’s
Organizational Chart 525
Calculating the Operating and Cash Cycles 526
The Operating Cycle 527
The Cash Cycle 527
Interpreting the Cash Cycle 528
16.3 Some Aspects of Short-Term Financial Policy 530
The Size of the Firm’s Investment in Current Assets 530
Alternative Financing Policies for Current Assets 532
Which Financing Policy Is Best? 534
Current Assets and Liabilities in Practice 535
16.4 The Cash Budget 536
Sales and Cash Collections 536
Cash Outflows 537
The Cash Balance 537
16.5 Short-Term Borrowing 539
Unsecured Loans 539
Secured Loans 539
Accounts Receivable Financing 539
Inventory Loans 540
Other Sources 540
16.6 A Short-Term Financial Plan 541
Summary and Conclusions 542
Chapter Review and Self-Test Problems 542
Answers to Chapter Review and Self-Test Problems 543
Critical Thinking and Concepts Review 544
Questions and Problems 545
What’s on the Web? 551
Excel Master It! Problem 551
Chapter Case: Piepkorn Manufacturing Working Capital
Management, Part 1 552
17 Working Capital Management 553
17.1 Float and Cash Management 553
Reasons for Holding Cash 554
The Speculative and Precautionary Motives 554
The Transaction Motive 554
Benefits of Holding Cash 554
Understanding Float 555
Disbursement Float 555
Collection Float and Net Float 555
Float Management 556
Ethical and Legal Questions 557
Electronic Data Interchange and Check 21: The End of
Float? 557
17.2 Cash Management: Collection, Disbursement, and
Investment 558
Cash Collection and Concentration 558
Components of Collection Time 558
Cash Collection 559
Lockboxes 559
Cash Concentration 559
Managing Cash Disbursements 560
Increasing Disbursement Float 560
Controlling Disbursements 561
Investing Idle Cash 562
Temporary Cash Surpluses 563
Characteristics of Short-Term Securities 563
Some Different Types of Money Market Securities 564
17.3 Credit and Receivables 565
Components of Credit Policy 565
Terms of Sale 566
The Basic Form 566
The Credit Period 566
Cash Discounts 567
Credit Instruments 568
Optimal Credit Policy 569
The Total Credit Cost Curve 569
Organizing the Credit Function 569
Credit Analysis 570
Credit Information 570
Credit Evaluation and Scoring 571
Collection Policy 571
Monitoring Receivables 571
Collection Effort 572
17.4 Inventory Management 573
The Financial Manager and Inventory Policy 573
Inventory Types 573
Inventory Costs 574
17.5 Inventory Management Techniques 574
The ABC Approach 574
The Economic Order Quantity Model 575
Inventory Depletion 576
Carrying Costs 576
Shortage Costs 577
Total Costs 577
Extensions to the EOQ Model 579
Safety Stocks 579
Reorder Points 579
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C O N T E N T S xxxv
Managing Derived-Demand Inventories 579
Materials Requirements Planning 580
Just-in-Time Inventory 581
Summary and Conclusions 582
Chapter Review and Self-Test Problems 582
Answers to Chapter Review and Self-Test Problems 583
Critical Thinking and Concepts Review 583
Questions and Problems 585
What’s on the Web? 587
Chapter Case: Piepkorn Manufacturing Working
Capital Management, Part 2 588
PART NINE TOPICS IN BUSINESS FINANCE
18 International Aspects of Financial
Management 589
18.1 Terminology 590
18.2 Foreign Exchange Markets and Exchange Rates 591
Exchange Rates 592
Exchange Rate Quotations 593
Cross-Rates and Triangle Arbitrage 593
Types of Transactions 595
18.3 Purchasing Power Parity 596
Absolute Purchasing Power Parity 596
Relative Purchasing Power Parity 598
The Basic Idea 598
The Result 599
Currency Appreciation and Depreciation 600
18.4 Exchange Rates and Interest Rates 600
Covered Interest Arbitrage 600
Interest Rate Parity 601
18.5 Exchange Rate Risk 602
Short-Run Exposure 602
Long-Run Exposure 603
Translation Exposure 604
Managing Exchange Rate Risk 605
18.6 Political Risk 605
The Tax Cuts and Jobs Act 606
Managing Political Risk 606
Summary and Conclusions 607
Chapter Review and Self-Test Problems 608
Answers to Chapter Review and Self-Test Problems 608
Critical Thinking and Concepts Review 609
Questions and Problems 611
What’s on the Web? 613
Excel Master It! Problem 614
Chapter Case: S&S Air Goes International 615
Appendix A Mathematical Tables 616
Appendix B Key Equations 624
Appendix C Answers to Selected End-
of-Chapter Problems 627
Appendix D Using the HP-10B and TI BA II Plus Financial
Calculators 631
Glossary 634
Name Index 641
Subject Index 642
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xxxvi
FINANCE MATTERS
CHAPTER 1 Corporate Ethics 11
CHAPTER 2 What Is Warren Buffett’s Tax Rate? 33
CHAPTER 3 How Fast Is Too Fast? 71
What’s in a Ratio? 79
CHAPTER 4 Collectibles as Investments? 111
CHAPTER 5 Jackpot! 128
An Unwelcome Christmas Present 150
CHAPTER 6 Exotic Bonds 186
CHAPTER 7 The Wild, Wild West of Stock Trading 226
CHAPTER 9 When Things Go Wrong . . . 292
CHAPTER 10 The Super Guide to Investing 331
Can the Pros Beat the Market? 339
CHAPTER 11 Beta, Beta, Who’s Got the Beta? 367
CHAPTER 12 EVA: An Old Idea Moves into the Modern Age 399
The Cost of Capital, Texas Style 402
CHAPTER 13 Bankruptcy, “Prepack” Style 447
CHAPTER 14 Stock Buybacks: No End in Sight 470
CHAPTER 15 IPO Underpricing around the World 502
The (Mis)Pricing of Palm, Inc. 504
Anatomy of an IPO 510
CHAPTER 16 Cash Cycle Comparison 529
CHAPTER 17 Supply Chain Management 581
CHAPTER 18 McPricing 598
List of Boxes
ros13952_fm_i-xxxvi.indd 36 1/4/19 12:19 PM
Please visit us at essentialsofcorporatefinance.blogspot.com for the latest developments in the world of corporate finance.
1
Please visit us at essentialsofcorporatefinance.blogspot.com for the latest developments in the world of corporate finance.
In 2009, Travis Kalanick and Garrett Camp started the ride-sharing app Uber. Uber shot out of the gate, completing more than five
billion rides by the middle of 2017. Even though Uber was losing
more than $100 million per quarter, its market value reached $70
billion, with Kalanick’s personal wealth exceeding $6 billion. Unfor-
tunately, Kalanick was accused of knowing about sexual harass-
ment in the company and doing nothing to resolve the problem.
Then, he was videotaped berating an Uber driver. As a result, he
was forced to step down as CEO of the company in June 2017, al-
though he remained the chair of the company’s board of directors.
And, reminiscent of a runaway car, in August 2017, Kalanick was
sued by a major shareholder for fraud, breach of contract, and
breach of fiduciary responsibility. In 2018, Kalanick became the CEO
of start-up City Storage Systems, which focuses on distressed real
estate, such as parking lots and abandoned malls, and turning them
into spaces for new industries.
Understanding Kalanick’s journey from the founder of a ride-sharing app, to corporate
executive, to embattled board chair, and finally to CEO takes us into issues involving the
corporate form of organization, corporate goals, and corporate control—all of which we dis-
cuss in this chapter. And if you are willing to share the ride with us, you’re going to learn an
uber-lot as you read.
Introduction to Financial
Management1
LEARNING OBJECTIVES
After studying this chapter, you should
be able to:
LO 1 Discuss the basic types of financial
management decisions and the
role of the financial manager.
LO 2 Identify the goal of financial
management.
LO 3 Compare the financial implications
of the different forms of business
organizations.
LO 4 Describe the conflicts of interest
that can arise between managers
and owners.
PART ONE Overview of Financial Management
To begin our study of financial management, we address two central issues. First: What is corporate, or business, finance, and what is the role of the financial manager? Second:
What is the goal of financial management?
ros13952_ch01_001-021.indd 1 12/22/18 5:46 PM
2 P A R T 1 Overview of Financial Management
FINANCE: A QUICK LOOK
Before we plunge into our study of “corp. fin.,” we think a quick overview of the finance
field might be a good idea. Our goal is to clue you in on some of the most important areas
in finance and some of the career opportunities available in each. We also want to illustrate
some of the ways finance fits in with other areas such as marketing, management, and
accounting.
The Four Basic Areas
Traditionally, financial topics are grouped into four main areas:
1. Corporate finance
2. Investments
3. Financial institutions
4. International finance
We discuss each of these next.
Corporate Finance The first of these four areas, corporate finance, is the main sub-
ject of this book. We begin covering this subject in our next section, so we will wait until
then to get into any details. One thing we should note is that the term corporate finance
seems to imply that what we cover is only relevant to corporations, but the truth is that al-
most all of the topics we consider are much broader than that. Maybe business finance
would be a little more descriptive, but even this is too narrow because at least half of the
subjects we discuss in the pages ahead are really basic financial ideas and principles applica-
ble across all the various areas of finance and beyond.
Investments Broadly speaking, the investments area deals with financial assets such as
stocks and bonds. Some of the more important questions include
1. What determines the price of a financial asset, such as a share of stock?
2. What are the potential risks and rewards associated with investing in financial assets?
3. What is the best mixture of financial assets to hold?
Students who specialize in the investments area have various career opportunities. Being a
stockbroker is one of the most common. Stockbrokers often work for large companies such
as Merrill Lynch, advising customers on what types of investments to consider and helping
them make buy and sell decisions. Financial advisers play a similar role but are not necessar-
ily brokers.
Portfolio management is a second investments-related career path. Portfolio managers,
as the name suggests, manage money for investors. For example, individual investors fre-
quently buy into mutual funds. Such funds are a means of pooling money that is then in-
vested by a portfolio manager. Portfolio managers also invest and manage money for pension
funds, insurance companies, and many other types of institutions.
Security analysis is a third area. A security analyst researches individual investments,
such as stock in a particular company, and makes a determination as to whether the price is
right. To do so, an analyst delves deeply into company and industry reports, along with a
variety of other information sources. Frequently, brokers and portfolio managers rely on
security analysts for information and recommendations.
These investments-related areas, like many areas in finance, share an interesting feature.
If they are done well, they can be very rewarding financially (translation: You can make a lot
1.1
For job descriptions in
finance and other areas,
visit www.careers-in
-business.com.
ros13952_ch01_001-021.indd 2 12/22/18 5:46 PM
C H A P T E R 1 Introduction to Financial Management 3
of money). The bad news, of course, is that they can be very demanding and very competi-
tive, so they are definitely not for everybody.
Financial Institutions Financial institutions are basically businesses that deal pri-
marily in financial matters. Banks and insurance companies would probably be the most
familiar to you. Institutions such as these employ people to perform a wide variety of fi-
nance-related tasks. For example, a commercial loan officer at a bank would evaluate
whether a particular business has a strong enough financial position to warrant extending a
loan. At an insurance company, an analyst would decide whether a particular risk was suit-
able for insuring and what the premium should be.
International Finance International finance isn’t so much an area as it is a special-
ization within one of the main areas we described earlier. In other words, careers in interna-
tional finance generally involve international aspects of either corporate finance,
investments, or financial institutions. For example, some portfolio managers and security
analysts specialize in non-U.S. companies. Similarly, many U.S. businesses have extensive
overseas operations and need employees familiar with such international topics as exchange
rates and political risk. Banks frequently are asked to make loans across country lines, so
international specialists are needed there as well.
Why Study Finance?
Who needs to know finance? In a word, you. In fact, there are many reasons you need a
working knowledge of finance even if you are not planning a finance career. We explore
some of these reasons next.
Marketing and Finance If you are interested in marketing, you need to know finance
because, for example, marketers constantly work with budgets, and they need to understand
how to get the greatest payoff from marketing expenditures and programs. Analyzing costs
and benefits of projects of all types is one of the most important aspects of finance, so the
tools you learn in finance are vital in marketing research, the design of marketing and distri-
bution channels, and product pricing, to name a few areas.
Financial analysts rely heavily on marketing analysts, and the two frequently work to-
gether to evaluate the profitability of proposed projects and products. As we will see in a
later chapter, sales projections are a key input in almost every type of new product analysis,
and such projections are often developed jointly between marketing and finance.
Beyond this, the finance industry employs marketers to help sell financial products
such as bank accounts, insurance policies, and mutual funds. Financial services marketing
is one of the most rapidly growing types of marketing, and successful financial services
marketers are very well compensated. To work in this area, you obviously need to under-
stand financial products.
Accounting and Finance For accountants, finance is required reading. In smaller
businesses in particular, accountants often are required to make financial decisions as well
as perform traditional accounting duties. Further, as the financial world continues to grow
more complex, accountants have to know finance to understand the implications of many of
the newer types of financial contracts and the impact they have on financial statements.
Beyond this, cost accounting and business finance are particularly closely related, sharing
many of the same subjects and concerns.
Financial analysts make extensive use of accounting information; they are some of the
most important end users. Understanding finance helps accountants recognize what types
ros13952_ch01_001-021.indd 3 12/22/18 5:46 PM
4 P A R T 1 Overview of Financial Management
of information are particularly valuable and, more generally, how accounting information is
actually used (and abused) in practice.
Management and Finance One of the most important areas in management is
strategy. Thinking about business strategy without simultaneously thinking about financial
strategy is an excellent recipe for disaster, and, as a result, management strategists must have
a very clear understanding of the financial implications of business plans.
In broader terms, management employees of all types are expected to have a strong
understanding of how their jobs affect profitability, and they also are expected to be able to
work within their areas to improve profitability. This is precisely what studying finance
teaches you: What are the characteristics of activities that create value?
You and Finance Perhaps the most important reason to know finance is that you will
have to make financial decisions that will be very important to you personally. Today, for
example, when you go to work for almost any type of company, you will be asked to decide
how you want to invest your retirement funds. We’ll see in a later chapter that what you
choose to do can make an enormous difference in your future financial well-being. On a
different note, is it your dream to start your own business? Good luck if you don’t under-
stand basic finance before you start; you’ll end up learning it the hard way. Want to know
how big your student loan payments are going to be before you take out that next loan?
Maybe not, but we’ll show you how to calculate them anyway.
These are just a few of the ways that finance will affect your personal and business lives.
Whether you want to or not, you are going to have to examine and understand financial is-
sues, and you are going to have to make financial decisions. We want you to do so wisely, so
keep reading.
CONCEPT QUESTIONS
1.1a What are the major areas in finance?
1.1b Besides wanting to pass this class, why do you need to understand finance?
BUSINESS FINANCE AND
THE FINANCIAL MANAGER
Now we proceed to define business finance and the financial manager’s job.
What Is Business Finance?
Imagine you were to start your own business. No matter what type of business you started,
you would have to answer the following three questions in some form or another:
1. What long-term investments should you take on? That is, what lines of business will
you be in, and what sorts of buildings, machinery, and equipment will you need?
2. Where will you get the long-term financing to pay for your investments? Will you bring
in other owners, or will you borrow the money?
3. How will you manage your everyday financial activities, such as collecting from
customers and paying suppliers?
1.2
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C H A P T E R 1 Introduction to Financial Management 5
These are not the only questions, but they are among the most important. Business finance,
broadly speaking, is the study of ways to answer these three questions. We’ll be looking at
each of them in the chapters ahead.
The Financial Manager
The financial management function is usually associated with a top officer of the firm, often
called the chief financial officer (CFO) or vice president of finance. Figure 1.1 is a simpli-
fied organizational chart that highlights the finance activity in a large firm. As shown, the
vice president of finance coordinates the activities of the treasurer and the controller. The
controller’s office handles cost and financial accounting, tax payments, and management
information systems. The treasurer’s office is responsible for managing the firm’s cash and
credit, its financial planning, and its capital expenditures. These treasury activities are all
related to the three general questions raised above, and the chapters ahead deal primarily
with these issues. Our study thus bears mostly on activities usually associated with the trea-
surer’s office. In a smaller firm, the treasurer and controller might be the same person, and
there would be only one office.
Financial Management Decisions
As our preceding discussion suggests, the financial manager must be concerned with three
basic types of questions. We consider these in greater detail next.
For current issues facing
CFOs, see www.cfo.com.
A simplified
organizational chart
The exact titles and
organization differ from
company to company.
FIGURE 1.1
Board of Directors
Chairman of the Board and
Chief Executive Officer (CEO)
President and Chief
Operations Officer (COO)
Vice President
Production
Treasurer Controller
Cash Manager Credit Manager Tax Manager Cost Accounting
Manager
Capital
Expenditures
Financial
Planning
Financial
Accounting
Manager
Data Processing
Manager
Vice President
Finance (CFO)
Vice President
Marketing
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6 P A R T 1 Overview of Financial Management
Capital Budgeting The first question concerns the firm’s long-term investments. The
process of planning and managing a firm’s long-term investments is called capital budgeting.
In capital budgeting, the financial manager tries to identify investment opportunities that
are worth more to the firm than they cost to acquire. Loosely speaking, this means that the
value of the cash flow generated by an asset exceeds the cost of that asset.
Regardless of the specific investment under consideration, financial managers must be
concerned with how much cash they expect to receive, when they expect to receive it, and
how likely they are to receive it. Evaluating the size, timing, and risk of future cash flows is
the essence of capital budgeting. In fact, whenever we evaluate a business decision, the size,
timing, and risk of the cash flows will be, by far, the most important things we will
consider.
Capital Structure The second question for the financial manager concerns how the
firm obtains the financing it needs to support its long-term investments. A firm’s
capital structure (or financial structure) refers to the specific mixture of long-term debt and
equity the firm uses to finance its operations. The financial manager has two concerns in
this area. First: How much should the firm borrow? Second: What are the least expensive
sources of funds for the firm?
In addition to deciding on the financing mix, the financial manager has to decide
exactly how and where to raise the money. The expenses associated with raising long-term
financing can be considerable, so different possibilities must be evaluated carefully. Also,
businesses borrow money from a variety of lenders in a number of different ways. Choos-
ing among lenders and among loan types is another job handled by the financial
manager.
Working Capital Management The third question concerns working capital man-
agement. The term working capital refers to a firm’s short-term assets, such as inventory, and
its short-term liabilities, such as money owed to suppliers. Managing the firm’s working
capital is a day-to-day activity that ensures the firm has sufficient resources to continue its
operations and avoid costly interruptions. This involves a number of activities related to the
firm’s receipt and disbursement of cash.
Some questions about working capital that must be answered are the following: (1)
How much cash and inventory should we keep on hand? (2) Should we sell on credit to our
customers? (3) How will we obtain any needed short-term financing? (4) If we borrow in
the short term, how and where should we do it? This is just a small sample of the issues that
arise in managing a firm’s working capital.
Conclusion The three areas of corporate financial management we have described—
capital budgeting, capital structure, and working capital management—are very broad cate-
gories. Each includes a rich variety of topics, and we have indicated only a few of the
questions that arise in the different areas. The chapters ahead contain greater detail.
CONCEPT QUESTIONS
1.2a What is the capital budgeting decision?
1.2b What do you call the specific mixture of long-term debt and equity that a firm
chooses to use?
1.2c Into what category of financial management does cash management fall?
capital budgeting
The process of planning
and managing a firm’s
long-term investments.
capital structure
The mixture of debt and
equity maintained by a
firm.
working capital
A firm’s short-term assets
and liabilities.
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C H A P T E R 1 Introduction to Financial Management 7
FORMS OF BUSINESS ORGANIZATION
Large firms in the United States, such as IBM and Apple, are almost all organized as
corporations. We examine the three different legal forms of business organization—sole
proprietorship, partnership, and corporation—to see why this is so.
Sole Proprietorship
A sole proprietorship is a business owned by one person. This is the simplest type of busi-
ness to start and is the least regulated form of organization. For this reason, there are more
proprietorships than any other type of business, and many businesses that later become
large corporations start out as small proprietorships.
The owner of a sole proprietorship keeps all the profits. That’s the good news. The bad
news is that the owner has unlimited liability for business debts. This means that creditors
can look to the proprietor’s personal assets for payment. Similarly, there is no distinction
between personal and business income, so all business income is taxed as personal
income.
The life of a sole proprietorship is limited to the owner’s life span, and, importantly, the
amount of equity that can be raised is limited to the proprietor’s personal wealth. This lim-
itation often means that the business is unable to exploit new opportunities because of insuf-
ficient capital. Ownership of a sole proprietorship may be difficult to transfer because this
requires the sale of the entire business to a new owner.
Partnership
A partnership is similar to a proprietorship, except that there are two or more owners (part-
ners). In a general partnership, all the partners share in gains or losses, and all have unlim-
ited liability for all partnership debts, not just some particular share. The way partnership
gains (and losses) are divided is described in the partnership agreement. This agreement can
be an informal oral agreement, such as “let’s start a lawn mowing business,” or a lengthy,
formal written document.
In a limited partnership, one or more general partners will run the business and have
unlimited liability, but there will be one or more limited partners who do not actively partic-
ipate in the business. A limited partner’s liability for business debts is limited to the amount
that partner contributes to the partnership. This form of organization is common in real
estate ventures, for example.
The advantages and disadvantages of a partnership are basically the same as those for a
proprietorship. Partnerships based on a relatively informal agreement are easy and inexpen-
sive to form. General partners have unlimited liability for partnership debts, and the part-
nership terminates when a general partner wishes to sell out or dies. All income is taxed as
personal income to the partners, and the amount of equity that can be raised is limited to
the partners’ combined wealth. Ownership by a general partner is not easily transferred be-
cause a new partnership must be formed. A limited partner’s interest can be sold without
dissolving the partnership, but finding a buyer may be difficult.
Because a partner in a general partnership can be held responsible for all partnership
debts, having a written agreement is very important. Failure to spell out the rights and
duties of the partners frequently leads to misunderstandings later on. Also, if you are a
limited partner, you must not become deeply involved in business decisions unless you are
willing to assume the obligations of a general partner. The reason is that if things go
badly, you may be deemed to be a general partner even though you say you are a limited
partner.
1.3
sole proprietorship
A business owned by a
single individual.
For more information on
forms of business
organization, visit www
.nolo.com.
partnership
A business formed by two
or more individuals or
entities.
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8 P A R T 1 Overview of Financial Management
Based on our discussion, the primary disadvantages of sole proprietorships and part-
nerships as forms of business organization are (1) unlimited liability for business debts on
the part of the owners, (2) limited life of the business, and (3) difficulty of transferring
ownership. These three disadvantages add up to a single, central problem: The ability of
such businesses to grow can be seriously limited by an inability to raise cash for
investment.
Corporation
The corporation is the most important form (in terms of size) of business organization in
the United States. A corporation is a legal “person” separate and distinct from its owners,
and it has many of the rights, duties, and privileges of an actual person. Corporations can
borrow money and own property, can sue and be sued, and can enter into contracts. A cor-
poration can even be a general partner or a limited partner in a partnership, and a corpora-
tion can own stock in another corporation.
Not surprisingly, starting a corporation is somewhat more complicated than starting
the other forms of business organization. Forming a corporation involves preparing articles
of incorporation (or a charter) and a set of bylaws. The articles of incorporation must contain
a number of things, including the corporation’s name, its intended life (which can be for-
ever), its business purpose, and the number of shares that can be issued. This information
must normally be supplied to the state in which the firm will be incorporated. For most le-
gal purposes, the corporation is a “resident” of that state.
The bylaws are rules describing how the corporation regulates its own existence. For
example, the bylaws describe how directors are elected. The bylaws may be amended or ex-
tended from time to time by the stockholders.
In a large corporation, the stockholders and the managers are usually separate groups.
The stockholders elect the board of directors, who then select the managers. Management
is charged with running the corporation’s affairs in the stockholders’ interests. In principle,
stockholders control the corporation because they elect the directors.
As a result of the separation of ownership and management, the corporate form has
several advantages. Ownership (represented by shares of stock) can be readily transferred,
and the life of the corporation is, therefore, not limited. The corporation borrows money in
its own name. As a result, the stockholders in a corporation have limited liability for corpo-
rate debts. The most they can lose is what they have invested.
The relative ease of transferring ownership, the limited liability for business debts, and
the unlimited life of the business are the reasons the corporate form is superior when it
comes to raising cash. If a corporation needs new equity, it can sell new shares of stock and
attract new investors. The number of owners can be huge; larger corporations have many
thousands or even millions of stockholders. For example, the General Electric Company
(better known as GE) has about 8.7 billion shares outstanding and 4 million shareholders.
The corporate form has a significant disadvantage. Because a corporation is a legal
person, it must pay taxes. Moreover, money paid out to stockholders in the form of divi-
dends is taxed again as income to those stockholders. This is double taxation, meaning that
corporate profits are taxed twice: at the corporate level when they are earned and again at
the personal level when they are paid out.
Today, all 50 states have enacted laws allowing for the creation of a relatively new form
of business organization, the limited liability company (LLC). The goal of this entity is to
operate and be taxed like a partnership but retain limited liability for owners. Thus, an LLC
is essentially a hybrid of a partnership and a corporation. Although states have differing
definitions for LLCs, the more important scorekeeper is the Internal Revenue Service
corporation
A business created as a
distinct legal entity owned
by one or more individuals
or entities.
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C H A P T E R 1 Introduction to Financial Management 9
(IRS). The IRS will consider an LLC a corporation, thereby subjecting it to double taxation,
unless it meets certain specific criteria. In essence, an LLC cannot be too corporation-like,
or it will be treated as one by the IRS. LLCs have become common. For example, Goldman
Sachs, one of Wall Street’s last remaining partnerships, decided to convert from a private
partnership to an LLC (it later “went public,” becoming a publicly held corporation). Large
accounting firms and law firms by the score have converted to LLCs.
A Corporation by Another Name . . .
The corporate form has many variations around the world. Exact laws and regulations
differ, of course, but the essential features of public ownership and limited liability remain.
These firms are often called joint stock companies, public limited companies, or limited liabil-
ity companies.
Table 1.1 gives the names of a few well-known international corporations, their country
of origin, and a translation of the abbreviation that follows the company name.
CONCEPT QUESTIONS
1.3a What are the three forms of business organization?
1.3b What are the primary advantages and disadvantages of sole proprietorships and
partnerships?
1.3c What is the difference between a general and a limited partnership?
1.3d Why is the corporate form superior when it comes to raising cash?
THE GOAL OF FINANCIAL MANAGEMENT
To study financial decision making, we first need to understand the goal of financial man-
agement. Such an understanding is important because it leads to an objective basis for mak-
ing and evaluating financial decisions.
Profit Maximization
Profit maximization would probably be the most commonly cited business goal, but this is
not a very precise objective. Do we mean profits this year? If so, then actions such as defer-
ring maintenance, letting inventories run down, and other short-run, cost-cutting measures
will tend to increase profits now, but these activities aren’t necessarily desirable.
You can find the translation
for any business type at
www.corporate
information.com.
1.4
Company Country of Origin Type of Company Translation
Bayerische Motoren
Werke (BMW) AG
Germany Aktiengesellschaft Corporation
Montblanc GmbH Germany Gesellschaft mit
beschränkter Haftung
Company with limited
liability
Rolls-Royce PLC United Kingdom Public limited company Public limited company
Shell UK Ltd. United Kingdom Limited Corporation
Unilever NV Netherlands Naamloze Vennootschap Limited liability company
Fiat SpA Italy Società per Azioni Public limited company
Saab AB Sweden Aktiebolag Joint stock company
Peugeot SA France Société Anonyme Joint stock company
International
corporations
TABLE 1.1
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10 P A R T 1 Overview of Financial Management
The goal of maximizing profits may refer to some sort of “long-run” or “average”
profits, but it’s unclear exactly what this means. First, do we mean something like ac-
counting net income or earnings per share? As we will see, these numbers may have little
to do with what is good or bad for the firm. Second, what do we mean by the long run?
As a famous economist once remarked: “In the long run, we’re all dead!” More to the
point, this goal doesn’t tell us the appropriate trade-off between current and future
profits.
The Goal of Financial Management in a Corporation
The financial manager in a corporation makes decisions for the stockholders of the firm.
Given this, instead of listing possible goals for the financial manager, we really need to an-
swer a more fundamental question: From the stockholders’ point of view, what is a good fi-
nancial management decision?
If we assume stockholders buy stock because they seek to gain financially, then the answer
is obvious: Good decisions increase the value of the stock, and poor decisions decrease it.
Given our observations, it follows that the financial manager acts in the shareholders’
best interests by making decisions that increase the value of the stock. The appropriate goal
for the financial manager in a corporation can thus be stated quite easily:
The goal of financial management is to maximize the current value per share of the
existing stock.
The goal of maximizing the value of the stock avoids the problems associated with the
different goals we discussed earlier. There is no ambiguity in the criterion, and there is no
short-run versus long-run issue. We explicitly mean that our goal is to maximize the current
stock value. Of course, maximizing stock value is the same thing as maximizing the market
price per share.
A More General Financial Management Goal
Given our goal as stated earlier (maximize the value of the stock), an obvious question
comes up: What is the appropriate goal when the firm has no traded stock? Corporations
are certainly not the only type of business, and the stock in many corporations rarely
changes hands, so it’s difficult to say what the value per share is at any given time.
As long as we are dealing with for-profit businesses, only a slight modification is
needed. The total value of the stock in a corporation is equal to the value of the owners’
equity. Therefore, a more general way of stating our goal is:
Maximize the market value of the existing owners’ equity.
With this goal in mind, it doesn’t matter whether the business is a proprietorship, a
partnership, or a corporation. For each of these, good financial decisions increase the mar-
ket value of the owners’ equity and poor financial decisions decrease it.
Finally, our goal does not imply that the financial manager should take illegal or uneth-
ical actions in the hope of increasing the value of the equity in the firm. What we mean is
that the financial manager best serves the owners of the business by identifying goods and
services that add value to the firm because they are desired and valued in the free market-
place. Our nearby Finance Matters box discusses some recent ethical issues and problems
faced by well-known corporations.
Business ethics are
considered at www.3
blassociation.com.
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Corporate Ethics
Large companies are sometimes guilty of unethical behav-ior. Often, this unethical behavior takes the form of false or
misleading financial statements. In one of the largest corpo-
rate fraud cases in history, energy giant Enron Corporation
was forced to file for bankruptcy in December 2001 amid al-
legations that the company’s financial statements were delib-
erately misleading and false. Enron’s bankruptcy destroyed
not only that company, but its auditor Arthur Andersen as well.
Often, unethical behavior is also illegal and can result in
a jail sentence for an individual or fines for a corporation. For
example, in March 2018, the investment bank and financial
services company Barclays reached a settlement with the
U.S. Department of Justice (DOJ). The DOJ claimed that Bar-
clays had misrepresented the quality of the mortgages it
packaged and sold to investors. To settle the claim, Barclays
agreed to pay $2 billion. Barclays was not the first bank to
settle a mortgage-related claim with the DOJ. Banks with
particularly large settlements with the DOJ regarding mort-
gages were Bank of America ($7 billion), JPMorgan ($13 bil-
lion), and Citigroup ($16.7 billion).
The difference between ethical and unethical behavior
can sometimes be murky. For example, many U.S. compa-
nies have relocated to Bermuda for reasons beyond the
beautiful pink beaches; namely, Bermuda has no corporate
income taxes. With a population of less than 65,000, the
island is home to more than 13,000 international companies.
Stanley Black & Decker, the well-known maker of Stanley
tools, was among the U.S. corporations that considered a
move to the island paradise. By doing so, Stanley estimated
that it would save $30 million per year in taxes. Stanley ulti-
mately decided against the move, but two of its rivals,
Cooper and Ingersoll-Rand, did move to Bermuda. Because
the goal of the corporation is to maximize shareholder
wealth, this would seem like a good move, and the practice
is entirely legal. But is it ethical? What are the issues?
Another corporate activity that has generated much
controversy is the practice of outsourcing, or offshoring, jobs
to other countries. U.S. corporations engage in this practice
when labor costs in another country are substantially lower
than they are domestically. Again, this is done to maximize
shareholder wealth. But the ethical dilemma in this case is
even trickier. Some U.S. workers do lose jobs when offshor-
ing occurs. On the other hand, the Milken Institute estimated
that every $1 spent on offshoring a service job to India gen-
erated a net value to the United States of $1.13, along with
another $.33 to India. And it gets even more complicated:
What about foreign companies such as BMW and Toyota
that “insource” jobs by building plants in the United States?
Is it unethical to outsource U.S. jobs while, at the same time,
insourcing jobs from other countries?
FINANCE MATTERS
11
Sarbanes-Oxley Act
In response to corporate scandals involving companies such as Enron, WorldCom, Tyco,
and Adelphia, Congress enacted the Sarbanes-Oxley Act in 2002. The act, which is better
known as “Sarbox,” is intended to strengthen protection against corporate accounting fraud
and financial malpractice. Key elements of Sarbox took effect on November 15, 2004.
Sarbox contains a number of requirements designed to ensure that companies tell the
truth in their financial statements. For example, the officers of a public corporation must
review and sign the annual report. They must attest that the annual report does not contain
false statements or material omissions and also that the financial statements fairly represent
the company’s financial results. In essence, Sarbox makes management personally responsi-
ble for the accuracy of a company’s financial statements.
Because of its extensive requirements, compliance with Sarbox can be very costly,
which has led to some unintended results. Since its implementation, hundreds of public
firms have chosen to “go dark,” meaning that their shares are no longer traded in the major
stock markets, in which case Sarbox does not apply. Most of these companies stated that
their reason was to avoid the cost of compliance. Ironically, in such cases, the law had the
effect of eliminating public disclosure instead of improving it.
Sarbox also probably has affected the number of companies going public in the United
States. Recently, many U.S.-based companies have chosen to go public on the London Stock
Exchange’s Alternative Investment Market (AIM) instead. The cost savings can be
To find out more about
Sarbanes-Oxley, go to
www.soxlaw.com.
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12 P A R T 1 Overview of Financial Management
enormous, especially for small companies. For example, Protonex Technologies, a fuel cell
developer based in Southborough, Massachusetts, estimated that it costs about $1 million
per year in compliance costs and mailings to stockholders to be listed on the AIM. In con-
trast, the annual cost to be listed on the NASDAQ would be about $3 million, with a large
part of the increase due to Sarbox compliance costs.
CONCEPT QUESTIONS
1.4a What is the goal of financial management?
1.4b What are some shortcomings of the goal of profit maximization?
THE AGENCY PROBLEM AND CONTROL
OF THE CORPORATION
We’ve seen that the financial manager in a corporation acts in the best interests of the stock-
holders by taking actions that increase the value of the firm’s stock. However, we’ve also
seen that in large corporations, ownership can be spread over a huge number of stockhold-
ers. This dispersion of ownership arguably means that management effectively controls the
firm. In this case, will management necessarily act in the best interests of the stockholders?
Put another way, might not management pursue its own goals at the stockholders’ expense?
We briefly consider some of the arguments in this section.
Agency Relationships
The relationship between stockholders and management is called an agency relationship.
Such a relationship exists whenever someone (the principal) hires another (the agent) to
represent his or her interest. For example, you might hire someone (an agent) to sell a car
that you own while you are away at school. In all such relationships, there is a possibility of
conflict of interest between the principal and the agent. Such a conflict is called an
agency problem.
Suppose you hire someone to sell your car and you agree to pay her a flat fee when she
sells the car. The agent’s incentive in this case is to make the sale, not necessarily to get you
the best price. If you paid a commission of, say, 10 percent of the sales price instead of a flat
fee, then this problem might not exist. This example illustrates that the way an agent is com-
pensated is one factor that affects agency problems.
Management Goals
To see how management and stockholder interests might differ, imagine that a corporation
is considering a new investment. The new investment is expected to favorably affect the
stock price, but it is also a relatively risky venture. The owners of the firm will wish to take
the investment (because the share value will rise), but management may not because there
is the possibility that things will turn out badly and management jobs will be lost. If manage-
ment does not take the investment, then the stockholders may lose a valuable opportunity.
This is one example of an agency cost.
It is sometimes argued that, left to themselves, managers would tend to maximize the
amount of resources over which they have control, or, more generally, business power or
wealth. This goal could lead to an overemphasis on business size or growth. For example,
cases where management is accused of overpaying to buy another company just to increase
1.5
agency problem
The possibility of conflict
of interest between the
owners and management
of a firm.
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C H A P T E R 1 Introduction to Financial Management 13
the size of the business or to demonstrate corporate power are not uncommon. Obviously,
if overpayment does take place, such a purchase does not benefit the owners of the purchas-
ing company.
Our discussion indicates that management may tend to overemphasize organizational
survival to protect job security. Also, management may dislike outside interference, so inde-
pendence and corporate self-sufficiency may be important goals.
Do Managers Act in the Stockholders’ Interests?
Whether managers will, in fact, act in the best interests of stockholders depends on two fac-
tors. First, how closely are management goals aligned with stockholder goals? This question
relates to the way managers are compensated. Second, can management be replaced if they
do not pursue stockholder goals? This issue relates to control of the firm. As we will discuss,
there are a number of reasons to think that, even in the largest firms, management has a
significant incentive to act in the interests of stockholders.
Managerial Compensation Management will frequently have a significant eco-
nomic incentive to increase share value for two reasons. First, managerial compensation,
particularly at the top, is usually tied to financial performance in general and oftentimes to
share value in particular. For example, managers are frequently given the option to buy
stock at a fixed price. The more the stock is worth, the more valuable is this option. The
second incentive managers have relates to job prospects. Better performers within the firm
will tend to get promoted. More generally, those managers who are successful in pursuing
stockholder goals will be in greater demand in the labor market and thus command higher
salaries.
In fact, managers who are successful in pursuing stockholder goals can reap enormous
rewards. For example, Hock Tan, CEO of Broadcom, received about $103 million in 2017,
which is less than Floyd Mayweather ($300 million) and Manny Pacquiao ($160 million).
Information on executive compensation, along with a ton of other information, can be easily
found on the web for almost any public company. Our nearby Work the Web box shows you
how to get started.
Control of the Firm Control of the firm ultimately rests with stockholders. They elect
the board of directors, who, in turn, hires and fires management. The mechanism by which
unhappy stockholders can act to replace existing management is called a proxy fight. A
proxy is the authority to vote someone else’s stock. A proxy fight develops when a group
solicits proxies in order to replace the existing board, and thereby replace existing
management.
For example, in July 2017, Trian Partners, headed by activist investor Nelson Peltz, en-
gaged in a proxy fight with Procter & Gamble in an attempt to gain a seat on the board of
directors. This was the largest proxy fight in history, with Trian owning $3.3 billion worth of
shares in the $223 billion company. Peltz cited disappointing financial results, weak share-
holder returns, deteriorating market share, and excessive cost and bureaucracy as reasons
for the proxy fight. P&G had fought off a previous proxy fight in 2012 when William Ack-
man attempted to gain a seat on the board. Ackman ultimately lost his battle and sold the
last of his P&G stock in May 2014.
Another way that management can be replaced is by takeover. Firms that are poorly
managed are more attractive as acquisitions than well-managed firms because a greater
profit potential exists. Thus, avoiding a takeover by another firm gives management another
incentive to act in the stockholders’ interests. Unhappy prominent shareholders can suggest
different business strategies to a firm’s top management. For example, in June 2017, Verizon
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14 P A R T 1 Overview of Financial Management
The web is a great place to learn about individual companies, and there are a slew of sites avail-able to help you. Try pointing your web browser to finance.yahoo.com. Once there, you should
see a box with “Quote Lookup.” To look up a company, you need its “ticker symbol” (or ticker for
short), which is a unique one-to-five-letter identifier. Or you can type in a company’s name to find
the ticker. For example, we typed in “SIRI,” which is the ticker symbol for Sirius XM Holdings, the
satellite radio provider. Here is a portion of what we found:
W R K T H E W E B
QUESTIONS
1. Go to finance.yahoo.com and find the current stock prices for Southwest Airlines (LUV),
Harley-Davidson (HOG), and Starwood Hotels & Resorts (HOT).
2. Get a quote for American Express (AXP) and follow the “Statistics” link. What informa-
tion is available on this link? What do “mrq,” “ttm,” “yoy,” and “lfy” mean?
There is a lot of information here and a lot of other links for you to explore, so have at it. By
the end of the term, we hope it all makes sense to you!
completed its $4.5 billion takeover of Yahoo! The management of Yahoo! had been under
fire for several years due to the company’s poor performance. Verizon hoped that the com-
bined company could create a third alternative in the digital advertising market to challenge
Google and Facebook. Yahoo! CEO Marissa Mayer wasn’t part of the plans going forward,
although she did receive $127 million when she was let go.
Conclusion The available theory and evidence are consistent with the view that stock-
holders control the firm and that stockholder wealth maximization is the relevant goal of
the corporation. Even so, there will undoubtedly be times when management goals are pur-
sued at the expense of the stockholders, at least temporarily.
Source: finance.yahoo.com
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C H A P T E R 1 Introduction to Financial Management 15
Agency problems are not unique to corporations; they exist whenever there is a separa-
tion of ownership and management. This separation is most pronounced in corporations,
but it certainly exists in partnerships and proprietorships as well.
Stakeholders
Our discussion thus far implies that management and stockholders are the only parties with
an interest in the firm’s decisions. This is an oversimplification, of course. Employees, cus-
tomers, suppliers, and even the government all have a financial interest in the firm.
These various groups are called stakeholders in the firm. In general, a stakeholder is
someone other than a stockholder or creditor who potentially has a claim on the cash flows
of the firm. Such groups also will attempt to exert control over the firm, perhaps to the det-
riment of the owners.
CONCEPT QUESTIONS
1.5a What is an agency relationship?
1.5b What are agency problems, and how do they arise? What are agency costs?
1.5c What incentives do managers in large corporations have to maximize share value?
FINANCIAL MARKETS AND
THE CORPORATION
We’ve seen that the primary advantages of the corporate form of organization are that owner-
ship can be transferred more quickly and easily than with other forms and that money can be
raised more readily. Both of these advantages are significantly enhanced by the existence of fi-
nancial markets, and financial markets play an extremely important role in corporate finance.
Cash Flows to and from the Firm
The interplay between the corporation and the financial markets is illustrated in Figure 1.2.
The arrows in Figure 1.2 trace the passage of cash from the financial markets to the firm
and from the firm back to the financial markets.
Suppose we start with the firm selling shares of stock and borrowing money to raise
cash. Cash flows to the firm from the financial markets (A). The firm invests the cash in
current and fixed (or long-term) assets (B). These assets generate some cash (C), some of
which goes to pay corporate taxes (D). After taxes are paid, some of this cash flow is rein-
vested in the firm (E). The rest goes back to the financial markets as cash paid to creditors
and shareholders (F).
A financial market, like any market, is a way of bringing buyers and sellers together. In
financial markets, it is debt and equity securities that are bought and sold. Financial markets
differ in detail, however. The most important differences concern the types of securities that
are traded, how trading is conducted, and who the buyers and sellers are. Some of these
differences are discussed next.
Primary versus Secondary Markets
Financial markets function as both primary and secondary markets for debt and equity
securities. The term primary market refers to the original sale of securities by governments
stakeholder
Someone other than a
stockholder or creditor
who potentially has a
claim on the cash flows of
the firm.
1.6
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16 P A R T 1 Overview of Financial Management
and corporations. The secondary markets are those in which these securities are bought and
sold after the original sale. Equities are, of course, issued solely by corporations. Debt secu-
rities are issued by both governments and corporations. In the discussion that follows, we
focus on corporate securities only.
Primary Markets In a primary market transaction, the corporation is the seller, and
the transaction raises money for the corporation. Corporations engage in two types of pri-
mary market transactions: public offerings and private placements. A public offering, as the
name suggests, involves selling securities to the general public, whereas a private placement
is a negotiated sale involving a specific buyer.
By law, public offerings of debt and equity must be registered with the Securities and
Exchange Commission (SEC). Registration requires the firm to disclose a great deal of in-
formation before selling any securities. The accounting, legal, and selling costs of public of-
ferings can be considerable.
Partly to avoid the various regulatory requirements and the expense of public offerings,
debt and equity often are sold privately to large financial institutions such as life insurance
companies or mutual funds. Such private placements do not have to be registered with the
SEC and do not require the involvement of underwriters (investment banks that specialize
in selling securities to the public).
Secondary Markets A secondary market transaction involves one owner or creditor
selling to another. It is, therefore, the secondary markets that provide the means for transfer-
ring ownership of corporate securities. Although a corporation is only directly involved in a
primary market transaction (when it sells securities to raise cash), the secondary markets
are still critical to large corporations. The reason is that investors are much more willing to
To learn more about the
SEC, visit www.sec.gov.
To learn more about stock
exchanges, visit www.nyse
.com and www.nasdaq
.com.
B. Firm invests
in assets
Current assets
Fixed assets
Financial
markets
Short-term debt
Long-term debt
Equity shares
A. Firm issues securities
E. Reinvested cash flows F. Dividends and
debt payments
C. Cash flow from
firm’s assets
D. Government
Other stakeholders
A. Firm issues securities to raise cash. E. Reinvested cash flows are plowed back
B. Firm invests in assets. into firm.
C. Firm’s operations generate cash flow. F. Cash is paid out to investors in the form
D. Cash is paid to government as taxes. of interest and dividends.
Other stakeholders may receive cash.
Total value of the firm
to investors in
the financial markets
Total value of
firm’s assets
FIGURE 1.2
Cash flows between
the firm and the
financial markets
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C H A P T E R 1 Introduction to Financial Management 17
purchase securities in a primary market transaction when they know that those securities
can be resold later if desired.
Dealer Versus Auction Markets There are two kinds of secondary markets: auction
markets and dealer markets. Generally speaking, dealers buy and sell for themselves, at their
own risk. A car dealer, for example, buys and sells automobiles. In contrast, brokers and
agents match buyers and sellers, but they do not actually own the commodity that is bought
or sold. A real estate agent, for example, does not normally buy and sell houses.
Dealer markets in stocks and long-term debt are called over-the-counter (OTC) markets.
Most trading in debt securities takes place over the counter. The expression over the counter
refers to days of old when securities were literally bought and sold at counters in offices around
the country. Today, a significant fraction of the market for stocks and almost all of the market
for long-term debt have no central location; the many dealers are connected electronically.
Auction markets differ from dealer markets in two ways. First, an auction market, or ex-
change, has a physical location (like Wall Street). Second, in a dealer market, most of the buy-
ing and selling is done by the dealer. The primary purpose of an auction market, on the other
hand, is to match those who wish to sell with those who wish to buy. Dealers play a limited role.
Trading in Corporate Securities The equity shares of most of the large firms in the United
States trade in organized auction markets. The largest such market is the New York Stock
Exchange (NYSE), which accounts for more than 85 percent of all the shares traded in
auction markets.
In addition to the stock exchanges, there is a large OTC market for stocks. In 1971, the
National Association of Securities Dealers (NASD) made available to dealers and brokers
an electronic quotation system called NASDAQ (NASD Automated Quotations system,
pronounced “naz-dak”). There are more companies listed on NASDAQ than there are on
the NYSE, but they tend to be much smaller in size and trade less actively. There are excep-
tions, of course. Both Microsoft and Intel trade OTC, for example. Nonetheless, the total
value of NASDAQ stocks is significantly less than the total value of NYSE stocks.
There are many large and important financial markets outside the United States, of
course, and U.S. corporations are increasingly looking to these markets to raise cash. The
Tokyo Stock Exchange and the London Stock Exchange (TSE and LSE, respectively) are
two well-known examples. The fact that OTC markets have no physical location means that
national borders do not present a great barrier, and there is now a huge international OTC
debt market. Because of globalization, financial markets have reached the point where trad-
ing in many instruments never stops; it just travels around the world.
Listing Stocks that trade on an organized exchange (or market) are said to be listed on that
exchange. In order to be listed, firms must meet certain minimum criteria concerning, for
example, asset size and number of shareholders. These criteria differ for different exchanges.
NYSE has the most stringent requirements of the stock markets in the United States.
There are minimums on earnings, assets, and number and market value of shares
outstanding.
CONCEPT QUESTIONS
1.6a What is a dealer market? How do dealer and auction markets differ?
1.6b What is the largest auction market in the United States?
1.6c What does OTC stand for? What is the large OTC market for stocks called?
The Tokyo Stock Exchange
in English: www.jpx.co.jp
/english/.
The London Stock
Exchange: www.london
stockexchange.com.
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18 P A R T 1 Overview of Financial Management
SUMMARY AND CONCLUSIONS
This chapter has introduced you to some of the basic ideas in business finance. In it, we
saw that:
1. Business finance has three main areas of concern:
a. Capital budgeting. What long-term investments should the firm take?
b. Capital structure. Where will the firm get the long-term financing to pay for its
investments? In other words, what mixture of debt and equity should we use to
fund our operations?
c. Working capital management. How should the firm manage its everyday financial
activities?
2. The goal of financial management in a for-profit business is to make decisions that
increase the value of the stock, or, more generally, increase the market value of the
equity.
3. The corporate form of organization is superior to other forms when it comes to
raising money and transferring ownership interests, but it has the significant
disadvantage of double taxation.
4. There is the possibility of conflicts between stockholders and management in a large
corporation. We called these conflicts agency problems and discussed how they might
be controlled and reduced.
Of the topics we’ve discussed thus far, the most important is the goal of financial manage-
ment. Throughout the text, we will be analyzing many different financial decisions, but we
always ask the same question: How does the decision under consideration affect the value of
the equity in the firm?
POP QUIZ!
Can you answer the following questions? If your class is using Connect, log on to
SmartBook to see if you know the answers to these and other questions, check out
the study tools, and find out what topics require additional practice!
Section 1.2 What are the three main questions to be addressed if you wanted to
start your own business?
Section 1.3 What characteristics are important when considering a partnership?
Section 1.4 What does the Sarbanes-Oxley Act require of corporate officers?
Section 1.5 Who are the stakeholders in a firm?
Section 1.6 What are the defining features of a primary market?
CRITICAL THINKING AND CONCEPTS REVIEW
LO 1 1.1 The Financial Management Decision Process What are the three types of
financial management decisions? For each type of decision, give an
example of a business transaction that would be relevant.
LO 3 1.2 Sole Proprietorships and Partnerships What are the four primary
disadvantages to the sole proprietorship and partnership forms of business
ros13952_ch01_001-021.indd 18 12/22/18 5:46 PM
C H A P T E R 1 Introduction to Financial Management 19
organization? What benefits are there to these types of business
organization as opposed to the corporate form?
LO 3 1.3 Corporations What is the primary disadvantage of the corporate form of
organization? Name at least two of the advantages of corporate
organization.
LO 3 1.4 Corporate Finance Organization In a large corporation, what are the two
distinct groups that report to the chief financial officer? Which group is the
focus of corporate finance?
LO 2 1.5 Goal of Financial Management What goal should always motivate the
actions of the firm’s financial manager?
LO 4 1.6 Agency Problems Who owns a corporation? Describe the process
whereby the owners control the firm’s management. What is the main
reason that an agency relationship exists in the corporate form of
organization? In this context, what kinds of problems can arise?
LO 3 1.7 Primary versus Secondary Markets You’ve probably noticed coverage in
the financial press of an initial public offering (IPO) of a company’s
securities. The social networking company Snapchat is a relatively recent
example. Is an IPO a primary market transaction or a secondary market
transaction?
LO 3 1.8 Auction versus Dealer Markets What does it mean when we say the New
York Stock Exchange is an auction market? How are auction markets
different from dealer markets? What kind of market is NASDAQ?
LO 2 1.9 Not-for-Profit Firm Goals Suppose you were the financial manager of a
not-for-profit business (a not-for-profit hospital, perhaps). What kinds of
goals do you think would be appropriate?
LO 2 1.10 Ethics and Firm Goals Can our goal of maximizing the value of the stock
conflict with other goals, such as avoiding unethical or illegal behavior? In
particular, do you think subjects such as customer and employee safety, the
environment, and the general good of society fit in this framework, or are
they essentially ignored? Try to think of some specific scenarios to illustrate
your answer.
LO 2 1.11 International Firm Goal Would our goal of maximizing the value of the
stock be different if we were thinking about financial management in a
foreign country? Why or why not?
LO 4 1.12 Agency Problems Suppose you own stock in a company. The current
price per share is $25. Another company has just announced that it wants
to buy your company and will pay $35 per share to acquire all the
outstanding stock. Your company’s management immediately begins
fighting off this hostile bid. Is management acting in the shareholders’ best
interests? Why or why not?
LO 4 1.13 Agency Problems and Corporate Ownership Corporate ownership varies
around the world. Historically, individuals have owned the majority of
shares in public corporations in the United States. In Germany and Japan,
however, banks, other large financial institutions, and other companies own
most of the stock in public corporations. Do you think agency problems are
likely to be more or less severe in Germany and Japan than in the United
States? Why? In recent years, large financial institutions such as mutual
funds and pension funds have become the dominant owners of stock in the
ros13952_ch01_001-021.indd 19 12/22/18 5:46 PM
20 P A R T 1 Overview of Financial Management
United States, and these institutions are becoming more active in corporate
affairs. What are the implications of this trend for agency problems and
corporate control?
LO 4 1.14 Executive Compensation Critics have charged that compensation to top
management in the United States is too high and should be cut back. For
example, focusing on large corporations, in 2017, First Data CEO Frank
Bisignano made about $102 million and Live Nation CEO Michael Rapino
made about $71 million. Are such amounts excessive? In answering, it
might be helpful to recognize that superstar athletes such as LeBron James,
top entertainers such as Oprah Winfrey, and many others at the top of their
respective fields earn at least as much, if not more.
LO 4 1.15 Sarbanes-Oxley In response to the Sarbanes-Oxley Act, many small firms
in the United States have opted to “go dark” and delist their stock. Why
might a company choose this route? What are the costs of “going dark”?
WHAT’S ON
THE WEB?
1.1 Listing Requirements This chapter discussed some of the listing requirements for the
NYSE and NASDAQ. Find the complete listing requirements for the NYSE at www
.nyse.com and NASDAQ at www.nasdaq.com. Which has more stringent listing
requirements? Why don’t they have the same listing requirements?
1.2 Business Formation As you may (or may not) know, many companies incorporate in
Delaware for a variety of reasons. Visit BizFilings at www.bizfilings.com to find out why.
Which state has the highest fee for incorporation? For an LLC? While at the site, look at
the FAQ section regarding corporations and LLCs.
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C H A P T E R 1 Introduction to Financial Management 21
Because of the increased sales, Doc left his other
job, followed shortly by Lyn. The company hired addi-
tional workers to meet demand. Unfortunately, the fast
growth experienced by the company led to cash flow
and capacity problems. The company is currently pro-
ducing as many cakes as possible with the assets it
owns, but demand for its cakes is still growing. Further,
the company has been approached by a national super-
market chain with a proposal to put four of its cakes in
all of the chain’s stores, and a national restaurant chain
has contacted the company about selling McGee cakes
in its restaurants. The restaurant would sell the cakes
without a brand name.
Doc and Lyn have operated the company as a sole
proprietorship. They have approached you to help man-
age and direct the company’s growth. Specifically, they
have asked you to answer the following questions:
In early 2013, Doc and Lyn McGee formed the McGee Cake Company. The company produced a full line of
cakes, and its specialties included chess cake,* lemon
pound cake, and double-iced, double-chocolate cake.
The couple formed the company as an outside interest,
and both continued to work at their current jobs. Doc did
all the baking, and Lyn handled the marketing and distri-
bution. With good product quality and a sound market-
ing plan, the company grew rapidly. In early 2018, the
company was featured in a widely distributed entrepre-
neurial magazine. Later that year, the company was fea-
tured in Gourmet Desserts, a leading specialty food
magazine. After the article appeared in Gourmet Des-
serts, sales exploded, and the company began receiving
orders from all over the world.
CHAPTER CASE
The McGee Cake Company
*Chess cake is quite delicious and distinct from cheesecake. The origin
of the name is obscure.
1. What are the advantages and disadvantages of
changing the company organization from a sole
proprietorship to an LLC?
2. What are the advantages and disadvantages of
changing the company organization from a sole
proprietorship to a corporation?
3. Ultimately, what action would you recommend the
company undertake? Why?
Q U E S T I O N S
ros13952_ch01_001-021.indd 21 12/22/18 5:46 PM
22
PART TWO Understanding Financial Statements and Cash Flow
Please visit us at essentialsofcorporatefinance.blogspot.com for the latest developments in the world of corporate finance.
In December 2017, the Tax Cuts and Jobs Act was enacted into law beginning in 2018. The new law was a sweeping change to
corporate taxes in the United States. For example, rather than de-
preciating an asset over time for tax purposes, companies are al-
lowed to depreciate the entire purchase price in the first year.
Another change was a limit to the tax deductibility of interest ex-
pense. However, possibly the biggest change was the switch
from a graduated corporate income tax structure, with rates rang-
ing from 15 percent to 39 percent, to a flat 21 percent corporate
tax rate.
While the change in the corporate tax rate affects net income,
there is a more important impact. Because taxes are a key consid-
eration in making investment decisions, the change in the tax rate
could lead to a significant change in corporate investment and
financing decisions. Understanding why ultimately leads us to the main subject of this
chapter: that all-important substance known as cash flow.
Financial Statements,
Taxes, and Cash Flow 2
LEARNING OBJECTIVES
After studying this chapter, you should
be able to:
LO 1 Differentiate between accounting
value (or “book” value) and market
value.
LO 2 Distinguish accounting income
from cash flow.
LO 3 Explain the difference between
average and marginal tax rates.
LO 4 Determine a firm’s cash flow from
its financial statements.
In this chapter, we examine financial statements, taxes, and cash flow. Our emphasis is not on preparing financial statements. Instead, we recognize that financial statements are fre-
quently a key source of information for financial decisions, so our goal is to briefly examine
such statements and point out some of their more relevant features. We pay special atten-
tion to some of the practical details of cash flow.
As you read, pay particular attention to two important differences: (1) the difference
between accounting value and market value and (2) the difference between accounting
income and cash flow. These distinctions will be important throughout the book.
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C H A P T E R 2 Financial Statements, Taxes, and Cash Flow 23
THE BALANCE SHEET
The balance sheet is a snapshot of the firm. It is a convenient means of organizing and
summarizing what a firm owns (its assets), what a firm owes (its liabilities), and the differ-
ence between the two (the firm’s equity) at a given point in time. Figure 2.1 illustrates how
the balance sheet is constructed. As shown, the left-hand side lists the assets of the firm, and
the right-hand side lists the liabilities and equity.
Assets: The Left-Hand Side
Assets are classified as either current or fixed. A fixed asset is one that has a relatively long
life. Fixed assets can either be tangible, such as a truck or a computer, or intangible, such as
a trademark or patent. A current asset has a life of less than one year. This means that the
asset will normally convert to cash within 12 months. For example, inventory would nor-
mally be purchased and sold within a year and is thus classified as a current asset. Obvi-
ously, cash itself is a current asset. Accounts receivable (money owed to the firm by its
customers) are also a current asset.
Liabilities and Owners’ Equity: The Right-Hand Side
The firm’s liabilities are the first thing listed on the right-hand side of the balance sheet.
These are classified as either current or long term. Current liabilities, like current assets, have
a life of less than one year (meaning they must be paid within the year), and they are listed
before long-term liabilities. Accounts payable (money the firm owes to its suppliers) are one
example of a current liability.
A debt that is not due in the coming year is classified as a long-term liability. A loan
that the firm will pay off in five years is one such long-term debt. Firms borrow over the
long term from a variety of sources. We will tend to use the terms bonds and bondholders
generically to refer to long-term debt and long-term creditors, respectively.
Finally, by definition, the difference between the total value of the assets (current and
fixed) and the total value of the liabilities (current and long-term) is the shareholders’ equity,
also called common equity or owners’ equity. This feature of the balance sheet is intended to
reflect the fact that, if the firm were to sell all of its assets and use the money to pay off its
debts, then whatever residual value remained would belong to the shareholders. So, the
2.1
coverage online
Excel
Master
balance sheet
Financial statement
showing a firm’s
accounting value on a
particular date.
Two excellent sites for
company financial
information are finance
.yahoo.com and money
.cnn.com.
Disney has a good investor
site at thewaltdisney
company.com.
The balance sheet
Left side: Total value
of assets.
Right side: Total value
of liabilities and
shareholders’ equity.
FIGURE 2.1
Current liabilities
Long-term debt
Shareholders’ equity
Net
Working
Capital
Total Value of Assets Total Value of Liabilities
and Shareholders’ Equity
Current assets
Fixed assets
1. Tangible fixed
assets
2. Intangible fixed
assets
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24 P A R T 2 Understanding Financial Statements and Cash Flow
balance sheet “balances” because the value of the left-hand side always equals the value of
the right-hand side. That is, the value of the firm’s assets is equal to the sum of its liabilities
and shareholders’ equity:1
Assets = Liabilities + Shareholders’ equity [2.1]
This is the balance sheet identity, or equation, and it always holds because shareholders’
equity is defined as the difference between assets and liabilities.
Net Working Capital
As shown in Figure 2.1, the difference between a firm’s current assets and its current liabili-
ties is called net working capital. Net working capital is positive when current assets exceed
current liabilities. Based on the definitions of current assets and current liabilities, this
means that the cash that will become available over the next 12 months exceeds the cash
that must be paid over that same period. For this reason, net working capital is usually posi-
tive in a healthy firm.
Table 2.1 shows simplified balance sheets for the fictitious U.S. Corporation. There are
three particularly important things to keep in mind when examining a balance sheet: liquid-
ity, debt versus equity, and market value versus book value.
net working capital
Current assets less current
liabilities.
1The terms owners’ equity, shareholders’ equity, and stockholders’ equity are used interchangeably to refer to the eq-
uity in a corporation. The term net worth also is used. Variations exist in addition to these.
U.S. CORPORATION
Balance Sheets as of December 31, 2018 and 2019
($ in Millions)
2018 2019 2018 2019
Assets Liabilities and Owners’ Equity
Current assets Current liabilities
Cash $ 104 $ 160 Accounts payable $ 232 $ 266
Accounts receivable 455 688 Notes payable 196 123
Inventory 553 555 Total $ 428 $ 389
Total $1,112 $1,403
Fixed assets
Net fixed assets $1,644 $1,709 Long-term debt $ 408 $ 454
Owners’ equity
Common stock and paid-in surplus 600 640
Retained earnings 1,320 1,629
Total $1,920 $2,269
Total assets $2,756 $3,112 Total liabilities and owners’ equity $2,756 $3,112
Balance sheets for
U.S. Corporation
TABLE 2.1
EXAMPLE 2.1 Building the Balance Sheet
A firm has current assets of $100, net fixed assets of $500, short-term debt of $70, and long-term
debt of $200. What does the balance sheet look like? What is shareholders’ equity? What is net
working capital?
In this case, total assets are $100 + 500 = $600 and total liabilities are $70 + 200 = $270,
so shareholders’ equity is the difference: $600 − 270 = $330. The balance sheet would thus
look like:
(continued)
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C H A P T E R 2 Financial Statements, Taxes, and Cash Flow 25
Liquidity
Liquidity refers to the speed and ease with which an asset can be converted to cash. Gold is
a relatively liquid asset; a custom manufacturing facility is not. Liquidity really has two di-
mensions: ease of conversion versus loss of value. Any asset can be converted to cash
quickly if we cut the price enough. A highly liquid asset, therefore, is one that can be quickly
sold without significant loss of value. An illiquid asset is one that cannot be quickly con-
verted to cash without a substantial price reduction.
Assets are normally listed on the balance sheet in order of decreasing liquidity,
meaning that the most liquid assets are listed first. Current assets are relatively liquid
and include cash and those assets that we expect to convert to cash over the next
12 months. Accounts receivable, for example, represent amounts not yet collected
from customers on sales already made. Naturally, we hope these will convert to cash in
the near future. Inventory is probably the least liquid of the current assets, at least for
many businesses.
Fixed assets are, for the most part, relatively illiquid. These consist of tangible things
such as buildings and equipment that don’t convert to cash at all in normal business activity
(they are, of course, used in the business to generate cash). Intangible assets, such as trade-
marks, have no physical existence but can be very valuable. Like tangible fixed assets, they
won’t ordinarily convert to cash and are generally considered illiquid.
Liquidity is valuable. The more liquid a business is, the less likely it is to experience
financial distress (i.e., difficulty in paying debts or buying needed assets). Unfortunately,
liquid assets are generally less profitable to hold. For example, cash holdings are the most
liquid of all investments, but they sometimes earn no return at all—they just sit there.
There is, therefore, a trade-off between the advantages of liquidity and forgone potential
profits.
Debt versus Equity
To the extent that a firm borrows money, it usually gives first claim to the firm’s cash flow
to creditors. Equity holders are entitled only to the residual value, the portion left after
creditors are paid. The value of this residual portion is the shareholders’ equity in the firm,
which is the value of the firm’s assets less the value of the firm’s liabilities:
Shareholders’ equity = Assets − Liabilities
This is true in an accounting sense because shareholders’ equity is defined as this residual
portion. More importantly, it is true in an economic sense: If the firm sells its assets and
pays its debts, whatever cash is left belongs to the shareholders.
Annual and quarterly
financial statements (and
lots more) for most public
U.S. corporations can be
found in the EDGAR
data base at www.sec.gov.
The home page for the
Financial Accounting
Standards Board (FASB)
is www.fasb.org.
Assets Liabilities and Shareholders’ Equity
Current assets $6100 Current liabilities $ 70
Net fixed assets 500 Long-term debt 200
Shareholders’ equity 330
Total assets $600 Total liabilities and shareholders’ equity $600
Net working capital is the difference between current assets and current liabilities, or $100 − 70 = $30.
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26 P A R T 2 Understanding Financial Statements and Cash Flow
The use of debt in a firm’s capital structure is called financial leverage. The more
debt a firm has (as a percentage of assets), the greater is its degree of financial leverage.
As we discuss in later chapters, debt acts like a lever in the sense that using it can greatly
magnify both gains and losses. So, financial leverage increases the potential reward to
shareholders, but it also increases the potential for financial distress and business
failure.
Market Value versus Book Value
The true value of any asset is its market value, which is the amount of cash we would
get if we actually sold it. In contrast, the values shown on the balance sheet for the
firm’s assets are book values and generally are not what the assets are actually worth.
Under Generally Accepted Accounting Principles (GAAP), audited financial statements
in the United States generally show assets at historical cost. In other words, assets are
“carried on the books” at what the firm paid for them (minus accumulated deprecia-
tion), no matter how long ago they were purchased or how much they are worth
today.
For current assets, market value and book value might be somewhat similar because
current assets are bought and converted into cash over a relatively short span of time. In
other circumstances, they might differ quite a bit. Moreover, for fixed assets, it would be
purely a coincidence if the actual market value of an asset (what the asset could be sold for)
were equal to its book value. For example, a railroad might own enormous tracts of land
purchased a century or more ago. What the railroad paid for that land could be hundreds or
thousands of times less than what it is worth today. The balance sheet would nonetheless
show the historical cost. There are exceptions to this practice.
Managers and investors frequently will be interested in knowing the market value of the
firm. This information is not on the balance sheet. The fact that balance sheet assets are
listed at cost means that there is no necessary connection between the total assets shown
and the market value of the firm. Indeed, many of the most valuable assets that a firm might
have—good management, a good reputation, talented employees—don’t appear on the bal-
ance sheet at all. To give one example, one of the most valuable assets for many well-known
companies is their brand name. According to one source, the names “Coca-Cola,” “Micro-
soft,” and “IBM” are all worth in excess of $50 billion.
Similarly, the owners’ equity figure on the balance sheet and the true market value of
the equity need not be related. For financial managers, then, the accounting value of the
equity is not an especially important concern; it is the market value that matters. Hence-
forth, whenever we speak of the value of an asset or the value of the firm, we will normally
mean its market value. So, for example, when we say the goal of the financial manager is to
increase the value of the stock, we mean the market value of the stock.
Generally Accepted
Accounting
Principles (GAAP)
The common set of
standards and procedures
by which audited financial
statements are prepared.
EXAMPLE 2.2 Market versus Book Values
The Klingon Corporation has fixed assets with a book value of $700 and an appraised market
value of about $1,000. Current assets are $400 on the books, but approximately $600 would be
realized if they were liquidated. Klingon has $500 in long-term debt, both book value and market
value, and no current liabilities of any kind. What is the book value of the equity? What is the
market value?
We can construct two simplified balance sheets, one in accounting (book value) terms and one
in economic (market value) terms:
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C H A P T E R 2 Financial Statements, Taxes, and Cash Flow 27
CONCEPT QUESTIONS
2.1a What is the balance sheet identity?
2.1b What is liquidity? Why is it important?
2.1c What do we mean by financial leverage?
2.1d Explain the difference between accounting value and market value. Which is more
important to the financial manager? Why?
THE INCOME STATEMENT
The income statement measures performance over some period of time, usually a quarter
or a year. The income statement equation is:
Revenues − Expenses = Income [2.2]
If you think of the balance sheet as a snapshot, then you can think of the income statement
as a video recording covering the period between a before and an after picture. Table 2.2
gives a simplified income statement for U.S. Corporation.
2.2
income statement
Financial statement
summarizing a firm’s
performance over a period
of time.
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Income statement for
U.S. Corporation
TABLE 2.2U.S. CORPORATION
2019 Income Statement
($ in Millions)
Net sales $1,509
Cost of goods sold 750
Depreciation 89
Earnings before interest and taxes $ 670
Interest paid 70
Taxable income $ 600
Taxes (21%) 126
Net income $ 474
Dividends $165
Addition to retained earnings 309
KLINGON CORPORATION
Balance Sheets
Market Value versus Book Value
Book Market Book Market
Assets Liabilities and Shareholders’ Equity
Current assets $ 400 $ 600 Long-term debt $ 500 $ 500
Net fixed assets 700 1,000 Shareholders’ equity 600 1,100
$1,100 $1,600 $1,100 $1,600
In this example, shareholders’ equity is actually worth almost twice as much as what is shown on
the books. The distinction between book and market values is important precisely because book
values can be so different from true economic values.
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28 P A R T 2 Understanding Financial Statements and Cash Flow
The first thing reported on an income statement is usually revenue and expenses from
the firm’s principal operations. Subsequent parts include, among other things, financing
expenses such as interest paid. Taxes paid are reported separately. The last item is net
income (the so-called bottom line). Net income often is expressed on a per-share basis and
called earnings per share (EPS).
As indicated, U.S. paid cash dividends of $165. The difference between net income and
cash dividends, $309, is the addition to retained earnings for the year. This amount is added
to the cumulative retained earnings account on the balance sheet. If you look back at the
two balance sheets for U.S. Corporation, you’ll see that retained earnings did go up by this
amount, $1,320 + 309 = $1,629.
EXAMPLE 2.3 Earnings and Dividends per Share
Suppose U.S. Corporation had 200 million shares outstanding at the end of 2019. Based on the in-
come statement in Table 2.2, what was EPS? What were dividends per share?
From the income statement, U.S. Corporation had a net income of $474 million for the year.
Total dividends were $165 million. Because 200 million shares were outstanding, we can calculate
earnings per share and dividends per share as follows:
Earnings per share = Net income/Total shares outstanding
= $474 / 200 = $2.37 per share
Dividends per share = Total dividends/Total shares outstanding
= $165/200 = $.825 per share
When looking at an income statement, the financial manager needs to keep three things
in mind: GAAP, cash versus noncash items, and time and costs.
GAAP and the Income Statement
An income statement prepared using GAAP will show revenue when it accrues. This is not
necessarily when the cash comes in. The general rule (the recognition principle) is to recognize
revenue when the earnings process is virtually complete and the value of an exchange of goods
or services is known or can be reliably determined. In practice, this principle usually means that
revenue is recognized at the time of sale, which need not be the same as the time of collection.
Expenses shown on the income statement are based on the matching principle. The
basic idea here is to first determine revenues as described earlier and then match those rev-
enues with the costs associated with producing them. So, if we manufacture a product and
then sell it on credit, the revenue is recognized at the time of sale. The production and other
costs associated with the sale of that product likewise would be recognized at that time.
Once again, the actual cash outflows may have occurred at some very different times. Thus,
as a result of the way revenues and expenses are reported, the figures shown on the income
statement may not be at all representative of the actual cash inflows and outflows that oc-
curred during a particular period.
Noncash Items
A primary reason that accounting income differs from cash flow is that an income state-
ment contains noncash items. The most important of these is depreciation. Suppose a firm
noncash items
Expenses charged against
revenues that do not
directly affect cash flow,
such as depreciation.
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C H A P T E R 2 Financial Statements, Taxes, and Cash Flow 29
purchases a fixed asset for $5,000 and pays in cash. Obviously, the firm has a $5,000 cash
outflow at the time of purchase. However, instead of deducting the $5,000 as an expense, an
accountant might depreciate the asset over a five-year period.
If the depreciation is straight-line and the asset is written down to zero over that period,
then $5,000/5 = $1,000 would be deducted each year as an expense.2 The important thing
to recognize is that this $1,000 deduction isn’t cash—it’s an accounting number. The actual
cash outflow occurred when the asset was purchased.
The depreciation deduction is another application of the matching principle in ac-
counting. The revenues associated with an asset would generally occur over some length of
time. So, the accountant seeks to match the expense of purchasing the asset with the bene-
fits produced from owning it.
As we will see, for the financial manager, the actual timing of cash inflows and outflows
is critical in coming up with a reasonable estimate of market value, so we need to learn how
to separate the cash flows from the noncash accounting entries. In reality, the difference
between cash flow and accounting income can be pretty dramatic. For example, in the third
quarter of 2017, wireless infrastructure company Westell Technologies announced a net loss
of $14.5 million. Sounds bad, but the company also reported a positive cash flow of $26.6
million, a difference of $41.1 million.
Time and Costs
It is often useful to think of the future as having two distinct parts: the short run and the
long run. These are not precise time periods. The distinction has to do with whether costs
are fixed or variable. In the long run, all business costs are variable. Given sufficient time,
assets can be sold, debts can be paid, and so on.
If our time horizon is relatively short, however, some costs are effectively fixed—they
must be paid no matter what (e.g., property taxes). Other costs, such as wages to laborers
and payments to suppliers, are still variable. As a result, even in the short run, the firm can
vary its output level by varying expenditures in these areas.
The distinction between fixed and variable costs is important, at times, to the financial
manager, but the way costs are reported on the income statement is not a good guide as to
which costs are which. The reason is that, in practice, accountants tend to classify costs as
either product costs or period costs.
Product costs include such things as raw materials, direct labor expense, and manu-
facturing overhead. These are reported on the income statement as costs of goods sold,
but they include both fixed and variable costs. Similarly, period costs are incurred during
a particular time period and might be reported as selling, general, and administrative
expenses. Once again, some of these period costs may be fixed and others may be vari-
able. The company president’s salary is a period cost and is probably fixed, at least in the
short run.
The balance sheets and income statement we have been using thus far are hypothetical.
Our nearby Work the Web box shows how to find actual balance sheets and income state-
ments online for almost any public company.
2By “straight-line,” we mean that the depreciation deduction is the same every year. By “written down to zero,” we
mean that the asset is assumed to have no value at the end of five years.
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30 P A R T 2 Understanding Financial Statements and Cash Flow
Earnings Management
The way that firms are required by GAAP to report financial results is intended to be objec-
tive and precise. In reality, there is plenty of wiggle room, and, as a result, companies have
significant discretion over their reported earnings. For example, corporations frequently like
to show investors that they have steadily growing earnings. To do this, they might take steps
to overstate or understate earnings at various times to smooth out dips and surges. Doing so
is called earnings management, and it is a controversial practice.
QUESTIONS
1. Before the popularization of computers, electronic filing of documents with the SEC
was not available. Go to www.sec.gov and find the filings for General Electric. What is
the date of the oldest 10-K available on the website for General Electric? Look up the
10-K forms for IBM and Apple to see if the year of the first electronic filing is the same
for these companies.
2. Go to www.sec.gov and find out when the following forms are used: Form DEF 14A,
Form 8-K, and Form 6-K.
Source: www.sec.gov
As of the date of this search, EDGAR had 24 of these reports for Microsoft available for download-
ing. The 10-K is the annual report filed with the SEC. It includes, among other things, the list of
officers and their salaries, financial statements for the previous fiscal year, and an explanation by
the company for the financial results. Here is an exercise for you: Go to the “Descriptions of
SEC Forms” page and find the different forms companies must file with the SEC. What is a
10-Q report?
W R K T H E W E B
The U.S. Securities and Exchange Commission (SEC) requires that most public companies file regular reports, including annual and quarterly financial statements. The SEC has a public site
named EDGAR that makes these reports available for free at www.sec.gov. We went to “Company
Filings Search” and searched for “Microsoft.” When we got our results, we limited our search to
Form 10-K. Here is what we found:
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C H A P T E R 2 Financial Statements, Taxes, and Cash Flow 31
With the increasing globalization of business, accounting standards need to be more
alike across countries. In recent years, U.S. accounting standards have increasingly be-
come more closely tied to International Financial Reporting Standards (IFRS). In partic-
ular, the Financial Accounting Standards Board (in charge of U.S. GAAP) and the
International Accounting Standards Board (in charge of IFRS) have been working toward
a convergence of policies. Although GAAP and IFRS have become similar in several
areas, as of 2018, it appears that a full convergence of accounting policies is off the table,
at least for now.
CONCEPT QUESTIONS
2.2a What is the income statement equation?
2.2b What are the three things to keep in mind when looking at an income statement?
2.2c Why is accounting income not the same as cash flow?
TAXES
Taxes can be one of the largest cash outflows a firm experiences. For example, for fiscal year
2018, Walmart’s earnings before taxes were about $15.1 billion. Its tax bill, including all
taxes paid worldwide, was a whopping $4.6 billion, or about 30 percent of its pretax
earnings.
The size of a company’s tax bill is determined through the tax code, an often-amended
set of rules. In this section, we examine corporate tax rates and how taxes are calculated. If
the various rules of taxation seem a little bizarre or convoluted to you, keep in mind that the
tax code is the result of political, not economic, forces. As a result, there is no reason why it
has to make economic sense.
Corporate Tax Rates
As we discussed in our chapter introduction, after the passage of the Tax Cuts and Jobs
Act of 2017, the federal corporate tax rate in the United States became a flat 21 percent.
However, tax rates on other forms of business such as proprietorships, partnerships, and
LLCs did not become flat. To illustrate some important points about taxes for such enti-
ties, we take a look at personal tax rates in Table 2.3. As shown, in 2018, there are seven
tax brackets, ranging from 10 percent to a high of 37 percent, down from 39.6 percent
in 2017.
For more information
about IFRS, check out the
website www.ifrs.org.
2.3
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The IRS has a great
website! (www.irs.gov)
Taxable Income Tax Rate
$ 0− 9,525 10%
9,525− 38,700 12
38,700− 82,500 22
82,500− 157,500 24
157,500− 200,000 32
200,000− 500,000 35
500,000+ 37
Personal tax rates for
2018 (unmarried
individuals)
TABLE 2.3
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32 P A R T 2 Understanding Financial Statements and Cash Flow
Average versus Marginal Tax Rates
In making financial decisions, it is frequently important to distinguish between average
and marginal tax rates. Your average tax rate is your tax bill divided by your taxable
income; in other words, the percentage of your income that goes to pay taxes. Your
marginal tax rate is the extra tax you would pay if you earned one more dollar. The
percentage tax rates shown in Table 2.3 are all marginal rates. Put another way, the tax
rates in Table 2.3 apply to the part of income in the indicated range only, not all
income.
The difference between average and marginal tax rates can be best illustrated with a
simple example. Suppose you are single and your personal taxable income is $100,000.
What is your tax bill? From Table 2.3, we can figure your tax bill like this:
.10($9,525) = $ 952.50
.12($38,700 – 9,525) = 3,501.00
.22($82,500 – 38,700) = 9,636.00
.24($100,000 – 82,500) = 4,200.00
$18,289.50
Your total tax is $18,289.50.
In our example, what is the average tax rate? You had a taxable income of $100,000 and
a tax bill of $18,289.50, so the average tax rate is $18,289.50/$100,000 = .1829, or 18.29%.
What is the marginal tax rate? If you made one more dollar, the tax on that dollar would be
24 cents, so your marginal rate is 24 percent.
average tax rate
Total taxes paid divided by
total taxable income.
marginal tax rate
Amount of tax payable on
the next dollar earned.
EXAMPLE 2.4 Deep in the Heart of Taxes
Algernon, a small proprietorship owned by an unmarried individual, has a taxable income of
$80,000. What is its tax bill? What is its average tax rate? Its marginal tax rate?
From Table 2.3, we see that the tax rate applied to the first $9,525 is 10 percent; the rate
applied over that up to $38,700 is 12 percent; the rate applied after that up to our total of $80,000
is 22 percent. So Algernon must pay .10 × $9,525 + .12 × ($38,700 − 9,525) + .22 × ($80,000 −
38,700) = $13,540. The average tax rate is thus $13,540/$80,000 = .1692, or 16.92%. The marginal
rate is 22 percent because Algernon’s taxes would rise by 22 cents if it earned another dollar in
taxable income.
It will normally be the marginal tax rate that is relevant for financial decision making.
The reason is that any new cash flows will be taxed at that marginal rate. Because financial
decisions usually involve new cash flows or changes in existing ones, this rate will tell us the
marginal effect on our tax bill.
With a flat-rate tax, such as the U.S. federal corporate tax (as of 2018), there is only one
tax rate, so the rate is the same for all income levels. With such a tax system, the marginal
tax rate is always the same as the average tax rate.
Before moving on, we should note that the tax rates we have discussed in this section
relate to federal taxes only. Overall tax rates can be higher if state, local, and any other taxes
are considered.
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CONCEPT QUESTION
2.3a What is the difference between a marginal and an average tax rate?
CASH FLOW
At this point, we are ready to discuss perhaps one of the most important pieces of financial infor-
mation that can be gleaned from financial statements: cash flow. By cash flow, we mean the differ-
ence between the number of dollars that came in and the number that went out. For example, if you
were the owner of a business, you might be very interested in how much cash you actually took out
of your business in a given year. How to determine this amount is one of the things we discuss next.
There is no standard financial statement that presents this information in the way that
we wish. We will, therefore, discuss how to calculate cash flow for U.S. Corporation and
point out how the result differs from that of standard financial statement calculations.
2.4
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What Is Warren Buffett’s Tax Rate?
In 2011, famed investor Warren Buffett, one of the wealthi-est individuals in the world, created a stir when he publicly
stated that his tax rate was lower than the tax rate paid by
his secretary. The previous year, Buffett’s gross income was
about $63 million, on which he paid only a 15 percent tax
rate. (Remember, this was before the Tax Cuts and Jobs Act
of 2017.) His secretary (with a substantially lower income)
had a 31 percent marginal tax rate. Also in 2011, when Re-
publican presidential contender Mitt Romney released his
income taxes, it was revealed that he, too, paid an income
tax rate of only 15 percent on his $21 million annual
income.
Why do Buffett’s and Romney’s tax rates appear so
low? Currently, under the U.S. tax system, wage income is
taxed at a much higher rate than dividends and long-term
capital gains. In fact, in 2011, in the highest tax bracket, wage
income was taxed at 37 percent, while dividends and long-
term capital gains were taxed at 15 percent. For Buffett and
Romney, most of their annual income comes from their in-
vestments, not wages, hence the 15 percent rate.
So do rich guys get all the (tax) breaks? Former U.S.
President Barack Obama seems to think so. In his 2012 State
of the Union Address, with Buffett’s secretary Debbie
Bosanek joining First Lady Michelle Obama in her box as a
special guest, he called for the creation of a “Buffett tax.” As
he described it, such a tax would be an extra tax paid by
very high-income individuals. Maybe President Obama was
mad about the fact that he and the first lady paid (in 2013)
$98,169 in federal taxes on their joint income of $481,098,
implying an average tax rate of 20.4 percent.
Of course, you know that income received from divi-
dends is already taxed. Dividends are paid from corporate
income, which was taxed at 35 percent for larger dividend-
paying companies. Effectively, any tax on dividends is dou-
ble taxation on that money. The tax code realizes this. The
lower tax rate on dividends lowers the double tax rate. The
same thing is true for capital gains; taxes are paid on the
money before the investment is made.
In Buffett’s case, most of his wealth stems from his approx-
imately 30 percent ownership of Berkshire Hathaway Corpora-
tion. Based on its 23,000 (no typo!)-page tax return, Berkshire’s
2014 corporate tax bill was $7.9 billion on pretax income
of $28.1 billion—a 28 percent average rate. Buffett’s share of
Berkshire’s tax bill therefore amounts to something on the
order of $2.37 billion! If we include Berkshire’s corporate taxes,
Buffett’s average tax rate is more like 28 + 15 = 43 percent.
To give another example, consider the situation de-
scribed by N. Gregory Mankiw, the well-known economist
and textbook author. Mankiw considers taking a writing job
for $1,000. He figures that if he earns an 8 percent return and
there are no taxes, he would be able to leave his children
about $10,000 in 30 years when he passes on. However, be-
cause of federal, state, and Medicare taxes, he would receive
only about $523 after taxes today. And because of corporate
taxes and personal income taxes, his return on the same in-
vestment would be only about 4 percent, which will result in
a balance of $1,700 in 30 years. When he dies, his account
will be taxed using the marginal estate tax rate, which is as
high as 55 percent. As a result, his children will receive only
about $1,000, implying a tax rate of 90 percent!
FINANCE MATTERS
33
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34 P A R T 2 Understanding Financial Statements and Cash Flow
Important note: There is a standard financial accounting statement called the statement of
cash flows, but it is concerned with a somewhat different issue that should not be confused
with what is discussed in this section.
From the balance sheet identity, we know that the value of a firm’s assets is equal to the
value of its liabilities plus the value of its equity. Similarly, the cash flow from the firm’s as-
sets must equal the sum of the cash flow to creditors and the cash flow to stockholders (or
owners, if the business is not a corporation):
Cash flow from assets = Cash flow to creditors + Cash flow to stockholders [2.3]
This is the cash flow identity. What it reflects is the fact that a firm generates cash through
its various activities, and that cash either is used to pay creditors or else is paid out to the
owners of the firm. We discuss the various things that make up these cash flows next.
Cash Flow from Assets
Cash flow from assets involves three components: operating cash flow, capital spending,
and change in net working capital. Operating cash flow refers to the cash flow that results
from the firm’s day-to-day activities of producing and selling. Expenses associated with the
firm’s financing of its assets are not included because they are not operating expenses.
In the normal course of events, some portion of the firm’s cash flow is reinvested in the
firm. Capital spending refers to the net spending on fixed assets (purchases of fixed assets
less sales of fixed assets). Finally, the change in net working capital is the amount spent on
net working capital. It is measured as the change in net working capital over the period be-
ing examined and represents the net increase or decrease in current assets over current lia-
bilities. The three components of cash flow are examined in more detail next. In all our
examples, all amounts are in millions of dollars.
Operating Cash Flow To calculate operating cash flow (OCF), we want to calculate
revenues minus costs, but we don’t want to include depreciation because it’s not a cash out-
flow, and we don’t want to include interest because it’s a financing expense. We do want to
include taxes because taxes are, unfortunately, paid in cash.
If we look at U.S. Corporation’s income statement (Table 2.2), we see that earnings
before interest and taxes (EBIT) are $670. This is almost what we want because it doesn’t
include interest paid. We need to make two adjustments. First, recall that depreciation is a
noncash expense. To get cash flow, we first add back the $89 in depreciation because it
wasn’t a cash deduction. The other adjustment is to subtract the $126 in taxes because these
were paid in cash. The result is operating cash flow:
U.S. CORPORATION
2019 Operating Cash Flow
Earnings before interest and taxes $670
+ Depreciation 89
− Taxes 126
Operating cash flow $633
U.S. Corporation thus had a 2019 operating cash flow of $633.
Operating cash flow is an important number because it tells us, on a very basic level,
whether or not a firm’s cash inflows from its business operations are sufficient to cover its every-
day cash outflows. For this reason, a negative operating cash flow is often a sign of trouble.
There is an unpleasant possibility for confusion when we speak of operating cash flow. In
accounting practice, operating cash flow often is defined as net income plus depreciation. For
U.S. Corporation, this would amount to $474 + 89 = $563. The accounting definition of
cash flow from assets
The total of cash flow to
creditors and cash flow to
stockholders, consisting of
the following: operating
cash flow, capital
spending, and change in
net working capital.
operating cash flow
Cash generated from a
firm’s normal business
activities.
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C H A P T E R 2 Financial Statements, Taxes, and Cash Flow 35
operating cash flow differs from ours in one important way: Interest is deducted when net in-
come is computed. Notice that the difference between the $633 operating cash flow we calcu-
lated and this $563 is $70, the amount of interest paid for the year. This definition of cash flow
thus considers interest paid to be an operating expense. Our definition treats it properly as a
financing expense. If there were no interest expense, the two definitions would be the same.
To finish our calculation of cash flow from assets for U.S. Corporation, we need to
consider how much of the $633 operating cash flow was reinvested in the firm. We consider
spending on fixed assets first.
Capital Spending Net capital spending is money spent on fixed assets less money received
from the sale of fixed assets. At the end of 2018, net fixed assets for U.S. Corporation (Table 2.1)
were $1,644. During the year, we wrote off (depreciated) $89 worth of fixed assets on the in-
come statement. So, if we didn’t purchase any new fixed assets, net fixed assets would have been
$1,644 − 89 = $1,555 at year’s end. The 2019 balance sheet shows $1,709 in net fixed assets, so
we must have spent a total of $1,709 − 1,555 = $154 on fixed assets during the year:
Ending net fixed assets $1,709
− Beginning net fixed assets 1,644
+ Depreciation 89
Net investment in fixed assets $ 154
This $154 is our net capital spending for 2019.
Could net capital spending be negative? The answer is yes. This would happen if the
firm sold off more assets than it purchased. The net here refers to purchases of fixed assets
net of any sales of fixed assets.
Change in Net Working Capital In addition to investing in fixed assets, a firm
also will invest in current assets. For example, going back to the balance sheet in Table 2.1, we
see that at the end of 2019, U.S. had current assets of $1,403. At the end of 2018, current as-
sets were $1,112, so, during the year, U.S. invested $1,403 − 1,112 = $291 in current assets.
As the firm changes its investment in current assets, its current liabilities usu-
ally will change as well. To determine the change in net working capital, the easiest approach
is to take the difference between the beginning and ending net working capital (NWC) fig-
ures. Net working capital at the end of 2019 was $1,403 − 389 = $1,014. Similarly, at the
end of 2018, net working capital was $1,112 − 428 = $684. So, given these figures, we have:
Ending NWC $1,014
− Beginning NWC 684
Change in NWC $ 330
Net working capital thus increased by $330. Put another way, U.S. Corporation had a net
investment of $330 in NWC for the year.
Conclusion Given the figures we’ve come up with, we’re ready to calculate cash flow
from assets. The total cash flow from assets is given by operating cash flow less the amounts
invested in fixed assets and net working capital. So, for U.S., we have:
U.S. CORPORATION
2019 Cash Flow from Assets
Operating cash flow $633
− Net capital spending 154
− Change in NWC 330
Cash flow from assets $ 149
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36 P A R T 2 Understanding Financial Statements and Cash Flow
From the cash flow identity above, this $149 cash flow from assets equals the sum of the
firm’s cash flow to creditors and its cash flow to stockholders. We consider these next.
It wouldn’t be at all unusual for a growing corporation to have a negative cash flow. As
we shall see below, a negative cash flow means that the firm raised more money by borrow-
ing and selling stock than it paid out to creditors and stockholders that year.
A Note on “Free” Cash Flow Cash flow from assets sometimes goes by a different
name, free cash flow. Of course, there is no such thing as “free” cash (we wish!). Instead,
the name refers to cash that the firm is free to distribute to creditors and stockholders be-
cause it is not needed for working capital or fixed asset investments. We will stick with “cash
flow from assets” as our label for this important concept because, in practice, there is some
variation in exactly how free cash flow is computed; different users calculate it in different
ways. Nonetheless, whenever you hear the phrase “free cash flow,” you should understand
that what is being discussed is cash flow from assets or something quite similar.
Cash Flow to Creditors and Stockholders
The cash flows to creditors and stockholders represent the net payments to creditors and
owners during the year. They are calculated in a similar way. Cash flow to creditors is inter-
est paid less net new borrowing; cash flow to stockholders is dividends paid less net new
equity raised.
Cash Flow to Creditors Looking at the income statement in Table 2.2, we see that
U.S. Corporation paid $70 in interest to creditors. From the balance sheets in Table 2.1,
long-term debt rose by $454 − 408 = $46. So, U.S. Corporation paid out $70 in interest,
but it borrowed an additional $46. Net cash flow to creditors is thus:
U.S. CORPORATION
2019 Cash Flow to Creditors
Interest paid $70
− Net new borrowing 46
Cash flow to creditors $24
Cash flow to creditors is sometimes called cash flow to bondholders; we will use these
terms interchangeably.
Cash Flow to Stockholders From the income statement, dividends paid to stock-
holders amount to $165. To get net new equity raised, we need to look at the common stock
and paid-in surplus account. This account tells us how much stock the company has sold.
During the year, this account rose by $40, so $40 in net new equity was raised. Given this,
we have:
U.S. CORPORATION
2019 Cash Flow to Stockholders
Dividends paid $ 165
− Net new equity raised 40
Cash flow to stockholders $ 125
The cash flow to stockholders for 2019 was thus $125.
free cash flow
Another name for cash
flow from assets.
cash flow to creditors
A firm’s interest payments
to creditors less net new
borrowing.
cash flow to
stockholders
Dividends paid out by a
firm less net new equity
raised.
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C H A P T E R 2 Financial Statements, Taxes, and Cash Flow 37
Conclusion
The last thing that we need to do is to verify that the cash flow identity holds to be sure that
we didn’t make any mistakes. From above, cash flow from assets is $149. Cash flow to credi-
tors and stockholders is $24 + 125 = $149, so everything checks out. Table 2.4 contains a
summary of the various cash flow calculations for future reference.
An Example: Cash Flows for Dole Cola
This extended example covers the various cash flow calculations discussed in the chapter. It
also illustrates a few variations that may arise.
Operating Cash Flow During the year, Dole Cola, Inc., had sales and cost of goods
sold of $600 and $300, respectively. Depreciation was $150, and interest paid was $30.
Taxes were calculated at a straight 21 percent. Dividends were $30. (All figures are in mil-
lions of dollars.) What was operating cash flow for Dole? Why is this different from net
income?
The easiest thing to do here is to go ahead and create an income statement. We can
then pick up the numbers we need. Dole Cola’s income statement is given here:
DOLE COLA
2019 Income Statement
Net sales $600
Cost of goods sold 300
Depreciation 150
Earnings before interest and taxes $150
Interest paid 30
Taxable income $120
Taxes 25
Net income $ 95
Dividends $30
Addition to retained earnings 65
I. ….The cash flow identity
Cash flow from assets = Cash flow to creditors (bondholders)
+ Cash flow to stockholders (owners)
II. ….Cash flow from assets
Cash flow from assets = Operating cash flow
− Net capital spending
− Change in net working capital (NWC)
where
Operating cash flow = Earnings before interest and taxes (EBIT)
+ Depreciation − Taxes
Net capital spending = Ending net fixed assets − Beginning net fixed assets
+ Depreciation
Change in NWC = Ending NWC − Beginning NWC
III. ….Cash flow to creditors (bondholders)
Cash flow to creditors = Interest paid − Net new borrowing
IV. ….Cash flow to stockholders (owners)
Cash flow to stockholders = Dividends paid − Net new equity raised
Cash flow summary
TABLE 2.4
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38 P A R T 2 Understanding Financial Statements and Cash Flow
Net income for Dole was thus $95. We now have all the numbers we need. Referring
back to the U.S. Corporation example and Table 2.4, we have:
DOLE COLA
2019 Operating Cash Flow
Earnings before interest and taxes $150
+ Depreciation 150
− Taxes 25
Operating cash flow $275
As this example illustrates, operating cash flow is not the same as net income because
depreciation and interest are subtracted out when net income is calculated. If you recall our
earlier discussion, we don’t subtract these out in computing operating cash flow because
depreciation is not a cash expense and interest paid is a financing expense, not an operating
expense.
Net Capital Spending Suppose beginning net fixed assets were $500 and ending net
fixed assets were $750. What was the net capital spending for the year?
From the income statement for Dole, depreciation for the year was $150. Net fixed
assets rose by $250. Dole thus spent $250 along with an additional $150, for a total
of $400.
Change in NWC and Cash Flow from Assets Suppose Dole Cola started the
year with $2,130 in current assets and $1,620 in current liabilities. The corresponding end-
ing figures were $2,260 and $1,710. What was the change in NWC during the year? What
was cash flow from assets? How does this compare to net income?
Net working capital started out as $2,130 − 1,620 = $510 and ended up at $2,260 −
1,710 = $550. The change in NWC was thus $550 − 510 = $40. Putting together all the
information for Dole Cola, we have:
DOLE COLA
2019 Cash Flow from Assets
Operating cash flow $275
− Net capital spending 400
− Change in NWC 40
Cash flow from assets −$165
Dole had cash flow from assets of −$165. Net income was positive at $95. Is the fact that
cash flow from assets was negative a cause for alarm? Not necessarily. The cash flow here is
negative primarily because of a large investment in fixed assets. If these are good invest-
ments, then the resulting negative cash flow is not a worry.
Cash Flow to Creditors and Stockholders We saw that Dole Cola had cash
flow from assets of −$165. The fact that this is negative means that Dole raised more
money in the form of new debt and equity than it paid out for the year. For example,
suppose we know that Dole didn’t sell any new equity for the year. What was cash flow to
stockholders? To creditors?
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C H A P T E R 2 Financial Statements, Taxes, and Cash Flow 39
Because it didn’t raise any new equity, Dole’s cash flow to stockholders is equal to the
cash dividend paid:
DOLE COLA
2019 Cash Flow to Stockholders
Dividends paid $30
− Net new equity 0
Cash flow to stockholders $30
Now, from the cash flow identity, the total cash paid to creditors and stockholders was
−$165. Cash flow to stockholders is $30, so cash flow to creditors must be equal to −$165
− 30 = −$195:
Cash flow to creditors + Cash flow to stockholders = –$165
Cash flow to creditors + $30 = –$165
Cash flow to creditors = –$195
Because we know that cash flow to creditors is −$195 and interest paid is $30 (from
the income statement), we can now determine net new borrowing. Dole must have
borrowed $225 during the year to help finance the fixed asset expansion:
DOLE COLA
2019 Cash Flow to Creditors
Interest paid $ 30
− Net new borrowing 225
Cash flow to creditors −$195
CONCEPT QUESTIONS
2.4a What is the cash flow identity? Explain what it says.
2.4b What are the components of operating cash flow?
2.4c Why is interest paid not a component of operating cash flow?
SUMMARY AND CONCLUSIONS
This chapter has introduced you to some of the basics of financial statements, taxes, and
cash flow. In it, we saw that:
1. The book values on an accounting balance sheet can be very different from market
values. The goal of financial management is to maximize the market value of the
stock, not its book value.
2. Net income, as it is computed on the income statement, is not cash flow. A primary
reason is that depreciation, a noncash expense, is deducted when net income is
computed.
3. Marginal and average tax rates can be different, and it is the marginal tax rate that is
relevant for most financial decisions.
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40 P A R T 2 Understanding Financial Statements and Cash Flow
4. After the Tax Cuts and Jobs Act of 2017, the U.S. corporate income tax is a flat
21 percent.
5. There is a cash flow identity much like the balance sheet identity. It says that cash
flow from assets equals cash flow to creditors and stockholders.
The calculation of cash flow from financial statements isn’t difficult. Care must be
taken in handling noncash expenses, such as depreciation, and in not confusing operating
costs with financing costs. Most of all, it is important not to confuse book values with mar-
ket values and accounting income with cash flow.
POP QUIZ!
Can you answer the following questions? If your class is using Connect, log on to
SmartBook to see if you know the answers to these and other questions, check out
the study tools, and find out what topics require additional practice!
Section 2.1 What is the relationship between current assets and current liabilities in
a healthy firm?
Section 2.2 What is the purpose of the income statement?
Section 2.3 If you make an extra $1,000 in income and your marginal tax rate is
32 percent while your average tax rate is 20 percent, what will you pay in taxes on
this extra income?
Section 2.4 What are the components of cash flow from assets?
CHAPTER REVIEW AND SELF-TEST PROBLEM
2.1 Cash Flow for Rasputin Corporation This problem will give you some practice
working with financial statements and figuring cash flow. Based on the following
information for Rasputin Corporation, prepare an income statement for 2019 and
balance sheets for 2018 and 2019. Next, following our U.S. Corporation examples in
the chapter, calculate cash flow from assets for Rasputin, cash flow to creditors, and
cash flow to stockholders for 2019. Use a 21 percent tax rate throughout. You can
check your answers below. (See Problem 20.)
2018 2019
Sales $3,790 $3,990
Cost of goods sold 2,043 2,137
Depreciation 975 1,018
Interest 225 267
Dividends 275 305
Current assets 2,140 2,346
Net fixed assets 6,770 7,087
Current liabilities 994 1,126
Long-term debt 2,869 2,962
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C H A P T E R 2 Financial Statements, Taxes, and Cash Flow 41
■ Answer to Chapter Review and Self-Test Problem
2.1 In preparing the balance sheets, remember that shareholders’ equity is the residual.
With this in mind, Rasputin’s balance sheets are as follows:
RASPUTIN CORPORATION
Balance Sheets as of December 31, 2018 and 2019
2018 2019 2018 2019
Current assets $2,140 $2,346 Current liabilities $ 994 $1,126
Net fixed assets 6,770 7,087 Long-term debt 2,869 2,962
Equity 5,047 5,345
Total liabilities and
Total assets $8,910 $9,433 shareholders’ equity $8,910 $9,433
The income statement is straightforward:
RASPUTIN CORPORATION
2019 Income Statement
Sales $3,990
Cost of goods sold 2,137
Depreciation 1,018
Earnings before interest and taxes $ 835
Interest paid 267
Taxable income $ 568
Taxes (21%) 119
Net income $ 449
Dividends $305
Addition to retained earnings 144
Notice that we’ve used a flat 21 percent tax rate. Also, notice that the addition to
retained earnings is net income less cash dividends.
We can now pick up the figures we need to get operating cash flow:
RASPUTIN CORPORATION
2019 Operating Cash Flow
Earnings before interest and taxes $ 835
+ Depreciation 1,018
− Current taxes 119
Operating cash flow $1,734
Next, we get the capital spending for the year by looking at the change in fixed
assets, remembering to account for the depreciation:
Ending fixed assets $7,087
− Beginning fixed assets 6,770
+ Depreciation 1,018
Net investment in fixed assets $1,335
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42 P A R T 2 Understanding Financial Statements and Cash Flow
After calculating beginning and ending NWC, we take the difference to get the
change in NWC:
Ending NWC $1,220
− Beginning NWC 1,146
Change in NWC $ 74
We now combine operating cash flow, net capital spending, and the change in
net working capital to get the total cash flow from assets:
RASPUTIN CORPORATION
2019 Cash Flow from Assets
Operating cash flow $1,734
− Net capital spending 1,335
− Change in NWC 74
Cash flow from assets $ 325
To get cash flow to creditors, notice that long-term borrowing increased by $93
during the year and that interest paid was $267, so:
RASPUTIN CORPORATION
2019 Cash Flow to Creditors
Interest paid $267
− Net new borrowing 93
Cash flow to creditors $174
Finally, dividends paid were $305. To get net new equity, we have to do some
extra calculating. Total equity was up by $5,345 − 5,047 = $298. Of this increase,
$144 was from additions to retained earnings, so $154 in new equity was raised during
the year. Cash flow to stockholders was thus:
RASPUTIN CORPORATION
2019 Cash Flow to Stockholders
Dividends paid $305
− Net new equity 154
Cash flow to stockholders $ 151
As a check, notice that cash flow from assets ($325) does equal cash flow to
creditors plus cash flow to stockholders ($174 + 151 = $325).
CRITICAL THINKING AND CONCEPTS REVIEW
LO 1 2.1 Liquidity What does liquidity measure? Explain the trade-off a firm faces
between high-liquidity and low-liquidity levels.
LO 2 2.2 Accounting and Cash Flows Why is it that the revenue and cost figures
shown on a standard income statement may not be representative of the
actual cash inflows and outflows that occurred during a period?
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C H A P T E R 2 Financial Statements, Taxes, and Cash Flow 43
LO 1 2.3 Book Values versus Market Values In preparing a balance sheet, why do
you think standard accounting practice focuses on historical cost rather
than market value?
LO 2 2.4 Operating Cash Flow In comparing accounting net income and operating
cash flow, what two items do you find in net income that are not in
operating cash flow? Explain what each is and why it is excluded in
operating cash flow.
LO 1 2.5 Book Values versus Market Values Under standard accounting rules, it is
possible for a company’s liabilities to exceed its assets. When this occurs,
the owners’ equity is negative. Can this happen with market values? Why or
why not?
LO 4 2.6 Cash Flow from Assets Suppose a company’s cash flow from assets was
negative for a particular period. Is this necessarily a good sign or a bad sign?
LO 4 2.7 Operating Cash Flow Suppose a company’s operating cash flow was
negative for several years running. Is this necessarily a good sign or a bad sign?
LO 4 2.8 Net Working Capital and Capital Spending Could a company’s change in
NWC be negative in a given year? (Hint: Yes.) Explain how this might come
about. What about net capital spending?
LO 4 2.9 Cash Flow to Stockholders and Creditors Could a company’s cash flow
to stockholders be negative in a given year? (Hint: Yes.) Explain how this
might come about. What about cash flow to creditors?
LO 4 2.10 Firm Values In February 2017, Toshiba announced that it was writing off
$6.3 billion due to its acquisition of nuclear power plant construction firm
CB&I Stone & Webster only a year before. We would argue that Toshiba’s
stockholders probably didn’t suffer as a result of the reported loss.
QUESTIONS AND PROBLEMS
BASIC (Questions 1–12)
1. Building a Balance Sheet Grey Wolf, Inc., has current assets of $2,090,
net fixed assets of $9,830, current liabilities of $1,710, and long-term debt of
$4,520. What is the value of the shareholders’ equity account for this firm?
How much is net working capital?
2. Building an Income Statement Sidewinder, Inc., has sales of $634,000,
costs of $328,000, depreciation expense of $73,000, interest expense of
$38,000, and a tax rate of 21 percent. What is the net income for this firm?
3. Dividends and Retained Earnings Suppose the firm in Problem 2 paid out
$68,000 in cash dividends. What is the addition to retained earnings?
4. Per-Share Earnings and Dividends Suppose the firm in Problem 3 had
35,000 shares of common stock outstanding. What is the earnings per share,
or EPS, figure? What is the dividends per share figure?
5. Calculating Taxes Duela Dent is single and had $189,000 in taxable income.
Using the rates from Table 2.3 in the chapter, calculate her income taxes.
6. Tax Rates In Problem 5, what is the average tax rate? What is the marginal
tax rate?
Select problems are available in McGraw-Hill Connect. Please see the pack-
aging options section of the preface for more information.
LO 1
LO 2
LO 2
LO 2
LO 3
LO 3
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44 P A R T 2 Understanding Financial Statements and Cash Flow
7. Calculating OCF Benson, Inc., has sales of $38,530, costs of $12,750,
depreciation expense of $2,550, and interest expense of $1,850. If the tax
rate is 21 percent, what is the operating cash flow, or OCF?
8. Calculating Net Capital Spending Rottweiler Obedience School’s
December 31, 2018, balance sheet showed net fixed assets of $1,945,000, and
the December 31, 2019, balance sheet showed net fixed assets of $2,137,000.
The company’s 2019 income statement showed a depreciation expense of
$335,000. What was the company’s net capital spending for 2019?
9. Calculating Additions to NWC The December 31, 2018, balance sheet
of Justin’s Golf Shop, Inc., showed current assets of $1,490 and current
liabilities of $1,210. The December 31, 2019, balance sheet showed current
assets of $1,675 and current liabilities of $1,290. What was the company’s
2019 change in net working capital, or NWC?
10. Cash Flow to Creditors The December 31, 2018, balance sheet of Whelan,
Inc., showed long-term debt of $1,350,000, and the December 31, 2019,
balance sheet showed long-term debt of $1,470,000. The 2019 income
statement showed an interest expense of $97,500. What was the firm’s cash
flow to creditors during 2019?
11. Cash Flow to Stockholders The December 31, 2018, balance sheet
of Whelan, Inc., showed $120,000 in the common stock account and
$2,289,000 in the additional paid-in surplus account. The December 31,
2019, balance sheet showed $137,000 and $2,568,000 in the same two
accounts, respectively. If the company paid out $149,500 in cash dividends
during 2019, what was the cash flow to stockholders for the year?
12. Calculating Cash Flows Given the information for Whelan, Inc., in
Problems 10 and 11, suppose you also know that the firm’s net capital
spending for 2019 was $745,000 and that the firm reduced its net working
capital investment by $94,300. What was the firm’s 2019 operating cash
flow, or OCF?
INTERMEDIATE (Questions 13–22)
13. Market Values and Book Values Klingon Widgets, Inc., purchased new
cloaking machinery three years ago for $6 million. The machinery can be
sold to the Romulans today for $4.6 million. Klingon’s current balance sheet
shows net fixed assets of $3.15 million, current liabilities of $830,000, and
net working capital of $210,000. If all the current accounts were liquidated
today, the company would receive $950,000 in cash. What is the book value
of Klingon’s total assets today? What is the sum of the market value of NWC
and the market value of fixed assets?
14. Calculating Cash Flows Weiland Co. shows the following information
on its 2019 income statement: sales = $178,000; costs = $103,600; other
expenses = $5,100; depreciation expense = $12,100; interest expense =
$8,900; taxes = $12,705; dividends = $10,143. In addition, you’re told that
the firm issued $2,900 in new equity during 2019 and redeemed $4,000 in
outstanding long-term debt.
a. What is the 2019 operating cash flow?
b. What is the 2019 cash flow to creditors?
LO 2
LO 4
LO 4
LO 4
LO 4
LO 4
LO 1
LO 4
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C H A P T E R 2 Financial Statements, Taxes, and Cash Flow 45
c. What is the 2019 cash flow to stockholders?
d. If net fixed assets increased by $23,140 during the year, what was the
addition to NWC?
15. Using Income Statements Given the following information for Ted’s Dread
Co., calculate the depreciation expense: sales = $68,500; costs = $51,700;
addition to retained earnings = $4,500; dividends paid = $2,420; interest
expense = $2,130; tax rate = 21 percent.
16. Preparing a Balance Sheet Prepare a balance sheet for Alaskan Peach
Corp. as of December 31, 2019, based on the following information: cash =
$207,000; patents and copyrights = $871,000; accounts payable = $293,000;
accounts receivable = $265,000; tangible net fixed assets = $5,270,000;
inventory = $579,000; notes payable = $201,000; accumulated retained
earnings = $4,676,000; long-term debt = $1,680,000.
17. Residual Claims Tremonti, Inc., is obligated to pay its creditors $7,900
during the year.
a. What is the value of the shareholders’ equity if assets equal $9,100?
b. What if assets equal $6,900?
18. Net Income and OCF During the year, Belyk Paving Co. had sales of
$2,275,000. Cost of goods sold, administrative and selling expenses, and
depreciation expense were $1,285,000, $535,000, and $420,000, respectively.
In addition, the company had an interest expense of $245,000 and a tax
rate of 21 percent. (Ignore any tax loss carryforward provision and assume
interest expense is fully deductible.)
a. What is the company’s net income?
b. What is its operating cash flow?
c. Explain your results in parts (a) and (b).
19. Accounting Values versus Cash Flows In Problem 18, suppose Belyk
Paving Co. paid out $370,000 in cash dividends. Is this possible? If net
capital spending was zero, no new investments were made in net working
capital, and no new stock was issued during the year, what do you know
about the firm’s long-term debt account?
20. Calculating Cash Flows Prescott Football Manufacturing had the
following operating results for 2019: sales = $29,874; cost of goods sold =
$21,632; depreciation expense = $3,470; interest expense = $514;
dividends paid = $825. At the beginning of the year, net fixed assets were
$19,872, current assets were $3,557, and current liabilities were $3,110.
At the end of the year, net fixed assets were $22,987, current assets were
$4,381, and current liabilities were $2,981. The tax rate for 2019 was
24 percent.
a. What is net income for 2019?
b. What is the operating cash flow for 2019?
c. What is the cash flow from assets for 2019? Is this possible? Explain.
d. If no new debt was issued during the year, what is the cash flow
to creditors? What is the cash flow to stockholders? Explain and
interpret the positive and negative signs of your answers in parts (a)
through (d).
LO 2
LO 1
LO 1
LO 2
LO 2
LO 4
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46 P A R T 2 Understanding Financial Statements and Cash Flow
21. Calculating Cash Flows Consider the following abbreviated financial
statements for Cabo Wabo, Inc.:
LO 4
CABO WABO, INC.
Partial Balance Sheets as of December 31, 2018 and 2019
2018 2019 2018 2019
Assets Liabilities and Owners’ Equity
Current assets $ 62,989 $ 3,169 Current liabilities $1,291 $1,898
Net fixed assets 13,862 14,493 Long-term debt 7,161 8,221
CABO WABO, INC.
2019 Income Statement
Sales $44,730
Costs 22,432
Depreciation 3,777
Interest paid 1,032
a. What is owners’ equity for 2018 and 2019?
b. What is the change in net working capital for 2019?
c. In 2019, the company purchased $7,876 in new fixed assets. How much
in fixed assets did the company sell? What is the cash flow from assets
for the year? (The tax rate is 22 percent.)
d. During 2019, the company raised $2,371 in new long-term debt. How
much long-term debt must the company have paid off during the year?
What is the cash flow to creditors?
22. Cash Flow Identity Graffiti Advertising, Inc., reported the following
financial statements for the last two years. Construct the cash flow identity
for the company. Explain what each number means.
2019 Income Statement
Sales $750,727
Cost of goods sold 430,821
Selling and administrative 165,676
Depreciation 72,489
EBIT $ 81,741
Interest 25,630
EBT $ 56,111
Taxes 14,028
Net income $ 42,083
Dividends $ 14,200
Addition to retained earnings 27,883
GRAFFITI ADVERTISING, INC.
Balance Sheet as of December 31, 2018
Cash $ 17,691 Accounts payable $ 12,721
Accounts receivable 25,228 Notes payable 19,149
Inventory 18,321 Current liabilities $ 31,870
Current assets $ 61,240 Long-term debt $181,000
Net fixed assets
Total assets
$ 457,454
$518,964
Owners’ equity
Total liabilities and
owners’ equity
$305,824
$518,694
LO 4
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C H A P T E R 2 Financial Statements, Taxes, and Cash Flow 47
GRAFFITI ADVERTISING, INC.
Balance Sheet as of December 31, 2019
Cash $ 19,003 Accounts payable $ 13,962
Accounts receivable 28,025 Notes payable 21,872
Inventory 30,222 Current liabilities $ 35,834
Current assets $ 77,250 Long-term debt $201,900
Net fixed assets
Total assets
$539,679
$616,929
Owners’ equity
Total liabilities and
owners’ equity
$379,195
$616,929
CHALLENGE (Question 23)
23. Net Fixed Assets and Depreciation On the balance sheet, the net fixed
assets (NFA) account is equal to the gross fixed assets (FA) account
(which records the acquisition cost of fixed assets) minus the accumulated
depreciation (AD) account (which records the total depreciation taken by
the firm against its fixed assets). Using the fact that NFA = FA − AD,
show that the expression given in the chapter for net capital spending,
NFAend − NFAbeg + D (where D is the depreciation expense during the
year), is equivalent to FAend − FAbeg.
LO 4
WHAT’S ON
THE WEB?
2.1 Change in Net Working Capital Visit Alcoa at www.alcoa.com. Find the most
recent annual report and locate the balance sheets for the past two years. Use these
balance sheets to calculate the change in net working capital. How do you interpret
this number?
2.2 Book Values versus Market Values The home page for The Coca-Cola Company can
be found at www.coca-cola.com. Locate the most recent annual report, which contains a
balance sheet for the company. What is the book value of equity for Coca-Cola? The
market value of a company is the number of shares of stock outstanding times the price
per share. This information can be found at finance.yahoo.com using the ticker symbol
for Coca-Cola (KO). What is the market value of equity? Which number is more relevant
for shareholders?
2.3 Net Working Capital Duke Energy is one of the world’s largest energy companies.
Go to the company’s home page at www.duke-energy.com, follow the link to the
investors’ page, and locate the annual reports. What was Duke Energy’s net working
capital for the most recent year? Does this number seem low to you given Duke’s current
liabilities? Does this indicate that Duke Energy may be experiencing financial problems?
Why or why not?
2.4 Cash Flows to Stockholders and Creditors Cooper Tire & Rubber Company
provides financial information for investors on its website at www.coopertire.com.
Follow the “Investors” link and find the most recent annual report. Using the
consolidated statement of cash flows, calculate the cash flow to stockholders and the
cash flow to creditors.
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48 P A R T 2 Understanding Financial Statements and Cash Flow
EXCEL MASTER IT! PROBLEM
Using Excel to find the marginal tax rate can be accomplished using the VLOOKUP func-
tion. However, calculating the total tax bill is a little more difficult. Here we show a copy of
the IRS tax table for an individual for 2018 (the income thresholds are indexed to inflation
and change through time). Often, tax tables are presented in this format.
If taxable income
is over…
But not over…
The tax is:
$ 0 $ 9,525 10% of the amount over $0
9,525 38,700 $952.50 plus 12% of the amount over $9,525
38,700 82,500 $4,453.50 plus 22% of the amount over $38,700
82,500 157,500 $14,089.50 plus 24% of the amount over $82,500
157,500 200,000 $32,089.50 plus 32% of the amount over $157,500
200,000 500,000 $45,689.50 plus 35% of the amount over $200,000
500,000 $150,689.50 plus 37% of the amount over $500,00
In reading this table, the marginal tax rate for taxable income less than $9,525 is 10%.
If the taxable income is between $9,525 and $38,700, the tax bill is $952.50 plus the mar-
ginal taxes. The marginal taxes are calculated as the taxable income minus $9,525 times the
marginal tax rate of 12%.
Below, we have the tax table for a married couple filing jointly.
Taxable income is greater
than or equal to…
But less than…
Tax rate
$ 0 $ 19,050 10%
19,050 77,400 12
77,400 165,000 22
165,000 315,000 24
315,000 400,000 32
400,000 600,000 35
600,000 37
a. Create a tax table in Excel for a married couple similar to the individual tax table
shown earlier. Your spreadsheet should then calculate the marginal tax rate, the
average tax rate, and the tax bill for any level of taxable income input by a user.
b. For a taxable income of $335,000, what is the marginal tax rate?
c. For a taxable income of $335,000, what is the total tax bill?
d. For a taxable income of $335,000, what is the average tax rate?
coverage online
Excel
Master
ros13952_ch02_022-049.indd 48 12/22/18 5:47 PM
C H A P T E R 2 Financial Statements, Taxes, and Cash Flow 49
2018 2019
Cost of goods sold $224,359 $283,281
Cash 32,372 34,394
Depreciation 63,334 71,584
Interest expense 13,783 15,780
Selling and administrative
expenses
44,121 57,586
Accounts payable 57,220 63,479
Net fixed assets 279,419 348,508
Sales 440,122 536,483
Accounts receivable 22,939 29,755
Notes payable 26,079 28,474
Long-term debt 141,040 158,368
Inventory 48,272 66,244
New equity 0 27,157
Sunset Boards currently pays out 50 percent of net
income as dividends to Tad and the other original inves-
tors and has a 21 percent tax rate. You are Jameson’s
assistant, and he has asked you to prepare the
following:
1. An income statement for 2018 and 2019.
2. A balance sheet for 2018 and 2019.
3. Operating cash flow for each year.
4. Cash flow from assets for 2019.
5. Cash flow to creditors for 2019.
6. Cash flow to stockholders for 2019.
Sunset Boards is a small company that manufactures and sells surfboards in Malibu. Tad Marks, the
founder of the company, is in charge of the design and
sale of the surfboards, but his background is in surfing,
not business. As a result, the company’s financial
records are not well maintained.
The initial investment in Sunset Boards was pro-
vided by Tad and his friends and family. Because the ini-
tial investment was relatively small, and the company
has made surfboards only for its own store, the investors
haven’t required detailed financial statements from Tad.
But thanks to word of mouth among professional surf-
ers, sales have picked up recently, and Tad is consider-
ing a major expansion. His plans include opening
another surfboard store in Hawaii, as well as supplying
his “sticks” (surfer lingo for boards) to other sellers.
Tad’s expansion plans require a significant invest-
ment, which he plans to finance with a combination of
additional funds from outsiders plus some money bor-
rowed from banks. Naturally, the new investors and
creditors require more organized and detailed financial
statements than Tad has previously prepared. At the
urging of his investors, Tad has hired financial analyst
Jameson Reid to evaluate the performance of the com-
pany over the past year.
After rooting through old bank statements, sales re-
ceipts, tax returns, and other records, Jameson has as-
sembled the following information:
CHAPTER CASE
Cash Flows and Financial Statements at Sunset Boards, Inc.
1. How would you describe Sunset Boards’s cash
flows for 2019? Write a brief discussion.
2. In light of your discussion in the previous question,
what do you think about Tad’s expansion plans?
Q U E S T I O N S
ros13952_ch02_022-049.indd 49 12/22/18 5:47 PM
50
Please visit us at essentialsofcorporatefinance.blogspot.com for the latest developments in the world of corporate finance.
In June 2018, shares of jet manufacturer Boeing were trading for about $370. At that price, Boeing had a price-earnings, or PE,
ratio of 24, meaning that investors were willing to pay $24 for every
dollar in income earned by Boeing. At the same time, investors
were willing to pay $274 for each dollar earned by Amazon.com,
but only a meager $6 and $7 for each dollar earned by Ford and
Comcast, respectively. And then there were stocks like Tesla, which,
despite having no earnings (a loss actually), had a stock price of
about $318 per share. Meanwhile, the average stock in the Stan-
dard & Poor’s (S&P) 500 index, which contains 500 of the largest
publicly traded companies in the United States, had a PE ratio of
about 24, so Boeing was average in this regard.
As we look at these numbers, an obvious question arises: Why
were investors willing to pay so much for a dollar of Amazon’s earn-
ings but so much less for a dollar earned by Comcast? To understand the answer, we need
to delve into subjects such as relative profitability and growth potential, and we also need to
know how to compare financial and operating information across companies. By a remark-
able coincidence, that is precisely what this chapter is about.
The PE ratio is just one example of a financial ratio. As we will see in this chapter, there
are a wide variety of such ratios, all designed to summarize specific aspects of a firm’s finan-
cial position. In addition to discussing financial ratios and what they mean, we will have quite
a bit to say about who uses this information and why.
Everybody needs to understand ratios. Managers will find that almost every business
characteristic, from profitability to employee productivity, is summarized in some kind of
ratio. Marketers examine ratios dealing with costs, markups, and margins. Production
Working with Financial
Statements 3
LEARNING OBJECTIVES
After studying this chapter, you should
be able to:
LO 1 Standardize financial statements
for comparison purposes.
LO 2 Compute and, more importantly,
interpret some common ratios.
LO 3 Assess the determinants of a firm’s
profitability and growth.
LO 4 Identify and explain some of the
problems and pitfalls in financial
statement analysis.
ros13952_ch03_050-096.indd 50 12/22/18 5:48 PM
personnel focus on ratios dealing with issues such as operating efficiency. Accountants need
to understand ratios because, among other things, ratios are one of the most common and
important forms of financial statement information.
In fact, regardless of your field, you very well may find that your compensation is tied to
some ratio or group of ratios. Perhaps that is the best reason to study up!
In Chapter 2, we discussed some of the essential concepts of financial statements and cash flows. This chapter continues where our earlier discussion left off. Our goal here is to
expand your understanding of the uses (and abuses) of financial statement information.
A good working knowledge of financial statements is desirable because such state-
ments, and numbers derived from those statements, are the primary means of communicat-
ing financial information both within the firm and outside the firm. In short, much of the
language of business finance is rooted in the ideas we discuss in this chapter.
In the best of all worlds, the financial manager has full market value information about
all of the firm’s assets. This will rarely (if ever) happen. So, the reason we rely on account-
ing figures for much of our financial information is that we are almost always unable to
obtain all (or even part) of the market information that we want. The only meaningful yard-
stick for evaluating business decisions is whether or not they create economic value (see
Chapter 1). However, in many important situations, it will not be possible to make this
judgment directly because we can’t see the market value effects.
We recognize that accounting numbers are often a pale reflection of economic real-
ity, but they frequently are the best available information. For privately held corpora-
tions, not-for-profit businesses, and smaller firms, for example, very little direct market
value information exists at all. The accountants’ reporting function is crucial in these
circumstances.
Clearly, one important goal of an accountant is to report financial information to the
user in a form useful for decision making. Ironically, the information frequently does not
come to the user in such a form. In other words, financial statements don’t come with a
user’s guide. This chapter is a first step in filling this gap.
STANDARDIZED FINANCIAL STATEMENTS
One obvious thing we might want to do with a company’s financial statements is to compare
them to those of other, similar companies. We would immediately have a problem, however.
It’s almost impossible to directly compare the financial statements for two companies
because of differences in size.
For example, Ford and GM are obviously serious rivals in the auto market, but GM was
historically much larger (in terms of assets), so it was difficult to compare them directly. For
that matter, it’s difficult to even compare financial statements from different points in time
for the same company if the company’s size has changed. The size problem is compounded
if we try to compare GM and, say, Toyota. If Toyota’s financial statements are denominated
in yen, then we have a size and a currency difference.
Company financial
information can be found
in many places on the
web, including www.sec
.gov and finance.google
.com.
3.1
coverage online
Excel
Master
51
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52 P A R T 2 Understanding Financial Statements and Cash Flow
PRUFROCK CORPORATION
Balance Sheets as of December 31, 2018 and 2019
($ in millions)
2018 2019
Assets
Current assets
Cash $ 84 $ 98
Accounts receivable 165 188
Inventory 393 422
Total $ 642 $ 708
Fixed assets
Net plant and equipment $2,731 $2,922
Total assets $3,373 $3,620
Liabilities and Owners’ Equity
Current liabilities
Accounts payable $ 312 $ 344
Notes payable 231 204
Total $ 543 $ 548
Long-term debt $ 531 $ 457
Owners’ equity
Common stock and paid-in surplus $ 500 $ 510
Retained earnings 1,799 2,115
Total $2,299 $2,625
Total liabilities and owners’ equity $3,373 $3,630
TABLE 3.1
To start making comparisons, one obvious thing we might try to do is to somehow
standardize the financial statements. One very common and useful way of doing this is to
work with percentages instead of total dollars. The resulting financial statements are called
common-size statements. We consider these next.
Common-Size Balance Sheets
For easy reference, Prufrock Corporation’s 2018 and 2019 balance sheets are provided in
Table 3.1. Using these, we construct common-size balance sheets by expressing each item as
a percentage of total assets. Prufrock’s 2018 and 2019 common-size balance sheets are
shown in Table 3.2.
Notice that some of the totals don’t check exactly because of rounding errors. Also
notice that the total change has to be zero because the beginning and ending numbers must
add up to 100 percent.
In this form, financial statements are relatively easy to read and compare. For example,
looking at the two balance sheets for Prufrock, we see that current assets were 19.5 percent
of total assets in 2019, up from 19.0 percent in 2018. Current liabilities declined from 16.1
percent to 15.1 percent of total liabilities and equity over that same time. Similarly, total
equity rose from 68.2 percent of total liabilities and equity to 72.3 percent.
Overall, Prufrock’s liquidity, as measured by current assets compared to current liabili-
ties, increased over the year. Simultaneously, Prufrock’s indebtedness diminished as a per-
centage of total assets. We might be tempted to conclude that the balance sheet has grown
“stronger.”
common-size
statement
A standardized financial
statement presenting all
items in percentage terms.
Balance sheet items are
shown as a percentage of
assets and income
statement items as a
percentage of sales.
IBM’s website has a
good guide to reading
financial statements. Visit
www.ibm.com/investor.
ros13952_ch03_050-096.indd 52 12/22/18 5:48 PM
C H A P T E R 3 Working with Financial Statements 53
PRUFROCK CORPORATION
Common-Size Balance Sheets
December 31, 2018 and 2019
2018 2019 Change
Assets
Current assets
Cash 2.5% 2.7% + .2%
Accounts receivable 4.9 5.2 + .3
Inventory 11.7 11.6 + .0
Total 19.0% 19.5% + .5%
Fixed assets
Net plant and equipment 81.0% 80.5% − .5%
Total assets 100.0% 100.0% 0%
Liabilities and Owners’ Equity
Current liabilities
Accounts payable 9.2% 9.5% + .2%
Notes payable 6.8 5.6 − 1.2
Total 16.1% 15.1% − 1.0%
Long-term debt 15.7% 12.6% − 3.2%
Owners’ equity
Common stock and paid-in surplus 14.8% 14.0% − .8%
Retained earnings 53.3 58.3 + 4.9
Total 68.2% 72.3% + 4.2%
Total liabilities and owners’ equity 100.0% 100.0% 0%
TABLE 3.2
PRUFROCK CORPORATION
2019 Income Statement
($ in millions)
Sales $2,361
Cost of goods sold 1,344
Depreciation 276
Earnings before interest and taxes $ 741
Interest paid 141
Taxable income $ 600
Taxes (21%) 126
Net income $ 474
Dividends $158
Addition to retained earnings 316
TABLE 3.3
Common-Size Income Statements
A useful way of standardizing the income statement shown in Table 3.3 is to express each
item as a percentage of total sales, as illustrated for Prufrock in Table 3.4.
This income statement tells us what happens to each dollar in sales. For Prufrock,
interest expense eats up $.060 out of every sales dollar, and taxes take another $.053.
When all is said and done, $.201 of each dollar flows through to the bottom line (net in-
come), and that amount is split into $.134 retained in the business and $.067 paid out in
dividends.
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54 P A R T 2 Understanding Financial Statements and Cash Flow
These percentages are very useful in comparisons. For example, a relevant figure is the
cost percentage. For Prufrock, $.569 of each $1.00 in sales goes to pay for goods sold. It
would be interesting to compute the same percentage for Prufrock’s main competitors to see
how Prufrock stacks up in terms of cost control.
CONCEPT QUESTIONS
3.1a Why is it often necessary to standardize financial statements?
3.1b Describe how common-size balance sheets and income statements are formed.
RATIO ANALYSIS
Another way of avoiding the problems involved in comparing companies of different sizes is
to calculate and compare financial ratios. Such ratios are ways of comparing and investigat-
ing the relationships between different pieces of financial information. We cover some of
the more common ratios next, but there are many others that we don’t touch on.
One problem with ratios is that different people and different sources frequently don’t
compute them in exactly the same way, and this leads to much confusion. The specific defi-
nitions we use here may or may not be the same as ones you have seen or will see elsewhere.
If you are ever using ratios as a tool for analysis, you should be careful to document how you
calculate each one, and, if you are comparing your numbers to those of another source, be
sure you know how their numbers are computed.
We will defer much of our discussion of how ratios are used and some problems that
come up with using them until a bit later in the chapter. For now, for each of the ratios we
discuss, several questions come to mind:
1. How is it computed?
2. What is it intended to measure, and why might we be interested?
3. What is the unit of measurement?
4. What might a high or low value be telling us? How might such values be misleading?
5. How could this measure be improved?
3.2
coverage online
Excel
Master
financial ratios
Relationships determined
from a firm’s financial
information and used for
comparison purposes.
PRUFROCK CORPORATION
Common-Size Income Statement
2019
Sales 100.0%
Cost of goods sold 56.9
Depreciation 11.7
Earnings before interest and taxes 31.4%
Interest paid 6.0
Taxable income 25.4%
Taxes (21%) 5.3
Net income 20.1%
Dividends 6.7%
Addition to retained earnings 13.4
TABLE 3.4
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C H A P T E R 3 Working with Financial Statements 55
Financial ratios are traditionally grouped into the following categories:
1. Short-term solvency, or liquidity, ratios.
2. Long-term solvency, or financial leverage, ratios.
3. Asset management, or turnover, ratios.
4. Profitability ratios.
5. Market value ratios.
We will consider each of these in turn. In calculating these numbers for Prufrock, we will
use the ending balance sheet (2019) figures unless we explicitly say otherwise. Also notice
that the various ratios are color-keyed to indicate which numbers come from the income
statement and which come from the balance sheet.
Short-Term Solvency, or Liquidity, Measures
As the name suggests, short-term solvency ratios as a group are intended to provide informa-
tion about a firm’s liquidity, and these ratios are sometimes called liquidity measures. The
primary concern is the firm’s ability to pay its bills over the short run without undue stress.
Consequently, these ratios focus on current assets and current liabilities.
For obvious reasons, liquidity ratios are particularly interesting to short-term creditors.
Because financial managers are constantly working with banks and other short-term lend-
ers, an understanding of these ratios is essential.
One advantage of looking at current assets and liabilities is that their book values and
market values are likely to be similar. Often (though not always), these assets and liabilities
don’t live long enough for the two to get seriously out of step. On the other hand, like any
type of near cash, current assets and liabilities can and do change fairly rapidly, so today’s
amounts may not be a reliable guide to the future.
Current Ratio One of the best-known and most widely used ratios is the current ratio.
As you might guess, the current ratio is defined as:
Current ratio = Current assets ____________ Current liabilities [3.1]
For Prufrock, the 2019 current ratio is:
Current ratio = $708 ____ $548 = 1.29 times
Because current assets and liabilities are, in principle, converted to cash over the following 12
months, the current ratio is a measure of short-term liquidity. The unit of measurement is ei-
ther dollars or times. So, we could say Prufrock has $1.29 in current assets for every $1 in
current liabilities, or we could say Prufrock has its current liabilities covered 1.29 times over.
To a creditor, particularly a short-term creditor such as a supplier, the higher the cur-
rent ratio, the better. To the firm, a high current ratio indicates liquidity, but it also may in-
dicate an inefficient use of cash and other short-term assets. Absent some extraordinary
circumstances, we would expect to see a current ratio of at least 1 because a current ratio of
less than 1 would mean that net working capital (current assets less current liabilities) is
negative. This would be unusual in a healthy firm, at least for most types of businesses.
The current ratio, like any ratio, is affected by various types of transactions. For exam-
ple, suppose the firm borrows over the long term to raise money. The short-run effect would
be an increase in cash from the issue proceeds and an increase in long-term debt. Current
liabilities would not be affected, so the current ratio would rise.
Finally, note that an apparently low current ratio may not be a bad sign for a company
with a large reserve of untapped borrowing power.
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56 P A R T 2 Understanding Financial Statements and Cash Flow
Quick (or Acid-Test) Ratio Inventory is often the least liquid current asset. It’s also
the one for which the book values are least reliable as measures of market value because the
quality of the inventory isn’t considered. Some of the inventory may later turn out to be
damaged, obsolete, or lost.
More to the point, relatively large inventories are often a sign of short-term trouble. The
firm may have overestimated sales and overbought or overproduced as a result. In this case,
the firm may have a substantial portion of its liquidity tied up in slow-moving inventory.
To further evaluate liquidity, the quick, or acid-test, ratio is computed like the current
ratio, except inventory is omitted:
Quick ratio =
Current assets – Inventory
__________________ Current liabilities [3.2]
Notice that using cash to buy inventory does not affect the current ratio, but it reduces the
quick ratio. Again, the idea is that inventory is relatively illiquid compared to cash. For Pru-
frock, this ratio in 2019 was:
Quick ratio = $708 – 422 _______ $548 = .52 times
The quick ratio here tells a somewhat different story than the current ratio because inven-
tory accounts for more than half of Prufrock’s current assets. To exaggerate the point, if this
inventory consisted of, say, unsold nuclear power plants, then this would be a cause for
concern.
To give an example of current versus quick ratios, based on recent financial statements,
Walmart and ManpowerGroup had current ratios of .85 and 1.39, respectively. However,
ManpowerGroup carries no inventory to speak of, whereas Walmart’s current assets are
virtually all inventory. As a result, Walmart’s quick ratio was only .22, and Manpower-
Group’s was 1.39, the same as its current ratio.
Cash Ratio A very short-term creditor might be interested in the cash ratio.
Cash ratio = Cash ____________ Current liabilities [3.3]
You can verify that this works out to be .18 times for Prufrock.
EXAMPLE 3.1 Current Events
Suppose a firm were to pay off some of its suppliers and short-term creditors. What would happen
to the current ratio? Suppose a firm buys some inventory. What happens in this case? What hap-
pens if a firm sells some merchandise?
The first case is a trick question. What happens is that the current ratio moves away from 1. If it
is greater than 1 (the usual case), it will get bigger, but if it is less than 1, it will get smaller. To see this,
suppose the firm has $4 in current assets and $2 in current liabilities for a current ratio of 2. If we
use $1 in cash to reduce current liabilities, then the new current ratio is ($4 – 1)/($2 – 1) = 3. If we
reverse the original situation to $2 in current assets and $4 in current liabilities, then the change will
cause the current ratio to fall to 1/3 from 1/2.
The second case is not quite as tricky. Nothing happens to the current ratio because cash
goes down while inventory goes up—total current assets are unaffected.
In the third case, the current ratio would usually rise because inventory is normally shown at
cost, and the sale would normally be at something greater than cost (the difference is the markup).
The increase in either cash or receivables is therefore greater than the decrease in inventory. This
increases current assets, and the current ratio rises.
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C H A P T E R 3 Working with Financial Statements 57
Long-Term Solvency Measures
Long-term solvency ratios are intended to address the firm’s long-run ability to meet its ob-
ligations, or, more generally, its financial leverage. These ratios are sometimes called finan-
cial leverage ratios or leverage ratios. We consider three commonly used measures and some
variations.
Total Debt Ratio The total debt ratio takes into account all debts of all maturities to all
creditors. It can be defined in several ways, the easiest of which is:
Total debt ratio =
Total assets – Total equity
__________________ Total assets [3.4]
=
$3,630 – 2,625
______________ $3,630 = .28 times
In this case, an analyst might say that Prufrock uses 28 percent debt.1 Whether this is high
or low or whether it even makes any difference depends on whether or not capital structure
matters, a subject we discuss in a later chapter.
Prufrock has $.28 in debt for every $1 in total assets. Therefore, there is $.72 in equity
(= $1 − .28) for every $.28 in debt. With this in mind, we can define two useful variations
on the total debt ratio, the debt-equity ratio and the equity multiplier:
Debt-equity ratio = Total debt/Total equity [3.5]
= $.28/$).72 = .)38 times
Equity multiplier = Total assets / Total equity [3.6]
= $1 / $.72 = 1.38 times
The fact that the equity multiplier is 1 plus the debt-equity ratio is not a coincidence:
Equity multiplier = Total assets / Total equity = $1 / $.72 = 1.38 times
= (Total equity + Total debt)/ Total equity
= 1 + Debt-equity ratio = 1.38 times
The thing to notice here is that given any one of these three ratios, you can immediately
calculate the other two, so they all say exactly the same thing.
Times Interest Earned Another common measure of long-term solvency is the times
interest earned (TIE) ratio. Once again, there are several possible (and common) definitions,
but we’ll stick with the most traditional:
Times interest earned ratio = EBIT _______ Interest [3.7]
= $741 _____ $141 = 5.26 times
As the name suggests, this ratio measures how well a company has its interest obligations
covered, and it is often called the interest coverage ratio. For Prufrock, the interest bill is
covered 5.26 times over.
1Total equity here includes preferred stock (discussed in Chapter 7), if there is any. An equivalent numerator in this
ratio would be (Current liabilities + Long-term debt).
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58 P A R T 2 Understanding Financial Statements and Cash Flow
Cash Coverage A problem with the TIE ratio is that it is based on EBIT, which is not
really a measure of cash available to pay interest. The reason is that depreciation, a noncash
expense, has been deducted out. Because interest is most definitely a cash outflow (to credi-
tors), one way to define the cash coverage ratio is:
Cash coverage ratio =
EBIT + Depreciation
_________________ Interest [3.8]
= $741 + 276 __________ $141 =
$1,)017
______ $141 = 7.21 times
The numerator here, EBIT plus depreciation, is often abbreviated EBITD (earnings before
interest, taxes, and depreciation—say “ebbit-dee”). It is a basic measure of the firm’s ability
to generate cash from operations, and it is frequently used as a measure of cash flow avail-
able to meet financial obligations.
A common variation on EBITD is earnings before interest, taxes, depreciation, and
amortization (EBITDA—say “ebbit-dah”). Here amortization refers to a noncash deduction
similar conceptually to depreciation, except it applies to an intangible asset (such as a pat-
ent) rather than a tangible asset (such as a machine). Note that the word amortization here
does not refer to the repayment of debt, a subject we discuss in a later chapter.
Asset Management, or Turnover, Measures
We next turn our attention to the efficiency with which Prufrock uses its assets. The mea-
sures in this section are sometimes called asset utilization ratios. The specific ratios we dis-
cuss all can be interpreted as measures of turnover. What they are intended to describe is
how efficiently, or intensively, a firm uses its assets to generate sales. We first look at two
important current assets: inventory and receivables.
Inventory Turnover and Days’ Sales in Inventory During the year, Prufrock
had a cost of goods sold of $1,344. Inventory at the end of the year was $422. With these
numbers, inventory turnover can be calculated as:
Inventory turnover =
Cost of goods sold
________________ Inventory [3.9]
=
$1,344
______ $422 = 3.18 times
In a sense, we sold off, or turned over, the entire inventory 3.18 times. As long as we are not
running out of stock and thereby forgoing sales, the higher this ratio is, the more efficiently
we are managing inventory.
If we know that we turned our inventory over 3.18 times during the year, then we can
immediately figure out how long it took us to turn it over, on average. The result is the aver-
age days’ sales in inventory:
Days’ sales in inventory =
365 days
________________ Inventory turnover [3.10]
= 365 ____ 3.18 = 114.61 days
This tells us that, roughly speaking, inventory sits about 115 days, on average, before it is
sold. Alternatively, assuming we used the most recent inventory and cost figures, it will take
about 115 days to work off our current inventory.
For example, in early 2018, the auto industry had a 35-day supply of cars and trucks.
Of course, not all manufacturers had the same inventory level. At that same time, General
ros13952_ch03_050-096.indd 58 12/22/18 5:48 PM
C H A P T E R 3 Working with Financial Statements 59
Motors had a 68-day supply. This inventory level means that at the then-current rate of
sales, it would have taken General Motors 68 days to deplete the available supply, or,
equivalently, that General Motors had 68 days of vehicle sales in inventory. At the same
time, Ford had a 115-day supply. This type of information is useful to auto manufacturers
in planning future marketing and production decisions. Historically, a 60-day supply of
inventory has been considered normal in the automobile industry, so these figures pointed
to manufacturing continuing at the same level for GM, and likely decreasing for Ford,
in 2018.
It might make more sense to use the average inventory in calculating turnover. Inven-
tory turnover would then be $l,344/[($393 + 422)/2] = 3.30 times.2 Whether we use the
ending inventory or average inventory depends on the purpose of the calculation. If we are
interested in how long it will take us to sell our current inventory, then using the ending
figure (as we did initially) is probably better.
In many of the ratios we discuss in the following pages, average figures could just as
well be used. Again, it depends on whether we are worried about the past, in which case
averages are appropriate, or the future, in which case ending figures might be better. Also,
using ending figures is common in reporting industry averages; so, for comparison pur-
poses, ending figures should be used in such cases. In any event, using ending figures is defi-
nitely less work, so we’ll continue to use them.
Receivables Turnover and Days’ Sales in Receivables Our inventory mea-
sures give some indication of how fast we can sell products. We now look at how fast we
collect on those sales. The receivables turnover is defined in the same way as inventory
turnover:
Receivables turnover = Sales _________________ Accounts receivable [3.11]
=
$2,361
_____ $188 = 12.56 times
Loosely speaking, we collected our outstanding credit accounts and reloaned the money
12.56 times during the year.3
This ratio makes more sense if we convert it to days, so the days’ sales in receivables is:
Days’ sales in receivables
=
365 days
_______________ Receivables turnover
=
365 ____ 12.56 = 29.06 days
[3.12]
Therefore, on average, we collect on our credit sales in about 30 days. For obvious reasons,
this ratio is very frequently called the average collection period (ACP).
Also note that if we are using the most recent figures, we can say that we have 30 days’
worth of sales currently uncollected. We will learn more about this subject when we study
credit policy in a later chapter.
2Notice that we calculated the average as (Beginning value + Ending value)/2.
3Here we have implicitly assumed that all sales are credit sales. If they were not, then we would use total credit sales
in these calculations, not total sales.
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60 P A R T 2 Understanding Financial Statements and Cash Flow
Total Asset Turnover Moving away from specific accounts like inventory or receiv-
ables, we can consider an important “big picture” ratio, the total asset turnover ratio. As the
name suggests, total asset turnover is:
Total asset turnover
=
Sales _________ Total assets
=
$2,361
_____ $3,630 = .65 times
[3.13]
In other words, for every dollar in assets, we generated $.65 in sales.
A closely related ratio, the capital intensity ratio, is the reciprocal of (that is, 1 divided
by) total asset turnover. It can be interpreted as the dollar investment in assets needed to
generate $1 in sales. High values correspond to capital-intensive industries (such as public
utilities). For Prufrock, total asset turnover is .65, so, if we flip this over, we get that capital
intensity is $l/.65 = $1.54. That is, it takes Prufrock $1.54 in assets to create $1 in sales.
It might seem that a high total asset turnover ratio is always a good sign for a com-
pany, but it isn’t necessarily. Consider a company with old assets. The assets would be al-
most fully depreciated and might be very outdated. In this case, the book value of assets
is low, contributing to a higher asset turnover. Plus, the high turnover might mean that the
company will need to make major capital outlays in the near future. A low asset turnover
might seem bad, but it could indicate the opposite: The company could have just pur-
chased a lot of new equipment, which implies that the book value of assets is relatively
high. These new assets could be more productive and efficient than those used by the
company’s competitors.
The eXtensible Business
Reporting Language
(XBRL) is designed to
make extracting EDGAR
data easier. You can
learn more about it at
www.xbrl.org.
EXAMPLE 3.2 Payables Turnover
Here is a variation on the receivables collection period. How long, on average, does it take for Pru-
frock Corporation to pay its bills? To answer, we need to calculate the accounts payable turnover
rate using cost of goods sold. We will assume that Prufrock purchases everything on credit.
The cost of goods sold is $1,344, and accounts payable are $344. The turnover is therefore
$1,344/$344 = 3.91 times. So, days’ costs in payables was about 365/3.91 = 93.42 days. On average,
then, Prufrock takes about 93 days to pay. As a potential creditor, we might take note of this fact.
EXAMPLE 3.3 More Turnover
Suppose you find that a particular company generates $.40 in sales for every dollar in total assets.
How often does this company turn over its total assets?
The total asset turnover here is .40 times per year. It takes 1/.40 = 2.5 years to turn assets over
completely.
Profitability Measures
The three measures we discuss in this section are probably the best known and most widely
used of all financial ratios. In one form or another, they are intended to measure how
efficiently the firm uses its assets and how efficiently the firm manages its operations. The
focus in this group is on the bottom line—net income.
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C H A P T E R 3 Working with Financial Statements 61
Profit Margin Companies pay a great deal of attention to their profit margin:
Profit margin
=
Net income ________ Sales
=
$474 _____ $2,361 = .2008, or 20.08%
[3.14]
This tells us that Prufrock, in an accounting sense, generates about 20 cents in profit for
every dollar in sales.
All other things being equal, a relatively high profit margin is obviously desirable. This
situation corresponds to low expense ratios relative to sales. However, we hasten to add that
other things are often not equal.
For example, lowering our sales price usually will increase unit volume, but nor-
mally will cause profit margins to shrink. Total profit (or, more importantly, operating cash
flow) may go up or down, so the fact that margins are smaller isn’t necessarily bad. After all,
isn’t it possible that, as the saying goes, “Our prices are so low that we lose money on every-
thing we sell, but we make it up in volume!”?4
Return on Assets Return on assets (ROA) is a measure of profit per dollar of assets. It
can be defined several ways, but the most common is:
Return on assets
=
Net income _________ Total assets
=
$474 _____ $3,630 = .1306, or 13.06%
[3.15]
Return on Equity Return on equity (ROE) is a measure of how the stockholders fared
during the year. Because benefiting shareholders is our goal, ROE is, in an accounting sense,
the true bottom-line measure of performance. ROE is usually measured as:
Return on equity
=
Net income _________ Total equity
=
$474 _____ $2,625 = ).1806,) or 18.06%
[3.16]
Therefore, for every dollar in equity, Prufrock generated 18.06 cents in profit, but, again,
this is only correct in accounting terms.
Because ROA and ROE are such commonly cited numbers, we stress that it is im-
portant to remember they are accounting rates of return. For this reason, these measures
should properly be called return on book assets and return on book equity. In addition,
ROE is sometimes called return on net worth. Whatever it’s called, it would be inappropri-
ate to compare the result to, for example, an interest rate observed in the financial
markets.
The fact that ROE exceeds ROA reflects Prufrock’s use of financial leverage. We will
examine the relationship between these two measures in more detail later.
Market Value Measures
Our final group of measures is based, in part, on information not necessarily contained in
financial statements—the market price per share of the stock. Obviously, these measures can
be calculated directly only for publicly traded companies.
4No, it’s not; margins can be small, but they do need to be positive!
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62 P A R T 2 Understanding Financial Statements and Cash Flow
We assume that Prufrock has 33 million shares outstanding and the stock sold for $115
per share at the end of the year. If we recall that Prufrock’s net income was $474 million,
then we can calculate that its earnings per share were:
EPS = Net income ______________ Shares outstanding =
$474 ____ 33 = $14).)36 [3.17]
Price-Earnings Ratio The first of our market value measures, the price-earnings, or
PE, ratio (or multiple), is defined as:
PE ratio
=
Price per share
______________ Earnings per share
=
$115 ______ $14.36 = 8.01 times
[3.18]
In the vernacular, we would say that Prufrock shares sell for about eight times earnings, or
we might say that Prufrock shares have, or “carry,” a PE multiple of 8.
Because the PE ratio measures how much investors are willing to pay per dollar of cur-
rent earnings, higher PEs are often taken to mean that the firm has significant prospects for
future growth. Of course, if a firm had no or almost no earnings, its PE would probably be
quite large; so, as always, care is needed in interpreting this ratio.
Price-Sales Ratio In some cases, companies will have negative earnings for extended
periods, so their PE ratios are not very meaningful. A good example is a recent start-up.
Such companies usually do have some revenues, so analysts will often look at the price-sales
ratio:
Price-sales ratio = Price per share/Sales per share [3.19]
In Prufrock’s case, sales were $2,361, so here is the price-sales ratio:
Price-sales ratio = $115/($2,361/33) = $115/$71.55 = 1.61 times
As with PE ratios, whether a particular price-sales ratio is high or low depends on the indus-
try involved.
Market-to-Book Ratio A second commonly quoted measure is the market-to-book
ratio:
Market-to-book ratio
=
Market value per share
________________ Book value per share
=
$115 ________ $2,625/33 =
$115 ______ $79.55 = 1.45 times
[3.20]
Notice that book value per share is total equity (not just common stock) divided by the
number of shares outstanding.
Because book value per share is an accounting number, it reflects historical costs.
Therefore, in a loose sense, the market-to-book ratio compares the market value of the firm’s
investments to their costs. A value less than 1 could mean that the firm has not been suc-
cessful overall in creating value for its stockholders.
Enterprise Value-EBITDA Ratio A company’s enterprise value is an estimate of the
market value of the company’s operating assets. By operating assets, we mean all the assets
of the firm except cash. Of course, it’s not practical to work with the individual assets of a
firm because market values would usually not be available. Instead, we can use the right-
hand side of the balance sheet and calculate the enterprise value as:
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C H A P T E R 3 Working with Financial Statements 63
I. Short-term solvency, or liquidity, ratios
Current ratio = Current assets ____________ Current liabilities
Quick ratio =
Current assets − Inventory
__________________ Current liabilities
Cash ratio = Cash ____________ Current liabilities
II. Long-term solvency, or financial leverage, ratios
Total debt ratio =
Total assets − Total equity
__________________ Total assets
Debt-equity ratio = Total debt/Total equity
99999Equity multiplier = Total assests/Total equity
Times interest earned ratio = EBIT ______ Interest
Cash coverage ratio =
EBIT + Depreciation
______________ Interest
III. Asset utilization, or turnover, ratios
Inventory turnover =
Cost of goods sold
_____________ Inventory
Days’ sales in inventory =
365 days
_____________ Inventory turnover
Receivables turnover = Sales ______________ Accounts receivable
Payables turnover =
Cost of goods sold
_____________ Accounts payable
Days’ sales in receivables =
365 days
_______________ Receivables turnover
Days’ costs in payables =
365 days
_____________ Payables turnover
Total asset turnover = Sales _________ Total assets
Capital intensity = Total assets _________ Sales
IV. Profitability ratios
Profit margin = Net9 income ________ Sales
Return on assets (ROA9) = Net income _________ Total assets
Return on equity (ROE9) = Net income _________ Total equity
ROE = Net income ________ Sales ×
Sales _____ Assets ×
Assets _____ Equity
V. Market value ratios
Price-earnings ratio =
Price per share
______________ Earnings per share
Price-sales ratio =
Price per share
___________ Sales per share
Market-to-book ratio =
Market value per share
________________ Book value per share
EBITDA ratio =
Enterprise value
____________ EBITDA
Common financial ratiosTABLE 3.5
Enterprise value = Total market value of the stock + Book value of all liabilities − Cash [3.21]
We use the book value for liabilities because we typically can’t get the market values, at least
not for all of them. However, book value is usually a reasonable approximation for market
value when it comes to liabilities, particularly short-term debts. Notice that the sum of the
market values of the stock and all liabilities equals the value of the firm’s assets from
the balance sheet identity. Once we have this number, we subtract the cash to get the enter-
prise value.
Enterprise value is frequently used to calculate the EBITDA ratio (or multiple):
EBITDA ratio = Enterprise value/EBITDA [3.22]
This ratio is similar in spirit to the PE ratio, but it relates the value of all the operating assets
(the enterprise value) to a measure of the operating cash flow generated by those assets
(EBITDA).
This completes our definition of some common ratios. We could tell you about more of
them, but these are enough for now. We’ll leave it here and go on to discuss some ways of
using these ratios instead of just how to calculate them. Table 3.5 summarizes the ratios
we’ve discussed. Table 3.6 provides some information for the well-known home supply
stores Lowe’s and The Home Depot for their fiscal years ending in 2018. As you can see,
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64 P A R T 2 Understanding Financial Statements and Cash Flow
The Home Depot has a higher current ratio, debt-equity ratio, and total asset turnover. The
Home Depot also has higher profitability ratios. Because of its increased use of leverage and
better profitability, The Home Depot has a higher ROE, something we will discuss in the
next section.
The price-earnings ratio is similar for Lowe’s and The Home Depot, although The
Home Depot’s market-to-book ratio is more than 10 times as large as Lowe’s. Overall, The
Home Depot appears to be performing better than Lowe’s based on this abbreviated finan-
cial analysis. Of course, if we really want to examine these two companies, we would want to
look at more ratios than the ones presented here.
CONCEPT QUESTIONS
3.2a What are the five groups of ratios? Give two or three examples of each kind.
3.2b Turnover ratios all have one of two figures as the numerator. What are these two
figures? What do these ratios measure? How do you interpret the results?
3.2c Profitability ratios all have the same figure in the numerator. What is it? What do
these ratios measure? How do you interpret the results?
3.2d Given the total debt ratio, what other two ratios can be computed? Explain how.
THE DUPONT IDENTITY
As we mentioned in discussing ROA and ROE, the difference between these two profitabil-
ity measures is a reflection of the use of debt financing, or financial leverage. We illustrate
the relationship between these measures in this section by investigating a famous way of
decomposing ROE into its component parts.
3.3
Financial information
from 2018 for Lowe’s
and The Home Depot
(numbers in millions
except for per-share
data)
Lowe’s The Home Depot
Sales $68,819 $100,904
Net income 3,447 8,630
Current assets 12,772 18,933
Current liabilities 12,096 16,194
Total assets 35,291 44,529
Total debt 29,418 43,075
Total equity 5,873 1,454
Price per share 100.50 199.64
Book value per share 7.12 1.25
Earnings per share 4.18 7.44
Current ratio 1.06 1.17
Debt-equity ratio 5.01 29.63
Total asset turnover 1.95 2.27
Profit margin 5.01% 8.55%
ROE 58.69% 593.54%
ROA 9.77% 19.38%
Market-to-book ratio 14.11 159.27
Price-earnings ratio 24.04 26.83
TABLE 3.6
Source: Lowe’s; Home Depot.
coverage online
Excel
Master
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C H A P T E R 3 Working with Financial Statements 65
To begin, let’s recall the definition of ROE:
Return )on equity = Net income _________ Total equity
If we were so inclined, we could multiply this ratio by Assets/Assets without changing
anything:
Return on equity
=
Net income _________ Total equity =
Net income _________ Total equity ×
Assets _____ Assets
=
Net income ________ Assets ×
Assets __________ Total equity
Notice that we have expressed the ROE as the product of two other ratios—ROA and the
equity multiplier:
ROE = ROA × Equity multiplier = ROA × (1 + Debt-equity ratio)
Looking back at Prufrock, we see that the debt-equity ratio was .38 and ROA was 13.06
percent. Our work here implies that Prufrock’s ROE, as we previously calculated, is:
ROE = .1306 × 1.38 = .1806, or 18.06%
We can further decompose ROE by multiplying the top and bottom by total sales:
ROE = Sales ____ Sales ×
Net income ________ Assets ×
Assets ________ Total equity
If we rearrange things a bit, ROE is
ROE = Net income __________ Sales ×
Sales ______ Assets ×
Assets __________ Total equity [3.23]
Return on assets
= Profit margin × Total asset turnover × Equity multiplier
What we have now done is to partition ROA into its two component parts, profit margin
and total asset turnover. This last expression is called the DuPont identity, after the DuPont
Corporation, which popularized its use.
We can check this relationship for Prufrock by noting that the profit margin was
20.08 percent and the total asset turnover was .65. ROE should thus be:
ROE = Profit margin × Total asset turnover × Equity multiplier
= .2008 × .65 )) × 1.38
= .1806, or 18.06%
This 18.06 percent ROE is exactly what we had before.
The DuPont identity tells us that ROE is affected by three things:
1. Operating efficiency (as measured by profit margin).
2. Asset use efficiency (as measured by total asset turnover).
3. Financial leverage (as measured by the equity multiplier).
Weakness in either operating or asset use efficiency (or both) will show up in a diminished
return on assets, which will translate into a lower ROE.
Considering the DuPont identity, it appears that a firm could leverage up its ROE by
increasing its amount of debt. It turns out this will happen only if the ratio of EBIT to total
assets is greater than the interest rate. More importantly, the use of debt financing has a
DuPont identity
Popular expression
breaking ROE into three
parts: operating efficiency,
asset use efficiency, and
financial leverage.
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66 P A R T 2 Understanding Financial Statements and Cash Flow
number of other effects, and, as we discuss at some length in later chapters, the amount of
leverage a firm uses is governed by its capital structure policy.
The decomposition of ROE we’ve discussed in this section is a convenient way of
systematically approaching financial statement analysis. If ROE is unsatisfactory by some
measure, then the DuPont identity tells you where to start looking for the reasons. To give
an example, take a look at the information about Internet marketplace companies Amazon
and Alibaba in Table 3.7. As you can see, in 2017, Amazon had an ROE of
15.0 percent, down from its ROE in 2015 of 16.7 percent. In contrast, also in 2017, Alibaba
had an ROE of 15.7 percent, down from its ROE in 2015 of 16.7 percent. Given this infor-
mation, it would appear that the two companies operate in a similar fashion, but as we
see, that is not true.
Looking at the DuPont breakdown, we see that Amazon’s profit margin is in the 2 to 3
percent range, while Alibaba’s profit has ranged from 27.6 percent to an astounding 70.7
percent. However, Amazon’s ROE is similar to Alibaba’s because Amazon has a higher asset
utilization, as measured by total asset turnover, and a higher leverage, as measured by the
equity multiplier.
An Expanded DuPont Analysis
So far, we’ve seen how the DuPont equation lets us break down ROE into its basic three
components: profit margin, total asset turnover, and financial leverage. We now extend this
analysis to take a closer look at how key parts of a firm’s operations feed into ROE. To get
going, we went to the SEC website (www.sec.gov) and found the 10-K for chemical products
giant DowDuPont. In the 10-K, we located the financial statements for 2017. What we found
is summarized in Table 3.8.
Using the information in Table 3.8, Figure 3.1 shows how we can construct an ex-
panded DuPont analysis for DowDuPont and present that analysis in chart form. The ad-
vantage of the extended DuPont chart is that it lets us examine several ratios at once,
thereby getting a better overall picture of a company’s performance and also allowing us to
determine possible items to improve.
Looking at the left-hand side of our DuPont chart in Figure 3.1, we see items related to
profitability. As always, profit margin is calculated as net income divided by sales. But, as
our chart emphasizes, net income depends on sales and a variety of costs, such as cost of
goods sold (CoGS) and selling, general, and administrative (SG&A) expenses. DuPont can
increase its ROE by increasing sales and also by reducing one or more of these costs. In
The regulatory filings of
publicly traded
corporations may be found
at www.sec.gov.
DuPont analysis for
Amazon and Alibaba
Amazon.com
Year ROE = Profit margin × Total asset turnover × Equity multiplier
2017 15.0% = 2.3% × 1.355 × 4.74
2016 21.7% = 3.1% × 1.631 × 4.32
2015 16.7% = 2.1% × 1.653 × 4.84
Alibaba
Year ROE = Profit margin × Total asset turnover × Equity multiplier
2017 15.7% = 27.6% × .312 × 1.82
2016 32.9% = 70.7% × .278 × 1.68
2015 16.7% = 31.8% × .298 × 1.76
TABLE 3.7
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C H A P T E R 3 Working with Financial Statements 67
FINANCIAL STATEMENTS FOR DOWDUPONT
12 months ending December 31, 2017
(All numbers are in millions)
Income Statement Balance Sheet
Sales $62,484 Current assets Current liabilities
CoGS 48,008 Cash $ 16,088 Accounts payable $ 11,601
Gross profit $14,476 Accounts receivable 16,813 Notes payable 50,203
SG&A expense 7,232 Inventory 16,992 Total $ 61,804
R&D expense 4,017 Total $ 49,893 Total long-term debt $ 30,030
EBIT $ 3,227 Fixed assets $142,271 Total equity $100,330
Interest 1,082 Total assets $192,164 Total liabilities and equity $192,164
EBT $ 2,145
Taxes 476
Net income $ 1,669
TABLE 3.8
Divided by
Subtracted
from
Selling, gen. &
admin. expense
$7,232
Total costs
$60,815
Net income
$1,669
Profit margin
2.67%
Sales
$62,484
Sales
$62,484
Cost of goods
sold
$48,008
Plus
Interest
$1,082
Depreciation
$4,017
Taxes
$476
Divided by
Fixed assets
$142,271
Sales
$62,484
Total asset
turnover
.33
Current assets
$49,893
Cash
$16,088
Accounts
receivable
$16,813
Inventory
$16,992
Total assets
$192,164
Multiplied
by
Multiplied by
Return on
assets
0.87%
Return on
equity
1.66%
Equity
multiplier
1.92
FIGURE 3.1 Extended DuPont chart for DowDuPont
Source: DowDuPont
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68 P A R T 2 Understanding Financial Statements and Cash Flow
other words, if we want to improve profitability, our chart clearly shows us the areas on
which we should focus.
Turning to the right-hand side of Figure 3.1, we have an analysis of the key factors un-
derlying total asset turnover. Thus, we see that reducing inventory holdings through more
efficient management reduces current assets, which reduces total assets, which then im-
proves total asset turnover.
CONCEPT QUESTIONS
3.3a Return on assets, or ROA, can be expressed as the product of two ratios. Which two?
3.3b Return on equity, or ROE, can be expressed as the product of three ratios. Which
three?
INTERNAL AND SUSTAINABLE
GROWTH
A firm’s return on assets and return on equity are frequently used to calculate two addi-
tional numbers, both of which have to do with the firm’s ability to grow. We examine these
next, but first we introduce two basic ratios.
Dividend Payout and Earnings Retention
As we have seen in various places, a firm’s net income gets divided into two pieces. The first
piece is cash dividends paid to stockholders. Whatever is left over is the addition to retained
earnings. For example, from Table 3.3, Prufrock’s net income was $474, of which $158 was
paid out in dividends. If we express dividends paid as a percentage of net income, the result
is the dividend payout ratio:
Dividend payout ratio
=
Cash dividends / Net income
= $158 / $474
=
.3333,) or 33).)33%
[3.24]
What this tells us is that Prufrock pays out about 33 percent of its net income in dividends.
Anything Prufrock does not pay out in the form of dividends must be retained in the
firm, so we can define the retention ratio as:
Retention ratio
=
Addition to retained earnings / Net income
=
$316 / $474
= .6667,) or 66.67%
[3.25]
So, Prufrock retains about 67 percent of its net income. The retention ratio also is known as
the plowback ratio because it is, in effect, the portion of net income that is plowed back into
the business.
Notice that net income must be either paid out or plowed back, so the dividend payout
and plowback ratios have to add up to 1. Put differently, if you know one of these figures,
you can figure the other one out immediately.
3.4
You can find growth rates
under the “Analysis” link at
finance.yahoo.com.
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C H A P T E R 3 Working with Financial Statements 69
ROA, ROE, and Growth
Investors and others are frequently interested in knowing how rapidly a firm’s sales can grow.
The important thing to recognize is that if sales are to grow, assets have to grow as well, at
least over the long run. Further, if assets are to grow, then the firm must somehow obtain the
money to pay for the needed acquisitions. In other words, growth has to be financed, and as
a direct corollary, a firm’s ability to grow depends on its financing policies.
A firm has two broad sources of financing: internal and external. Internal financing
refers to what the firm earns and subsequently plows back into the business. External
financing refers to funds raised by either borrowing money or selling stock.
The Internal Growth Rate Suppose a firm has a policy of financing growth using
only internal financing. This means that the firm won’t borrow any funds and won’t sell any
new stock. How rapidly can the firm grow? The answer is given by the internal growth rate:
Internal growth rate = ROA × b ___________ 1 − ROA × b [3.26]
where ROA is, as usual, return on assets and b is the retention, or plowback, ratio we just
discussed.
For Prufrock Corporation, we earlier calculated ROA as 13.06 percent. We also saw
that the retention ratio is 66.67 percent, so the internal growth rate is:
Internal growth rate = ROA × b ___________ 1 − ROA × b
= .1306 × .6667 _______________ 1 − .1306 × .6667
= .0954,) or 9.54%
Thus, if Prufrock relies solely on internally generated financing, it can grow at a maximum
rate of 9.54 percent per year.
The Sustainable Growth Rate If a firm only relies on internal financing, then,
through time, its total debt ratio will decline. The reason is that assets will grow, but total
debt will remain the same (or even fall if some is paid off). Frequently, firms have a particu-
lar total debt ratio or equity multiplier that they view as optimal (why this is so is the subject
of Chapter 13).
With this in mind, we now consider how rapidly a firm can grow if (1) it wishes to
maintain a particular total debt ratio and (2) it is unwilling to sell new stock. There are vari-
ous reasons a firm might wish to avoid selling stock, and equity sales by established firms
are actually a relatively rare occurrence. Given these two assumptions, the maximum growth
rate that can be achieved, called the sustainable growth rate, is:
Sustainable growth rate = ROE × b ___________ 1 − ROE × b [3.27]
internal growth rate
The maximum possible
growth rate a firm can
achieve without external
financing of any kind.
sustainable growth
rate
The maximum possible
growth rate a firm can
achieve without external
equity financing while
maintaining a constant
debt-equity ratio.
EXAMPLE 3.4 Payout and Retention
The Manson-Marilyn Corporation routinely pays out 40 percent of net income in the form of divi-
dends. What is its plowback ratio? If net income was $800, how much did stockholders actually
receive?
If the payout ratio is 40 percent, then the retention, or plowback, ratio must be 60 percent
because the two have to add up to 100 percent. Dividends were 40 percent of $800, or $320.
ros13952_ch03_050-096.indd 69 12/22/18 5:48 PM
70 P A R T 2 Understanding Financial Statements and Cash Flow
Notice that this is the same as the internal growth rate, except that ROE is used instead of
ROA.
Looking at Prufrock, we earlier calculated ROE as 18.06 percent, and we know that the
retention ratio is 66.67 percent, so we can easily calculate sustainable growth as:
Sustainable growth rate = ROE × b ___________ 1 − ROE × b
= .1806 × .6667 __________________ 1 − .1806 × .6667
= .1369, or 13.69%
If you compare this sustainable growth rate of 13.69 percent to the internal growth rate of
9.54 percent, you might wonder why it is larger. The reason is that, as the firm grows, it will
have to borrow additional funds if it is to maintain a constant debt ratio. This new borrow-
ing is an extra source of financing in addition to internally generated funds, so Prufrock can
expand more rapidly.
Determinants of Growth In our previous section, we saw that the return on equity,
or ROE, could be decomposed into its various components using the DuPont identity. Be-
cause ROE appears so prominently in the determination of the sustainable growth rate, the
factors important in determining ROE are also important determinants of growth.
As we saw, ROE can be written as the product of three factors:
ROE = Profit margin × Total asset turnover × Equity multiplier
If we examine our expression for the sustainable growth rate, we see that anything that in-
creases ROE will increase the sustainable growth rate by making the numerator larger and
the denominator smaller. Increasing the plowback ratio will have the same effect.
Putting it all together, what we have is that a firm’s ability to sustain growth depends
explicitly on the following four factors:
1. Profit margin. An increase in profit margin will increase the firm’s ability to generate
funds internally and thereby increase its sustainable growth.
2. Total asset turnover. An increase in the firm’s total asset turnover increases the sales
generated for each dollar in assets. This decreases the firm’s need for new assets as
sales grow and thereby increases the sustainable growth rate. Notice that increasing
total asset turnover is the same thing as decreasing capital intensity.
3. Financial policy. An increase in the debt-equity ratio increases the firm’s financial
leverage. Because this makes additional debt financing available, it increases the
sustainable growth rate.
4. Dividend policy. A decrease in the percentage of net income paid out as dividends will
increase the retention ratio. This increases internally generated equity and thus
increases internal and sustainable growth.
The sustainable growth rate is a very useful number. What it illustrates is the explicit rela-
tionship between the firm’s four major areas of concern: its operating efficiency as mea-
sured by profit margin, its asset use efficiency as measured by total asset turnover, its
financial policy as measured by the debt-equity ratio, and its dividend policy as measured by
the retention ratio. If sales are to grow at a rate higher than the sustainable growth rate, the
firm must increase profit margins, increase total asset turnover, increase financial leverage,
increase earnings retention, or sell new shares.
The two growth rates, internal and sustainable, are summarized in Table 3.9. The
nearby Finance Matters box discusses some issues related to growth rates.
ros13952_ch03_050-096.indd 70 12/22/18 5:48 PM
How Fast Is Too Fast?
Growth rates are an important tool for evaluating a com-pany, and, as we will see later, an important tool for valu-
ing a company’s stock. When thinking about (and calculating)
growth rates, a little common sense goes a long way. For
example, in 2018, retailing giant Walmart had about 785 mil-
lion square feet of stores, distribution centers, and so forth.
Suppose the company wants to expand its square footage
by 6 percent over the next year. This increase doesn’t sound
too outrageous, but can Walmart grow its square footage at
6 percent indefinitely?
We’ll get into the calculation in our next chapter, but if
you assume that Walmart grows at 6 percent per year over
the next 202 years, the company will have about 100 trillion
square feet of property, which is about the total land mass of
the entire United States! In other words, if Walmart keeps
growing at 6 percent, the entire country will eventually be
one big Walmart. Scary.
Facebook is another example. The company had total
revenues of about $1.97 billion in 2010 and $40.65 billion in
2017. This represents an annual rate of increase of 54 per-
cent! How likely do you think it is that the company can con-
tinue this growth rate? If this growth continued, the company
would have revenues of about $26.67 trillion in just 15 years,
which exceeds the gross domestic product (GDP) of the
United States. Obviously, Facebook’s growth rate will slow
substantially in the next several years.
What about growth in cash flow? As of the beginning of
2018, cash flow for Internet travel booking website Priceline
.com grew at an annual rate of about 37 percent for the past
10 years. The company was expected to generate about
$4.48 billion in cash flow for 2018. If Priceline.com’s cash
flow grew at the same rate for the next 19 years, the com-
pany would generate about $1.77 trillion per year, or slightly
more than the $1.63 trillion of U.S. currency circulating in the
world.
As these examples show, growth rates can be deceiv-
ing. It is fairly easy for a small company to grow very fast. If a
company has $100 in sales, it only has to increase sales by
another $100 to have a 100 percent increase in sales. If the
company’s sales are $10 billion, it has to increase sales by
another $10 billion to achieve the same 100 percent in-
crease. So, long-term growth rate estimates must be chosen
very carefully. As a rule of thumb, for really long-term growth
estimates, you should probably assume that a company will
not grow much faster than the economy as a whole, which is
about 1 to 3 percent (inflation-adjusted).
FINANCE MATTERS
I. Internal growth rate
Internal growth rate = ROA × b ___________ 1 − ROA × b
where:
ROA = Return on assets = Net income/Total assets
b = Plowback (retention) ratio
= Addition to retained earnings/Net income
= 1 – Dividend payout ratio
The internal growth rate is the maximum growth rate that can be achieved with no external
financing of any kind.
II. Sustainable growth rate
Sustainable growth rate = ROE × b ___________ 1 − ROE × b
where:
ROE = Return on equity = Net income/Total equity
b = Plowback (retention) ratio
= Addition to retained earnings/Net income
= 1 – Dividend payout ratio
The sustainable growth rate is the maximum growth rate that can be achieved with no
external equity financing while maintaining a constant debt-equity ratio.
Summary of internal
and sustainable
growth rates
TABLE 3.9
71
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72 P A R T 2 Understanding Financial Statements and Cash Flow
A Note on Sustainable Growth Rate Calculations Very commonly, the sus-
tainable growth rate is calculated using just the numerator in our expression, ROE × b. This
causes some confusion, which we can clear up here. The issue has to do with how ROE is
computed. Recall that ROE is calculated as net income divided by total equity. If total eq-
uity is taken from an ending balance sheet (as we have done consistently, and is commonly
done in practice), then our formula is the right one. However, if total equity is from the be-
ginning of the period, then the simpler formula is the correct one.
In principle, you’ll get exactly the same sustainable growth rate regardless of which way
you calculate it (as long as you match up the ROE calculation with the right formula). In
reality, you may see some differences because of accounting-related complications. By the
way, if you use the average of beginning and ending equity (as some advocate), yet another
formula is needed. Also, all of our comments here apply to the internal growth rate as well.
A simple example is useful to illustrate these points. Suppose a firm has a net income
of $20 and a retention ratio of .60. Beginning assets are $100. The debt-equity ratio is .25,
so beginning equity is $80.
If we use beginning numbers, we get the following:
ROE = $20 / $80 = .25,) or 25%
Sustainable growth = .25 × .60 = .15,) or 15%
For the same firm, ending equity is $80 + .60 × $20 = $92. So, we can calculate this:
ROE = $20/$92 = .2174, or 21.74%
Sustainable growth = .2174 × .60/(1 − .2174 × .60) = .15, or 15%
These growth rates are exactly the same. See if you don’t agree that the internal growth rate
is 12 percent.
CONCEPT QUESTIONS
3.4a What does a firm’s internal growth rate tell us?
3.4b What does a firm’s sustainable growth rate tell us?
3.4c Why is the sustainable growth rate likely to be larger than the internal growth rate?
USING FINANCIAL STATEMENT INFORMATION
Our last task in this chapter is to discuss in more detail some practical aspects of financial
statement analysis. In particular, we will look at reasons for doing financial statement analy-
sis, how to go about getting benchmark information, and some of the problems that come
up in the process.
Why Evaluate Financial Statements?
As we have discussed, the primary reason for looking at accounting information is that we don’t
have, and can’t reasonably expect to get, market value information. It is important to emphasize
that, whenever we have market information, we will use it instead of accounting data. Also, if
there is a conflict between accounting and market data, market data should be given precedence.
Financial statement analysis is essentially an application of “management by excep-
tion.” In many cases, such analysis will boil down to comparing ratios for one business with
some kind of average or representative ratios. Those ratios that seem to differ the most from
the averages are tagged for further study.
3.5
coverage online
Excel
Master
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C H A P T E R 3 Working with Financial Statements 73
Internal Uses Financial statement information has a variety of uses within a firm.
Among the most important of these is performance evaluation. For example, managers
are frequently evaluated and compensated on the basis of accounting measures of perfor-
mance such as profit margin and return on equity. Also, firms with multiple divisions
frequently compare the performance of those divisions using financial statement
information.
Another important internal use of financial statement information involves planning for
the future. Historical financial statement information is very useful for generating projections
about the future and for checking the realism of assumptions made in those projections.
External Uses Financial statements are useful to parties outside the firm, including
short-term and long-term creditors and potential investors. For example, we would find such
information quite useful in deciding whether or not to grant credit to a new customer.
We also would use this information to evaluate suppliers, and suppliers would use our
statements before deciding to extend credit to us. Large customers use this information to
decide if we are likely to be around in the future. Credit-rating agencies rely on financial
statements in assessing a firm’s overall creditworthiness. The common theme here is that
financial statements are a prime source of information about a firm’s financial health.
We also would find such information useful in evaluating our main competitors. We
might be thinking of launching a new product. A prime concern would be whether the com-
petition would jump in shortly thereafter. In this case, we would be interested in our com-
petitors’ financial strength to see if they could afford the necessary development.
Finally, we might be thinking of acquiring another firm. Financial statement informa-
tion would be essential in identifying potential targets and deciding what to offer.
Choosing a Benchmark
Given that we want to evaluate a division or a firm based on its financial statements, a basic
problem immediately comes up. How do we choose a benchmark, or a standard of compari-
son? We describe in this section some ways of getting started.
Time-Trend Analysis One standard we could use is history. Suppose we found that
the current ratio for a particular firm is 2.4 based on the most recent financial statement
information. Looking back over the last 10 years, we might find that this ratio has declined
fairly steadily over that period.
Based on this, we might wonder if the liquidity position of the firm has deteriorated. It
could be, of course, that the firm has made changes that allow it to use its current assets
more efficiently, that the nature of the firm’s business has changed, or that business prac-
tices have changed. If we investigate, we might find any of these possible explanations. This
is an example of what we mean by management by exception—a deteriorating time trend
may not be bad, but it does merit investigation.
Peer Group Analysis The second means of establishing a benchmark is to identify
firms similar in the sense that they compete in the same markets, have similar assets, and
operate in similar ways. In other words, we need to identify a peer group. There are obvious
problems with doing this since no two companies are identical. Ultimately, the choice of
which companies to use as a basis for comparison is subjective.
One common way of identifying potential peers is based on Standard
Industrial Classification (SIC) codes. These are four-digit codes established by the U.S. gov-
ernment for statistical reporting purposes. Firms with the same SIC code are frequently as-
sumed to be similar.
Standard Industrial
Classification (SIC)
code
U.S. government code
used to classify a firm by
its type of business
operations.
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74 P A R T 2 Understanding Financial Statements and Cash Flow
The first digit in an SIC code establishes the general type of business. For example,
firms engaged in finance, insurance, and real estate have SIC codes beginning with 6. Each
additional digit narrows down the industry. So, companies with SIC codes beginning with
60 are mostly banks and banklike businesses; those with codes beginning with 602 are
mostly commercial banks; and SIC code 6025 is assigned to national banks that are mem-
bers of the Federal Reserve system. Table 3.10 is a list of selected two-digit codes (the first
two digits of the four-digit SIC codes) and the industries they represent.
Beginning in 1997, a new industry classification system was instituted. Specifically, the
North American Industry Classification System (NAICS, pronounced “nakes”) is intended
to replace the older SIC codes, and it probably will eventually. Currently, however, SIC
codes are widely used.
SIC codes are far from perfect. Suppose you were examining financial statements for
Walmart, the largest retailer in the United States. In a quick scan of the nearest financial
database, you might find about 20 large, publicly owned corporations with this same SIC
code, but you might not be too comfortable with some of them. Target would seem to be a
reasonable peer, but Neiman Marcus also carries the same industry code. Are Walmart and
Neiman Marcus really comparable?
As this example illustrates, it is probably not appropriate to blindly use SIC code-based
averages. Instead, analysts often identify a set of primary competitors and then compute a
set of averages based on this group. Also, we may be more concerned with a group of the
top firms in an industry, not the average firm. Such a group is called an aspirant group be-
cause we aspire to be like them. In this case, a financial statement analysis reveals how far
we have to go.
We can now take a look at a specific industry. Suppose we are in the retail hardware
business. Table 3.11 contains some condensed common-size financial statements for this
industry from RMA, one of many sources of such information. Table 3.12 contains selected
ratios from the same source.
There is a large amount of information here, most of which is self-explanatory. On
the right in Table 3.11, we have current information reported for different groups based
on sales. Within each sales group, common-size information is reported. For example,
Learn more about NAICS at
www.naics.com.
Selected two-digit
SIC codes
Agriculture, Forestry, and Fishing
01 Agriculture production: crops
02 Forestry
Mining
10 Metal mining
13 Oil and gas extraction
Construction
15 Building construction
16 Construction other than building
Manufacturing
28 Chemicals and allied products
29 Petroleum refining
35 Machinery, except electrical
37 Transportation equipment
Transportation, Communication, Electric, Gas,
and Sanitary Service
45 Transportation by air
49 Electric, gas, and sanitary services
Retail Trade
54 Food stores
55 Auto dealers and gas stations
58 Eating and drinking places
Finance, Insurance, and Real Estate
60 Banking
63 Insurance
65 Real Estate
Services
78 Motion pictures
80 Health services
82 Educational services
TABLE 3.10
ros13952_ch03_050-096.indd 74 12/22/18 5:48 PM
C H A P T E R 3 Working with Financial Statements 75
Selected financial statement information
M = $ thousand; MM = $ million.
Interpretation of Statement Studies Figures: RMA cautions that the studies be regarded only as a general guideline and not as an absolute industry
norm. This is due to limited samples within categories, the categorization of companies by their primary NAICS code only, and different methods of
operations by companies within the same industry. For these reasons, RMA recommends that the figures be used only as general guidelines in
addition to other methods of financial analysis.
© 2017 by RMA. All rights reserved. No part of this table may be reproduced or utilized in any form or by any means, electronic or mechanical, including
photocopying, recording, or by any information storage and retrieval system, without permission in writing from RMA, Risk Management Association.
TABLE 3.11
Manufacturing—Wineries NAICS 312130
Comparative Historical Data Current Data Sorted by Sales
Type of Statement
38 33 29 Unqualified 1 2 4 22
40 53 41 Reviewed 2 15 15 9
17 15 12 Compiled 1 2 3 3 2 1
24 25 26 Tax Returns 11 6 4 4 1
100 150 150 Other 24 35 20 18 26 27
31 (4/1–9/30/15) 227 (10/1/15–3/31/16)
4/1/13–
3/31/14
ALL
219
4/1/14–
3/31/15
ALL
276
4/1/15 –
3/31/16
ALL
258
NUMBER OF
STATEMENTS
0-1
MM
37
1-3 MM
45
3-5 MM
27
5-10
MM
42
10-25
MM
48
25MM
& OVER
59
Assets
5.2% 5.3% 5.0% Cash & Equivalents 6.8% 5.0% 8.7% 5.2% 2.0% 4.4%
8.4 8.1 9.2 Trade Receivables (net) 5.6 7.3 7.5 9.0 11.0 12.3
44.4 47.4 47.3 Inventory 52.0 50.1 49.4 42.6 47.0 44.9
2.4 1.9 1.7 All Other Current .6 1.6 .7 1.8 1.6 2.8
60.5 62.7 63.1 Total Current 65.0 64.0 66.3 58.6 61.6 64.3
32.0 29.2 29.8 Fixed Assets (net) 28.4 32.6 22.9 36.3 29.4 27.6
3.5 4.0 3.7 Intangibles (net) 4.5 1.5 3.7 3.1 5.0 4.1
4.0 4.1 3.4 All Other Non-Current 2.0 2.0 7.1 2.0 3.9 4.0
100.0 100.0 100.0 Total 100.0 100.0 100.0 100.0 100.0 100.0
Liabilities
14.1 16.8 15.7 Notes Payable—Short Term 17.7 14.3 10.0 12.3 18.8 18.1
2.1 1.8 1.3 Cur. Mat.-L.T.D. .9 1.0 .9 2.0 1.4 1.6
8.8 8.9 8.8 Trade Payables 5.9 9.0 7.2 7.8 12.2 9.3
.2 .2 .2 Income Taxes Payable .4 .3 .0 .3 .0 .1
6.0 6.0 6.5 All Other Current 7.6 4.8 6.0 4.1 8.7 7.4
31.2 33.8 32.6 Total Current 32.5 29.3 24.1 26.5 41.2 36.5
19.8 17.4 18.5 Long-Term Debt 20.5 17.5 17.8 22.5 17.4 16.6
.4 .3 .4 Deferred Taxes .0 .0 .2 .7 .7 .4
6.3 6.7 6.6 All Other Non-Current 13.5 5.6 17.8 7.5 4.4 3.6
42.2 41.8 41.9 Net Worth 33.5 17.5 50.1 42.8 36.3 42.9
100.0 100.0 100.0 Total Liabilities & Net Worth 100.0 100.0 100.0 100.0 100.0 100.0
Income Data
100.0 100.0 100.0 Net Sales 100.0 100.0 100.0 100.0 100.0 100.0
48.9 50.0 49.3 Gross Profit 57.1 54.1 55.8 49.5 45.0 41.0
37.2 37.9 37.9 Operating Expenses 51.4 44.5 39.4 38.2 32.5 27.8
11.7 12.0 11.4 Operating Profit 5.7 9.7 16.4 11.3 12.5 13.3
2.7 2.6 2.6 All Other Expenses (net) 3.4 1.9 1.1 4.3 2.9 2.1
9.0 9.5 8.8 Profit Before Taxes 2.3 7.8 15.3 7.1 9.6 11.2
ros13952_ch03_050-096.indd 75 12/22/18 5:48 PM
76 P A R T 2 Understanding Financial Statements and Cash Flow
Selected ratios
Manufacturing—Wineries NAICS 312130
Comparative Historical Data Current Data Sorted by Sales
38
40
17
24
100
33
53
15
25
150
29
41
12
26
150
Type of
Statement
Unqualified
Reviewed
Compiled
Tax Returns
Other
1
1
11
29
2
2
6
35
3
4
20
2
15
3
4
18
4
15
2
1
26
22
9
1
27
31 (4/1–9/30/15) 227 (10/1/15–3/31/16)
4/1/13–
3/31/14
ALL 219
4/1/14–
3/31/15
ALL 276
4/1/15–
3/31/16
ALL 258
NUMBER OF
STATEMENTS
0–1 MM
37
1–3 MM
45
3–5 MM
27
5–10 MM
42
10–25 MM
48
25 MM &
OVER 59
4.0
2.1
1.4
4.5
2.0
1.4
4.0
2.1
1.4
Ratios
Current
4.1
2.7
1.4
5.8
2.3
1.5
5.9
3.3
1.8
3.8
2.3
1.8
2.4
1.5
1.2
3.4
1.9
1.3
.9
.3
.2
.9
.3
.2
.9
.3
.2
Quick
1.2
.3
.1
1.1
.3
.2
1.9
.5
.2
1.2
.4
.2
.6
.3
.1
.7
.4
.2
16
30
51
23.0
12.2
7.1
15
34
52
24.8
10.6
7.0
15
31
52
23.7
11.8
7.0
Sales/
Receivables
0
10
46
UND
35.6
7.9
2
28
50
49.3
12.9
7.3
11
20
39
32.8
18.3
9.4
16
29
57
22.4
12.6
6.4
21
37
56
17.2
9.8
6.5
28
41
59
13.1
8.9
6.2
261
456
730
1.4
.8
.5
332
521
912
1.1
.7
.4
304
521
730
1.2
.7
.5
Cost of Sales/
Inventory
192
608
912
1.9
.6
.4
304
608
912
1.2
.6
.4
261
608
730
1.4
.6
.5
304
608
730
1.2
.6
.5
365
521
730
1.0
.7
.5
261
365
608
1.4
1.0
.6
14
24
38
14.4
6.6
3.6
26
59
122
14.0
6.2
3.0
21
51
107
17.3
7.2
3.4
Cost of Sales/
Payables
0
48
166
UND
7.6
2.2
10
53
146
36.2
6.9
2.5
21
35
70
17.2
10.3
5.2
23
47
122
16.0
7.8
3.0
36
69
122
10.1
5.3
3.0
23
51
76
16.1
7.2
4.8
1.4
2.7
6.6
1.3
2.4
5.1
1.3
2.6
5.2
Sales/Working
Capital
1.2
2.0
7.8
1.2
2.8
5.8
1.1
2.3
4.0
1.3
2.1
2.8
2.0
3.7
6.7
1.9
2.9
6.0
(200)
9.7
3.9
1.9
(252)
11.4
4.7
1.7
(235)
14.3
3.7
1.3
EBIT/Interest (31)
4.5
1.0
−2.1
(36)
7.9
3.60
1.2
(25)
31.5
9.0
2.1
(40)
12.3
2.3
1.1
(46)
13.0
4.1
1.2
(57)
19.9
5.7
2.8
(42)
8.0
4.8
1.9
(55)
9.1
5.0
2.6
(45)
9.5
5.9
2.6
Net Profit + Depr.,
Dep., Amort./
Cur. Mat. L/T/D
(10)
6.9
3.5
1.8
(24)
17.3
7.7
4.3
.3
.8
1.6
.2
.7
1.4
.2
.7
1.5
Fixed/Worth
.2
.6
4.5
.2
.7
1.5
.1
.4
1.1
.4
1.0
1.5
.2
.8
1.9
.3
.8
1.3
.6
1.5
4.1
.6
1.4
3.0
.6
1.4
3.9
Debt/Worth
.5
2.6
24.2
.5
1.0
2.7
.4
1.2
4.3
.6
1.4
2.8
1.2
2.1
4.3
.8
1.1
3.2
(194)
32.8
14.8
2.7
(253)
33.9
15.6
3.3
(230)
32.7
13.6
2.7
% Profit Before
Taxes/Tangible
Net Worth
(29)
34.2
5.5
−8.9
(41)
25.0
11.8
4.6
(25)
47.0
20.5
3.3
(38)
20.0
7.4
.4
(43)
42.2
19.6
3.7
(54)
27.9
18.3
10.2
TABLE 3.12
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C H A P T E R 3 Working with Financial Statements 77
firms with sales in the $10 million to $25 million range have cash and equivalents
equal to 2.0 percent of total assets. There are 48 companies in this group, out of 258
in all.
On the left, we have three years’ worth of summary historical information for the entire
group. For example, operating profit decreased slightly from 11.7 percent of sales to 11.4
percent over that time.
Table 3.12 contains some selected ratios, again reported by sales groups on the right
and time period on the left. To see how we might use this information, suppose our firm has
a current ratio of 2. Based on the ratios, is this value unusual?
Looking at the current ratio for the overall group for the most recent year (third column
from the left in Table 3.12), we see that three numbers are reported. The one in the middle,
2.1, is the median, meaning that half of the 258 firms had current ratios that were lower and
half had higher current ratios. The other two numbers are the upper and lower quartiles. So,
25 percent of the firms had a current ratio larger than 4.0 and 25 percent had a current ratio
smaller than 1.4. Our value of 2 falls comfortably within these bounds, so it doesn’t appear
too unusual. This comparison illustrates how knowledge of the range of ratios is important in
addition to knowledge of the average. Notice how stable the current ratio has been for the
last three years.
43 (4/1–9/30/10) 326 (10/1/10–3/31/11)
4/1/13–
3/31/14
ALL 219
4/1/14–
3/31/15
ALL 276
4/1/15–
3/31/16
ALL 258
NUMBER OF
STATEMENTS
0–1 MM
37
1–3 MM
45
3–5 MM
27
5–10 MM
42
10–25 MM
48
25 MM
& OVER
59
12.0
5.1
.7
12.8
5.6
.9
12.1
4.8
.6
% Profit
Before Taxes/
Total Assets
13.6
1.4
−5.0
9.1
5.2
.8
23.9
7.2
1.5
8.7
2.7
.2
13.4
4.4
.8
13.1
7.0
3.0
7.4
2.5
1.1
9.5
3.0
1.1
8.6
2.9
1.2
Sales/Net
Fixed Assets
7.3
5.0
2.4
6.8
2.3
1.5
13.9
5.1
1.7
3.9
1.4
.9
33.5
2.1
1.0
9.0
3.3
1.4
1.1
.7
.5
1.0
.7
.5
1.1
.7
.5
Sales/Total
Assets
1.1
.7
.5
1.1
.7
.5
1.2
.8
.5
1.0
.6
.4
1.1
.7
.4
1.1
.7
.5
(171)
2.4
5.2
8.3
(270)
2.4
5.1
8.1
(199)
2.1
5.3
8.4
% Depr.,
Dep., Amort./
Sales
(22)
3.4
5.9
14.3
(31)
1.6
5.8
8.7
(40)
1.1
3.9
9.6
(35)
2.7
7.1
9.1
(29)
2.3
6.1
9.3
(56)
1.4
4.0
7.1
(27)
3.1
4.3
7.7
(201)
2.7
4.1
9.5
(33)
2.6
4.1
7.3
% Officers’,
Directors’, Owners’
Comp/Sales
4892971M
6963108M
8360552M
8811913M
5519014M
8435750M
Net Sales ($)
Total Assets ($)
19825M
49293M
82307M
161278M
103312M
147637M
287163M
602723M
774866M
1722233M
4251541M
5752586M
M = $ thousand; MM = $ million.
© 2017 by RMA. All rights reserved. No part of this table may be reproduced or utilized in any form or by any means, electronic or mechanical,
including photocopying, recording, or by any information storage and retrieval system, without permission in writing from RMA, Risk Management
Association.
TABLE 3.12 Selected ratios (continued”)
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78 P A R T 2 Understanding Financial Statements and Cash Flow
There are many sources of ratio information in addition to the one we examine here.
The nearby Work the Web box shows how to get this information for most publicly traded
companies, along with some very useful benchmarking information. Be sure to look it over
and then benchmark your favorite company.
EXAMPLE 3.5 More Ratios
Take a look at the most recent numbers reported for Cost of Sales/Inventory and EBIT/lnterest in
Table 3.12. What are the overall median values? What are these ratios?
If you look back at our discussion, you will see that these are the inventory turnover and the
times interest earned, or TIE, ratios. The median value for inventory turnover for the entire group is
.7 times. So, the days’ sales in inventory would be 365/.7 = 521 days, which is the boldfaced number
reported. While this is long compared to other industries, this doesn’t seem like very long for fine
wines. The median for the TIE is 3.7 times. The number in parentheses indicates that the calculation
is meaningful for, and therefore based on, only 235 of the 258 companies. In this case, the reason
is that only 235 companies paid any significant amount of interest.
As we discussed in this chapter, ratios are an important tool for examining a company’s perfor-mance, but gathering the necessary information can be tedious and time-consuming. Fortu-
nately, many sites on the web provide this information for free. We went to www.reuters.com,
entered the ticker symbol “BBY” (for Best Buy), and then went to the financials page. Here is an
abbreviated look at the results:
W R K T H E W E B
QUESTIONS
1. Go to www.reuters.com and find the major ratio categories listed on this website. How
do the categories differ from the categories listed in the textbook?
2. Go to www.reuters.com and find all the ratios for Best Buy. How is the company per-
forming in each ratio category presented on this website?
In looking at the Management Effectiveness ratios (or what we call profitability ratios), Best
Buy has outperformed the company and sector for both the 1-year and 5-year periods reported.
Source: www.reuters.com
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C H A P T E R 3 Working with Financial Statements 79
Problems with Financial Statement Analysis
We close out our chapter on working with financial statements by discussing some addi-
tional problems that can arise in using financial statements. In one way or another, the basic
problem with financial statement analysis is that there is no underlying theory to help us
identify which items or ratios to look at and to guide us in establishing benchmarks.
As we discuss in other chapters, there are many cases in which financial theory and
economic logic provide guidance in making judgments about value and risk. Very little such
help exists with financial statements. This is why we can’t say which ratios matter the most
and what a high or low value might be.
One particularly severe problem is that many firms, such as General Electric (GE), are
conglomerates owning more or less unrelated lines of business. The consolidated financial
statements for such firms don’t really fit any neat industry category. More generally, the
kind of peer group analysis we have been describing is going to work best when the firms are
strictly in the same line of business, the industry is competitive, and there is only one way of
operating.
Another problem that is becoming increasingly common is that major competitors and
natural peer group members in an industry may be scattered around the globe. The automo-
bile industry is an obvious example. The problem here is that financial statements from
outside the United States do not necessarily conform at all to GAAP (more precisely, differ-
ent countries can have different GAAPs). The existence of different standards and proce-
dures makes it very difficult to compare financial statements across national borders.
What’s in a Ratio?
Abraham Briloff, a well-known financial commentator, famously remarked that “financial statements are like
fine perfume; to be sniffed but not swallowed.” As you prob-
ably have figured out by now, his point is that information
gleaned from financial statements—and ratios and growth
rates computed from that information—should be taken with
a grain of salt.
For example, looking back at our chapter opener re-
garding PE ratios, investors must really think that Amazon
.com will have extraordinary growth. After all, they are willing
to pay about $274 for every dollar the company currently
earns, which definitely makes it look like a growth company.
Looking back, from 2012 to 2017, Amazon’s revenue in-
creased by 22 percent per year. More important, looking
ahead, the well-known independent investment research
company Value Line projected revenue growth of 21 percent
per year and earnings growth of 48 percent per year over
the next five years for Amazon.
A problem that can occur with ratio analysis is negative
equity. Let’s look at retailer Sears Holdings, for example. The
company reported a loss of about $383 million during 2017,
and its book value of equity was negative $3.7 billion. If you
calculate the ROE for the company, you will find that it is
about 10 percent, which is pretty good. Unfortunately, if you
examine the ROE a little closer, you will find something un-
usual: The more the company loses, the higher the ROE be-
comes. Also, in this case, both the market-to-book and PE
ratios are negative. How do you interpret a negative PE?
We’re not really sure either. Whenever a company has a
negative book value of equity, it means the losses for the
company have been so large that it has erased all the book
equity. In this case, ROE, PE ratios, and market-to-book ra-
tios are usually not reported because they lack meaning.
Even if a company’s book equity is positive, you still
have to be careful. For example, consider Boeing, which had
a market-to-book ratio of about 500 in early 2018. Because
this ratio measures the value created by the company for
shareholders, things look pretty good for the company. But a
closer look shows that Boeing’s book value of equity per
share was $19.90 in 2013, but it dropped to $.60 in 2017
even though the company posted a positive net income for
the year. As it happens, the drop was due to accounting
charges related to the company’s 747, 747-8, and KC-46A
programs.
Financial ratios are important tools used in evaluating
companies of all types, but you cannot take a number as
given. Instead, before doing any analysis, the first step is to
ask whether the number actually makes sense.
FINANCE MATTERS
79
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80 P A R T 2 Understanding Financial Statements and Cash Flow
Even companies that are clearly in the same line of business may not be comparable.
For example, electric utilities engaged primarily in power generation are all classified in the
same group (SIC 4911). This group is often thought to be relatively homogeneous. However,
utilities generally operate as regulated monopolies, so they don’t compete with each other.
Many have stockholders, and many are organized as cooperatives with no stockholders.
There are several different ways of generating power, ranging from hydroelectric to nuclear,
so the operating activities can differ quite a bit. Finally, profitability is strongly affected by
the regulatory environment, so utilities in different locations can be very similar but show
very different profits.
Several other general problems frequently crop up. First, different firms use differ-
ent accounting procedures—for inventory, for example. This makes it difficult to compare
statements. Second, different firms end their fiscal years at different times. For firms in
seasonal businesses (such as a retailer with a large Christmas season), this can lead to
difficulties in comparing balance sheets because of fluctuations in accounts during the
year. Finally, for any particular firm, unusual or transient events, such as a one-time
profit from an asset sale, may affect financial performance. In comparing firms, such
events can give misleading signals. Our nearby Finance Matters box discusses some ad-
ditional issues.
CONCEPT QUESTIONS
3.5a What are some uses for financial statement analysis?
3.5b What are SIC codes and how might they be useful?
3.5c Why do we say that financial statement analysis is management by exception?
3.5d What are some of the problems that can arise with financial statement analysis?
SUMMARY AND CONCLUSIONS
This chapter has discussed aspects of financial statement analysis, including:
1. Standardized financial statements. We explained that differences in firm size make it
difficult to compare financial statements, and we discussed how to form common-size
statements to make comparisons easier.
2. Ratio analysis. Evaluating ratios of accounting numbers is another way of comparing
financial statement information. We therefore defined and discussed a number of the
most commonly reported and used financial ratios. We also discussed the famous
DuPont identity as a way of analyzing financial performance, and we examined the
connection between profitability, financial policy, and growth.
3. Using financial statements. We described how to establish benchmarks for
comparison purposes and discussed some of the types of information that are
available. We then examined some of the potential problems that can arise.
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C H A P T E R 3 Working with Financial Statements 81
After you have studied this chapter, we hope that you will have some perspective on the
uses and abuses of financial statements. You also should find that your vocabulary of busi-
ness and financial terms has grown substantially.
POP QUIZ!
Can you answer the following questions? If your class is using Connect, log on to
SmartBook to see if you know the answers to these and other questions, check out
the study tools, and find out what topics require additional practice!
Section 3.1 A common-size balance sheet expresses all accounts as a percentage
of what?
Section 3.2 What are the categories of traditional financial ratios?
Section 3.3 According to the DuPont identity, what factors affect ROE?
Section 3.4 Bubbles, Inc., has a return on equity of 12 percent and its retention ratio
is 60 percent. What is its sustainable growth rate?
Section 3.5 When should market information be used when analyzing financial
transactions?
CHAPTER REVIEW AND SELF-TEST PROBLEMS
3.1 Common-Size Statements Here are the most recent financial statements for
Wildhack. Prepare a common-size income statement based on this information. How
do you interpret the standardized net income? What percentage of sales goes to cost
of goods sold? (See Problem 15.)
WILDHACK CORPORATION
2019 Income Statement
($ in millions)
Sales $3,756
Cost of goods sold 2,453
Depreciation 490
Earnings before interest and taxes $ 813
Interest paid 613
Taxable income $ 200
Taxes (21%) 42
Net income $ 158
Dividends $72
Addition to retained earnings 86
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82 P A R T 2 Understanding Financial Statements and Cash Flow
3.2 Financial Ratios Based on the balance sheets and income statement in the previous
problem, calculate the following ratios for 2019: (See Problem 35.)
Current ratio
Quick ratio
Cash ratio
Inventory turnover
Receivables turnover
Days’ sales in inventory
Days’ sales in receivables
Total debt ratio
Times interest earned ratio
Cash coverage ratio
3.3 ROE and the DuPont Identity Calculate the 2019 ROE for the Wildhack
Corporation and then break down your answer into its component parts using the
DuPont identity. (See Problem 36.)
3.4 Sustainable Growth Based on the following information, what growth rate can
Corwin maintain if no external financing is used? What is the sustainable growth
rate? (See Problems 20, 21.)
WILDHACK CORPORATION
Balance Sheets as of December 31, 2018 and 2019
($ in millions)
2018 2019 2018 2019
Assets Liabilities and Owners’ Equity
Current assets Current liabilities
Cash $ 120 $ 88 Accounts payable $ 124 $ 144
Accounts receivable 224 192 Notes payable 1,412 1,039
Inventory 424 368 Total $1,536 $1,183
Total $ 768 $ 648 Long-term debt $1,804 $2,077
Fixed assets Owners’ equity
Net plant and equipment $5,228 $5,354 Common stock and
paid-in surplus $ 300 $ 300
Retained earnings 2,356 2,442
Total assets $5,996 $6,002 Total $2,656 $2,742
Total liabilities and
owners’ equity $5,996 $6,002
CORWIN COMPANY
Financial Statements
Income Statement Balance Sheet
Sales $2,750 Current assets $ 600 Long-term debt $ 200
Cost of sales 2,450 Net fixed assets 800 Equity 1,200
Tax (21%) 63 Total $1,400 Total $1,400
Net income $ 237
Dividends $ 79
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C H A P T E R 3 Working with Financial Statements 83
■ Answers to Chapter Review and Self-Test Problems
3.1 We’ve calculated the common-size income statement below. Remember that we
divide each item by total sales.
WILDHACK CORPORATION
2019 Common-Size Income Statement
Sales 100.0%
Cost of goods sold 65.3
Depreciation 13.0
Earnings before interest and taxes 21.6
Interest paid 16.3
Taxable income 5.3
Taxes (21%) 1.1
Net income 4.2%
Dividends 1.9%
Addition to retained earnings 2.3
Net income is 4.2 percent of sales. Because this is the percentage of each sales dollar
that makes its way to the bottom line, the standardized net income is the firm’s profit
margin. Cost of goods sold is 65.3 percent of sales.
3.2 We’ve calculated the ratios below based on the ending figures. If you don’t
remember a definition, refer back to Table 3.5.
Current ratio $648/$1,183 = .55 times
Quick ratio $280/$1,183 = .24 times
Cash ratio $88/$1,183 = .07 times
Inventory turnover $2,453/$368 = 6.67 times
Receivables turnover $3,756/$192 = 19.56 times
Days’ sales in inventory 365/6.67 = 54.76 days
Days’ sales in receivables 365/19.56 = 18.66 days
Total debt ratio $3,260/$6,002 = .54 times
Times interest earned ratio $813/$613 = 1.33 times
Cash coverage ratio $1,303/$613 = 2.13 times
3.3 The return on equity is the ratio of net income to total equity. For Wildhack, this is
$158/$2,742 = .0576, or 5.76%, which is not outstanding. Given the DuPont identity,
ROE can be written as:
ROE = Profit margin × Total asset turnover × Equity multiplier
= $158/$3,756 × $3,756/$6,002 × $6,002/$2,742
= .0421 × .6258 × 2.1889
= .0576, or 5.76%
Notice that return on assets, ROA, is .0421 × .6258 = .0263, or 2.63%.
3.4 Corwin retains $158/$237 = 2 ⁄ 3 ≈ .6667 of net income. Return on assets is:
$237/$1,400 = .1693, or 16.93%. The internal growth rate is
ROA × b ________ 1 − ROA × b =
.1693 × .6667 ____________ 1 − .1693 × .6667 = .1272, or 12.72%
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84 P A R T 2 Understanding Financial Statements and Cash Flow
Return on equity for Corwin is $237 /$1,200 = .1975, or 19.75%, so we can calculate
the sustainable growth rate as:
ROE × b ________ 1 − ROE × b =
.1975 × .6667 _____________ 1 − .1975 × .6667 = .1516, or 15.16%
CRITICAL THINKING AND CONCEPTS REVIEW
LO 2 3.1 Current Ratio What effect would the following actions have on a firm’s
current ratio? Assume that net working capital is positive.
a. Inventory is purchased.
b. A supplier is paid.
c. A short-term bank loan is repaid.
d. A long-term debt is paid off early.
e. A customer pays off a credit account.
f. Inventory is sold at cost.
g. Inventory is sold for a profit.
LO 2 3.2 Current Ratio and Quick Ratio In recent years, Dixie Co. has greatly
increased its current ratio. At the same time, the quick ratio has fallen.
What has happened? Has the liquidity of the company improved?
LO 2 3.3 Current Ratio Explain what it means for a firm to have a current ratio
equal to .50. Would the firm be better off if the current ratio were 1.50?
What if it were 15.0? Explain your answers.
LO 2 3.4 Financial Ratios Fully explain the kind of information the following
financial ratios provide about a firm:
a. Quick ratio
b. Cash ratio
c. Capital intensity ratio
d. Total asset turnover
e. Equity multiplier
f. Times interest earned ratio
g. Profit margin
h. Return on assets
i. Return on equity
j. Price-earnings ratio
LO 1 3.5 Standardized Financial Statements What types of information do
common-size financial statements reveal about the firm? What is the best
use for these common-size statements?
LO 2 3.6 Peer Group Analysis Explain what peer group analysis means. As a
financial manager, how could you use the results of peer group analysis to
evaluate the performance of your firm? How is a peer group different from
an aspirant group?
LO 3 3.7 DuPont Identity Why is the DuPont identity a valuable tool for analyzing
the performance of a firm? Discuss the types of information it reveals as
compared to ROE considered by itself.
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C H A P T E R 3 Working with Financial Statements 85
LO 2 3.8 Industry-Specific Ratios Specialized ratios are sometimes used in specific
industries. For example, the so-called book-to-bill ratio is closely watched
for semiconductor manufacturers. A ratio of .93 indicates that for every
$100 worth of chips shipped over some period, only $93 worth of new
orders were received. In the first quarter of 2018, the North American
semiconductor equipment industry’s book-to-bill ratio was 1.14, down from
1.27 in the first quarter of 2017. The most recent low occurred in October
2016 when it reached .91. What is this ratio intended to measure? Why do
you think it is so closely followed?
LO 2 3.9 Industry-Specific Ratios So-called same-store sales are a very important
measure for companies as diverse as McDonald’s and Target. As the name
suggests, examining same-store sales means comparing revenues from the
same stores or restaurants at two different points in time. Why might
companies focus on same-store sales rather than total sales?
LO 2 3.10 Industry-Specific Ratios There are many ways of using standardized
financial information beyond those discussed in this chapter. The usual
goal is to put firms on an equal footing for comparison purposes. For
example, for auto manufacturers, it is common to express sales, costs, and
profits on a per-car basis. For each of the following industries, give an
example of an actual company and discuss one or more potentially useful
means of standardizing financial information:
a. Public utilities
b. Large retailers
c. Airlines
d. Online services
e. Hospitals
f. College textbook publishers
LO 2 3.11 Financial Statement Analysis You are examining the common-size
income statements for a company for the past five years and have noticed
that the cost of goods as a percentage of sales has been increasing steadily.
At the same time, EBIT as a percentage of sales has been decreasing. What
might account for the trends in these ratios?
LO 2 3.12 Financial Statement Analysis In the previous question, what actions
might managers take to improve these ratios?
Select problems are available in McGraw-Hill Connect. Please see the pack-
aging options section of the Preface for more information.
QUESTIONS AND PROBLEMS
1. Calculating Liquidity Ratios SDJ, Inc., has net working capital of $2,135,
current liabilities of $5,320, and inventory of $2,470. What is the current
ratio? What is the quick ratio?
2. Calculating Profitability Ratios Wims, Inc., has sales of $15.2 million, total
assets of $9.8 million, and total debt of $3.7 million. If the profit margin is 6
percent, what is net income? What is ROA? What is ROE?
LO 2
BASIC (Questions 1–26)
LO 2
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86 P A R T 2 Understanding Financial Statements and Cash Flow
3. Calculating the Average Collection Period Trout Lumber Yard has a
current accounts receivable balance of $527,164. Credit sales for the year just
ended were $6,787,626. What is the receivables turnover? The days’ sales in
receivables? How long did it take, on average, for credit customers to pay off
their accounts during the past year?
4. Calculating Inventory Turnover A7X Corporation has ending
inventory of $625,817, and cost of goods sold for the year just ended was
$9,758,345. What is the inventory turnover? The days’ sales in inventory?
How long, on average, did a unit of inventory sit on the shelf before it
was sold?
5. Calculating Leverage Ratios Bello, Inc., has a total debt ratio of .43. What
is its debt-equity ratio? What is its equity multiplier?
6. Calculating Market Value Ratios Dove, Inc., had additions to retained
earnings for the year just ended of $486,000. The firm paid out $175,000
in cash dividends, and it has ending total equity of $6.825 million. If the
company currently has 335,000 shares of common stock outstanding, what
are earnings per share? Dividends per share? What is book value per share?
If the stock currently sells for $46 per share, what is the market-to-book
ratio? The price-earnings ratio? If total sales were $15.4 million, what is the
price-sales ratio?
7. DuPont Identity If jPhone, Inc., has an equity multiplier of 1.67, total asset
turnover of 1.45, and a profit margin of 5.9 percent, what is its ROE?
8. DuPont Identity Croc Gator Removal has a profit margin of 6.4 percent,
total asset turnover of 1.73, and ROE of 14.3 percent. What is this firm’s
debt-equity ratio?
9. Calculating Average Payables Period For the past year, Hawkeye, Inc.,
had a cost of goods sold of $95,318. At the end of the year, the accounts
payable balance was $22,816. How long, on average, did it take the company
to pay off its suppliers during the year? What might a large value for this
ratio imply?
10. Equity Multiplier and Return on Equity Pickler Company has a debt-equity
ratio of .65. Return on assets is 7.2 percent, and total equity is $815,000.
What is the equity multiplier? Return on equity? Net income?
11. Internal Growth If Levine, Inc., has an ROA of 7.8 percent and a payout
ratio of 25 percent, what is its internal growth rate?
12. Sustainable Growth If the Crash Davis Driving School has an ROE of
14.6 percent and a payout ratio of 20 percent, what is its sustainable growth
rate?
13. Sustainable Growth Based on the following information, calculate the
sustainable growth rate for Northern Lights Co.:
Profit margin = 6.7%
Capital intensity ratio = .45
Debt–equity ratio = .35
Net income = $135,000
Dividends = $65,000
LO 2
LO 2
LO 2
LO 2
LO 3
LO 3
LO 2
LO 2
LO 3
LO 3
LO 3
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C H A P T E R 3 Working with Financial Statements 87
14. Sustainable Growth Assuming the following ratios are constant, what is the
sustainable growth rate?
Total asset turnover =2.95
Profit margin =5.9%
Equity multiplier =1.31
Payout ratio =40%
Bethesda Mining Company reports the following balance sheet information for
2018 and 2019. Use this information to work Problems 15 through 17.
LO 3
BETHESDA MINING COMPANY
Balance Sheets as of December 31, 2018 and 2019
2018 2019 2018 2019
Assets Liabilities and Owners’ Equity
Current assets Current liabilities
Cash $ 21,182 $ 24,141 Accounts payable $180,108 $190,767
Accounts receivable 51,036 59,935 Notes payable 83,179 98,175
Inventory 120,589 142,718 Total $263,287 $288,942
Total $192,807 $226,794 Long-term debt $305,000 $340,000
Owners’ equity
Common stock and paid-in surplus $165,000 $178,000
Fixed assets Accumulated retained earnings 235,445 283,578
Net plant and equipment $775,925 $863,726 Total $400,445 $461,578
Total assets $968,732 $1,090,520 Total liabilities and owners’ equity $968,732 $1,090,520
15. Preparing Standardized Financial Statements Prepare the 2018 and 2019
common-size balance sheets for Bethesda Mining.
16. Calculating Financial Ratios Based on the balance sheets given for
Bethesda Mining, calculate the following financial ratios for each year:
a. Current ratio
b. Quick ratio
c. Cash ratio
d. Debt-equity ratio and equity multiplier
e. Total debt ratio
17. DuPont Identity Suppose that the Bethesda Mining Company had sales
of $2,751,332 and net income of $86,432 for the year ending December 31,
2019. Calculate the DuPont identity.
18. DuPont Identity The Taylor Company has an ROA of 7.6 percent, a profit
margin of 5.2 percent, and an ROE of 14 percent. What is the company’s
total asset turnover? What is the equity multiplier?
19. Return on Assets Borland, Inc., has a profit margin of 5.6 percent on sales
of $13.6 million. If the firm has debt of $6.4 million and total assets of $9.8
million, what is the firm’s ROA?
20. Calculating Internal Growth The most recent financial statements for
Minnie’s Manufacturing Co. are shown here:
LO 1
LO 2
LO 3
LO 3
LO 2
LO 3
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88 P A R T 2 Understanding Financial Statements and Cash Flow
Assets and costs are proportional to sales. Debt and equity are not. The com-
pany maintains a constant 40 percent dividend payout ratio. No external fi-
nancing is possible. What is the internal growth rate?
21. Calculating Sustainable Growth For Minnie’s Manufacturing in Problem
20, what is the sustainable growth rate?
22. Total Asset Turnover Kaleb’s Karate Supply had a profit margin of 6.7
percent, sales of $14.2 million, and total assets of $6.75 million. What was
total asset turnover? If management set a goal of increasing total asset
turnover to 2.75 times, what would the new sales figure need to be, assuming
no increase in total assets?
23. Return on Equity Barrett, Inc., has a total debt ratio of .65, total debt of
$353,000, and net income of $20,750. What is the company’s return on
equity?
24. Market Value Ratios Wilson, Inc., has a current stock price of $64. For the
past year, the company had net income of $9.1 million, total equity of $24.7
million, sales of $49.6 million, and 4.9 million shares of stock outstanding.
What are earnings per share (EPS)? Price-earnings ratio? Price-sales ratio?
Book value per share? Market-to-book ratio?
25. Profit Margin PXG Co. has total assets of $8.42 million and a total asset
turnover of 1.5 times. If the return on assets is 8.3 percent, what is its profit
margin?
26. Enterprise Value-EBITDA Multiple The market value of the equity of
Skipper, Inc., is $745,000. The balance sheet shows $46,000 in cash and
$235,000 in debt, while the income statement has EBIT of $96,700 and a
total of $144,000 in depreciation and amortization. What is the enterprise
value-EBITDA multiple for this company?
LO 3
LO 2
LO 2
LO 2
LO 3
LO 2
Income Statement Balance Sheet
Sales $87,600 Current assets $ 29,000 Debt $ 38,400
Costs 64,350 Fixed assets 91,400 Equity 82,000
Taxable income $23,250 Total $120,400 Total $120,400
Tax (21%) 4,883
Net Income $18,368
INTERMEDIATE (Questions 27–46)
27. Using the DuPont Identity Y3K, Inc., has sales of $12,840, total assets of
$4,730, and a debt-equity ratio of .25. If its return on equity is 14 percent,
what is its net income?
28. Ratios and Fixed Assets The Plainfield Company has a long-term debt
ratio (i.e., the ratio of long-term debt to long-term debt plus equity) of .35
and a current ratio of 1.25. Current liabilities are $2,510, sales are $12,840,
profit margin is 8 percent, and ROE is 12.8 percent. What is the amount of
the firm’s net fixed assets?
LO 3
LO 2
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C H A P T E R 3 Working with Financial Statements 89
29. Profit Margin In response to complaints about high prices, a grocery chain
runs the following advertising campaign: “If you pay your child $2 to go buy
$50 worth of groceries, then your child makes twice as much on the trip as
we do.” You’ve collected the following information from the grocery chain’s
financial statements:
(in millions)
Sales $685.00
Net income 13.70
Total assets 365.00
Total debt 229.80
Evaluate the grocery chain’s claim. What is the basis for the statement? Is this
claim misleading? Why or why not?
30. Using the DuPont Identity The Moraine Company has net income of
$158,230. There are currently 28.45 days’ sales in receivables. Total assets
are $804,320, total receivables are $155,218, and the debt-equity ratio
is .25. What is the company’s profit margin? Its total asset turnover? Its
ROE?
31. Calculating the Cash Coverage Ratio Delectable Parsnip, Inc.’s, net
income for the most recent year was $8,417. The tax rate was 21 percent.
The firm paid $4,632 in total interest expense and deducted $5,105 in
depreciation expense. What was the company’s cash coverage ratio for the
year?
32. Calculating the Times Interest Earned Ratio For the most recent year,
Camargo, Inc., had sales of $534,000, cost of goods sold of $241,680,
depreciation expense of $60,400, and additions to retained earnings
of $72,800. The firm currently has 20,000 shares of common stock
outstanding, and the previous year’s dividends per share were $1.35.
Assuming a 22 percent income tax rate, what was the times interest earned
ratio?
33. Return on Assets A fire has destroyed a large percentage of the financial
records of the Inferno Company. You have the task of piecing together
information in order to release a financial report. You have found the
return on equity to be 11.6 percent. Sales were $1.79 million, the total debt
ratio was .43, and total debt was $693,000. What is the return on assets
(ROA)?
34. Ratios and Foreign Companies Prince Albert Canning PLC had a net loss
of £32,415 on sales of £515,380. What was the company’s profit margin?
Does the fact that these figures are quoted in a foreign currency make any
difference? Why? In dollars, sales were $689,785. What was the net loss in
dollars?
Some recent financial statements for Smolira Golf, Inc., follow. Use this informa-
tion to work Problems 35 through 38.
LO 2
LO 3
LO 2
LO 2
LO 2
LO 2
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90 P A R T 2 Understanding Financial Statements and Cash Flow
SMOLIRA GOLF, INC.
Balance Sheets as of December 31, 2018 and 2019
2018 2019 2018 2019
Assets Liabilities and Owners’ Equity
Current assets Current liabilities
Cash $ 5,298 5,827 Accounts payable $ 3,754 $ 3,986
Accounts receivable 7,707 8,477 Notes payable 3,045 3,318
Inventory 12,150 21,956 Other 152 179
Total $ 25,155 $ 36,260 Total $ 6,951 $ 7,483
Long-term debt $ 24,700 $ 16,000
Owners’ equity
Common stock and paid-in surplus $ 40,000 $ 37,000
Fixed assets Accumulated retained earnings 28,805 55,189
Net plant and equipment $ 75,301 $ 79,412 Total $ 68,805 $ 92,189
Total assets $100,456 $115,672 Total liabilities and owners’ equity $100,456 $115,672
SMOLIRA GOLF, INC.
2019 Income Statement
Sales $229,854
Cost of goods sold 184,317
Depreciation 8,730
EBIT $ 36,807
Interest paid 1,811
Taxable income $ 34,996
Taxes 7,349
Net income $ 27,647
Dividends $16,000
Addition to retained earnings 11,647
35. Calculating Financial Ratios Find the following financial ratios for Smolira
Golf (use year-end figures rather than average values where appropriate):
Short-term solvency ratios
a. Current ratio ________________
b. Quick ratio ________________
c. Cash ratio ________________
Asset utilization ratios
d. Total asset turnover ________________
e. Inventory turnover ________________
f. Receivables turnover ________________
Long-term solvency ratios
g. Total debt ratio ________________
h. Debt–equity ratio ________________
i. Equity multiplier ________________
j. Times interest earned ratio ________________
k. Cash coverage ratio ________________
LO 2
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C H A P T E R 3 Working with Financial Statements 91
Profitability ratios
l. Profit margin ________________
m. Return on assets ________________
n. Return on equity ________________
36. DuPont Identity Construct the DuPont identity for Smolira Golf.
37. Market Value Ratios Smolira Golf has 10,000 shares of common stock
outstanding, and the market price for a share of stock at the end of 2019 was
$73. What is the price-earnings ratio? What is the price-sales ratio? What are
the dividends per share? What is the market-to-book ratio at the end of 2019?
38. Interpreting Financial Ratios After calculating the ratios for Smolira Golf,
you have uncovered the following industry ratios for 2019:
Lower Quartile Median Upper Quartile
Current ratio
Total asset turnover
Debt-equity ratio
Profit margin
1.3
2.1
.23
8.4%
2.6
2.7
.50
11.2%
5.3
4.1
.60
16.3%
How is Smolira Golf performing based on these ratios?
39. Growth and Profit Margin Jasmine Manufacturing wishes to maintain a
sustainable growth rate of 7 percent a year, a debt-equity ratio of .65, and
a dividend payout ratio of 25 percent. The ratio of total assets to sales is
constant at 1.25. What profit margin must the firm achieve?
40. Market Value Ratios Abercrombie & Fitch and American Eagle Outfitters
(AEO) reported the following numbers (in millions except for the share
price) for fiscal year 2018. Calculate the earnings per share, market-to-book
ratio, and price-earnings ratio for each company.
Abercrombie AEO
Net income $ 7.09 $ 9302.79
Shares outstanding 67.79 9 176.61
Stock price $ 26.43 $ 924.56
Total equity $1,242.38 $1,246.79
41. Growth and Assets A firm wishes to maintain an internal growth rate of
5.3 percent and a dividend payout ratio of 40 percent. The current profit
margin is 6.8 percent and the firm uses no external financing sources. What
must total asset turnover be?
42. Sustainable Growth Based on the following information, calculate the
sustainable growth rate for Groot, Inc.:
Profit margin = 7.1%
Total asset turnover = 1.90
Total debt ratio = .45
Payout ratio = 20%
What is the ROA here?
LO 3
LO 2
LO 2
LO 3
LO 2
LO 3
LO 3
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92 P A R T 2 Understanding Financial Statements and Cash Flow
43. Sustainable Growth and Outside Financing You’ve collected the following
information about Gandalf, Inc.:
Sales = $295,000
Net income = $18,400
Dividends = $9,100
Total debt = $68,000
Total equity = $94,000
What is the sustainable growth rate for the company? If it does grow at this
rate, how much new borrowing will take place in the coming year, assuming a
constant debt-equity ratio? What growth rate could be supported with no out-
side financing at all?
44. Constraints on Growth High Flyer, Inc., wishes to maintain a growth rate
of 12 percent per year and a debt-equity ratio of .25. The profit margin is
5 percent, and total asset turnover is constant at 1.20. Is this growth rate
possible? To answer, determine what the dividend payout ratio must be. How
do you interpret the result?
45. Internal and Sustainable Growth Rates Best Buy reported the following
numbers (in millions) for the years ending January 28, 2017, and February
3, 2018. What are the internal and sustainable growth rates? What are the
internal and sustainable growth rates using ROE × b and ROA × b and
the end-of-period equity (assets)? What are the growth rates if you use the
beginning of period equity in this equation? Why aren’t the growth rates
the same? What is your best estimate of the internal and sustainable growth
rates?
2017 2018
Net income $ 1,000
Dividends 409
Total assets $13,856 13,049
Total equity 4,709 3,612
46. Expanded DuPont Identity Hershey Co. reported the following income
statement and balance sheet (in millions) for 2017. Construct the expanded
DuPont identity similar to Figure 3.1. What is the company’s return on
equity?
LO 3
LO 4
LO 3
LO 3
Income Statement
Sales $7,515.426
CoGS 4,065.760
SG&A 1,896.643
Other costs 344.043
EBIT $1,208.980
Interest 98.282
EBT $1,110.698
Taxes 354.131
Net income $ 756.567
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C H A P T E R 3 Working with Financial Statements 93
3.1 DuPont Identity You can find financial statements for The Walt Disney Company at
Disney’s home page, thewaltdisneycompany.com. For the three most recent years, calculate
the DuPont identity for Disney. How has ROE changed over this period? How have changes
in each component of the DuPont identity affected ROE over this period?
3.2 Ratio Analysis You want to examine the financial ratios for Johnson & Johnson. Go to
www.reuters.com and type in the ticker symbol for the company (JNJ). Next, go to the
financials link.
a. What do TTM and MRQ mean?
b. How do JNJ’s recent profitability ratios compare to their values over the past five
years? To the industry averages? To the sector averages? To the S&P 500 averages?
Which is the better comparison group for JNJ: the industry, sector, or S&P 500
averages? Why?
c. In what areas does JNJ seem to outperform its competitors based on the financial
ratios? Where does JNJ seem to lag behind its competitors?
3.3 Standardized Financial Statements Go to www.att.com and find the income statements
and balance sheets for the two most recent years at this link. Using this information,
prepare the common-size income statements and balance sheets for the two years.
3.4 Asset Utilization Ratios Find the most recent financial statements for Walmart at www
.walmart.com and Boeing at www.boeing.com. Calculate the asset utilization ratio for these
two companies. What does this ratio measure? Is the ratio similar for both companies? Why
or why not?
WHAT’S ON
THE WEB?
Balance Sheet
Assets Liabilities & Equity
Current assets Current liabilities $2,076.543
Cash $ 380.179
Accounts receivable 588.262 Long-term debt $2,545.618
Inventory 1,033.469
Total $2,001.910 Shareholders’ equity $ 931.565
Fixed assets $3,551.816
Total assets $5,553.726 Total liabilities and $5,553.726
shareholders’ equity
Source: Hershey Co.
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94 P A R T 2 Understanding Financial Statements and Cash Flow94 P A R T 2 Understanding Financial Statements and Cash Flow
EXCEL MASTER IT! PROBLEM
The eXtensible Business Reporting Language (XBRL) is likely the future of financial report-
ing. XBRL is a computer language that “tags” each item and specifies what that item is.
XBRL reporting already has been adopted for use in Australia, Japan, and the United King-
dom. XBRL reporting will allow investors to quickly download financial statements for
analysis.
Currently, several companies voluntarily submit financial statements in XBRL format.
For this assignment, go to the SEC website at www.sec.gov. When you click the link for a
particular filing, the XBRL results are shown at the bottom of the page. Download the in-
come statement and balance sheet from the annual report for a company of your choice.
Using these reports, calculate the financial ratios for the company from the data available
for the past two years. Do you notice any changes in these ratios that might indicate the
need for further investigation?
coverage online
Excel
Master
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C H A P T E R 3 Working with Financial Statements 95 C H A P T E R 3 Working with Financial Statements 95
partial payment before the order is complete. In con-
trast, a commercial airplane may take one and one-half
to two years to manufacture once the order is placed.
Mark and Todd have provided the following finan-
cial statements. Chris has gathered the industry ratios
for the light airplane manufacturing industry.
Chris Guthrie was recently hired by S&S Air, Inc., to assist the company with its financial planning and to
evaluate the company’s performance. Chris graduated
from college five years ago with a finance degree. He
has been employed in the finance department of a For-
tune 500 company since then.
S&S Air was founded 10 years ago by friends Mark
Sexton and Todd Story. The company has manufactured
and sold light airplanes over this period, and the com-
pany’s products have received high reviews for safety
and reliability. The company has a niche market in that it
sells primarily to individuals who own and fly their own
airplanes. The company has two models: the Birdie,
which sells for $53,000, and the Eagle, which sells for
$78,000.
While the company manufactures aircraft, its opera-
tions are different from commercial aircraft companies.
S&S Air builds aircraft to order. By using prefabricated
parts, the company is able to complete the manufacture
of an airplane in only five weeks. The company also re-
ceives a deposit on each order, as well as another
CHAPTER CASE
Ratios and Financial Planning at S&S Air, Inc.
S&S AIR, INC.
2019 Income Statement
Sales $26,501,600
Cost of goods sold 19,780,200
Other expenses 3,166,700
Depreciation 864,500
EBIT $ 2,690,200
Interest 479,200
Taxable income $ 2,211,000
Taxes (21%) 464,310
Net income $ 1,746,690
Dividends $270,600
Additions to retained 1,476,090
earnings
S&S AIR, INC.
2019 Balance Sheet
Assets Liabilities and Equity
Current assets Current liabilities
Cash $ 481,852 Accounts payable $ 9999 944,698
Accounts receivable 2,025,778 Notes payable 1,909,248
Inventory 1,634,820 Total current liabilities $ 99 2,853,946
Total current assets $ 4,142,450
Fixed assets Long-term debt $99 5,060,000
Net plant and $16,256,698 Shareholder equity
equipment Common stock $ 9999 190,000
Retained earnings 12,295,202
Total equity $12,485,202
Total assets $20,399,148 Total liabilities and equity $20,399,148
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96 P A R T 2 Understanding Financial Statements and Cash Flow
Light Airplane Industry Ratios
Lower Quartile Median Upper Quartile
Current ratio .50 1.43 1.89
Quick ratio .64 .84 1.05
Cash ratio .08 .21 .39
Total asset turnover .68 .85 1.13
Inventory turnover 4.89 6.15 10.89
Receivables turnover 6.27 9.82 11.51
Total debt ratio .31 .52 .61
Debt-equity ratio .58 1.08 1.56
Equity multiplier 1.58 2.08 2.56
Times interest earned 5.18 8.06 9.83
Cash coverage ratio 5.84 8.43 10.27
Profit margin 4.05% 6.75% 8.47%
Return on assets 6.05% 10.53% 13.21%
Return on equity 9.93% 16.54% 26.15%
1. Calculate the ratios for S&S Air that are shown for
the industry.
2. Mark and Todd agree that a ratio analysis can pro-
vide a measure of the company’s performance.
They have chosen Boeing as an aspirant com-
pany. Would you choose Boeing as an aspirant
company? Why or why not?
3. Compare the performance of S&S Air to the indus-
try. For each ratio, comment on why it might be
viewed as positive or negative relative to the in-
dustry. Suppose you create an inventory ratio cal-
culated by inventory divided by current liabilities.
How do you think S&S Air’s ratio would compare
to the industry average?
4. Calculate the internal growth rate and sustainable
growth rate for S&S Air. What do these numbers
mean?
Q U E S T I O N S
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97
As you are probably aware, the U.S. government has a signifi-cant amount of debt. That debt, which is widely owned by in-
vestors, comes in different varieties, including Series EE U.S.
Treasury savings bonds. With a Series EE bond, you pay a particular
amount today of, say, $25, and the bond accrues interest over the
time you hold it. In the middle of 2018, the U.S. Treasury promised to
pay .10 percent per year on EE savings bonds. In an interesting (and
important) wrinkle, if you hold the bond for 20 years, the Treasury
promises to “step up” the value to double your cost. That is, if the
$25 bond you purchased and all the accumulated interest earned is
worth less than $50, the Treasury will automatically increase the
value of the bond to $50.
Is giving up $25 in exchange for $50 in 20 years a good deal?
On the plus side, you get back $2 for every $1 you put up. That
probably sounds good, but, on the downside, you have to wait 20
years to get it. What you need to know is how to analyze this trade-off. This chapter gives
you the tools you need.
Specifically, our goal here is to introduce you to one of the most important principles in
finance, the time value of money. What you will learn is how to determine the value today of
some cash flow to be received later. This is a very basic business skill, and it underlies the
analysis of many different types of investments and financing arrangements. In fact, almost
all business activities, whether they originate in marketing, management, operations, or
strategy, involve comparing outlays made today to benefits projected for the future. How
to do this comparison is something everyone needs to understand; this chapter gets
you started.
Introduction to Valuation:
The Time Value of Money4
LEARNING OBJECTIVES
After studying this chapter, you should
be able to:
LO 1 Determine the future value of an
investment made today.
LO 2 Determine the present value of
cash to be received at a future
date.
LO 3 Calculate the return on an
investment.
LO 4 Predict how long it takes for an
investment to reach a desired
value.
PART THREE Valuation of Future Cash Flows
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98 P A R T 3 Valuation of Future Cash Flows
One of the basic problems faced by the financial manager is how to determine the value today of cash flows expected in the future. For example, the jackpot in a PowerBallTM
lottery drawing was $110 million. Does this mean the winning ticket was worth $110 mil-
lion? The answer is no because the jackpot was actually going to pay out over a 20-year pe-
riod at a rate of $5.5 million per year. How much was the ticket worth then? The answer
depends on the time value of money, the subject of this chapter.
In the most general sense, the phrase time value of money refers to the fact that a dollar
in hand today is worth more than a dollar promised at some time in the future. On a practi-
cal level, one reason for this is that you could earn interest while you waited; so, a dollar
today would grow to more than a dollar later. The trade-off between money now and money
later thus depends on, among other things, the rate you can earn by investing. Our goal in
this chapter is to explicitly evaluate this trade-off between dollars today and dollars at some
future time.
A thorough understanding of the material in this chapter is critical to understanding
material in subsequent chapters, so you should study it with particular care. We present a
number of examples in this chapter. In many problems, your answer may differ from ours
slightly. This can happen because of rounding and is not a cause for concern.
FUTURE VALUE AND COMPOUNDING
The first thing we will study is future value. Future value (FV) refers to the amount of money
an investment will grow to over some period of time at some given interest rate. Put another
way, future value is the cash value of an investment at some time in the future. We start out
by considering the simplest case, a single-period investment.
Investing for a Single Period
Suppose you were to invest $100 in a savings account that pays 10 percent interest per year.
How much would you have in one year? You would have $110. This $110 is equal to your
original principal of $100 plus $10 in interest that you earn. We say that $110 is the future
value of $100 invested for one year at 10 percent, and we mean that $100 today is worth
$110 in one year, given that 10 percent is the interest rate.
In general, if you invest for one period at an interest rate of r, your investment will grow
to (1 + r) per dollar invested. In our example, r is 10 percent, so your investment grows to
1 + .10 = 1.10 dollars per dollar invested. You invested $100 in this case, so you ended up
with $100 × 1.10 = $110.
Investing for More Than One Period
Going back to our $100 investment, what will you have after two years, assuming the inter-
est rate doesn’t change? If you leave the entire $110 in the bank, you will earn $110 × .10 =
$11 in interest during the second year, so you will have a total of $110 + 11 = $121. This
$121 is the future value of $100 in two years at 10 percent. Another way of looking at it is
that one year from now you are effectively investing $110 at 10 percent for a year. This is a
single-period problem, so you’ll end up with $1.10 for every dollar invested, or $110 × 1.1 =
$121 total.
This $121 has four parts. The first part is the $100 original principal. The second part
is the $10 in interest you earn in the first year, and the third part is another $10 you earn in
the second year, for a total of $120. The last $1 you end up with (the fourth part) is interest
you earn in the second year on the interest paid in the first year: $10 × .10 = $1.
To find out more about
U.S. savings bonds and
other government
securities, go to www
.treasurydirect.gov.
4.1
coverage online
Excel
Master
future value (FV)
The amount an investment
is worth after one or more
periods. Also compound
value.
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C H A P T E R 4 Introduction to Valuation: The Time Value of Money 99
This process of leaving your money and any accumulated interest in an investment for
more than one period, thereby reinvesting the interest, is called compounding. Compound-
ing the interest means earning interest on interest, so we call the result compound interest.
With simple interest, the interest is not reinvested, so interest is earned each period only on
the original principal.
compounding
The process of
accumulating interest in
an investment over time to
earn more interest.
interest on interest
Interest earned on the
reinvestment of previous
interest payments.
compound interest
Interest earned on both
the initial principal and the
interest reinvested from
prior periods.
simple interest
Interest earned only on
the original principal
amount invested.
EXAMPLE 4.1 Interest on Interest
Suppose you locate a two-year investment that pays 14 percent per year. If you invest $325, how
much will you have at the end of the two years? How much of this is simple interest? How much is
compound interest?
At the end of the first year, you will have $325 × 1.14 = $370.50. If you reinvest this entire
amount, and thereby compound the interest, you will have $370.50 × 1.14 = $422.37 at the end of
the second year. The total interest you earn is thus $422.37 − 325 = $97.37. Your $325 original
principal earns $325 × .14 = $45.50 in interest each year, for a two-year total of $91 in simple inter-
est. The remaining $97.37 − 91 = $6.37 results from compounding. You can check this by noting
that the interest earned in the first year is $45.50. The interest on interest earned in the second
year thus amounts to $45.50 × .14 = $6.37, as we calculated.
We now take a closer look at how we calculated the $121 future value. We multiplied
$110 by 1.1 to get $121. The $110, however, was $100 also multiplied by 1.1. In other words:
$121 = $110 × 1.1
= ($100 × 1.1) × 1.1
= $100 × (1.1 × 1.1)
= $100 × 1.12
= $100 × 1.21
At the risk of belaboring the obvious, let’s ask: How much would our $100 grow to after
three years? Once again, in two years, we’ll be investing $121 for one period at 10 percent.
We’ll end up with $1.1 for every dollar we invest, or $121 × 1.1 = $133.1 total. This $133.1
is thus:
$133.1 = $121 × 1.1
= ($110 × 1.1) × 1.1
= ($100 × 1.1) × 1.1 × 1.1
= $100 × (1.1 × 1.1 × 1.1)
= $100 × 1.13
= $100 × 1.331
You’re probably noticing a pattern to these calculations, so we can now go ahead and
state the general result. As our examples suggest, the future value of $1 invested for t periods
at a rate of r per period is:
Future value = $1 × (1 + r)t [4.1]
The expression (1 + r)t is sometimes called the future value interest factor (or future value
factor) for $1 invested at r percent for t periods. It can be abbreviated as FVIF(r, t).
In our example, what would your $100 be worth after five years? We can first compute
the relevant future value factor as:
(1 + r)t = (1 + .10)5 = 1.15 = 1.6105
ros13952_ch04_097-121.indd 99 12/22/18 5:49 PM
100 P A R T 3 Valuation of Future Cash Flows
Your $100 will thus grow to:
$100 × 1.6105 = $161.05
The growth of your $100 each year is illustrated in Table 4.1. As shown, the interest
earned in each year is equal to the beginning amount multiplied by the interest rate of
10 percent.
In Table 4.1, notice that the total interest you earn is $61.05. Over the five-year span of
this investment, the simple interest is $100 × .10 = $10 per year, so you accumulate $50
this way. The other $11.05 is from compounding.
Figure 4.1 illustrates the growth of the compound interest in Table 4.1. Notice how the
simple interest is constant each year, but the compound interest you earn gets bigger every
year. The size of the compound interest keeps increasing because more and more interest
builds up and there is thus more to compound.
Future values depend critically on the assumed interest rate, particularly for long-lived
investments. Figure 4.2 illustrates this relationship by plotting the growth of $1 for different
rates and lengths of time. Notice that the future value of $1 after 10 years is about $6.20 at
a 20 percent rate, but it is only about $2.60 at 10 percent. In this case, doubling the interest
rate more than doubles the future value.
A brief introduction to
key financial concepts is
available at www
.teachmefinance.com.
Future value of $100
at 10 percent
TABLE 4.1 Year Beginning Amount Interest Earned Ending Amount
1 $100.00 $10.00 $110.00
2 110.00 11.00 121.00
3 121.00 12.10 133.10
4 133.10 13.31 146.41
5 146.41 14.64 161.05
Total interest $61.05
160
150
140
130
120
110
100
$110
$121
$133.10
$146.41
$161.05
Future
value ($)
1 2 3 4 5
0
Growth of $100 original amount at 10% per year. Blue
shaded area represents the portion of the total that results
from compounding of interest.
Time
(years)
FIGURE 4.1
Future value, simple
interest, and
compound interest
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C H A P T E R 4 Introduction to Valuation: The Time Value of Money 101
To solve future value problems, we need to come up with the relevant future value fac-
tors. There are several different ways of doing this. In our example, we could have multiplied
1.1 by itself five times. This would work fine, but it would get to be very tedious for, say, a
30-year investment.
Fortunately, there are several easier ways to get future value factors. Most calculators
have a key labeled “yx”. You can usually enter 1.1, press this key, enter 5, and press the “= ”
key to get the answer. This is an easy way to calculate future value factors because it’s quick
and accurate.
Alternatively, you can use a table that contains future value factors for some common
interest rates and time periods. Table 4.2 contains some of these factors. Table A.1 in
Appendix A at the end of the book contains a much larger set. To use the table, find the
column that corresponds to 10 percent. Then look down the rows until you come to five
periods. You should find the factor that we calculated, 1.6105.
Tables such as Table 4.2 are not as common as they once were because they predate
inexpensive calculators and are only available for a relatively small number of rates. Interest
rates often are quoted to three or four decimal places, so the tables needed to deal with
these accurately would be quite large. As a result, the “real world” has moved away from us-
ing them. We will emphasize the use of a calculator in this chapter.
These tables still serve a useful purpose. To make sure you are doing the calculations
correctly, pick a factor from the table and then calculate it yourself to see that you get the
same answer. There are plenty of numbers to choose from.
Future value of $1 for
different periods and
rates
FIGURE 4.2Future
value
of $1 ($)
20%
15%
10%
5%
0%
7
6
5
4
3
2
1
54321 109876
Time
(years)
Future value interest
factors
TABLE 4.2Number of
Periods
Interest Rates
5% 10% 15% 20%
1 1.0500 1.1000 1.1500 1.2000
2 1.1025 1.2100 1.3225 1.4400
3 1.1576 1.3310 1.5209 1.7280
4 1.2155 1.4641 1.7490 2.0736
5 1.2763 1.6105 2.0114 2.4883
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102 P A R T 3 Valuation of Future Cash Flows
The effect of compounding is not great over short time periods, but it really starts
to add up as the time horizon grows. To take an extreme case, suppose one of your
more frugal ancestors had invested $5 for you at a 6 percent interest rate 200 years ago.
How much would you have today? The future value factor is a substantial 1.06200 =
115,125.90 (you won’t find this one in a table), so you would have $5 × 115,125.90 =
$575,629.52 today. Notice that the simple interest is $5 × .06 = $.30 per year. After
200 years, this amounts to $60. The rest is from reinvesting. Such is the power of compound
interest!
How much do you need at
retirement? Locate the
“Retirement Calculator”
link at www.bankrate.com.
EXAMPLE 4.2 Compound Interest
You’ve located an investment that pays 12 percent. That rate sounds good to you, so you invest
$400. How much will you have in three years? How much will you have in seven years? At the end
of seven years, how much interest have you earned? How much of that interest results from
compounding?
Based on our discussion, we can calculate the future value factor for 12 percent and three
years as:
(1 + r)t = 1.123 = 1.4049
Your $400 thus grows to:
$400 × 1.4049 = $561.97
After seven years, you will have:
$400 × 1.127 = $400 × 2.2107 = $884.27
Thus, you will more than double your money over seven years.
Because you invested $400, the interest in the $884.27 future value is $884.27 − 400 =
$484.27. At 12 percent, your $400 investment earns $400 × .12 = $48 in simple interest every year.
Over seven years, the simple interest thus totals 7 × $48 = $336. The other $484.27 − 336 =
$148.27 is from compounding.
EXAMPLE 4.3 How Much for That Island?
To further illustrate the effect of compounding for long horizons, consider the case of Peter Minuit
and the Indians. In 1626, Minuit bought all of Manhattan Island for about $24 in goods and trinkets.
This sounds cheap, but the Indians may have gotten the better end of the deal. To see why, sup-
pose the Indians had sold the goods and invested the $24 at 10 percent. How much would it be
worth today?
Roughly 392 years have passed since the transaction. At 10 percent, $24 will grow by quite a
bit over that time. How much? The future value factor is approximately:
(1 + r)t = 1.1392 ≃ 16,824,000,000,000,000
That is, 17 followed by 15 zeroes. The future value is thus on the order of $24 × 16.824 quadrillion,
or about $404 quadrillion (give or take a few hundreds of trillions).
Well, $404 quadrillion is a lot of money. How much? If you had it, you could buy the United
States. All of it. Cash. With money left over to buy Canada, Mexico, and the rest of the world, for that
matter.
This example is something of an exaggeration, of course. In 1626, it would not have been
easy to locate an investment that would pay 10 percent every year without fail for the next
392 years.
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C H A P T E R 4 Introduction to Valuation: The Time Value of Money 103
USING A FINANCIAL CALCULATOR
Although there are the various ways of calculating future values we have described so far, many of you
will decide that a financial calculator is the way to go. If you are planning on using one, you should read
this extended hint; otherwise, skip it.
A financial calculator is an ordinary calculator with a few extra features. In particular, it knows some
of the most commonly used financial formulas, so it can directly compute things like future values.
Financial calculators have the advantage that they handle a lot of the computation, but that is really
all. In other words, you still have to understand the problem; the calculator does some of the arithmetic.
In fact, there is an old joke (somewhat modified) that goes like this: Anyone can make a mistake on a
time value of money problem, but to really screw one up takes a financial calculator! We therefore have
two goals for this section. First, we’ll discuss how to compute future values. After that, we’ll show you
how to avoid the most common mistakes people make when they start using financial calculators.
How to Calculate Future Values with a Financial Calculator Examining a typical financial cal-
culator, you will find five keys of particular interest. They usually look like this:
For now, we need to focus on four of these. The keys labeled PV and FV are what you
would guess: present value and future value. The key labeled N refers to the number of periods,
which is what we have been calling t. Finally, I/Y stands for the interest rate, which we have called r.1
If we have the financial calculator set up correctly (see our next section), then calculating a future
value is very simple. Take a look back at our question involving the future value of $100 at 10 percent for
five years. We have seen that the answer is $161.05. The exact keystrokes will differ depending on what
type of calculator you use, but here is basically all you do:
1. Enter −100. Press the PV key. (The negative sign is explained below.)
2. Enter 10. Press the I/Y key. (Notice that we entered 10, not .10; see below.)
3. Enter 5. Press the N key.
Now we have entered all of the relevant information. To solve for the future value, we need to ask
the calculator what the FV is. Depending on your calculator, you either press the button labeled
“CPT” (for compute) and then press FV “, or else you press FV “. Either way, you should get 161.05. If
you don’t (and you probably won’t if this is the first time you have used a financial calculator!), we offer
some help in our next section.
Before we explain the kinds of problems that you are likely to run into, we want to establish a stand-
ard format for showing you how to use a financial calculator. Using the example we just looked at, in the
future, we will illustrate such problems like this:
Enter 5 10 −100
FV
Solve for 161.05
Here is an important tip: Appendix D in the back of the book contains more detailed instructions for
the most common types of financial calculators. See if yours is included, and, if it is, follow the instructions
there if you need help. Of course, if all else fails, you can read the manual that came with the calculator.
How to Get the Wrong Answer Using a Financial Calculator There are a couple of common
(and frustrating) problems that cause a lot of trouble with financial calculators. In this section, we provide
some important dos and don’ts. If you can’t seem to get a problem to work out, you should refer back to
this section.
CALCULATOR
HINTS
1The reason financial calculators use N and I/Y is that the most common use for these calculators is determining
loan payments. In this context, N is the number of payments and I/Y is the interest rate on the loan. But, as we will
see, there are many other uses of financial calculators that don’t involve loan payments and interest rates.
(continued)
ros13952_ch04_097-121.indd 103 12/22/18 5:49 PM
104 P A R T 3 Valuation of Future Cash Flows
There are two categories we examine: three things you need to do only once and three things you
need to do every time you work a problem. The things you need to do only once deal with the following
calculator settings:
1. Make sure your calculator is set to display a large number of decimal places. Most financial
calculators only display two decimal places; this causes problems because we frequently work
with numbers—like interest rates—that are very small.
2. Make sure your calculator is set to assume only one payment per period or per year. Some
financial calculators assume monthly payments (12 per year) unless you say otherwise.
3. Make sure your calculator is in “end” mode. This is usually the default, but you can accidentally
change to “begin” mode.
If you don’t know how to set these three things, see Appendix D or your calculator’s operating manual.
There are also three things you need to do every time you work a problem:
1. Before you start, completely clear out the calculator. This is very important. Failure to do this is
the number one reason for wrong answers; you must get in the habit of clearing the calculator
every time you start a problem. How you do this depends on the calculator (see Appendix D), but
you must do more than just clear the display. For example, on a Texas Instruments BA II Plus, you
must press 2nd then CLR TVM for clear time value of money. There is a similar command on
your calculator. Learn it!
Note that turning the calculator off and back on won’t do it. Most financial calculators
remember everything you enter, even after you turn them off. In other words, they remember all
your mistakes unless you explicitly clear them out. Also, if you are in the middle of a problem and
make a mistake, clear it out and start over. Better to be safe than sorry.
2. Put a negative sign on cash outflows. Most financial calculators require you to put a negative
sign on cash outflows and a positive sign on cash inflows. As a practical matter, this usually
means that you should enter the present value amount with a negative sign (because normally
the present value represents the amount you give up today in exchange for cash inflows later).
You enter a negative value on the BA II Plus by first entering a number and then pressing the
+/– key. By the same token, when you solve for a present value, you shouldn’t be surprised
to see a negative sign.
3. Enter the rate correctly. Financial calculators assume that rates are quoted in percent, so if the
rate is .08 (or 8 percent), you should enter 8, not .08.
If you follow these guidelines (especially the one about clearing out the calculator), you should
have no problem using a financial calculator to work almost all of the problems in this and the next few
chapters. We’ll provide some additional examples and guidance where appropriate.
CONCEPT QUESTIONS
4.1a What do we mean by the future value of an investment?
4.1b What does it mean to compound interest? How does compound interest differ from
simple interest?
4.1c In general, what is the future value of $1 invested at r per period for t periods?
PRESENT VALUE AND DISCOUNTING
When we discuss future value, we are thinking of questions such as the following: What will
my $2,000 investment grow to if it earns a 6.5 percent return every year for the next
six years? The answer to this question is what we call the future value of $2,000 invested at
6.5 percent for six years (verify that the answer is about $2,918).
4.2
coverage online
Excel
Master
ros13952_ch04_097-121.indd 104 12/22/18 5:49 PM
C H A P T E R 4 Introduction to Valuation: The Time Value of Money 105
There is another type of question that comes up even more often in financial manage-
ment that is obviously related to future value. Suppose you need to have $10,000 in
10 years, and you can earn 6.5 percent on your money. How much do you have to invest
today to reach your goal? You can verify that the answer is $5,327.26. How do we know
this? Read on.
The Single-Period Case
We’ve seen that the future value of $1 invested for one year at 10 percent is $1.10. We
now ask a slightly different question: How much do we have to invest today at 10 percent
to get $1 in one year? In other words, we know the future value here is $1, but what is
the present value (PV)? The answer isn’t too hard to figure out. Whatever we invest
today will be 1.1 times bigger at the end of the year. Because we need $1 at the end of
the year:
Present value × 1.1 = $1
Or solving for the present value:
Present value = $1/1.1 = $.909
In this case, the present value is the answer to the following question: What amount,
invested today, will grow to $1 in one year if the interest rate is 10 percent? Present value is
thus the reverse of future value. Instead of compounding the money forward into the future,
we discount it back to the present.
present value (PV)
The current value of future
cash flows discounted at
the appropriate discount
rate.
EXAMPLE 4.4 Single-Period PV
Suppose you need $800 to buy textbooks next year. You can earn 7 percent on your money. How
much do you have to put up today?
We need to know the PV of $800 in one year at 7 percent. Proceeding as earlier:
Present value × 1.07 = $800
We can now solve for the present value:
Present value = $800 × (1/1.07) = $747.66
Thus, $747.66 is the present value. Again, this means that investing this amount for one year at
7 percent will result in a future value of $800.
discount
Calculation of the present
value of some future
amount.
From our examples, the present value of $1 to be received in one period is generally
given as:
PV = $1 × [1/(1 + r)] = $1/(1 + r)
We next examine how to get the present value of an amount to be paid in two or more peri-
ods into the future.
Present Values for Multiple Periods
Suppose you need to have $1,000 in two years. If you can earn 7 percent, how much do you
have to invest to make sure that you have the $1,000 when you need it? In other words, what
is the present value of $1,000 in two years if the relevant rate is 7 percent?
ros13952_ch04_097-121.indd 105 12/22/18 5:49 PM
106 P A R T 3 Valuation of Future Cash Flows
Based on your knowledge of future values, you know that the amount invested must
grow to $1,000 over the two years. In other words, it must be the case that:
$1,000 = PV × 1.07 × 1.07
= PV × 1.072
= PV × 1.1449
Given this, we can solve for the present value:
Present value = $1,000/1.1449 = $873.44
Therefore, $873.44 is the amount you must invest in order to achieve your goal.
EXAMPLE 4.5 Saving Up
You would like to buy a new automobile. You have $50,000, but the car costs $68,500. If you can
earn 9 percent, how much do you have to invest today to buy the car in two years? Do you have
enough? Assume the price will stay the same.
What we need to know is the present value of $68,500 to be paid in two years, assuming a 9
percent rate. Based on our discussion, this is:
PV = $68,500/1.092 = $68,500/1.1881 = $57,655.08
You’re still about $7,655 short, even if you’re willing to wait two years.
As you have probably recognized by now, calculating present values is quite similar to
calculating future values, and the general result looks much the same. The present value of
$1 to be received t periods into the future at a discount rate of r is:
PV = $1 × [1/(1 + r)t] = $1/(1 + r)t [4.2]
The quantity in brackets, 1/(1 + r)t, goes by several different names. Because it’s used to
discount a future cash flow, it is often called a discount factor. With this name, it is not sur-
prising that the rate used in the calculation is often called the discount rate. We tend to call
it this in talking about present values. The quantity in brackets also is called the present value
interest factor (or just present value factor) for $1 at r percent for t periods and is sometimes
abbreviated as PVIF(r, t). Finally, calculating the present value of a future cash flow to de-
termine its worth today is commonly called discounted cash flow (DCF) valuation.
To illustrate, suppose you need $1,000 in three years. You can earn 15 percent on your
money. How much do you have to invest today? To find out, we have to determine the pres-
ent value of $1,000 in three years at 15 percent. We do this by discounting $1,000 back three
periods at 15 percent. With these numbers, the discount factor is:
1/1.153 = 1/1.5209 = .6575
The amount you must invest is thus:
$1,000 × .6575 = $657.52
We say that $657.52 is the present, or discounted, value of $1,000 to be received in
three years at 15 percent.
There are tables for present value factors as there are tables for future value factors, and
you use them in the same way (if you use them at all). Table 4.3 contains a small set of these
factors. A much larger set can be found in Table A.2 in Appendix A.
discount rate
The rate used to calculate
the present value of future
cash flows.
discounted cash
flow (DCF) valuation
(a) Calculating the present
value of a future cash flow
to determine its value
today. (b) The process of
valuing an investment by
discounting its future cash
flows.
ros13952_ch04_097-121.indd 106 12/22/18 5:49 PM
C H A P T E R 4 Introduction to Valuation: The Time Value of Money 107
In Table 4.3, the discount factor we calculated, .6575, can be found by looking down the
column labeled “15%” until you come to the third row. Of course, you could use a financial
calculator, as we illustrate nearby.
As the length of time until payment grows, present values decline. As Example 4.6
illustrates, present values tend to become small as the time horizon grows. If you look out
far enough, they will always get close to zero. Also, for a given length of time, the higher the
discount rate is, the lower is the present value. Put another way, present values and discount
rates are inversely related. Increasing the discount rate decreases the PV and vice versa.
EXAMPLE 4.6 Deceptive Advertising
Recently, some businesses have been saying things like “Come try our product. If you do, we’ll give
you $100 just for coming by!” If you read the fine print, what you find out is that they will give you a
savings certificate that will pay you $100 in 25 years or so. If the going interest rate on such certifi-
cates is 10 percent per year, how much are they really giving you today?
What you’re actually getting is the present value of $100 to be paid in 25 years. If the discount
rate is 10 percent per year, then the discount factor is:
1 / 1.125 = 1 / 10.8347 = .0923
This tells you that a dollar in 25 years is worth a little more than nine cents today, assuming a 10
percent discount rate. Given this, the promotion is actually paying you about .0923 × $100 = $9.23.
Maybe this is enough to draw customers, but it’s not $100.
You solve present value problems on a financial calculator like you do future value problems. For the
example we just examined (the present value of $1,000 to be received in three years at 15 percent), you
would do the following:
Enter 3 15 1,000
FV
Solve for −657.52
Notice that the answer has a negative sign; as we discussed earlier, that’s because it represents an out-
flow today in exchange for the $1,000 inflow later.
CALCULATOR
HINTS
Present value
interest factors
TABLE 4.3Number of
Periods
Interest Rates
5% 10% 15% 20%
1 .9524 .9091 .8696 .8333
2 .9070 .8264 .7561 .6944
3 .8638 .7513 .6575 .5787
4 .8227 .6830 .5718 .4823
5 .7835 .6209 .4972 .4019
The relationship between time, discount rates, and present values is illustrated in
Figure 4.3. Notice that by the time we get to 10 years, the present values are all substantially
smaller than the future amounts.
ros13952_ch04_097-121.indd 107 12/22/18 5:49 PM
108 P A R T 3 Valuation of Future Cash Flows
CONCEPT QUESTIONS
4.2a What do we mean by the present value of an investment?
4.2b The process of discounting a future amount back to the present is the opposite of
doing what?
4.2c What do we mean by discounted cash flow, or DCF, valuation?
4.2d In general, what is the present value of $1 to be received in t periods, assuming a
discount rate of r per period?
MORE ON PRESENT AND FUTURE VALUES
If you look back at the expressions we came up with for present and future values, you will
see there is a very simple relationship between the two. We explore this relationship and
some related issues in this section.
Present versus Future Value
What we called the present value factor is just the reciprocal of (that is, 1 divided by) the
future value factor:
Future value factor = (1 + r)t
Present value factor = 1 / (1 + r()t
In fact, the easy way to calculate a present value factor on many calculators is to first calcu-
late the future value factor and then press the 1/X key to flip it over.
If we let FVt stand for the future value after t periods, then the relationship between
future value and present value can be written as one of the following:
PV × (1 + r()t = FVt
PV = FVt / (1 + r()
t = FVt × [1 / (1 + r()
t] [4.3]
4.3
coverage online
Excel
Master
For a downloadable,
Windows-based financial
calculator, go to www
.calculator.org.
Present
value
of $1 ($)
1.00
.90
.80
.70
.60
.50
.40
.30
.20
.10
r = 0%
r = 5%
r = 10%
r = 15%
r = 20%
54321 109876
Time
(years)
FIGURE 4.3
Present value of $1
for different periods
and rates
ros13952_ch04_097-121.indd 108 12/22/18 5:49 PM
C H A P T E R 4 Introduction to Valuation: The Time Value of Money 109
We will call this last result the basic present value equation, and we use it throughout the
text. There are a number of variations that come up, but this simple equation underlies
many of the most important ideas in finance.
EXAMPLE 4.7 Evaluating Investments
To give you an idea of how we will be using present and future values, consider the following sim-
ple investment. Your company proposes to buy an asset for $335. This investment is very safe. You
will sell the asset in three years for $400. You know you could invest the $335 elsewhere at
10 percent with very little risk. What do you think of the proposed investment?
This is not a good investment. Why not? Because you can invest the $335 elsewhere at
10 percent. If you do, after three years it will grow to:
$335 × (1 + r)t = $335 × 1.13
= $335 × 1.331
= $445.89
Because the proposed investment only pays out $400, it is not as good as other alternatives we
have. Another way of saying the same thing is to notice that the present value of $400 in three
years at 10 percent is:
$400 × [1/(1 + r)t] = $400/1.13 = $400 / 1.331 = $300.53
This tells us that we only have to invest about $300 to get $400 in three years, not $335. We will
return to this type of analysis later on.
Determining the Discount Rate
It will turn out that we frequently need to determine what discount rate is implicit in an in-
vestment. We can do this by looking at the basic present value equation:
PV = FVt!!/(1 + r)
t
There are only four parts to this equation: the present value (PV), the future value (FVt), the
discount rate (r), and the life of the investment (t). Given any three of these, we can always
find the fourth.
EXAMPLE 4.8 Finding r for a Single-Period Investment
You are considering a one-year investment. If you put up $1,250, you will get back $1,350. What rate
is this investment paying?
First, in this single-period case, the answer is fairly obvious. You are getting a total of $100 in
addition to your $1,250. The implicit rate on this investment is thus $100/$1,250 = .08, or
8 percent.
More formally, from the basic present value equation, the present value (the amount you must
put up today) is $1,250. The future value (what the present value grows to) is $1,350. The time
involved is one period, so we have:
$1,250 = $1,350/(1 + r)t
1 + r = $1,350 / $1,250 = 1.08
r = .08, or 8%
In this simple case, of course, there was no need to go through this calculation, but, as we describe
later, it gets a little harder when there is more than one period.
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110 P A R T 3 Valuation of Future Cash Flows
To illustrate what happens with multiple periods, let’s say that we are offered an invest-
ment that costs us $100 and will double our money in eight years. To compare this to other
investments, we would like to know what discount rate is implicit in these numbers. This
discount rate is called the rate of return, or sometimes just return, on the investment. In this
case, we have a present value of $100, a future value of $200 (double our money), and an
eight-year life. To calculate the return, we can write the basic present value equation as:
PV = FVt/(1 + r)
t
$100 = $200/(1 + r)8
It also could be written as:
(1 + r)8 = $200 / $100 = 2
We now need to solve for r. There are three ways we could do it:
1. Use a financial calculator. (See below.)
2. Solve the equation for 1 + r by taking the eighth root of both sides. Because this is the
same thing as raising both sides to the power of ⅛, or .125, this is actually easy to do
with the yx key on a calculator. Just enter 2, then press yx , enter .125, and press
the = key. The eighth root should be about 1.09, which implies that r is 9 percent.
3. Use a future value table. The future value factor for eight years is equal to 2. If you
look across the row corresponding to eight periods in Table A.1, you will see that a
future value factor of 2 corresponds to the 9 percent column, again implying that the
return here is 9 percent.
Actually, in this particular example, there is a useful “back of the envelope” means of
solving for r—the Rule of 72. For reasonable rates of return, the time it takes to double your
money is given approximately by 72/r%. In our example, this means that 72/r% = 8 years,
implying that r is 9 percent as we calculated. This rule is fairly accurate for discount rates in
the 5 percent to 20 percent range.
The nearby Finance Matters box provides some examples of rates of return on collecti-
bles. See if you can verify the numbers reported there.
Why does the Rule of 72
work? See www.money
chimp.com.
EXAMPLE 4.9 Double Your Fun
You have been offered an investment that promises to double your money every 10 years. What is
the approximate rate of return on the investment?
From the Rule of 72, the rate of return is given approximately by 72/r% = 10, so the rate is ap-
proximately 72/10 = .072, or 7.2%. Verify that the exact answer is 7.177 percent.
A slightly more extreme example involves money bequeathed by Benjamin Franklin,
who died on April 17, 1790. In his will, he gave 1,000 pounds sterling to Massachusetts and
the city of Boston. He gave a like amount to Pennsylvania and the city of Philadelphia. The
money was paid to Franklin when he held political office, but he believed that politicians
should not be paid for their service (it appears that this view is not widely shared by mod-
ern-day politicians).
Franklin originally specified that the money should be paid out 100 years after his
death and used to train young people. Later, however, after some legal wrangling, it was
agreed that the money would be paid out in 1990, 200 years after Franklin’s death. By that
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Collectibles as Investments?
It used to be that trading in collectibles such as baseball cards, art, and old toys occurred mostly at auctions, swap
meets, and collectible shops, all of which were limited to re-
gional traffic. However, with the growing popularity of online
auctions such as eBay, trading in collectibles has expanded
to an international arena. The most visible form of collectible
is probably the baseball card, but Furbies, Beanie Babies,
and Pokémon cards have been extremely hot collectibles in
the recent past. However, it’s not just fad items that spark
interest from collectors; virtually anything of sentimental
value from days gone by is considered collectible, and, more
and more, collectibles are being viewed as investments.
Collectibles typically provide no cash flows until they
are sold, and condition and buyer sentiment are the major
determinants of value. The rates of return have been amaz-
ing at times, but care is needed in interpreting them. For ex-
ample, in 2018, a 1915-S Panama-Pacific Round $50 Gold
Piece sold for $336,000. While that looks like a whopping
price increase to the untrained eye, check for yourself that
the actual return on the investment was only about 8.93 per-
cent per year. Not too bad, but nowhere near the return
most people expect from looking at the sales price.
Comic books have recently grown in popularity among
collectors. The first issue of Batman was the Spring 1940
issue, sold at a cover price of 10 cents. In 2018, one of the
original comics was auctioned off for $227,050. This gain
seems like a very high return to the untrained eye, and
indeed it is! See if you don’t agree that the return was about
20.64 percent per year.
Stamp collecting (or philately) is another popular activ-
ity. Possibly the most famous stamp in the world is the British
Guiana One-Cent Black on Magenta stamp, issued in 1856.
There is only one known example of this stamp left in exis-
tence and it has been out of public view since 1986. In
June 2014, the stamp sold at auction for $9,480,000.
Although this is almost 1 billion times the original price of
the stamp, verify for yourself that the annual return is about
13.98 percent.
FINANCE MATTERS
time, the Pennsylvania bequest had grown to about $2 million; the Massachusetts bequest
had grown to $4.5 million. The money was used to fund the Franklin Institutes in Boston
and Philadelphia. Assuming that 1,000 pounds sterling was equivalent to 1,000 dollars (the
dollar did not become the official U.S. currency until 1792), what rate of return did the two
states earn?
For Pennsylvania, the future value is $2 million and the present value is $1,000. There
are 200 years involved, so we need to solve for r in the following:
$1,000 = $2,000,000/(1 + r)200
(1 + r)200 = 2,000
Solving for r, we see that the Pennsylvania money grew at about 3.87 percent per year. The
Massachusetts money did better; verify that the rate of return in this case was 4.3 percent.
Small differences can add up!
We can illustrate how to calculate unknown rates using a financial calculator with these numbers. For
Pennsylvania, you would do the following:
Enter 200 −1,000 2,000,000
I/ Y
Solve for 3.87
As in our previous examples, notice the minus sign on the present value, representing Franklin’s outlay
made many years ago. What do you change to work the problem for Massachusetts?
CALCULATOR
HINTS
111
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112 P A R T 3 Valuation of Future Cash Flows
EXAMPLE 4.10 Saving for College
You estimate that you will need about $80,000 to send your child to college in eight years. You
have about $35,000 now. If you can earn 20 percent per year, will you make it? At what rate will you
just reach your goal?
If you can earn 20 percent, the future value of your $35,000 in eight years will be:
FV = $35,000 × 1.208 = $35,000 × 4.2998 = $150,493.59
So, you will make it easily. The minimum rate is the unknown r in the following:
FV = $35,000 × (1 + r)8 = $80,000
(1 + r)8 = $80,000/35,000 = 2.2857
Therefore, the future value factor is 2.2857. Looking at the row in Table A.1 that corresponds to
eight periods, we see that our future value factor is roughly halfway between the ones shown
for 10 percent (2.1436) and 12 percent (2.4760), so you will reach your goal if you earn approxi-
mately 11 percent. To get the exact answer, we could use a financial calculator or we could
solve for r:
(1 + r)8 = $80,000/35,000 = 2.2857
1 + r = 2.2857(1/8) = 2.2857.125 = 1.1089
r = 10.89%
EXAMPLE 4.11 Only 18,262.5 Days to Retirement
You would like to retire in 50 years as a millionaire. If you have $10,000 today, what rate of return
do you need to earn to achieve your goal?
The future value is $1,000,000. The present value is $10,000, and there are 50 years until
retirement. We need to calculate the unknown discount rate in the following:
$10,000 = $1,000,000/(1 + r)50
(1 + r)50 = 100
The future value factor is thus 100. You can verify that the implicit rate is about 9.65 percent.
Finding the Number of Periods
Suppose we were interested in purchasing an asset that costs $50,000. We currently have
$25,000. If we can earn 12 percent on this $25,000, how long until we have the $50,000?
Finding the answer involves solving for the last variable in the basic present value equation,
the number of periods. You already know how to get an approximate answer to this particu-
lar problem. Notice that we need to double our money. From the Rule of 72, this will take
about 72/12 = 6 years at 12 percent.
To come up with the exact answer, we again can manipulate the basic present value
equation. The present value is $25,000, and the future value is $50,000. With a 12 percent
discount rate, the basic equation takes one of the following forms:
$25,000 = $50,000/1.12t
$50,000/$25,000 = 1.12t = 2
We thus have a future value factor of 2 for a 12 percent rate. We now need to solve for t. If
you look down the column in Table A.1 that corresponds to 12 percent, you will see that a
future value factor of 1.9738 occurs at six periods. It will thus take about six years, as we
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C H A P T E R 4 Introduction to Valuation: The Time Value of Money 113
This example finishes our introduction to basic time value of money concepts.
Table 4.4 summarizes present value and future value calculations for future reference. As
the Work the Web box in this section shows, online calculators are widely available to handle
these calculations, but it is still important to know what is going on.
I. ((((Symbols
PV = Present value, what future cash flows are worth today
FVt = Future value, what cash flows are worth in the future
r = Interest rate, rate of return, or discount rate per period—typically, but not always,
one year
t = Number of periods—typically, but not always, the number of years
C = Cash amount
II. ((((Future value of C invested at r percent per period for t periods
FVt = C × (1 + r)
t
The term (1 + r)t is called the future value factor.
III. ((((Present value of C to be received in t periods at r percent per period
PV = C/(1 + r)t
The term 1/(1 + r)t is called the present value factor.
IV. (((( The basic present value equation giving the relationship between present and future
value is:
PV = FVt /(1 + r)
t
Summary of time
value of money
calculations
TABLE 4.4
calculated. To get the exact answer, we have to explicitly solve for t (or use a financial calcu-
lator). If you do this, you will find that the answer is 6.1163 years, so our approximation was
quite close in this case.
If you do use a financial calculator, here are the relevant entries:
Enter 12 −25,000 50,000
N
Solve for 6.1163
CALCULATOR
HINTS
EXAMPLE 4.12 Waiting for Godot
You’ve been saving up to buy the Godot Company. The total cost will be $10 million. You currently
have about $2.3 million. If you can earn 5 percent on your money, how long will you have to wait?
At 16 percent, how long must you wait?
At 5 percent, you’ll have to wait a long time. From the basic present value equation:
$2.3 = $10/1.05t
1.05t = 4.35
t = 30.12 years
At 16 percent, things are a little better. Verify for yourself that it will take about 10 years.
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114 P A R T 3 Valuation of Future Cash Flows
QUESTIONS
1. Use the present value calculator on this website to answer the following: Suppose you
want to have $140,000 in 25 years. If you can earn a 10 percent return, how much do
you have to invest today?
2. Use the future value calculator on this website to answer the following question: Sup-
pose you have $8,000 today that you plan to save for your retirement in 40 years. If
you earn a return of 10.8 percent per year, how much will this account be worth when
you are ready to retire?
Who said time value of money calculations are hard?
W R K T H E W E B
How important is the time value of money? A recent web search returned more than 996 mil-lion hits! It is important to understand the calculations behind the time value of money, but the
advent of financial calculators and spreadsheets has eliminated the need for tedious calculations.
In fact, many websites offer time value of money calculators. The following is an example from
Moneychimp’s website, www.moneychimp.com. You need $150,000 in 25 years and will invest
your money at 9.2 percent. How much do you need to deposit today? To use the calculator, you
enter the values and hit “Calculate.” The results look like this:
USING A SPREADSHEET FOR TIME VALUE OF MONEY CALCULATIONS
More and more, businesspeople from many different areas (and not just finance and accounting) rely on
spreadsheets to do all the different types of calculations that come up in the real world. As a result, in
this section, we show you how to use a spreadsheet to handle the various time value of money problems
we presented in this chapter. We will use Microsoft ExcelTM, but the commands are similar for other types
of software. We assume you are already familiar with basic spreadsheet operations.
As we have seen, you can solve for any one of the following four potential unknowns: future value,
present value, the discount rate, or the number of periods. With a spreadsheet, there is a separate for-
mula for each. In Excel, these are as follows:
To Find Enter This Formula
Future value = FV(rate, nper, pmt, pv)
Present value = PV(rate, nper, pmt, fv)
Discount rate = RATE(nper, pmt, pv, fv)
Number of periods = NPER(rate, pmt, pv, fv)
In these formulas, pv and fv are present and future value; nper is the number of periods; and rate is the
discount, or interest, rate.
Learn more about using
Excel for time value of
money and other
calculations at www
.studyfinance.com.
SPREADSHEET
STRATEGIES
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C H A P T E R 4 Introduction to Valuation: The Time Value of Money 115
CONCEPT QUESTIONS
4.3a What is the basic present value equation?
4.3b What is the Rule of 72?
There are two things that are a little tricky here. First, unlike a financial calculator, the spreadsheet
requires that the rate be entered as a decimal. Second, as with most financial calculators, you have to
put a negative sign on either the present value or the future value to solve for the rate or the number of
periods. For the same reason, if you solve for a present value, the answer will have a negative sign un-
less you input a negative future value. The same is true when you compute a future value.
To illustrate how you might use these formulas, we will go back to an example in the chapter. If you
invest $25,000 at 12 percent per year, how long until you have $50,000? You might set up a spread-
sheet like this:
A B C D E F G H
1
2 Using a spreadsheet for time value of money calculations
3
4 If we invest $25,000 at 12 percent, how long until we have $50,000? We need to solve for the
5 unknown number of periods, so we use the formula NPER (rate, pmt, pv, fv).
6
7 Present value (pv): $25,000
8 Future value (fv): $50,000
9 Rate: .12
10
11 Periods: 6.116255
12
13 The formula entered in cell B11 is =NPER(B9,0,-B7,B8); notice that pmt is zero and that pv has a
14 negative sign on it. Also notice that the rate is entered as a decimal, not a percentage.
SUMMARY AND CONCLUSIONS
This chapter has introduced you to the basic principles of present value and discounted cash
flow valuation. In it, we explained a number of things about the time value of money,
including:
1. For a given rate of return, the value at some point in the future of an investment made
today can be determined by calculating the future value of that investment.
2. The current worth of a future cash flow can be determined for a given rate of return
by calculating the present value of the cash flow involved.
3. The relationship between present value and future value for a given rate, r, and time, t,
is given by the basic present value equation:
PV = FVt/(1 + r)
t
As we have shown, it is possible to find any one of the four components (PV, FVt, r,
or t) given the other three.
The principles developed in this chapter will figure prominently in the chapters to
come. The reason for this is that most investments, whether they involve real assets or
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116 P A R T 3 Valuation of Future Cash Flows
financial assets, can be analyzed using the discounted cash flow, or DCF, approach. As a
result, the DCF approach is broadly applicable and widely used in practice. Before going on,
therefore, you might want to do some of the problems below.
POP QUIZ!
Can you answer the following questions? If your class is using Connect, log on to
SmartBook to see if you know the answers to these and other questions, check out
the study tools, and find out what topics require additional practice!
Section 4.1 If you invest $500 for one year at a rate of 8 percent per year, how
much interest will you earn?
Section 4.2 What is the formula used to calculate the present value of a future
amount?
Section 4.3 Suppose you invest $100 now and receive $259.37 in 10 years. What
rate of interest did you earn?
CHAPTER REVIEW AND SELF-TEST PROBLEMS
4.1 Calculating Future Values Assume you deposit $1,000 today in an account that
pays 8 percent interest. How much will you have in four years? (See Problem 2.)
4.2 Calculating Present Values Suppose you have just celebrated your 19th birthday.
A rich uncle set up a trust fund for you that will pay you $100,000 when you turn 25.
If the relevant discount rate is 11 percent, how much is this fund worth today? (See
Problem 3.)
4.3 Calculating Rates of Return You’ve been offered an investment that will double
your money in 12 years. What rate of return are you being offered? Check your
answer using the Rule of 72. (See Problem 4.)
4.4 Calculating the Number of Periods You’ve been offered an investment that will
pay you 7 percent per year. If you invest $10,000, how long until you have $20,000?
How long until you have $30,000? (See Problem 5.)
■ Answers to Chapter Review and Self-Test Problems
4.1 We need to calculate the future value of $1,000 at 8 percent for four years. The
future value factor is:
1.084 = 1.3605
The future value is thus $1,000 × 1.3605 = $1,360.49.
4.2 We need the present value of $100,000 to be paid in six years at 11 percent. The
discount factor is:
1/1.116 = 1/1.8704 = .5346
The present value is thus about $53,464.
4.3 Suppose you invest, say, $100. You will have $200 in 12 years with this investment.
So, $100 is the amount you have today, the present value, and $200 is the amount
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C H A P T E R 4 Introduction to Valuation: The Time Value of Money 117
you will have in 12 years, or the future value. From the basic present value
equation, we have:
$200 = $100 × (1 × r)12
2 = (1 × r)12
From here, we need to solve for r, the unknown rate. As shown in the chapter, there
are several different ways to do this. We will take the 12th root of 2 (by raising 2 to
the power of 1/12):
21/12 = 1 + r
1.0595 = 1 + r
r = .0595, or 5.95%
Using the Rule of 72, we have 72/t = r%, or 72/12 = 6%, so our answer looks good
(remember that the Rule of 72 is only an approximation).
4.4 The basic equation is:
$20,000 = $10,000 × (1 + .07)t
2 = (1 + 07)t
If we solve for t, we get that t = 10.24 years. Using the Rule of 72, we get 72/7 = 10.29
years, so, once again, our answer looks good. To get $30,000, verify for yourself that
you will have to wait 16.24 years.
CRITICAL THINKING AND CONCEPTS REVIEW
LO 1 4.1 Compounding What is compounding? What is discounting?
LO 1 4.2 Compounding and Periods As you increase the length of time involved,
what happens to future values? What happens to present values?
LO 1 4.3 Compounding and Interest Rates What happens to a future value if you
increase the rate, r? What happens to a present value?
LO 1 4.4 Future Values Suppose you deposit a large sum in an account that earns a
low interest rate and simultaneously deposit a small sum in an account with
a high interest rate. Which account will have the larger future value?
LO 3 4.5 Ethical Considerations Take a look back at Example 4.6. Is it deceptive
advertising? Is it unethical to advertise a future value like this without a
disclaimer?
Use the following information for the next five questions: On March 28, 2008, Toyota
Motor Credit Corporation (TMCC), a subsidiary of Toyota Motor, offered some
securities for sale to the public. Under the terms of the deal, TMCC promised to
repay the owner of one of these securities $100,000 on March 28, 2038, but inves-
tors would receive nothing until then. Investors paid TMCC $24,099 for each of
these securities; so they gave up $24,099 on March 28, 2008, for the promise of a
$100,000 payment 30 years later.
LO 2 4.6 Time Value of Money Why would TMCC be willing to accept such a
small amount today ($24,099) in exchange for a promise to repay about
four times that amount ($100,000) in the future?
LO 3 4.7 Call Provisions TMCC has the right to buy back the securities on the
anniversary date at a price established when the securities were issued (this
feature is a term of this particular deal). What impact does this feature have
on the desirability of this security as an investment?
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118 P A R T 3 Valuation of Future Cash Flows
LO 3 4.8 Time Value of Money Would you be willing to pay $24,099 today in exchange
for $100,000 in 30 years? What would be the key considerations in answering
yes or no? Would your answer depend on who is making the promise to repay?
LO 3 4.9 Investment Comparison Suppose that when TMCC offered the security
for $24,099, the U.S. Treasury had offered an essentially identical security.
Do you think it would have had a higher or lower price? Why?
LO 3 4.10 Length of Investment The TMCC security is bought and sold on the New
York Stock Exchange. If you looked at the price today, do you think the
price would exceed the $24,099 original price? Why? If you looked in 2022,
do you think the price would be higher or lower than today’s price? Why?
QUESTIONS AND PROBLEMS
Select problems are available in McGraw-Hill Connect. Please see the pack-
aging options section of the Preface for more information.
BASIC (Questions 1–15)
1. Simple Interest versus Compound Interest First City Bank pays 7 percent
simple interest on its savings account balances, whereas Second City Bank
pays 7 percent interest compounded annually. If you made a deposit of
$7,900 in each bank, how much more money would you earn from your
Second City Bank account at the end of 10 years?
2. Calculating Future Values For each of the following, compute the future value:
Present Value Years Interest Rate Future Value
$ 2,960 7 13%
7,846 16 7
85,381 19 9
221,614 26 5
3. Calculating Present Values For each of the following, compute the
present value:
Present Value Years Interest Rate Future Value
15 7% $ 19,415
8 11 47,382
13 10 312,176
25 13 629,381
4. Calculating Interest Rates Solve for the unknown interest rate in each of
the following:
Present Value Years Interest Rate Future Value
$ 715 9 $ 1,381
905 12 1,718
15,000 26 141,832
70,300 15 312,815
LO 1
LO 1
LO 2
LO 3
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C H A P T E R 4 Introduction to Valuation: The Time Value of Money 119
5. Calculating the Number of Periods Solve for the unknown number of years
in each of the following:
Present Value Years Interest Rate Future Value
$ 195 8% $ 873
2,105 11 3,500
47,800 10 326,500
38,650 15 213,380
6. Calculating Rates of Return Assume the total cost of a college education
will be $235,000 when your child enters college in 18 years. You presently
have $53,000 to invest. What annual rate of interest must you earn on your
investment to cover the cost of your child’s college education?
7. Calculating the Number of Periods At 5.3 percent interest, how long does
it take to double your money? To quadruple it?
8. Calculating Rates of Return In 2018, one of the first copper pennies struck
at the Philadelphia mint in 1793 was sold for $300,000. What was the rate of
return on this investment?
9. Calculating the Number of Periods You’re trying to save to buy a new
$175,000 Ferrari. You have $35,000 today that can be invested at your bank.
The bank pays 2.9 percent annual interest on its accounts. How long will it
be before you have enough to buy the car?
10. Calculating Present Values Imprudential, Inc., has an unfunded pension
liability of $645 million that must be paid in 25 years. To assess the value of the
firm’s stock, financial analysts want to discount this liability back to the present. If
the relevant discount rate is 5.5 percent, what is the present value of this liability?
11. Calculating Present Values You have just received notification that you
have won the $1 million first prize in the Centennial Lottery. However, the
prize will be awarded on your 100th birthday (assuming you’re around to
collect), 80 years from now. What is the present value of your windfall if the
appropriate discount rate is 8.45 percent?
12. Calculating Future Values Your coin collection contains fifty 1952 silver
dollars. If your grandparents purchased them for their face value when they
were new, how much will your collection be worth when you retire in 2063,
assuming they appreciate at an annual rate of 4.8 percent?
13. Calculating Growth Rates and Future Values In 1895, the first U.S. Open
Golf Championship was held. The winner’s prize money was $150. In 2018,
the winner’s check was $2,160,000. What was the annual percentage increase
in the winner’s check over this period? If the winner’s prize increases at the
same rate, what will it be in 2048?
14. Calculating Rates of Return In 2018, an Action Comics No. 1, featuring the
first appearance of Superman, was sold at auction for $573,600. The comic
book was originally sold in 1938 for $.10. What was the annual increase in
the value of this comic book?
15. Calculating Rates of Return Although appealing to more refined tastes,
art as a collectible has not always performed so profitably. During 2010,
Deutscher-Menzies sold Arkie under the Shower, a painting by renowned
Australian painter Brett Whiteley, at auction for a price of $1,100,000.
LO 4
LO 3
LO 4
LO 3
LO 4
LO 2
LO 2
LO 1
LO 1
LO 3
LO 3
LO 3
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120 P A R T 3 Valuation of Future Cash Flows
Unfortunately for the previous owner, he had purchased it 3 years earlier at a
price of $1,680,000. What was his annual rate of return on this painting?
INTERMEDIATE (Questions 16–25)
16. Calculating Rates of Return Refer back to the Series EE savings bonds we
discussed at the very beginning of the chapter.
a. Assuming you purchased a $50 face value bond, what rate of return would
you earn if you held the bond for 20 years until it doubled in value?
b. If you purchased a $50 face value bond in early 2018 at the then-current
interest rate of .10 percent per year, how much would the bond be worth
in 2028?
c. In 2028, instead of cashing the bond in for its then-current value, you
decide to hold the bond until it doubles in face value in 2038. What rate
of return will you earn over the last 10 years?
17. Calculating Present Values Suppose you are still committed to owning
a $175,000 Ferrari (see Question 9). If you believe your mutual fund can
achieve an annual return of 11.2 percent, and you want to buy the car in 10
years on the day you turn 30, how much must you invest today?
18. Calculating Future Values You have just made your first $5,000
contribution to your individual retirement account. Assuming you earn an
annual rate of return of 10.2 percent and make no additional contributions,
what will your account be worth when you retire in 45 years? What if
you wait 10 years before contributing? (Does this suggest an investment
strategy?)
19. Calculating Future Values You are scheduled to receive $10,000 in two years.
When you receive it, you will invest it for six more years at 7.5 percent per year.
How much will you have in eight years?
20. Calculating the Number of Periods You expect to receive $30,000 at
graduation in two years. You plan on investing it at 7 percent until you have
$125,000. How long will you wait from now? (Better than the situation in
Question 9, but still no Ferrari.)
21. Calculating Future Values You have $5,800 to deposit. Regency Bank
offers 12 percent per year compounded monthly (1 percent per month),
while King Bank offers 12 percent but will only compound annually. How
much will your investment be worth in 20 years at each bank?
22. Calculating Rates of Return An investment offers to triple your money
in 24 months (don’t believe it). What rate per three months are you being
offered?
23. Calculating the Number of Periods You can earn .31 percent per month at
your bank. If you deposit $1,800, how long must you wait until your account
has grown to $3,100?
24. Calculating Present Values You need $85,000 in 10 years. If you can earn
.78 percent per month, how much will you have to deposit today?
25. Calculating Present Values You have decided that you want to be a
millionaire when you retire in 45 years. If you can earn an annual return of
11.4 percent, how much do you have to invest today? What if you can earn
5.7 percent?
LO 3
LO 2
LO 1
LO 1
LO 4
LO 1
LO 3
LO 4
LO 2
LO 2
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C H A P T E R 4 Introduction to Valuation: The Time Value of Money 121
CHALLENGE (Question 26)
26. Calculating Future Values You have $20,000 you want to invest for the
next 40 years. You are offered an investment plan that will pay you 6 percent
per year for the next 20 years and 10 percent per year for the last 20 years.
How much will you have at the end of the 40 years? Does it matter if the
investment plan pays you 10 percent per year for the first 20 years and 6
percent per year for the next 20 years? Why or why not?
LO 1
WHAT’S ON
THE WEB?
4.1 Calculating Future Values Go to www.dinkytown.net and find the “Savings
Calculators” link. If you currently have $10,000 and invest this money at 9 percent, how
much will you have in 30 years? Assume you will not make any additional contributions.
How much will you have if you can earn 11 percent?
4.2 Calculating the Number of Periods Go to www.dinkytown.net and find the “Cool
Million” calculator. You want to be a millionaire. You can earn 11.5 percent per year.
Using your current age, at what age will you become a millionaire if you have $25,000 to
invest, assuming you make no other deposits (ignore inflation)?
4.3 Calculating the Number of Periods Go to www.moneychimp.com and find the
“Compound Interest” calculator. You want to buy a Lamborghini Murciélago. Assume
the price of the car is $330,000 and you have $35,000. If you can earn an 11 percent
return, how long must you wait to buy this car (assuming the price stays the same)?
4.4 Calculating Rates of Return Use the “Return Rate” calculator at www.moneychimp
.com to solve the following problem. You still want to buy the Lamborghini Murciélago,
but you have $60,000 to invest and want to buy the car in 15 years. What interest rate do
you have to earn to accomplish this (assuming the price stays the same)?
4.5 Future Values and Taxes Taxes can greatly affect the future value of your investment.
The website at www.financialcalculators.com has a financial calculator that adjusts your
return for taxes. Go to this web page and find this calculator. Suppose you have $50,000
to invest today. If you can earn a 12 percent return, and you have no additional savings,
how much will you have in 20 years? (Enter 0 percent as the tax rate.) Now, assume that
your marginal tax rate is 27.5 percent. How much will you have at this tax rate?
EXCEL MASTER IT! PROBLEM
Before the advent of financial calculators (and Excel), tables often were used in the calcula-
tion of present values and future values. Using a two-way data table, create a future value
table and a present value table. To make the table a little more interesting, make sure that it
will calculate the future values and present values for different dollar amounts. One thing we
should note here is that you will not be able to copy and paste the tables presented earlier in
this workbook. When a data table is created, you cannot insert or delete rows or columns at
a later point in time.
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122
Please visit us at essentialsofcorporatefinance.blogspot.com for the latest developments in the world of corporate finance.
What do professional athletes Alex Avila, Yu Darvish, and Jimmy Garoppolo have in common? All three signed big
contracts in 2018. The contract values were reported as $8.25 mil-
lion, $126 million, and $137.5 million, respectively. That’s definitely
major league money, but, even so, reported numbers like these can
be misleading. For example, in January 2018, Avila signed with the
Arizona Diamondbacks. His contract called for a salary of $4 million
in 2018 and $4.25 million for 2019. Not bad, especially for someone
who makes a living using the “tools of ignorance” ( jock jargon for a
catcher’s equipment).
A closer look at the numbers shows that Alex, Yu, and Jimmy
did pretty well, but nothing like the quoted figures. Using Yu’s
contract as an example, although the value was reported to be
$126 million, it was actually payable over several years. The con-
tract consisted of $25 million to be paid in 2018, but only $18 million in 2023. Because the
payments were spread out over time, we must consider the time value of money, which
means his contract was worth less than reported. How much did he really get? This chapter
gives you the “tools of knowledge” to answer this question.
In our previous chapter, we learned how to examine single, lump-sum future payments
to determine their current, or present, value. This is a useful skill, but we need to go further
and figure out how to handle multiple future payments because that is the much more com-
mon situation. For example, most loans (including student loans) involve receiving a lump
sum today and making future payments.
More generally, most types of business decisions, including decisions concerning mar-
keting, operations, and strategy, involve the comparison of costs incurred today with cash
Discounted Cash
Flow Valuation 5
LEARNING OBJECTIVES
After studying this chapter, you should
be able to:
LO 1 Determine the future value and
present value of investments with
multiple cash flows.
LO 2 Calculate loan payments, and find
the interest rate on a loan.
LO 3 Describe how loans are amortized
or paid off.
LO 4 Explain how interest rates are
quoted (and misquoted).
ros13952_ch05_122-164.indd 122 12/24/18 4:40 PM
123
In our previous chapter, we covered the basics of discounted cash flow valuation. However, so far, we have only dealt with single cash flows. In reality, most investments have multiple
cash flows. If Target is thinking of opening a new department store, there will be a large
cash outlay in the beginning and then cash inflows for many years. In this chapter, we begin
to explore how to value such investments.
When you finish this chapter, you should have some very practical skills. For example,
you will know how to calculate your own car payments or student loan payments. You
also will be able to determine how long it will take to pay off a credit card if you make the
minimum payment each month (a practice we do not recommend). We will show you how to
compare interest rates to determine which are the highest and which are the lowest, and we
also will show you how interest rates can be quoted in different, and at times deceptive, ways.
FUTURE AND PRESENT VALUES OF
MULTIPLE CASH FLOWS
Thus far, we have restricted our attention to either the future value of a lump-sum present
amount or the present value of some single future cash flow. In this section, we begin to
study ways to value multiple cash flows. We start with future value.
Future Value with Multiple Cash Flows
Suppose you deposit $100 today in an account paying 8 percent. In one year, you will de-
posit another $100. How much will you have in two years? This particular problem is rela-
tively easy. At the end of the first year, you will have $108 plus the second $100 you deposit,
for a total of $208. You leave this $208 on deposit at 8 percent for another year. At the end
of this second year, the account is worth:
$208 × 1.08 = $224.64
Figure 5.1 is a time line that illustrates the process of calculating the future value of these
two $100 deposits. Figures such as this one are very useful for solving complicated prob-
lems. Any time you are having trouble with a present or future value problem, drawing a
time line will usually help you to see what is happening.
In the first part of Figure 5.1, we show the cash flows on the time line. The most im-
portant thing is that we write them down where they actually occur. Here, the first cash flow
occurs today, which we label as Time 0. We therefore put $100 at Time 0 on the time line.
The second $100 cash flow occurs one year from today, so we write it down at the point la-
beled as Time 1. In the second part of Figure 5.1, we calculate the future values one period
at a time to come up with the final $224.64.
5.1
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inflows hoped for later. Evaluating the cost-benefit trade-off requires the tools that we de-
velop in this chapter.
Because discounted cash flow valuation is so important, students who learn this mate-
rial well will find that life is much easier down the road. Getting it straight now will save you a
lot of headaches later.
ros13952_ch05_122-164.indd 123 12/24/18 4:40 PM
124 P A R T 3 Valuation of Future Cash Flows
Drawing and using a time line
A. The time line:
0
$100
1 2
Cash flows
B. Calculating the future value:
0 1 2
Cash flows
+108
$208
×1.08
$224.64Future values
×1.08
$100
$100 $100
Time
(years)
Time
(years)
FIGURE 5.1
EXAMPLE 5.1 Saving Up Revisited
You think you will be able to deposit $4,000 at the end of each of the next three years in a bank
account paying 8 percent interest. You currently have $7,000 in the account. How much will you
have in three years? In four years?
At the end of the first year, you will have:
$7,000 × 1.08 + 4,000 = $11,560
At the end of the second year, you will have:
$11,560 × 1.08 + 4,000 = $16,484.80
Repeating this for the third year gives:
$16,484.80 × 1.08 + 4,000 = $21,803.58
Therefore, you will have $21,803.58 in three years. If you leave this on deposit for one more year
(and don’t add to it), at the end of the fourth year, you’ll have:
$21,803.58 × 1.08 = $23,547.87
When we calculated the future value of the two $100 deposits, we calculated the bal-
ance as of the beginning of each year and then rolled that amount forward to the next year.
We could have done it another, quicker way. The first $100 is on deposit for two years at
8 percent, so its future value is:
$100 × 1.08 2 = $100 × 1.1664 = $116.64
The second $100 is on deposit for one year at 8 percent, and its future value is thus:
$100 × 1.08 = $108.00
The total future value, as we previously calculated, is equal to the sum of these two future
values:
$116.64 + 108 = $224.64
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C H A P T E R 5 Discounted Cash Flow Valuation 125
Time line for $2,000 per year for five years
0 1 2 3 4 5
$2,000 $2,000 $2,000 $2,000 $2,000
Time
(years)
FIGURE 5.2
Future value calculated by compounding forward one period at a time
0 1 2 3 4 5
$ 0
2,000
$2,000
Beginning amount
Additions
Ending amount
$0
0
$0
+
$2,200
2,000
$4,200
×1.1×1.1
$4,620
2,000
$6,620
×1.1
$7,282
2,000
$9,282
×1.1
$10,210.20
2,000.00
$12,210.20
×1.1
Time
(years)
FIGURE 5.3
Future value calculated by compounding each cash flow separately
0 1 2 3 4 5
$2,000 $2,000 $2,000 $2,000 $ 2,000
2,200.00
2,420.00
2,662.00
2,928.20
$12,210.20
×1.1
Time
(years)
×1.12
×1.13
×1.14
FIGURE 5.4
Based on this example, there are two ways to calculate future values for multiple cash
flows: (1) compound the accumulated balance forward one year at a time or (2) calculate
the future value of each cash flow first and then add these up. Both give the same answer, so
you can do it either way.
To illustrate the two different ways of calculating future values, consider the future
value of $2,000 invested at the end of each of the next five years. The current balance is
zero, and the rate is 10 percent. We first draw a time line as shown in Figure 5.2.
On the time line, notice that nothing happens until the end of the first year when we
make the first $2,000 investment. This first $2,000 earns interest for the next four (not five)
years. Also, notice that the last $2,000 is invested at the end of the fifth year, so it earns no
interest at all.
Figure 5.3 illustrates the calculations involved if we compound the investment one pe-
riod at a time. As illustrated, the future value is $12,210.20.
Figure 5.4 goes through the same calculations, but it uses the second technique. Natu-
rally, the answer is the same.
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126 P A R T 3 Valuation of Future Cash Flows
Present Value with Multiple Cash Flows
It will turn out that we will very often need to determine the present value of a series of fu-
ture cash flows. As with future values, there are two ways we can do it. We can either dis-
count back one period at a time, or we can calculate the present values individually and add
them up.
Suppose you need $1,000 in one year and $2,000 more in two years. If you can earn
9 percent on your money, how much do you have to put up today to exactly cover these
amounts in the future? In other words, what is the present value of the two cash flows at
9 percent?
The present value of $2,000 in two years at 9 percent is:
$2,000 / 1.092 = $1,683.36
The present value of $1,000 in one year is:
$1,000 / 1.09 = $917.43
Therefore, the total present value is:
$1,683.36 + 917.43 = $2,600.79
To see why $2,600.79 is the right answer, we can check to see that after the $2,000 is
paid out in two years, there is no money left. If we invest $2,600.79 for one year at 9 percent,
we will have:
$2,600.79 × 1.09 = $2,834.86
EXAMPLE 5.2 Saving Up Once Again
If you deposit $100 in one year, $200 in two years, and $300 in three years, how much will you
have in three years? How much of this is interest? How much will you have in five years if you don’t
add additional amounts? Assume a 7 percent interest rate throughout.
We will calculate the future value of each amount in three years. Notice that the $100 earns
interest for two years, and the $200 earns interest for one year. The final $300 earns no interest.
The future values are thus:
$100 × 1.072 %%= $114.49
$200 × 1.07 %%%%= 214.00
+ $300 %%%%%%=%%%%%%%%%%%%%%%%%300.00
Total future value = $628.49
The future value is thus $628.49. The total interest is:
$628.49 − (100 + 200 + 300) = $28.49
How much will you have in five years? We know that you will have $628.49 in three years. If you
leave that in for two more years, it will grow to:
$628.49 × 1.072 = $628.49 × 1.1449 = $719.56
Notice that we could have calculated the future value of each amount separately. Once again, be
careful about the lengths of time. As we previously calculated, the first $100 earns interest for only
four years, the second deposit earns three years’ interest, and the last earns two years’ interest:
$100 × 1.074 = $100 × 1.3108 = $131.08
$200 × 1.073 = $200 × 1.2250 = %%%245.01
+$300 × 1.072 = $300 × 1.1449 = 343.47
Total future value = $719.56
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C H A P T E R 5 Discounted Cash Flow Valuation 127
We take out $1,000, leaving $1,834.86. This amount earns 9 percent for another year, leav-
ing us with:
$1,834.86 × 1.09 = $2,000
This is as we planned. As this example illustrates, the present value of a series of future cash
flows is the amount that you would need today in order to exactly duplicate those future
cash flows (for a given discount rate).
An alternative way of calculating present values for multiple future cash flows is to
discount back to the present one period at a time. To illustrate, suppose we had an invest-
ment that was going to pay $1,000 at the end of every year for the next five years. To find the
present value, we could discount each $1,000 back to the present separately and then add
the results up. Figure 5.5 illustrates this approach for a 6 percent discount rate. As shown,
the answer is $4,212.36.
Alternatively, we could discount the last cash flow back one period and add it to the
next-to-the-last cash flow:
$1,000 / 1.06 + 1,000 = $943.40 + 1,000 = $1,943.40
We could then discount this amount back one period and add it to the Year 3 cash flow:
$1,943.40 / 1.06 + 1,000 = $1,833.39 + 1,000 = $2,833.39
This process could be repeated as necessary. Figure 5.6 illustrates this approach and the
remaining calculations.
As the accompanying Finance Matters box shows, calculating present values is a vital
step in comparing alternative cash flows. We will have much more to say on this subject in
subsequent chapters.
Present value
calculated by
discounting each
cash flow separately
FIGURE 5.50 1 2 3 4 5
$1,000 $1,000 $1,000 $1,000
$ 943.40
890.00
839.62
792.09
747.26
$4,212.36
× 1/1.06
Time
(years)
$1,000
×1/1.062
×1/1.063
×1/1.064
×1/1.065
Total present value
r = 6%
Present value
calculated by
discounting back one
period at a time
FIGURE 5.60 1 2 3 4 5
$4,212.36
0.00
$4,212.36
$3,465.11
1,000.00
$4,465.11
$2,673.01
1,000.00
$3,673.01
$1,833.39
1,000.00
$2,833.39
$ 943.40
1,000.00
$1,943.40
$ 0.00
1,000.00
$1,000.00
Time
(years)
Total present value = $4,212.36
r = 6%
ros13952_ch05_122-164.indd 127 12/24/18 4:40 PM
Jackpot!
If you, or someone you know, is a regular lottery player, you probably already understand that you are 20 times more
likely to be killed by a lightning bolt than to win a big lottery
jackpot. How bad are the odds? Below you will find a table
comparing your chances of winning the Mega Millions Lot-
tery to other events.
Big Game: Is It Worth the Gamble?
Odds of winning Mega Millions jackpot 1:135,145,920*
Odds of being killed by a venomous spider 1:57,018,763
Odds of being killed by a dog bite 1:11,403,753
Odds of being killed by lightning 1:6,479,405
Odds of being killed by drowning 1:690,300
Odds of being killed by falling from a bed
or other furniture
1:388,411
Odds of being killed in a car crash 1:6,029
*Source: Virginia Lottery website. All other odds from the National Safety
Council.
Sweepstakes may have different odds than lotteries,
but the odds may not be much better. Probably the largest
advertised grand prize ever was Pepsi’s “Play for a Billion,”
which, you guessed it, had a $1 billion (billion!) prize. Not bad
for a day’s work, but you still have to read the fine print. It
turns out that the winner would be paid $5 million per year
for the next 20 years, $10 million per year for Years 21 to 39,
and a lump sum of $710 million in 40 years. From what you
have learned, you know the value of the sweepstakes wasn’t
even close to $1 billion. In fact, at an interest rate of 10 per-
cent, the present value was about $70.7 million.
Lottery jackpots are often paid out over 20 or more
years, but the winner can usually choose to take a lump-sum
cash payment instead. For example, in June 2018, a Hacken-
sack, New Jersey, man won the $315 million Powerball lot-
tery. The man had the option of a single cash payment of
$183 million or payments of $10.5 million over the next
30 years. In this case, the man chose the cash option.
Some lotteries make your decision a little tougher. The
Ontario Lottery will pay you either $1,000 a day for the rest
of your life or $7 million now. (That’s in Canadian dollars, by
the way.) The fine print tells you that the lottery determines
the payout frequency. Assuming a payment of $365,000 is
made at the beginning of each year, if you only receive pay-
ments for 20 years, the break-even interest rate is about
.45 percent. Of course, if you manage to invest the $7 million
lump sum at a rate of return of about 5.5 percent per year,
you can have your cake and eat it, too, because the invest-
ment will return $365,000 at the beginning of each year for-
ever! A Quebec 18-year-old was faced with such a decision
when she went to buy a bottle of champagne to celebrate
her birthday and won $1,000 a week for life. She took the
weekly payment instead of a $1 million lump sum. Taxes
complicate the decision in this case because the lottery pay-
ments are all on an aftertax basis. Thus, the rates of return in
this example would have to be aftertax as well.
FINANCE MATTERS
EXAMPLE 5.3 How Much Is It Worth?
You are offered an investment that will pay you $200 in one year, $400 the next year, $600 the
next year, and $800 at the end of the next year. You can earn 12 percent on very similar invest-
ments. What is the most you should pay for this one?
We need to calculate the present value of these cash flows at 12 percent. Taking them one at
a time gives:
$200 × 1/1.121 = $200/1.1200 = $ 178.57
$400 × 1/1.122 = $400/1.2544 = %%%318.88
$600 × 1/1.123 = $600/1.4049 = %%%427.07
+$800 × 1/1.124 = $800/1.5735 = 508.41
Total present value = $1,432.93
If you can earn 12 percent on your money, then you can duplicate this investment’s cash flows for
$1,432.93, so this is the most you should be willing to pay.
128
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C H A P T E R 5 Discounted Cash Flow Valuation 129
EXAMPLE 5.4 How Much Is It Worth? Part 2
You are offered an investment that will make three $5,000 payments. The first payment will occur
four years from today. The second will occur in five years, and the third will follow in six years. If you
can earn 11 percent, what is the most this investment is worth today? What is the future value of the
cash flows?
We answer the questions in reverse order to illustrate a point. The future value of the cash
flows in six years is:
$5,000 × 1.112 + 5,000 × 1.11 + 5,000 = $6,160.50 + 5,550 + 5,000
= $16,710.50
The present value must be:
$16,710.50/1.116 = $8,934.12
Let’s check this. Taking them one at a time, the PVs of the cash flows are:
$5,000 × 1/1.116 = $5,000/1.8704 = $2,673.20
$5,000 × 1/1.115 = $5,000/1.6851 = 2,967.26
+$5,000 × 1/1.114 = $5,000/1.5181 = 3,293.65
Total present value = $8,934.12
This is as we previously calculated. The point we want to make is that we can calculate present and
future values in any order and convert between them using whatever way seems most convenient.
The answers will always be the same as long as we stick with the same discount rate and are care-
ful to keep track of the right number of periods.
HOW TO CALCULATE PRESENT VALUES WITH MULTIPLE FUTURE
CASH FLOWS USING A FINANCIAL CALCULATOR
To calculate the present value of multiple cash flows with a financial calculator, we will discount the indi-
vidual cash flows one at a time using the same technique we used in our previous chapter, so this is not
really new. There is a shortcut, however, that we can show you. We will use the numbers in Example 5.3
to illustrate.
To begin, of course, we first remember to clear out the calculator! Next, from Example 5.3, the first
cash flow is $200 to be received in one year and the discount rate is 12 percent, so we do the
following:
Enter 1 12 200
PV
Solve for −178.57
Now, you can write down this answer to save it, but that’s inefficient. All calculators have a memory
where you can store numbers. Why not save it there? Doing so cuts way down on mistakes because you
don’t have to write down and/or rekey numbers, and it’s much faster.
Next, we value the second cash flow. We need to change N to 2 and FV to 400. As long as we
haven’t changed anything else, we don’t have to reenter I/Y or clear out the calculator, so we have:
Enter 2 400
PV
Solve for −318.88
CALCULATOR
HINTS
(continued)
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130 P A R T 3 Valuation of Future Cash Flows
You save this number by adding it to the one you saved in our first calculation, and so on, for the remain-
ing two calculations.
As we will see in a later chapter, some financial calculators will let you enter all of the future cash
flows at once, but we’ll discuss that subject when we get to it.
A Note on Cash Flow Timing
In working present and future value problems, cash flow timing is critically important. In
almost all such calculations, it is implicitly assumed that the cash flows occur at the end of
each period. In fact, all the formulas we have discussed, all the numbers in a standard pres-
ent value or future value table, and, very importantly, all the preset (or default) settings on a
financial calculator or spreadsheet assume that cash flows occur at the end of each period.
Unless you are very explicitly told otherwise, you always should assume that this is what is
meant.
As a quick illustration of this point, suppose you are told that a three-year investment
has a first-year cash flow of $100, a second-year cash flow of $200, and a third-year cash
flow of $300. You are asked to draw a time line. Without further information, you should
always assume that the time line looks like this:
0 1
$100 $200 $300
2 3
On our time line, notice how the first cash flow occurs at the end of the first period,
the second at the end of the second period, and the third at the end of the third
period.
We will close this section by answering the question we posed at the beginning of the
chapter concerning baseball player Yu Darvish’s contract. The contract called for payments
of $25 million in 2018, $20 million in 2019, $22 million in 2020, $22 million in 2021,
$19 million in 2022, and $18 million in 2023. If 12 percent is the appropriate discount rate,
what kind of deal did the Cubs’ pitcher hurl?
To answer, we can calculate the present value by discounting each year’s salary
back to the present as follows (notice we assume that all the payments are made at
year-end):
Year 1(((( (2018): (((($25,000,000 × 1 / 1.12 (((((((= $22,321,428.57
Year 2 (2019): (((($20,000,000 × 1 / 1.122 = $15,943,877.55
Year 3 (2020): $22,000,000 × 1 / 1.123 = $15,659,165.45
. . .
. . .
. . .
Year 6 (2023): $18,000,000 ((((× 1 / 1.126 = $9,119,360.18
If you fill in the missing rows and then add (do it for practice), you will see that Yu’s
contract had a present value of about $87.8 million, or only about 70 percent of the stated
$126 million value (but still pretty good).
ros13952_ch05_122-164.indd 130 12/24/18 4:40 PM
C H A P T E R 5 Discounted Cash Flow Valuation 131
CONCEPT QUESTIONS
5.1a Describe how to calculate the future value of a series of cash flows.
5.1b Describe how to calculate the present value of a series of cash flows.
5.1c Unless we are explicitly told otherwise, what do we always assume about the timing
of cash flows in present and future value problems?
VALUING LEVEL CASH FLOWS: ANNUITIES
AND PERPETUITIES
We frequently encounter situations in which we have multiple cash flows that are all the
same amount. For example, a very common type of loan repayment plan calls for the bor-
rower to repay the loan by making a series of equal payments for some length of time. Al-
most all consumer loans (such as car loans) and home mortgages feature equal payments,
usually made each month.
5.2
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HOW TO CALCULATE PRESENT VALUES WITH MULTIPLE FUTURE
CASH FLOWS USING A SPREADSHEET
As we did in our previous chapter, we can set up a basic spreadsheet to calculate the present values of
the individual cash flows as follows. Notice that we have calculated the present values one at a time and
added them up.
SPREADSHEET
STRATEGIES
A B C D E F
1
2 Using a spreadsheet to value multiple cash flows
3
4 What is the present value of $200 in one year, $400 the next year, $600 the next year, and
5 $800 the last year if the discount rate is 12 percent?
6
7 Rate: .12
8
9 Year Cash flows Present values Formula used
10 1 $200 $178.57 = PV($B$7, A10,0,-B10)
11 2 $400 $318.88 = PV($B$7, A11,0,-B11)
12 3 $600 $427.07 = PV($B$7, A12,0,-B12)
13 4 $800 $508.41 = PV($B$7, A13,0,-B13)
14
15 Total PV: $1,432.93 = SUM(C10:C13)
16
17 Notice the negative signs inserted in the PV formulas. These make the present values have
positive signs. Also, the reference to the discount rate in cell B7 is entered as $B$7
(an “absolute” reference) because it is used over and over. We could have entered “.12” instead,
but our approach is more flexible.
18
19
20
21
22
ros13952_ch05_122-164.indd 131 12/24/18 4:40 PM
132 P A R T 3 Valuation of Future Cash Flows
More generally, a series of constant, or level, cash flows that occur at the end of each
period for some fixed number of periods is called an ordinary annuity; or, more correctly,
the cash flows are said to be in ordinary annuity form. Annuities appear very frequently in
financial arrangements, and there are some useful shortcuts for determining their values.
We consider these next.
Present Value for Annuity Cash Flows
Suppose we were examining an asset that promised to pay $500 at the end of each of the
next three years. The cash flows from this asset are in the form of a three-year, $500 ordi-
nary annuity. If we wanted to earn 10 percent on our money, how much would we offer for
this annuity?
From the previous section, we know that we can discount each of these $500 payments
back to the present at 10 percent to determine the total present value:
Present value = $500 / 1.11 + 500 / 1.12 + 500 / 1.13
= $500 / 1.10 + 500 / 1.21 + 500 / 1.331
= $454.55 + 413.22 + 375.66
= $1,243.43
This approach works fine. However, we will often encounter situations where the number of
cash flows is quite large. For example, a typical home mortgage calls for monthly payments
over 30 years, for a total of 360 payments. If we were trying to determine the present value
of those payments, it would be useful to have a shortcut.
Because the cash flows on an annuity are all the same, we can come up with a very
useful variation on the basic present value equation. It turns out that the present value of an
annuity of C dollars per period for t periods when the rate of return, or interest rate, is r is
given by:
Annuity present value = C ×( ( 1 − Present value factor _________________ r )
= C × { 1 − [1 /(1 + r)t ] __________ r } [5.1]
The term in parentheses on the first line is sometimes called the present value interest factor
for annuities and abbreviated PVIFA(r, t).
The expression for the annuity present value may look a little complicated, but it
isn’t difficult to use. Notice that the term in square brackets on the second line, 1/(1 + r)t,
is the same present value factor we’ve been calculating. In the preceding example, the
interest rate is 10 percent and there are three years involved. The usual present value factor
is thus:
Present value factor = 1 / 1.13 = 1 / 1.331 = .751315
To calculate the annuity present value factor, we plug this in:
Annuity present value factor = (1 − Present value factor) / r
= (1 − .751315) / .10
= .248685 / .10 = 2.48685
As we calculated before, the present value of our $500 annuity is then:
Annuity present value = $500 × 2.48685 = $1,243.43
annuity
A level stream of cash
flows for a fixed period of
time.
ros13952_ch05_122-164.indd 132 12/24/18 4:40 PM
C H A P T E R 5 Discounted Cash Flow Valuation 133
Annuity Tables Just as there are tables for ordinary present value factors, there are ta-
bles for annuity factors as well. Table 5.1 contains a few such factors; Appendix A.3 contains
a larger set. To find the annuity present value factor we just calculated, look for the row cor-
responding to three periods and then find the column for 10 percent. The number you see at
that intersection should be 2.4869 (rounded to four decimal places), as we calculated. Once
again, try calculating a few of these factors yourself and compare your answers to the ones in
the table to make sure you know how to do it. If you are using a financial calculator, enter $1
as the payment and calculate the present value; the result should be the annuity present
value factor.
Annuity present
value interest factors
TABLE 5.1Number of
Periods
Interest Rates
5% 10% 15% 20%
1 .9524 .9091 .8696 .8333
2 1.8594 1.7355 1.6257 1.5278
3 2.7232 2.4869 2.2832 2.1065
4 3.5460 3.1699 2.8550 2.5887
5 4.3295 3.7908 3.3522 2.9906
EXAMPLE 5.5 How Much Can You Afford?
After carefully going over your budget, you have determined you can afford to pay $632 per month
toward a new sports car. You call up your local bank and find out that the going rate is 1 percent per
month for 48 months. How much can you borrow?
To determine how much you can borrow, we need to calculate the present value of $632 per
month for 48 months at 1 percent per month. The loan payments are in ordinary annuity form, so the
annuity present value factor is:
Annuity PV factor = (1 − Present value factor)/r
= [1 − (1/1.0148)]/.01
= (1 − .62026)/.01
= 37.9740
With this factor, we can calculate the present value of the 48 payments of $632 each as:
Present value = $632 × 37.9740 = $24,000
Therefore, $24,000 is about what you can afford to borrow and repay.
ANNUITY PRESENT VALUES
To find annuity present values with a financial calculator, we need to use the PMT key (you were prob-
ably wondering what it was for). Compared to finding the present value of a single amount, there are two
important differences. First, we enter the annuity cash flow using the PMT key, and, second, we don’t
enter anything for the future value, FV . So, for example, the problem we have been examining is a
three-year, $500 annuity. If the discount rate is 10 percent, we need to do the following (after clearing
out the calculator!):
Enter 3 10 500
PV
Solve for −1,243.43
As usual, we get a negative sign on the PV.
CALCULATOR
HINTS
ros13952_ch05_122-164.indd 133 12/24/18 4:40 PM
134 P A R T 3 Valuation of Future Cash Flows
ANNUITY PRESENT VALUES
Using a spreadsheet to work the same problem goes like this:
SPREADSHEET
STRATEGIES
A B C D E F G
1
2 Using a spreadsheet to find annuity present values
3
4 What is the present value of $500 per year for 3 years if the discount rate is 10 percent?
5 We need to solve for the unknown present value, so we use the formula PV(rate, nper, pmt, fv).
6
7 Payment amount per period: $500
8 Number of payments: 3
9 Discount rate: .1
10
11 Annuity present value: $1,243.43
12
13 The formula entered in cell B11 is =PV(B9, B8, −B7, 0); notice that fv is zero and that pmt has a
14 negative sign on it. Also notice that the discount rate is entered as a decimal, not a percentage.
15
Finding the Payment Suppose you wish to start a new business that specializes
in the latest health food trend, frozen yak milk. To produce and market your product,
the Yakee Doodle Dandy, you need to borrow $100,000. Because it strikes you as
unlikely that this particular fad will be long-lived, you propose to pay off the loan quickly
by making five equal annual payments. If the interest rate is 18 percent, what will the
payments be?
In this case, we know that the present value is $100,000. The interest rate is 18 percent,
and there are five years to make payments. The payments are all equal, so we need to find
the relevant annuity factor and solve for the unknown cash flow:
Annuity present value = $100,000 = C × (1 − Present value factor) / r
$100,000 = C × (1 − 1 / 1.185) / .18
= C × (1 − .4371) / .18
= C × 3.1272
C = $100,000 / 3.1272 = $31,977.78
Therefore, you’ll make five payments of just under $32,000 each.
ANNUITY PAYMENTS
Finding annuity payments is easy with a financial calculator. In our example above, the PV is $100,000,
the interest rate is 18 percent, and there are five years. We find the payment as follows:
Enter 5 18 100,000
PMTPMTPMT
Solve for −31,977.78
Here we get a negative sign on the payment because the payment is an outflow for us.
CALCULATOR
HINTS
ros13952_ch05_122-164.indd 134 12/24/18 4:40 PM
C H A P T E R 5 Discounted Cash Flow Valuation 135
ANNUITY PAYMENTS
Using a spreadsheet to work the same problem goes like this:
SPREADSHEET
STRATEGIES
A B C D E F
1
2 Using a spreadsheet to find annuity payments
3
4 What is the annuity payment if the present value is $100,000, the interest rate is 18 percent, and
5 there are 5 periods? We need to solve for the unknown payment in an annuity, so we use the
6 formula PMT(rate, nper, pv, fv)
7
8 Annuity present value: $100,000
9 Number of payments: 5
10 Discount rate: .18
11
12 Annuity payment: ($31,977.78)
13
14 The formula entered in cell B12 is =PMT(B10, B9, B8); notice that the
15 payment is negative because it is an outflow to us.
EXAMPLE 5.6 Finding the Number of Payments
You ran a little short on your spring break vacation, so you put $1,000 on your credit card. You can
afford to make only the minimum payment of $20 per month. The interest rate on the credit card is
1.5 percent per month. How long will you need to pay off the $1,000?
What we have here is an annuity of $20 per month at 1.5 percent per month for some un-
known length of time. The present value is $1,000 (the amount you owe today). We need to do a
little algebra (or else use a financial calculator):
$1,000 = $20 × (1 − Present value factor)/.015
($1,000/20) × .015 = 1 − Present value factor
Present value factor = .25 = 1/(1 + r)t
1.015t = 1/.25 = 4
At this point, the problem boils down to asking the following question: How long does it take for
your money to quadruple at 1.5 percent per month? Based on our previous chapter, the answer is
about 93 months:
1.01593 ≈ 4
It will take you about 93/12 = 7.75 years at this rate.
FINDING THE NUMBER OF PAYMENTS
To solve this one on a financial calculator, do the following:
Enter 1.5 −20 1,000
N
Solve for 93.11
Notice that we put a negative sign on the payment you must make, and we have solved for the number
of months. You still have to divide by 12 to get our answer. Also, some financial calculators won’t report
a fractional value for N; they automatically (without telling you) round up to the next whole period (not to
the nearest value). With a spreadsheet, use the function =NPER(rate, pmt, pv, fv); be sure to put in a zero
for fv and to enter −20 as the payment.
CALCULATOR
HINTS
ros13952_ch05_122-164.indd 135 12/24/18 4:40 PM
136 P A R T 3 Valuation of Future Cash Flows
Finding the Rate The last question we might want to ask concerns the interest rate
implicit in an annuity. For example, an insurance company offers to pay you $1,000 per year
for 10 years if you pay $6,710 up front. What rate is implicit in this 10-year annuity?
In this case, we know the present value ($6,710), we know the cash flows ($1,000 per
year), and we know the life of the investment (10 years). What we don’t know is the dis-
count rate:
$6,710 = $1,000 × (1 − Present value factor() / r
$6,710 / 1,000 = 6.71 = { 1 − [(1 / (1 + r()10 ]} / r
So, the annuity factor for 10 periods is equal to 6.71, and we need to solve this equation for
the unknown value of r. Unfortunately, this is mathematically impossible to do directly. The
only way to do it is to use a table or trial and error to find a value for r.
If you look across the row corresponding to 10 periods in Appendix A.3, you will see a
factor of 6.7101 for 8 percent, so we see right away that the insurance company is offering
about 8 percent. Alternatively, we could start trying different values until we got very close
to the answer. Using this trial-and-error approach can be a little tedious, but, fortunately,
machines are good at that sort of thing.1
To illustrate how to find the answer by trial and error, suppose a relative of yours wants
to borrow $3,000. She offers to repay you $1,000 every year for four years. What interest
rate are you being offered?
The cash flows here have the form of a four-year, $1,000 annuity. The present value is
$3,000. We need to find the discount rate, r. Our goal in doing so is primarily to give you a
feel for the relationship between annuity values and discount rates.
We need to start somewhere, and 10 percent is probably as good a place as any to be-
gin. At 10 percent, the annuity factor is:
Annuity present value factor = (1 − 1 / 1.104() / .10 = 3.1699
The present value of the cash flows at 10 percent is thus:
Present value = $1,000 × 3.1699 = $3,169(.(87
You can see that we’re already in the right ballpark.
Is 10 percent too high or too low? Recall that present values and discount rates move in
opposite directions: Increasing the discount rate lowers the PV and vice versa. Our present
value here is too high, so the discount rate is too low. If we try 12 percent:
Present value = $1,000 × (1 − 1 / 1.12 4 () / .12 = $3,037.35
Now we’re almost there. We are still a little low on the discount rate (because the PV is a
little high), so we’ll try 13 percent:
Present value = $1,000 × (1 − 1 / 1.134() / .13 = $2,974.47
This is less than $3,000, so we now know that the answer is between 12 percent and 13 per-
cent, and it looks to be about 12.5 percent. For practice, work at it for a while longer and see
if you find that the answer is about 12.59 percent.
1Financial calculators rely on trial and error to find the answer. That’s why they sometimes appear to be “thinking”
before coming up with the answer. Actually, it is possible to directly solve for r if there are fewer than five periods,
but it’s usually not worth the trouble.
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C H A P T E R 5 Discounted Cash Flow Valuation 137
Future Value for Annuities
On occasion, it’s also handy to know a shortcut for calculating the future value of an annu-
ity. As you might guess, there are future value factors for annuities as well as present value
factors. In general, the future value factor for an annuity is given by:
Annuity FV factor = (Future value factor − 1)/r
= [(1 + r)t − 1]/r
[5.2]
To see how we use annuity future value factors, suppose you plan to contribute $2,000 every
year into a retirement account paying 8 percent. If you retire in 30 years, how much will
you have?
The number of years here, t, is 30, and the interest rate, r, is 8 percent, so we can calcu-
late the annuity future value factor as:
Annuity FV factor = (Future value factor − 1()(/ r
= (1.0830 − 1()(/ .08
= (10.0627 − 1()(/ .08
= 113.2832
The future value of this 30-year, $2,000 annuity is thus:
Annuity future value = $2,000 × 113.2832
= $226,566.42
FINDING THE RATE
Alternatively, you could use a financial calculator to do the following:
Enter 4 1,000 −3,000
I/ Y
Solve for 12.59
Notice that we put a negative sign on the present value (why?). With a spreadsheet, use the function
=RATE(nper, pmt, pv, fv); be sure to put in a zero for fv and to enter 1,000 as the payment and −3,000 as
the present value.
CALCULATOR
HINTS
A Note on Annuities Due
So far, we only have discussed ordinary annuities. These are the most important, but there
is a variation that is fairly common. Remember that with an ordinary annuity, the cash
flows occur at the end of each period. When you take out a loan with monthly payments,
ANNUITY FUTURE VALUES
Of course, you could solve this problem using a financial calculator by doing the following:
Enter 30 8 −2,000
FV
Solve for 226,566.42
Notice that we put a negative sign on the payment (why?). With a spreadsheet, use the function =FV(rate,
nper, pmt, pv); be sure to put in a zero for pv and to enter −2,000 as the payment.
CALCULATOR
HINTS
ros13952_ch05_122-164.indd 137 12/24/18 4:40 PM
138 P A R T 3 Valuation of Future Cash Flows
for example, the first loan payment normally occurs one month after you get the loan. How-
ever, when you lease an apartment, the first lease payment is usually due immediately. The
second payment is due at the beginning of the second month, and so on. A lease is an exam-
ple of an annuity due. An annuity due is an annuity for which the cash flows occur at the
beginning of each period. Almost any type of arrangement in which we have to prepay the
same amount each period is an annuity due.
There are several different ways to calculate the value of an annuity due. With a finan-
cial calculator, you switch it into “due” or “beginning” mode. It is very important to remem-
ber to switch it back when you are finished! Another way to calculate the present value of an
annuity due can be illustrated with a time line. Suppose an annuity due has five payments of
$400 each, and the relevant discount rate is 10 percent. The time line looks like this:
0 1
$400$400 $400
2
$400
3
$400
4 5
Notice how the cash flows here are the same as those for a four-year ordinary annuity, ex-
cept that there is an extra $400 at Time 0. For practice, verify that the present value of a
four-year $400 ordinary annuity at 10 percent is $1,267.95. If we add on the extra $400, we
get $1,667.95, which is the present value of this annuity due.
There is an even easier way to calculate the present or future value of an annuity due. If
we assume that cash flows occur at the end of each period when they really occur at the
beginning, then we discount each one by one period too many. We could fix this by multiply-
ing our answer by (1 + r), where r is the discount rate. In fact, the relationship between the
value of an annuity due and an ordinary annuity with the same number of payments is:
Annuity due value = Ordinary annuity value × (1 + r) [5.3]
This works for both present and future values, so calculating the value of an annuity due
involves two steps: (1) calculate the present or future value as though it were an ordinary
annuity and (2) multiply your answer by (1 + r).
Perpetuities
We’ve seen that a series of level cash flows can be valued by treating those cash flows as an
annuity. An important special case of an annuity arises when the level stream of cash flows
continues forever. Such an asset is called a perpetuity because the cash flows are perpetual.
Perpetuities also are called consols, particularly in Canada and the United Kingdom. See
Example 5.7 for an important example of a perpetuity.
Because a perpetuity has an infinite number of cash flows, we obviously can’t compute
its value by discounting each one. Fortunately, valuing a perpetuity turns out to be the easi-
est possible case. The present value of a perpetuity is:
Perpetuity PV = C/r [5.4]
For example, an investment offers a perpetual cash flow of $500 every year. The return you
require on such an investment is 8 percent. What is the value of this investment? The value
of this perpetuity is:
Perpetuity PV = C / r = $500 / .08 = $6,250
This concludes our discussion of valuing investments with multiple cash flows. For future
reference, Table 5.2 contains a summary of the annuity and perpetuity basic calculations we
described. By now, you probably think that you’ll use online calculators to handle annuity
problems. Before you do, see our nearby Work the Web box.
annuity due
An annuity for which the
cash flows occur at the
beginning of the period.
Time value applications
abound on the web. See,
for example, www.college
board.org and www
.fidelity.com/calculators
-tools/overview.
perpetuity
An annuity in which the
cash flows continue
forever.
consol
A type of perpetuity.
ros13952_ch05_122-164.indd 138 12/24/18 4:40 PM
C H A P T E R 5 Discounted Cash Flow Valuation 139
According to the Calculatoredge calculator, the answer is $139,288.47. How important is it to un-
derstand what you are doing? Calculate this one for yourself, and you should get $152,520.88.
Which one is right? You are, of course! What’s going on is that Calculatoredge assumes (but tells
you on a different page) that the annuity is in the form of an annuity due, not an ordinary annuity.
Recall that with an annuity due the payments occur at the beginning of the period rather than at
the end of the period. The moral of the story is clear: Caveat calculator.
QUESTIONS
1. Go to the calculator at www.calculatoredge.com and find out how much the website
says you could withdraw each year if you have $2,500,000, earn an 8 percent interest
rate, and make annual withdrawals for 35 years. How much more are the withdrawals
if they are in the form of an ordinary annuity?
2. Suppose you have $500,000 and want to make withdrawals each month for the next
10 years. The first withdrawal is today and the appropriate interest rate is 9 percent
compounded monthly. Using this website, how much are your withdrawals?
W R K T H E W E B
As we discussed in our previous chapter, many websites have financial calculators. One of these sites is Calculatoredge, which is located at www.calculatoredge.com. Suppose you retire with
$1,500,000 and want to withdraw an equal amount each year for the next 30 years. If you can earn
a 9.5 percent return, how much can you withdraw each year? Here is what Calculatoredge says:
Summary of annuity
and perpetuity
calculations
TABLE 5.2
I. Symbols
PV = Present value, what future cash flows are worth today
FVt = Future value, what cash flows are worth in the future at Time t
r = Interest rate, rate of return, or discount rate per period—typically, but not always,
one year
t = Number of periods—typically, but not always, the number of years
C = Cash amount
II. Future value of C invested per period for t periods at r percent per period
FVt = C × [(1 + r)
t − 1]/r
A series of identical cash flows paid for a set number of periods is called an annuity, and the
term [(1 + r)t − 1]/r is called the annuity future value factor.
III. Present value of C per period for t periods at r percent per period
PV = C × {1 − [1/(1 + r)t]}/r
The term {1 − [1/(1 + r)t]}/r is called the annuity present value factor.
IV. Present value of a perpetuity of C per period
PV = C/r
A perpetuity has the same cash flow every period forever.
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140 P A R T 3 Valuation of Future Cash Flows
CONCEPT QUESTIONS
5.2a In general, what is the present value of an annuity of C dollars per period at a
discount rate of r per period? The future value?
5.2b In general, what is the present value of a perpetuity?
COMPARING RATES: THE EFFECT
OF COMPOUNDING PERIODS
An important issue we need to discuss has to do with the way interest rates are quoted. This
subject causes a fair amount of confusion because rates are quoted in many different ways.
Sometimes the way a rate is quoted is the result of tradition, and sometimes it’s the result
of legislation. Unfortunately, at times, rates are quoted in deliberately deceptive ways to
mislead borrowers and investors. We discuss these topics in this section.
Effective Annual Rates and Compounding
If a rate is quoted as 10 percent compounded semiannually, then what this means is that the
investment actually pays 5 percent every six months. A natural question then arises: Is 5 percent
every six months the same thing as 10 percent per year? It’s easy to see that it is not. If you invest
$1 at 10 percent per year, you will have $1.10 at the end of the year. If you invest at 5 percent
every six months, then you’ll have the future value of $1 at 5 percent for two periods, or:
$1 × 1.05 2 = $1.1025
This is $.0025 more. The reason is very simple. What has occurred is that your account was
credited with $1 × .05 = 5 cents in interest after six months. In the following six months,
you earned 5 percent on that nickel, for an extra .05 × .05 = .0025 = .25 cents.
As our example illustrates, 10 percent compounded semiannually is actually equivalent
to 10.25 percent per year. Put another way, we would be indifferent between 10 percent
compounded semiannually and 10.25 percent compounded annually. Any time we have
compounding during the year, we need to be concerned about what the rate really is.
5.3
coverage online
Excel
Master
EXAMPLE 5.7 Preferred Stock
Preferred stock (or preference stock) is an important example of a perpetuity. When a corporation
sells preferred stock, the buyer is promised a fixed cash dividend every period (usually every quar-
ter) forever. This dividend must be paid before any dividend can be paid to regular stockholders,
hence the term preferred.
Suppose the Fellini Co. wants to sell preferred stock at $100 per share. A very similar issue of
preferred stock already outstanding has a price of $40 per share and offers a dividend of $1 every
quarter. What dividend will Fellini have to offer if the preferred stock is going to sell?
The issue that is already out has a present value of $40 and a cash flow of $1 every quarter
forever. Because this is a perpetuity:
Present value = $40 = $1 × (1/r)
r = .025, or 2.5%
To be competitive, the new Fellini issue also will have to offer 2.5 percent per quarter; so, if the
present value is to be $100, the dividend must be such that:
Present value = $100 = C × (1/.025)
C = $2.5 (per quarter)
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C H A P T E R 5 Discounted Cash Flow Valuation 141
In our example, the 10 percent is called a stated, or quoted, interest rate. Other
names are used as well. The 10.25 percent, which is actually the rate that you will earn, is
called the effective annual rate (EAR). To compare different investments or interest rates,
we will always need to convert to effective rates. Some general procedures for doing this are
discussed next.
Calculating and Comparing Effective Annual Rates
To see why it is important to work only with effective rates, suppose you’ve shopped around
and come up with the following three rates:
Bank A: 15 percent, compounded daily
Bank B: 15.5 percent, compounded quarterly
Bank C: 16 percent, compounded annually
Which of these is the best if you are thinking of opening a savings account? Which of these
is best if they represent loan rates?
To begin, Bank C is offering 16 percent per year. Because there is no compounding
during the year, this is the effective rate. Bank B is actually paying .155/4 = .03875, or 3.875
percent, per quarter. At this rate, an investment of $1 for four quarters would grow to:
$1 × 1.03875 4 = $1.1642
The EAR, therefore, is 16.42 percent. For a saver, this is much better than the 16 percent
rate Bank C is offering; for a borrower, it’s worse.
Bank A is compounding every day. This may seem a little extreme, but it is very com-
mon to calculate interest daily. In this case, the daily interest rate is actually:
.15 / 365 = .000411
This is .0411 percent per day. At this rate, an investment of $1 for 365 periods would grow to:
$1 × 1.000411 365 = $1.1618
The EAR is 16.18 percent. This is not as good as Bank B’s 16.42 percent for a saver and not
as good as Bank C’s 16 percent for a borrower.
This example illustrates two things. First, the highest quoted rate is not necessarily the
best. Second, compounding during the year can lead to a significant difference between the
quoted rate and the effective rate. Remember that the effective rate is what you get or what
you pay.
If you look at our examples, you see that we computed the EARs in three steps. We first
divided the quoted rate by the number of times that the interest is compounded. We then
added 1 to the result and raised it to the power of the number of times the interest is com-
pounded. Finally, we subtracted the 1. If we let m be the number of times the interest is
compounded during the year, these steps can be summarized as:
EAR = (1 + Quoted rate/m)m − 1 [5.5]
Suppose you were offered 12 percent compounded monthly. In this case, the interest is
compounded 12 times a year, so m is 12. You can calculate the effective rate as:
EAR = (1 + Quoted rate/m)m − 1
= (1 + .12/12)12 − 1
= 1.0112 − 1
= 1.126825 − 1
= .126825, or 12.6825%
stated interest rate
The interest rate
expressed in terms of the
interest payment made
each period. Also quoted
interest rate.
quoted interest rate
The interest rate
expressed in terms of the
interest payment made
each period. Also stated
interest rate.
effective annual rate
(EAR)
The interest rate
expressed as if it were
compounded once per
year.
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142 P A R T 3 Valuation of Future Cash Flows
EXAMPLE 5.8 What’s the EAR?
A bank is offering 12 percent compounded quarterly. If you put $100 in an account, how much
will you have at the end of one year? What’s the EAR? How much will you have at the end of
two years?
The bank is effectively offering 12%/4 = 3% every quarter. If you invest $100 for four periods at
3 percent per period, the future value is:
Future value = $100 × 1.034
= $100 × 1.1255
= $112.55
The EAR is 12.55 percent, so at the end of one year you will have $100 × 1.1255 = $112.55.
We can determine what you would have at the end of two years in two different ways. One
way is to recognize that two years is the same as eight quarters. At 3 percent per quarter, after eight
quarters, you would have:
$100 × 1.038 = $100 × 1.2668 = $126.68
Alternatively, we could determine the value after two years by using an EAR of 12.55 percent; so
after two years you would have:
$100 × 1.12552 = $100 × 1.2668 = $126.68
Thus, the two calculations produce the same answer. This illustrates an important point. Any time
we do a present or future value calculation, the rate we use must be an actual or effective rate. In
this case, the actual rate is 3 percent per quarter. The effective annual rate is 12.55 percent. It
doesn’t matter which one we use once we know the EAR.
EXAMPLE 5.9 Quoting a Rate
Now that you know how to convert a quoted rate to an EAR, consider going the other way. As a
lender, you know you want to actually earn 18 percent on a particular loan. You want to quote a rate
that features monthly compounding. What rate do you quote?
In this case, we know that the EAR is 18 percent, and we know that this is the result of monthly
compounding. Let q stand for the quoted rate. We thus have:
EAR = (1 + Quoted rate/m)m − 1
.18 = (1 + q/12)12 − 1
1.18 = (1 + q/12)12
We need to solve this equation for the quoted rate. This calculation is the same as the ones we did
to find an unknown interest rate in Chapter 4:
1.18(1/12) = 1 + q/12
1.18.08333 = 1 + q/12
1.0139 = 1 + q/12
q = .0139 × 12
= .1667, or 16.67%
Therefore, the rate you would quote is 16.67 percent, compounded monthly.
EARs and APRs
Sometimes it’s not altogether clear whether a rate is an effective annual rate or not. A case
in point concerns what is called the annual percentage rate (APR) on a loan. Truth-in-
lending laws in the United States require that lenders disclose an APR on virtually all
annual percentage
rate (APR)
The interest rate charged
per period multiplied by the
number of periods per year.
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C H A P T E R 5 Discounted Cash Flow Valuation 143
consumer loans. This rate must be displayed on a loan document in a prominent and unam-
biguous way.2
Given that an APR must be calculated and displayed, an obvious question arises: Is an
APR an effective annual rate? Put another way: If a bank quotes a car loan at 12 percent
APR, is the consumer actually paying 12 percent interest? Surprisingly, the answer is no.
There is some confusion over this point, which we discuss next.
The confusion over APRs arises because lenders are required by law to compute the
APR in a particular way. By law, the APR is equal to the interest rate per period multiplied
by the number of periods in a year. For example, if a bank is charging 1.2 percent per month
on car loans, then the APR that must be reported is 1.2% × 12 = 14.4%. So, an APR is in
fact a quoted, or stated, rate in the sense we’ve been discussing. For example, an APR of 12
percent on a loan calling for monthly payments is really 1 percent per month. The EAR on
such a loan is thus:
EAR = (1 + APR/12)12 − 1
= 1.0112 − 1
= .126825, or 12.6825%
2By law, lenders are required to report the APR on all consumer loans. We normally compute the APR as the inter-
est rate per period multiplied by the number of periods in a year. According to federal law, the APR is a measure
of the cost of consumer credit expressed as a yearly rate, and it includes interest and certain noninterest charges
and fees. In practice, the APR can be much higher than the interest rate on the loan if the lender charges substan-
tial fees that must be included in the federally mandated APR calculation.
EXAMPLE 5.10 What Rate Are You Paying?
A typical credit card agreement quotes an interest rate of 18 percent APR. Monthly payments are
required. What is the actual interest rate you pay on such a credit card?
Based on our discussion, an APR of 18 percent with monthly payments is really .18/12 = .015, or
1.5 percent, per month. The EAR is thus:
EAR = (1 + .18/12)12 − 1
= 1.01512 − 1
= 1.1956 − 1
= .1956, or 19.56%
This is the rate you actually pay.
The difference between an APR and an EAR probably won’t be all that great (as long
as the rates are relatively low), but it is somewhat ironic that truth-in-lending laws sometimes
require lenders to be untruthful about the actual rate on a loan.
There can be a huge difference between the APR and EAR when interest rates are
large. Consider “payday loans.” Payday loans are short-term loans made to consumers, often
for less than two weeks, and are offered by companies such as Check Into Cash and Na-
tional Payday. The loans work like this: You write a check today that is postdated (i.e., the
date on the check is in the future) and give it to the company. They give you some cash.
When the check date arrives, you either go to the store and pay the cash amount of the
check, or the company cashes it (or else automatically renews the loan).
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144 P A R T 3 Valuation of Future Cash Flows
For example, as of 2018 in one particular state, Check Into Cash allows you to write a
check for $352.94 dated 14 days in the future, for which they give you $300 today. So what
are the APR and EAR of this arrangement? First, we need to find the interest rate, which we
can find by the FV equation as follows:
FV = PV × (1 + r)1
$352.94 = $300 × (1 + r)1
1.1765 = (1 + r)
r = .1765, or 17.65%
That doesn’t seem too bad until you remember this is the interest rate for 14 days! The APR
of the loan is:
APR = .1765 × 365/14
APR = 4.6007, or 460.07%
And the EAR for this loan is:
EAR = (1 + Quoted rate/m)m − 1
EAR = (1 + .1765)365/14 − 1
EAR = 68.20089, or 6,820.09%
Now that’s an interest rate! Just to see what an impact a small difference in fees can make,
in another state, Check Into Cash will make you write a check for $335 for the same amount.
Check for yourself that the APR of this arrangement is 304.17 percent and the EAR is
1,675.97 percent.
EARs, APRs, Financial Calculators, and Spreadsheets
A financial calculator will convert a quoted rate (or an APR) to an EAR and back. Unfortu-
nately, the specific procedures are too different from calculator to calculator for us to illus-
trate in general terms; you’ll have to consult Appendix D or your calculator’s operating
manual. Typically, however, what we have called EAR is labeled “EFF ”(for effective) on a
calculator. More troublesome is the fact that what we have called a quoted rate (or an APR)
is labeled “NOM” (for nominal). Unfortunately, the term nominal rate has come to have a
different meaning that we will see in our next chapter. So, remember that nominal in this
context means quoted or APR.
With a spreadsheet, we can easily do these conversions. To convert a quoted rate (or an
APR) to an effective rate in Excel, for example, use the formula EFFECT(nominal_ rate,
npery), where nominal_rate is the quoted rate or APR and npery is the number of com-
pounding periods per year. Similarly, to convert an EAR to a quoted rate, use NOMI-
NAL(effect_rate, npery), where effect_rate is the EAR.
CONCEPT QUESTIONS
5.3a If an interest rate is given as 12 percent, compounded daily, what do we call this
rate?
5.3b What is an APR? What is an EAR? Are they the same thing?
5.3c In general, what is the relationship between a stated interest rate and an effective
interest rate? Which is more relevant for financial decisions?
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C H A P T E R 5 Discounted Cash Flow Valuation 145
LOAN TYPES AND LOAN AMORTIZATION
Whenever a lender extends a loan, some provision will be made for repayment of the princi-
pal (the original loan amount). A loan might be repaid in equal installments, for example, or
it might be repaid in a single lump sum. Because the way that the principal and interest are
paid is up to the parties involved, there are actually an unlimited number of possibilities.
In this section, we describe a few forms of repayment that come up quite often; more
complicated forms usually can be built up from these. The three basic types of loans are
pure discount loans, interest-only loans, and amortized loans. Working with these loans is a
very straightforward application of the present value principles that we already have
developed.
Pure Discount Loans
The pure discount loan is the simplest form of loan. With such a loan, the borrower receives
money today and repays a single lump sum at some time in the future. A one-year, 10 per-
cent pure discount loan, for example, would require the borrower to repay $1.1 in one year
for every dollar borrowed today.
Because a pure discount loan is so simple, we already know how to value one. Suppose
a borrower was able to repay $25,000 in five years. If we, acting as the lender, wanted a 12
percent interest rate on the loan, how much would we be willing to lend? Put another way,
what value would we assign today to that $25,000 to be repaid in five years? Based on our
work in Chapter 4, we know that the answer is the present value of $25,000 at 12 percent for
five years:
Present value = $25,000/1.125
= $25,000/1.7623
= $14,186
Pure discount loans are very common when the loan term is short, say, a year or less. In re-
cent years, they have become increasingly common for much longer periods.
5.4
coverage online
Excel
Master
EXAMPLE 5.11 Treasury Bills
When the U.S. government borrows money on a short-term basis (a year or less), it does so by sell-
ing what are called Treasury bills, or T-bills for short. A T-bill is a promise by the government to re-
pay a fixed amount at some time in the future, for example, 3 months or 12 months.
Treasury bills are pure discount loans. If a T-bill promises to repay $10,000 in 12 months, and
the market interest rate is 7 percent, how much will the bill sell for in the market?
The going rate is 7 percent, so the T-bill will sell for the present value of $10,000 to be paid in
one year at 7 percent, or:
Present value = $10,000/1.07 = $9,345.79
Interest-Only Loans
A second type of loan has a repayment plan that calls for the borrower to pay interest each
period and to repay the entire principal (the original loan amount) at some point in the fu-
ture. Such loans are called interest-only loans. Notice that if there is just one period, a pure
discount loan and an interest-only loan are the same thing.
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146 P A R T 3 Valuation of Future Cash Flows
For example, with a three-year, 10 percent, interest-only loan of $1,000, the borrower
would pay $1,000 × .10 = $100 in interest at the end of the first and second years. At the
end of the third year, the borrower would return the $1,000 along with another $100 in in-
terest for that year. Similarly, a 50-year interest-only loan would call for the borrower to pay
interest every year for the next 50 years and then repay the principal. In the extreme, the
borrower pays the interest every period forever and never repays any principal. As we dis-
cussed earlier in the chapter, the result is a perpetuity.
Most corporate bonds have the general form of an interest-only loan. Because we will
be considering bonds in some detail in the next chapter, we defer a further discussion of
them for now.
Amortized Loans
With a pure discount or interest-only loan, the principal is repaid all at once. An alternative
is an amortized loan, with which the lender may require the borrower to repay parts of the
loan amount over time. The process of paying off a loan by making regular principal reduc-
tions is called amortizing the loan.
A simple way of amortizing a loan is to have the borrower pay the interest each period
plus some fixed amount. This approach is common with medium-term business loans. Sup-
pose a business takes out a $5,000, five-year loan at 9 percent. The loan agreement calls for
the borrower to pay the interest on the loan balance each year and to reduce the loan bal-
ance each year by $1,000. Because the loan amount declines by $1,000 each year, it is fully
paid in five years.
In the case we are considering, notice that the total payment will decline each year. The
reason is that the loan balance goes down, resulting in a lower interest charge each year,
while the $1,000 principal reduction is constant. For example, the interest in the first year
will be $5,000 × .09 = $450. The total payment will be $1,000 + 450 = $1,450. In the
second year, the loan balance is $4,000, so the interest is $4,000 × .09 = $360, and the to-
tal payment is $1,360. We can calculate the total payment in each of the remaining years by
preparing an amortization schedule as follows:
Beginning Total Interest Principal Ending
Year Balance Payment Paid Paid Balance
1 $5,000 $1,450 $ 450 $1,000 $4,000
2 4,000 1,360 360 1,000 3,000
3 3,000 1,270 270 1,000 2,000
4 2,000 1,180 180 1,000 1,000
5 1,000 1,090 90 1,000 0
Totals $6,350 $1,350 $5,000
Notice that, in each year, the interest paid is given by the beginning balance multiplied by
the interest rate. Also, notice that the beginning balance is given by the ending balance from
the previous year.
Probably the most common way of amortizing a loan is to have the borrower make a
single, fixed payment every period. Almost all consumer loans (such as car loans) and mort-
gages work this way. Suppose our five-year, 9 percent, $5,000 loan was amortized this way.
How would the amortization schedule look?
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C H A P T E R 5 Discounted Cash Flow Valuation 147
We first need to determine the payment. From our discussion earlier in the chapter, we
know that this loan’s cash flows are in the form of an ordinary annuity. In this case, we can
solve for the payment as follows:
$5,000 = C × (1 − 1/1.095)/.09
= C × (1 − .6499)/.09
This gives us:
C = $5,000/3.8897
= $1,285.46
The borrower will, therefore, make five equal payments of $1,285.46. Will this pay off the
loan? We check by filling in an amortization schedule.
In our previous example, we knew the principal reduction each year. We then calcu-
lated the interest owed to get the total payment. In this example, we know the total payment.
We thus calculate the interest and then subtract it from the total payment to get the princi-
pal portion in each payment.
In the first year, the interest is $450, as we calculated before. Because the total payment
is $1,285.46, the principal paid in the first year must be:
Principal paid = $1,285.46 − 450 = $835.46
The ending loan balance is thus:
Ending balance = $5,000 − 835.46 = $4,164.54
The interest in the second year is $4,164.54 × .09 = $374.81, and the loan balance declines
by $1,285.46 − 374.81 = $910.65. We can summarize all of the relevant calculations in the
following schedule:
Beginning Total Interest Principal Ending
Year Balance Payment Paid Paid Balance
1 $5,000.00 $1,285.46 $ <<< 450.00 $ 835.46 $ 4,164.54
2 4,164.54 1,285.46 374.81 910.65 3,253.88
3 3,253.88 1,285.46 292.85 992.61 2,261.27
4 2,261.27 1,285.46 203.51 1,081.95 1,179.32
5 1,179.32 1,285.46 << 106.14 1,179.32 .00
Totals $6,427.31 $1,427.31 $5,000.00
Because the loan balance declines to zero, the five equal payments do pay off the loan. No-
tice that the interest paid declines each period. This isn’t surprising because the loan bal-
ance is going down. Given that the total payment is fixed, the principal paid must be rising
each period.
If you compare the two loan amortizations in this section, you see that the total interest
is greater for the equal total payment case, $1,427.31 versus $1,350. The reason for this is
that the loan is repaid more slowly early on, so the interest is somewhat higher. This doesn’t
mean that one loan is better than the other; it means that one is effectively paid off faster
than the other. For example, the principal reduction in the first year is $835.46 in the equal
total payment case compared to $1,000 in the first case. Many websites offer loan amortiza-
tion schedules. See our nearby Work the Web box for an example.
You can find a good loan
amortization schedule
online at www.myamor
tizationchart.com.
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148 P A R T 3 Valuation of Future Cash Flows
QUESTIONS
1. Suppose you take out a 30-year mortgage for $250,000 at an interest rate of 4.8 per-
cent. Use this website to construct an amortization table for the loan. What are the in-
terest payment and principal amounts in the 110th payment? How much in total interest
will you pay over the life of the loan?
2. You take out a 30-year mortgage for $275,000 at an interest rate of 5.1 percent. How
much will you pay in interest over the life of this loan? Now assume you pay an extra
$100 per month on this loan. How much is your total interest now? How much sooner
will the mortgage be paid off?
As you can see, the monthly payment will be $349.75. The first payment will consist of
$126.48 in principal and $223.27 in interest. Over the life of the loan you will pay a total of
$23,554.54 in interest.
W R K T H E W E B
Preparing an amortization table is one of the more tedious time value of money applications. Us-ing a spreadsheet makes it relatively easy, but there are also websites available that will prepare
an amortization table very quickly. One such site is www.bankrate.com. The website has a mortgage
calculator for home loans, but the same calculations apply to most other types of loans such as car
loans and student loans. According to one source, college graduates in 2017 left school with an av-
erage of $39,400 in student loans. Suppose you graduate with the average student loan and decide
to pay the loan off over the next 15 years at 6.8 percent, the maximum interest rate for unsubsidized
Stafford loans. What are your monthly payments? Using the calculator, for the first year, we get:
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C H A P T E R 5 Discounted Cash Flow Valuation 149
We close out this discussion by noting that one type of loan may be particularly impor-
tant to you. Student loans are an important source of financing for many college students,
helping to cover the cost of tuition, books, new cars, condominiums, and many other things.
Sometimes students do not seem to fully realize that such loans have a serious drawback:
They must be repaid. See our nearby Finance Matters box for a discussion.
CONCEPT QUESTIONS
5.4a What is a pure discount loan?
5.4b What does it mean to amortize a loan?
LOAN AMORTIZATION USING A SPREADSHEET
Loan amortization is a very common spreadsheet application. To illustrate, we will set up the problem
that we have just examined, a five-year, $5,000, 9 percent loan with constant payments. Our spread-
sheet looks like this:
SPREADSHEET
STRATEGIES
A B C D E F G H
1
2 Using a spreadsheet to amortize a loan
3
4 Loan amount: $5,000
5 Interest rate: .09
6 Loan term: 5
7 Loan payment: $1,285.46
8 Note: payment is calculated using PMT(rate, nper, -pv, fv).
9 Amortization table:
10
11 Year Beginning Total Interest Principal Ending
12 Balance Payment Paid Paid Balance
13 1 $5,000.00 $1,285.46 $450.00 $835.46 $4,164.54
14 2 4,164.54 1,285.46 374.81 910.65 3,253.88
15 3 3,253.88 1,285.46 292.85 992.61 2,261.27
16 4 2,261.27 1,285.46 203.51 1,081.95 1,179.32
17 5 1,179.32 1,285.46 106.14 1,179.32 .00
18 Totals $6,427.31 $1,427.31 $5,000.00
19
20 Formulas in the amortization table:
21
22 Year Beginning Total Interest Principal Ending
23 Balance Payment Paid Paid Balance
24 1 =+D4 =$D$7 =+$D$5*C13 =+D13-E13 =+C13-F13
25 2 =+G13 =$D$7 =+$D$5*C14 =+D14-E14 =+C14-F14
26 3 =+G14 =$D$7 =+$D$5*C15 =+D15-E15 =+C15-F15
27 4 =+G15 =$D$7 =+$D$5*C16 =+D16-E16 =+C16-F16
28 5 =+G16 =$D$7 =+$D$5*C17 =+D17-E17 =+C17-F17
29
30 Note: totals in the amortization table are calculated using the SUM formula.
31
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An Unwelcome Christmas Present
If you are reading this, we can assume that you are a col-lege student. While you will receive an education in col-
lege, and studies show that college graduates earn higher
salaries on average than nongraduates, you might receive
an unwelcome Christmas present when you graduate: stu-
dent loan payments. About one-half of all college students
graduate with student loans, and more than 90 percent of
the loans are Stafford loans. Stafford loans are available
through lenders such as Sallie Mae, online lenders, or, in
some cases, your college. Stafford loans must be paid off in
10 years, but there is a six-month grace period from the time
you graduate until the first payment must be made. The
maximum interest rate on unsubsidized Stafford loans made
after July 1, 2006, is 6.8 percent.
If you have student loans, you went through an intro-
ductory program. In case you forgot, here are several of the
repayment options. First, you can make equal monthly pay-
ments like most other loans. A second option is to pay only
the interest on the loan for up to four years, and then begin
making principal and interest payments. This means your
payments at the end of the loan are higher than the equal
payment option. A third option is to make payments based
on a percentage of your salary. A fourth option is a gradu-
ated payment option that increases your monthly payments
on a predetermined schedule. Finally, you can consolidate
your loans one time. If the loan balance is high enough, you
may be able to extend your payment for up to 30 years.
While we do not recommend it, some students rack up
an extraordinary amount of debt. For example, the son of
former Federal Reserve Chairman Ben Bernanke was re-
ported to be on track to graduate medical school with more
than $400,000 in student loans. That’s a lot, but it is esti-
mated that there are 101 individuals in the U.S. with student
loans greater than $1 million!
So how do student loans work in practice? A recent
graduate from the University of Maryland with a master’s
degree in creative writing graduated with $40,000 in stu-
dent loans. Her loan payments were $442 a month, a pay-
ment that was difficult to make on her salary as a fund-raiser.
She considered the percentage of salary option, which
would have lowered her monthly payments to about $200
per month. However, she realized that this was only putting
off the inevitable, so she took a second job to make up the
difference.
A dentist from Utah, who has more than $1 million in
student loans, is using a government program to help out.
He has agreed to pay 10 percent of his discretionary income
each month for the next 25 years. Without the government
program, his monthly payments would be about $10,500 per
month. In 25 years, he will have repaid about $1.6 million to-
ward his loan, but because his current payments don’t cover
the interest payments, the loan balance will be about $2 mil-
lion. This will be forgiven by the U.S. government, but unfor-
tunately will result in a tax bill of about $700,000.
A Chicago couple is using a third solution. Both the
husband and wife are doctors. The wife is out of her resi-
dency and employed full time, while the husband is finishing
his last year of residency. What is most unusual about this
couple is the amount of student loan debt. The wife’s stu-
dent loan balance is $234,000, the husband’s student loan
balance is $310,000, and the couple has a $156,000 mort-
gage! The wife’s student loan repayments al-
ready have started and amount to $1,750 per month. So how
is the couple handling this? They are paying a total of
$2,250 per month toward the wife’s student loans. This will
reduce the repayment period from 22 years to 13 years. The
couple also is paying an additional $100 per month on their
$1,500 mortgage payment. Fortunately, when the husband’s
residency ends, he expects his salary to triple. The couple
will need it. His loan payments will be $2,349 per month.
And you thought your student loan was high! Maybe MD
stands for “mucho debt”!
FINANCE MATTERS
SUMMARY AND CONCLUSIONS
This chapter rounds out your understanding of fundamental concepts related to the time
value of money and discounted cash flow valuation. Several important topics were covered,
including:
1. There are two ways of calculating present and future values when there are multiple
cash flows. Both approaches are straightforward extensions of our earlier analysis of
single cash flows.
150
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C H A P T E R 5 Discounted Cash Flow Valuation 151
2. A series of constant cash flows that arrive or are paid at the end of each period is
called an ordinary annuity, and we described some useful shortcuts for determining
the present and future values of annuities.
3. Interest rates can be quoted in a variety of ways. For financial decisions, it is
important that any rates being compared first be converted to effective rates. The
relationship between a quoted rate, such as an annual percentage rate, or APR, and an
effective annual rate, or EAR, is given by:
EAR = (1 + Quoted rate/m ) m − 1
where m is the number of times during the year the money is compounded, or, equiva-
lently, the number of payments during the year.
4. Many loans are annuities. The process of paying off a loan gradually is called amortizing
the loan, and we discussed how amortization schedules are prepared and interpreted.
POP QUIZ!
Can you answer the following questions? If your class is using Connect, log on to
SmartBook to see if you know the answers to these and other questions, check out
the study tools, and find out what topics require additional practice!
Section 5.1 In multiple cash flow calculations, when is it assumed that cash flows
occur?
Section 5.2 What is the present value of an ordinary annuity that pays $100 per
year for three years if the discount rate is 6 percent per year?
Section 5.3 You agree to repay $1,200 in two weeks for a $1,000 payday loan.
What is your EAR assuming that there are 52 weeks in a year?
Section 5.4 What is the simplest form of loan?
CHAPTER REVIEW AND SELF-TEST PROBLEMS
5.1 Present Values with Multiple Cash Flows A first-round draft choice quarterback
has been signed to a three-year, $10 million contract. The details provide for an
immediate cash bonus of $1 million. The player is to receive $2 million in salary at
the end of the first year, $3 million the next, and $4 million at the end of the last
year. Assuming a 10 percent discount rate, is this package worth $10 million? How
much is it worth? (See Problem 1.)
5.2 Future Value with Multiple Cash Flows You plan to make a series of deposits in an
interest-bearing account. You will deposit $1,000 today, $2,000 in two years, and
$8,000 in five years. If you withdraw $3,000 in three years and $5,000 in seven years,
how much will you have after eight years if the interest rate is 9 percent? What is the
present value of these cash flows? (See Problem 3.)
5.3 Annuity Present Value You are looking into an investment that will pay you
$12,000 per year for the next 10 years. If you require a 15 percent return, what is the
most you would pay for this investment? (See Problem 2.)
5.4 APR versus EAR The going rate on student loans is quoted as 9 percent APR. The
terms of the loan call for monthly payments. What is the effective annual rate, or
EAR, on such a student loan? (See Problem 19.)
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152 P A R T 3 Valuation of Future Cash Flows
5.5 It’s the Principal That Matters Suppose you borrow $10,000. You are going to
repay the loan by making equal annual payments for five years. The interest rate is
14 percent per year. Prepare an amortization schedule for the loan. How much
interest will you pay over the life of the loan? (See Problem 55.)
5.6 Just a Little Bit Each Month You’ve recently finished your MBA at the Darnit
School. Naturally, you must purchase a new BMW immediately. The car costs about
$42,000. The bank quotes an interest rate of 15 percent APR for a 72-month loan
with a 10 percent down payment. What will your monthly payment be? What is the
effective interest rate on the loan? (See Problem 20.)
■ Answers to Chapter Review and Self-Test Problems
5.1 Obviously, the package is not worth $10 million because the payments are spread
out over three years. The bonus is paid today, so it’s worth $1 million. The present
values for the three subsequent salary payments are:
$2/1.1 + $3/1.12 + $4/1.13 = $2/1.1 + $3/1.21 + $4/1.331
= $7.3028
The package is worth a total of $8.3028 million.
5.2 We will calculate the future value for each of the cash flows separately and then add
the results. Notice that we treat the withdrawals as negative cash flows:
$1,000 × 1.098 = $1,000 × 1.9926 = $ 1,992.56
$2,000 × 1.096 = $2,000 × 1.6771 = 3,354.20
−$3,000 × 1.095 = −$3,000 × 1.5386 = −4,615.87
$8,000 × 1.093 = $8,000 × 1.2950 = 10,360.23
−$5,000 × 1.091 = −$5,000 × 1.0900 = −5,450.00
Total future value = $ 5,641.12
To calculate the present value, we could discount each cash flow back to the present
or we could discount back a single year at a time. However, because we already know
that the future value in eight years is $5,641.12, the easy way to get the PV is to
discount this amount back eight years:
Present value = $5,641.12/1.098
= $5,641.12/1.9926
= $2,831.09
For practice, you can verify that this is what you get if you discount each cash flow
back separately.
5.3 The most you would be willing to pay is the present value of $12,000 per year for 10
years at a 15 percent discount rate. The cash flows here are in ordinary annuity
form, so the relevant present value factor is:
Annuity present value factor = [1 − (1/1.1510)]/.15
= (1 − .2472)/.15
= 5.0188
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C H A P T E R 5 Discounted Cash Flow Valuation 153
The present value of the 10 cash flows is thus:
Present value = $12,000 × 5.0188
= $60,225
This is the most you would pay.
5.4 A rate of 9 percent with monthly payments is actually 9%/12 = .75% per month.
The EAR is thus:
EAR = (1 + .09/12)12 − 1 = .0938, or 9.38%
5.5 We first need to calculate the annual payment. With a present value of $10,000, an
interest rate of 14 percent, and a term of five years, the payment can be determined
from:
$10,000 = Payment × (1 − 1/1.145)/.14
= Payment × 3.4331
Therefore, the payment is $10,000/3.4331 = $2,912.84 (actually, it’s $2,912.8355;
this will create some small rounding errors in the accompanying schedule). We can
now prepare the amortization schedule as follows:
Beginning Total Interest Principal Ending
Year Balance Payment Paid Paid Balance
1 $10,000.00 $ 2,912.84 $1,400.00 $ 1,512.84 $8,487.16
2 8,487.16 2,912.84 1,188.20 1,724.63 6,762.53
3 6,762.53 2,912.84 946.75 1,966.08 4,796.45
4 4,796.45 2,912.84 671.50 2,241.33 2,555.12
5 2,555.12 2,912.84 357.72 2,555.12 .00
Totals $14,564.18 $4,564.18 $10,000.00
5.6 The cash flows on the car loan are in annuity form, so we only need to find the
payment. The interest rate is 15%/12 = 1.25% per month, and there are 72 months.
The first thing we need is the annuity factor for 72 periods at 1.25 percent per period:
Annuity present value factor = (1 − Present value factor)/r
= [1 − (1/1.012572)]/.0125
= [1 − (1/2.4459)]/.0125
= (1 − .4088)/.0125
= 47.2925
The present value is the amount we finance. With a 10 percent down payment, we
will be borrowing 90 percent of $42,000, or $37,800.
So, to find the payment, we need to solve for C in the following:
$37,800
=
C × Annuity present value factor
=
C × 47.2925
Rearranging things a bit, we have:
C
=
$37,800 × (1 / 47.2925 )
= $37,800 × .02115
=
$799.28
Your payment is just under $800 per month.
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154 P A R T 3 Valuation of Future Cash Flows
The actual interest rate on this loan is 1.25 percent per month. Based on our
work in the chapter, we can calculate the effective annual rate as:
EAR = 1.0125 12 − 1 = .1608, or 16.08%
The effective rate is about one point higher than the quoted rate.
CRITICAL THINKING AND CONCEPTS REVIEW
5.1 Annuity Period As you increase the length of time involved, what happens
to the present value of an annuity? What happens to the future value?
5.2 Interest Rates What happens to the future value of an annuity if you
increase the rate, r ? What happens to the present value?
^a 5.3 Annuity Present Values Tri-State Megabucks Lottery advertises a $10
million grand prize. The winner receives $500,000 today and 19 annual
payments of $500,000. A lump-sum option of $5 million payable
immediately is also available. Is this deceptive advertising?
5.4 Annuity Present Values Suppose you won the Tri-State Megabucks Lottery
in the previous question. What factors should you take into account in
deciding whether you should take the annuity option or the lump-sum option?
5.5 Present Value If you were an athlete negotiating a contract, would you
want a big signing bonus payable immediately and smaller payments in the
future, or vice versa? How about looking at it from the team’s perspective?
5.6 Present Value Suppose two athletes sign 10-year contracts for $80 million. In
one case, we’re told that the $80 million will be paid in 10 equal installments. In
the other case, we’re told that the $80 million will be paid in 10 installments,
but the installments will increase by 5 percent per year. Who got the better deal?
5.7 APR and EAR Should lending laws be changed to require lenders to report
EARs instead of APRs? Why or why not?
5.8 Time Value On subsidized Stafford loans, a common source of financial
aid for college students, interest does not begin to accrue until repayment
begins. Who receives a bigger subsidy, a freshman or a senior? Explain.
5.9 Time Value In words, how would you go about valuing the subsidy on a
subsidized Stafford loan?
5.10 Time Value Eligibility for a subsidized Stafford loan is based on current
financial need. However, both subsidized and unsubsidized Stafford loans
are repaid out of future income. Given this, do you see a possible objection
to having two types?
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QUESTIONS AND PROBLEMS
Select problems are available in McGraw-Hill Connect. Please see the pack-
aging options section of the Preface for more information.
BASIC (Questions 1–28)
1. Present Value and Multiple Cash Flows Fox Co. has identified an
investment project with the following cash flows. If the discount rate is 10
percent, what is the present value of these cash flows? What is the present
value at 18 percent? At 24 percent?
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Year Cash Flow
1 $ 570
2 430
3 840
4 1,230
2. Present Value and Multiple Cash Flows Investment X offers to pay
you $3,100 per year for 9 years, whereas Investment Y offers to pay you
$4,800 per year for 5 years. Which of these cash flow streams has the
higher present value if the discount rate is 6 percent? If the discount rate
is 22 percent?
3. Future Value and Multiple Cash Flows Wells, Inc., has identified an
investment project with the following cash flows. If the discount rate is 8
percent, what is the future value of these cash flows in Year 4? What is the
future value at an interest rate of 11 percent? At 24 percent?
Year Cash Flow
1 $ 865
2 1,040
3 1,290
4 1,385
4. Calculating Annuity Present Values An investment offers $6,125 per year
for 15 years, with the first payment occurring one year from now. If the
required return is 8 percent, what is the value of the investment? What
would the value be if the payments occurred for 40 years? For 75 years?
Forever?
5. Calculating Annuity Cash Flows For each of the following annuities,
calculate the annual cash flow.
Present Value Years Interest Rate
$ 15,000 6 11%
21,400 8 7
145,300 15 8
325,000 20 6
6. Calculating Annuity Values For each of the following annuities, calculate
the present value.
Annuity Payment Years Interest Rate
$ 1,560 7 5%
1,280 9 10
20,000 18 8
53,200 28 14
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7. Calculating Annuity Cash Flows For each of the following annuities,
calculate the annuity payment.
Future Value Years Interest Rate
$ 21,800 8 5%
1,500,000 40 7
520,000 25 8
98,700 13 4
8. Calculating Annuity Values For each of the following annuities, calculate
the future value.
Annual Payment (Years Interest Rate
$2,100 10 8%
6,500 40 9
1,100 9 6
5,000 30 10
9. Calculating Annuity Values If you deposit $5,000 at the end of each year
for the next 20 years into an account paying 10.1 percent interest, how much
money will you have in the account in 20 years? How much will you have if
you make deposits for 40 years?
10. Calculating Perpetuity Values Larry’s Life Insurance Co. is trying to sell
you an investment policy that will pay you and your heirs $25,000 per year
forever. If the required return on this investment is 4 percent, how much will
you pay for the policy?
11. Calculating Perpetuity Values In the previous problem, suppose Larry’s
told you the policy costs $645,000. At what interest rate would this be a
fair deal?
12. Calculating EAR Find the EAR in each of the following cases.
( Stated Rate (APR) Number of Times Compounded Effective Rate (EAR)
10.2% Quarterly
18.0 Monthly
13.5 Daily
9.5 Semiannually
13. Calculating APR Find the APR, or stated rate, in each of the following
cases.
( Stated Rate (APR) Number of Times Compounded Effective Rate (EAR)
Semiannually 15.3%
Monthly 8.7
Weekly 9.4
Daily 14.9
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C H A P T E R 5 Discounted Cash Flow Valuation 157
14. Calculating EAR First National Bank charges 14.3 percent compounded
monthly on its business loans. First United Bank charges 14.7 percent
compounded semiannually. As a potential borrower, which bank would you
go to for a new loan?
15. Calculating APR Vandermark Credit Corp. wants to earn an effective
annual return on its consumer loans of 13.9 percent per year. The bank uses
daily compounding on its loans. What interest rate is the bank required by
law to report to potential borrowers? Explain why this rate is misleading to
an uninformed borrower.
16. Calculating Future Values What is the future value of $1,150 in 16 years
assuming an interest rate of 7.9 percent compounded semiannually?
17. Calculating Future Values Streamsong Credit Bank is offering
4.7 percent compounded daily on its savings accounts. If you deposit
$4,750 today, how much will you have in the account in 5 years? In
10 years? In 20 years?
18. Calculating Present Values An investment will pay you $100,000 in
9 years. If the appropriate discount rate is 5.5 percent compounded daily,
what is the present value?
19. EAR versus APR Ricky Ripov’s Pawn Shop charges an interest rate of
12.1 percent per month on loans to its customers. Like all lenders, Ricky
must report an APR to consumers. What rate should the shop report? What
is the effective annual rate?
20. Calculating Loan Payments You want to buy a new sports coupe for
$78,500, and the finance office at the dealership has quoted you a
loan with an APR of 4.9 percent for 60 months to buy the car. What will
your monthly payments be? What is the effective annual rate on this
loan?
21. Calculating Number of Periods One of your customers is delinquent on
his accounts payable balance. You’ve mutually agreed to a repayment
schedule of $400 per month. You will charge 1.4 percent per month interest
on the overdue balance. If the current balance is $17,320, how long will it
take for the account to be paid off?
22. Calculating EAR Friendly’s Quick Loans, Inc., offers you “Five for four, or
I knock on your door.” This means you get $4 today and repay $5 when you
get your paycheck in one week (or else). What’s the effective annual return
Friendly’s earns on this lending business? If you were brave enough to ask,
what APR would Friendly’s say you were paying?
23. Valuing Perpetuities Maybepay Life Insurance Co. is selling a perpetual
annuity contract that pays $2,750 monthly. The contract currently sells for
$400,000. What is the monthly return on this investment vehicle? What is
the APR? The effective annual return?
24. Calculating Annuity Future Values You are to make monthly deposits of
$500 into a retirement account that earns an APR of 9.5 percent
compounded monthly. If your first deposit will be made one month from
now, how large will your retirement account be in 35 years?
25. Calculating Annuity Future Values In the previous problem, suppose you
make $6,000 annual deposits into the same retirement account. How large
will your account balance be in 35 years?
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26. Calculating Annuity Present Values Beginning three months from now,
you want to be able to withdraw $2,500 each quarter from your bank
account to cover college expenses over the next 4 years. If the account pays
.47 percent interest per quarter, how much do you need to have in your bank
account today to meet your expense needs over the next 4 years?
27. Discounted Cash Flow Analysis If the appropriate discount rate for the
following cash flows is 8.15 percent, what is the present value of the cash
flows?
Year Cash Flow
1 $1,200
2 1,100
3 800
4 600
28. Discounted Cash Flow Analysis If the appropriate discount rate for the
following cash flows is 4.78 percent per year, what is the present value of the
cash flows?
Year Cash Flow
1 $1,400
2 1,900
3 3,400
4 4,300
INTERMEDIATE (Questions 29–56)
29. Simple Interest versus Compound Interest First Simple Bank pays
6.3 percent simple interest on its investment accounts. If First Complex
Bank pays interest on its accounts compounded annually, what rate should
the bank set if it wants to match First Simple Bank over an investment
horizon of 10 years?
30. Calculating Annuities Due You want to buy a new sports car from Muscle
Motors for $68,500. The contract is in the form of a 60-month annuity due
at an APR of 4.5 percent. What will your monthly payment be?
31. Calculating Interest Expense You receive a credit card application from
Shady Banks Savings and Loan offering an introductory rate of .9 percent
per year, compounded monthly for the first six months, increasing thereafter
to 18.5 percent compounded monthly. Assuming you transfer the $10,000
balance from your existing credit card and make no subsequent payments,
how much interest will you owe at the end of the first year?
32. Calculating the Number of Periods You are saving to buy a $255,000
house. There are two competing banks in your area, both offering
certificates of deposit yielding 4.8 percent. How long will it take your initial
$95,000 investment to reach the desired level at First Bank, which pays
simple interest? How long at Second Bank, which compounds interest
monthly?
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33. Calculating Future Values You have an investment that will pay you
1.38 percent per month. How much will you have per dollar invested in
one year? In two years?
34. Calculating Annuity Interest Rates Although you may know William
Shakespeare from his classic literature, what is not well-known is that he was
an astute investor. In 1604, when he was 40 and writing King Lear,
Shakespeare grew worried about his eventual retirement. Afraid that he
would become like King Lear in his retirement and beg hospitality from his
children, he purchased grain “tithes,” or shares in farm output, for 440
pounds. The tithes paid him 60 pounds per year for 31 years. Even though
he died at the age of 52, his children received the remaining payments. What
interest rate did the Bard of Avon receive on this investment?
35. Comparing Cash Flow Streams You’ve just joined the investment banking
firm of Dewey, Cheatum, and Howe. They’ve offered you two different salary
arrangements. You can have $6,100 per month for the next two years, or you
can have $5,100 per month for the next two years, along with a $25,000
signing bonus today. If the interest rate is 7 percent compounded monthly,
which do you prefer?
36. Calculating Present Value of Annuities Peter Lynchpin wants to sell you
an investment contract that pays equal $22,500 amounts at the end of each
year for the next 20 years. If you require an effective annual return of 8
percent on this investment, how much will you pay for the contract today?
37. Calculating Rates of Return You’re trying to choose between two different
investments, both of which have up-front costs of $30,000. Investment G
returns $65,000 in six years. Investment H returns $98,000 in nine years.
Which of these investments has the higher return?
38. Present Value and Interest Rates What is the relationship between the
value of an annuity and the level of interest rates? Suppose you just bought a
10-year annuity of $5,200 per year at the current interest rate of 10 percent
per year. What happens to the value of your investment if interest rates
suddenly drop to 5 percent? What if interest rates suddenly rise to 15
percent?
39. Calculating the Number of Payments You’re prepared to make monthly
payments of $250, beginning at the end of this month, into an account that
pays 8 percent interest compounded monthly. How many payments will you
have made when your account balance reaches $50,000?
40. Calculating Annuity Present Values You want to borrow $75,000 from
your local bank to buy a new sailboat. You can afford to make monthly
payments of $1,475, but no more. Assuming monthly compounding, what is
the highest rate you can afford on a 60-month APR loan?
41. Calculating Present Values In March 2018, the Buffalo Bills signed Star
Lotulelei to a contract reportedly worth $50 million. Lotulelei’s salary
(including bonuses) was to be paid as $17.1 million in 2018, $8.9 million in
2019, $7.5 million in 2020, and $8.25 million in 2021 and 2022. If the
appropriate interest rate is 11 percent, what kind of deal did the defensive
tackle sack? Assume all payments are paid at the end of each year.
42. Calculating Present Values The contract signed in February 2018 by
Jimmy Garoppolo that we discussed at the beginning of the chapter was
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160 P A R T 3 Valuation of Future Cash Flows
actually paid as a $35 million signing bonus to be paid immediately and a
$7.6 million salary for 2018. The remaining salary was $18.6 million in 2019,
$25.2 million in 2020, $25.5 million in 2021, and $25.6 million in 2022. If
the appropriate interest rate is 11 percent, what kind of deal did the
quarterback toss? Assume all payments other than the first $35 million are
paid at the end of each year.
43. EAR versus APR You have just purchased a new warehouse. To finance
the purchase, you’ve arranged for a 30-year mortgage loan for 80 percent of
the $3,500,000 purchase price. The monthly payment on this loan will be
$15,100. What is the APR on this loan? The EAR?
44. Annuity Values You are planning your retirement in 10 years. You
currently have $50,000 in a bond account and $250,000 in a stock account.
You plan to add $9,000 per year at the end of each of the next 10 years to
your bond account. The stock account will earn a return of 10.5 percent and
the bond account will earn a return of 7 percent. When you retire, you plan
to withdraw an equal amount for each of the next 25 years at the end of each
year and have nothing left. Additionally, when you retire you will transfer
your money to an account that earns 6.25 percent. How much can you
withdraw each year?
45. Calculating Annuities Due Interest Rates You have arranged for a loan on
your new car that will require the first payment today. The loan is for
$28,500, and the monthly payments are $525. If the loan will be paid off
over the next 60 months, what is the APR of the loan?
46. Calculating Annuities Due Suppose you are going to receive $7,800 per
year for five years. The appropriate discount rate is 7.5 percent.
a. What is the present value of the payments if they are in the form of an
ordinary annuity? What is the present value if the payments are an
annuity due?
b. Suppose you plan to invest the payments for five years. What is the
future value if the payments are an ordinary annuity? What if the
payments are an annuity due?
c. Which has the higher present value, the ordinary annuity or annuity
due? Which has the higher future value? Will this always be true?
47. Annuity and Perpetuity Values Mary is going to receive a 30-year annuity of
$9,500. Nancy is going to receive a perpetuity of $9,500. If the appropriate
discount rate is 5.4 percent, how much more is Nancy’s cash flow worth?
48. Calculating Present Values A 6-year annuity of twelve $7,375 semiannual
payments will begin 9 years from now, with the first payment coming
9.5 years from now. If the discount rate is 9 percent compounded
semiannually, what is the value of this annuity five years from now? What is
the value three years from now? What is the current value of the annuity?
49. Present Value and Multiple Cash Flows What is the present value of
$2,625 per year, at a discount rate of 6.9 percent, if the first payment is re ceived
six years from now and the last payment is received 20 years from now?
50. Variable Interest Rates A 10-year annuity pays $1,725 per month, and
payments are made at the end of each month. If the interest rate is
9 percent compounded monthly for the first four years, and 7 percent
compounded monthly thereafter, what is the value of the annuity today?
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51. Comparing Cash Flow Streams You have your choice of two investment
accounts. Investment A is a 10-year annuity that features end-of-month
$1,525 payments and has an interest rate of 7 percent compounded monthly.
Investment B is an annually compounded lump-sum investment with an
interest rate of 9 percent, also good for 10 years. How much money would
you need to invest in B today for it to be worth as much as Investment
A 10 years from now?
52. Calculating Present Value of a Perpetuity Given an interest rate of
6.35 percent per year, what is the value at Year 7 of a perpetual stream of
$7,000 payments that begin at Year 20?
53. Calculating EAR A local finance company quotes an interest rate of
16.7 percent on one-year loans. So, if you borrow $25,000, the interest for
the year will be $4,175. Because you must repay a total of $29,175 in one
year, the finance company requires you to pay $29,175/12, or $2,431.25 per
month over the next 12 months. Is the interest rate on this loan 16.7
percent? What rate would legally have to be quoted? What is the effective
annual rate?
54. Calculating Future Values If today is Year 0, what is the future value of
the following cash flows five years from now? What is the future value
10 years from now? Assume an interest rate of 6.1 percent per year.
Year Cash Flow
2 $15,000
3 24,000
5 33,000
55. Amortization with Equal Payments Prepare an amortization schedule for
a three-year loan of $57,000. The interest rate is 8 percent per year, and the
loan calls for equal annual payments. How much interest is paid in the third
year? How much total interest is paid over the life of the loan?
56. Amortization with Equal Principal Payments Rework Problem 55
assuming that the loan agreement calls for a principal reduction of $19,000
every year instead of equal annual payments.
CHALLENGE (Questions 57–60)
57. Discount Interest Loans This question illustrates what is known as
discount interest. Imagine you are discussing a loan with a somewhat
unscrupulous lender. You want to borrow $18,000 for one year. The interest
rate is 14.6 percent. You and the lender agree that the interest on the loan
will be .146 × $18,000 = $2,628. So, the lender deducts this interest amount
from the loan up front and gives you $15,372. In this case, we say that the
discount is $2,628. What’s wrong here?
58. Calculating Annuity Values You are serving on a jury. A plaintiff is suing
the city for injuries sustained after a freak street-sweeper accident. In the
trial, doctors testified that it will be five years before the plaintiff is able to
return to work. The jury already has decided in favor of the plaintiff. You are
the foreperson of the jury and propose that the jury give the plaintiff an
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award to cover the following: (a) The present value of two years’ back pay.
The plaintiff’s annual salary for the last two years would have been $44,000
and $47,000, respectively. (b) The present value of five years’ future salary.
You assume the salary will be $51,000 per year. (c) $200,000 for pain and
suffering. (d) $25,000 for court costs. Assume that the salary payments are
equal amounts paid at the end of each month. If the interest rate you choose
is an EAR of 7 percent, what is the size of the settlement? If you were the
plaintiff, would you like to see a higher or lower interest rate?
59. Calculating EAR with Points You are looking at a one-year loan of
$15,000. The interest rate is quoted as 12 percent plus two points. A point on
a loan is 1 percent (one percentage point) of the loan amount. Quotes
similar to this one are common with home mortgages. The interest rate
quotation in this example requires the borrower to pay two points to the
lender up front and repay the loan later with 12 percent interest. What rate
would you actually be paying here?
60. Future Value and Multiple Cash Flows An insurance company is offering
a new policy to its customers. Typically, the policy is bought by a parent or
grandparent for a child at the child’s birth. The details of the policy are as
follows: The purchaser (say, the parent) makes the following six payments to
the insurance company:
First birthday: $ 800
Second birthday: $ 800
Third birthday: $ 900
Fourth birthday: $ 900
Fifth birthday: $1,000
Sixth birthday: $1,000
After the child’s sixth birthday, no more payments are made. When the child
reaches age 65, he or she receives $150,000. If the relevant interest rate is
10 percent for the first six years and 5.75 percent for all subsequent years,
is the policy worth buying?
LO 4
LO 1
WHAT’S ON
THE WEB?
5.1 Annuity Future Value The Federal Reserve Bank of St. Louis has files listing
historical interest rates on its website www.stlouisfed.org. Find the link for “FRED®”
(Federal Reserve Economic Data). You will find listings for Moody’s Seasoned Aaa
Corporate Bond Yield and Moody’s Seasoned Baa Corporate Bond Yield. (These rates
are discussed in the next chapter.) If you invest $2,000 per year for the next 40 years at
the most recent Aaa yield, how much will you have? What if you invest the same amount
at the Baa yield?
5.2 Loan Payments Finding the time necessary until you pay off a loan is simple if you
make equal payments each month. However, when paying off credit cards, many
individuals only make the minimum monthly payment, which is generally $10 or 2
percent to 3 percent of the balance, whichever is greater. You can find a credit card
calculator at www.financialcalculators.com. You currently owe $10,000 on a credit card
with a 17 percent interest rate and a minimum payment of $10 or 2 percent of your
balance, whichever is greater. How soon will you pay off this debt if you make the
minimum payment each month? How much total interest will you pay?
(continued)
ros13952_ch05_122-164.indd 162 12/24/18 4:40 PM
C H A P T E R 5 Discounted Cash Flow Valuation 163
5.3 Annuity Payments Find the retirement calculator at www.moneychimp.com to
answer the following question: Suppose you have $1,500,000 when you retire and want
to withdraw an equal amount each year for the next 30 years. How much can you
withdraw each year if you earn 7 percent? What if you can earn 9 percent?
5.4 Annuity Payments The Federal Reserve Bank of St. Louis has files listing historical
interest rates on its website www.stlouisfed.org. Find the link for “FRED®” (Federal
Reserve Economic Data). You will find a listing for the Bank Prime Loan Rate. The file
lists the monthly prime rates since January 1949 (1949.01). What is the most recent
prime rate? What is the highest prime rate over this period? If you buy a house for
$150,000 at the current prime rate on a 30-year mortgage with monthly payments, how
much are your payments? If you had purchased the house at the same price when the
prime rate was at its highest, what would your monthly payments have been?
5.5 Loan Amortization Bankrate, located at www.bankrate.com, has a financial
calculator that will prepare an amortization table based on your inputs. First, find the
APR quoted on the website for a 30-year fixed rate mortgage. You want to buy a home
for $200,000 on a 30-year mortgage with monthly payments at the rate quoted on the
site. What percentage of your first month’s payment is principal? What percentage of
your last month’s payment is principal? What is the total interest paid on the loan?
EXCEL MASTER IT! PROBLEM
This is a classic retirement problem. A friend is celebrating her birthday and wants to start
saving for her anticipated retirement. She has the following years to retirement and retire-
ment spending goals:
Years until retirement: 30
Amount to withdraw each year: $90,000
Years to withdraw in retirement: 20
Interest rate: 8%
Because your friend is planning ahead, the first withdrawal will not take place until one
year after she retires. She wants to make equal annual deposits into her account for her
retirement fund.
a. If she starts making these deposits in one year and makes her last deposit on the day
she retires, what amount must she deposit annually to be able to make the desired
withdrawals at retirement?
b. Suppose your friend just inherited a large sum of money. Rather than making equal
annual payments, she decided to make one lump-sum deposit today to cover her
retirement needs. What amount does she have to deposit today?
c. Suppose your friend’s employer will contribute to the account each year as part of the
company’s profit-sharing plan. In addition, your friend expects a distribution from a
family trust several years from now. What amount must she deposit annually now to
be able to make the desired withdrawals at retirement?
Employer’s annual contribution: $ 1,500
Years until trust fund distribution: 20
Amount of trust fund distribution: $25,000
coverage online
Excel
Master
ros13952_ch05_122-164.indd 163 12/24/18 4:40 PM
164 P A R T 3 Valuation of Future Cash Flows
greatest interest savings. At Todd’s prompting, she goes
on to explain a bullet loan. The monthly payments of a
bullet loan would be calculated using a 30-year tradi-
tional mortgage. In this case, there would be a 5-year
bullet. This means that the company would make the
mortgage payments for the traditional 30-year mortgage
for the first five years, but immediately after the com-
pany makes the 60th payment, the bullet payment
would be due. The bullet payment is the remaining prin-
cipal of the loan. Chris then asks how the bullet payment
is calculated. Christie tells him that the remaining princi-
pal can be calculated using an amortization table, but it
is also the present value of the remaining 25 years of
mortgage payments for the 30-year mortgage.
Todd also has heard of an interest-only loan and
asks if this loan is available and what the terms would
be. Christie says that the bank offers an interest-only
loan with a term of 10 years and an APR of 3.5 percent.
She goes on to further explain the terms. The company
would be responsible for making interest payments
each month on the amount borrowed. No principal pay-
ments are required. At the end of the 10-year term, the
company would repay the $35 million. However, the
company can make principal payments at any time. The
principal payments would work just like those on a tradi-
tional mortgage. Principal payments would reduce the
principal of the loan and reduce the interest due on the
next payment.
Mark and Todd are satisfied with Christie’s answers,
but they are still unsure of which loan they should
choose. They have asked Chris to answer the following
questions to help them choose the correct mortgage.
Mark Sexton and Todd Story, the owners of S&S Air, Inc., were impressed by the work Chris had done on finan-
cial planning. Using Chris’s analysis, and looking at the de-
mand for light aircraft, they have decided that their existing
fabrication equipment is sufficient, but it is time to acquire
a bigger manufacturing facility. Mark and Todd have identi-
fied a suitable structure that is currently for sale, and they
believe they can buy and refurbish it for about $35 million.
Mark, Todd, and Chris are now ready to meet with Christie
Vaughan, the loan officer for First United National Bank.
The meeting is to discuss the mortgage options available
to the company to finance the new facility.
Christie begins the meeting by discussing a 30-year
mortgage. The loan would be repaid in equal monthly
installments. Because of the previous relationship be-
tween S&S Air and the bank, there would be no closing
costs for the loan. Christie states that the APR of the
loan would be 6.1 percent. Todd asks if a shorter mort-
gage loan is available. Christie says that the bank does
have a 20-year mortgage available at the same APR.
Mark decides to ask Christie about a “smart loan” he
discussed with a mortgage broker when he was refi-
nancing his home loan. A smart loan works as follows:
Every two weeks a mortgage payment is made that is
exactly one-half of the traditional monthly mortgage pay-
ment. Christie informs him that the bank does have smart
loans. The APR of the smart loan would be the same as
the APR of the traditional loan. Mark nods his head. He
then states this is the best mortgage option available to
the company because it saves interest payments.
Christie agrees with Mark, but then suggests that a
bullet loan, or balloon payment, would result in the
CHAPTER CASE
S&S Air’s Mortgage
1. What are the monthly payments for a 30-year
traditional mortgage? What are the payments for
a 20-year traditional mortgage?
2. Prepare an amortization table for the first six
months of the traditional 30-year mortgage. How
much of the first payment goes toward principal?
3. How long would it take for S&S Air to pay off the
smart loan assuming 30-year traditional mortgage
payments? Why is this shorter than the time
needed to pay off the traditional mortgage? How
much interest would the company save?
4. Assume S&S Air takes out a bullet loan under
the terms described. What are the payments on
the loan?
5. What are the payments for the interest-only loan?
6. Which mortgage is the best for the company?
Are there any potential risks in this action?
Q U E S T I O N S
ros13952_ch05_122-164.indd 164 12/24/18 4:40 PM
Please visit us at essentialsofcorporatefinance.blogspot.com for the latest developments in the world of corporate finance.
165
Generally, when you make an investment, you expect that you will get back more money in the future than you invested today.
But in December 2017, this wasn’t the case for many bond investors.
The yield on a five-year German government bond was about negative
.20 percent, and the yields on two-year and five-year Japanese gov-
ernment bonds were negative .14 percent and negative .09 percent,
respectively. In fact, in 2016, the amount of debt worldwide that had a
negative yield reached a record $13.4 trillion! And negative yields
were not restricted to government bonds, as at one point the yield on
a bond issued by chocolate maker Nestlé was negative as well.
So what happened? Central banks were in a race to the bot-
tom, lowering interest rates in an attempt to improve their domestic
economies.
This chapter takes what we have learned about the time value
of money and shows how it can be used to value one of the most
common of all financial assets, a bond. It then discusses bond fea-
tures, bond types, and the operation of the bond market.
What we will see is that bond prices depend critically on interest rates, so we will go on
to discuss some very fundamental issues regarding interest rates. Clearly, interest rates are
important to everybody because they underlie what businesses of all types—small and
large—must pay to borrow money.
Interest Rates and
Bond Valuation6
LEARNING OBJECTIVES
After studying this chapter, you should
be able to:
LO 1 Identify important bond features
and types of bonds.
LO 2 Describe bond values and why
they fluctuate.
LO 3 Discuss bond ratings and what
they mean.
LO 4 Evaluate the impact of inflation on
interest rates.
LO 5 Explain the term structure of
interest rates and the determinants
of bond yields.
PART FOUR Valuing Stocks and Bonds
Our goal in this chapter is to introduce you to bonds. We begin by showing how the techniques we developed in Chapters 4 and 5 can be applied to bond valuation. From
there, we go on to discuss bond features and how bonds are bought and sold. One important
thing we learn is that bond values depend, in large part, on interest rates. Thus, we close out
the chapter with an examination of interest rates and their behavior.
Please visit us at essentialsofcorporatefinance.blogspot.com for the latest developments in the world of corporate finance.
ros13952_ch06_165-204.indd 165 12/24/18 4:46 PM
166 P A R T 4 Valuing Stocks and Bonds
BONDS AND BOND VALUATION
When a corporation (or government) wishes to borrow money from the public on a long-
term basis, it usually does so by issuing, or selling, debt securities that are generically called
bonds. In this section, we describe the various features of corporate bonds and some of the
terminology associated with bonds. We then discuss the cash flows associated with a bond
and how bonds can be valued using our discounted cash flow procedure.
Bond Features and Prices
As we mentioned in our previous chapter, a bond is normally an interest-only loan, meaning
that the borrower will pay the interest every period, but none of the principal will be repaid
until the end of the loan. Suppose the Beck Corporation wants to borrow $1,000 for 30
years. The interest rate on similar debt issued by similar corporations is 12 percent. Beck
will thus pay .12 × $1,000 = $120 in interest every year for 30 years. At the end of 30 years,
Beck will repay the $1,000. As this example suggests, a bond is a fairly simple financing ar-
rangement. There is, however, a rich jargon associated with bonds, so we will use this exam-
ple to define some of the more important terms.
In our example, the $120 regular interest payments that Beck promises to make are
called the bond’s coupons. Because the coupon is constant and paid every year, the type of
bond we are describing is sometimes called a level coupon bond. The amount that will be re-
paid at the end of the loan is called the bond’s face value or par value. As in our example,
this par value is usually $1,000 for corporate bonds, and a bond that sells for its par value is
called a par value bond. Government bonds frequently have much larger face, or par, values.
Finally, the annual coupon divided by the face value is called the coupon rate on the bond; in
this case, because $120/$1,000 = .12, or 12 percent, the bond has a 12 percent coupon rate.
The number of years until the face value is paid is called the bond’s time to maturity. A
corporate bond will frequently have a maturity of 30 years when it is originally issued, but this
varies. Once the bond has been issued, the number of years to maturity declines as time goes by.
Bond Values and Yields
As time passes, interest rates change in the marketplace. The cash flows from a bond, how-
ever, stay the same. As a result, the value of the bond will fluctuate. When interest rates rise,
the present value of the bond’s remaining cash flows declines, and the bond is worth less.
When interest rates fall, the bond is worth more.
To determine the value of a bond at a particular point in time, we need to know the
number of periods remaining until maturity, the face value, the coupon, and the market in-
terest rate for bonds with similar features. This interest rate required in the market on a
bond is called the bond’s yield to maturity (YTM). This rate is sometimes called the bond’s
yield for short. Given all this information, we can calculate the present value of the cash
flows as an estimate of the bond’s current market value.
For example, suppose the Xanth (pronounced “zanth”) Co. were to issue a bond with
10 years to maturity. The Xanth bond has an annual coupon of $80. Similar bonds have a
yield to maturity of 8 percent. Based on our preceding discussion, the Xanth bond will pay
$80 per year for the next 10 years in coupon interest. In 10 years, Xanth will pay $1,000 to
the owner of the bond. The cash flows from the bond are shown in Figure 6.1. What would
this bond sell for?
As illustrated in Figure 6.1, the Xanth bond’s cash flows have an annuity component
(the coupons) and a lump sum (the face value paid at maturity). We thus estimate the mar-
ket value of the bond by calculating the present value of these two components separately
6.1
coverage online
Excel
Master
coupon
The stated interest
payment made on a
bond.
face value
The principal amount of a
bond that is repaid at the
end of the term. Also par
value.
par value
The principal amount of a
bond that is repaid at the
end of the term. Also face
value.
coupon rate
The annual coupon
divided by the face value
of a bond.
maturity
Specified date on which
the principal amount of a
bond is paid.
yield to maturity
(YTM)
The rate required in the
market on a bond.
ros13952_ch06_165-204.indd 166 12/24/18 4:46 PM
C H A P T E R 6 Interest Rates and Bond Valuation 167
and adding the results together. First, at the going rate of 8 percent, the present value of the
$1,000 paid in 10 years is:
Present value = $1,000 / 1.08 10 = $1,000 / 2.1589 = $463.19
Second, the bond offers $80 per year for 10 years; the present value of this annuity stream is:
Annuity present value = $80 × (1 − 1/1.0810)/.08
= $80 × (1 − 1/2.1589)/.08
= $80 × 6.7101
= $536.81
We can now add the values for the two parts together to get the bond’s value:
Total bond value = $463.19 + 536.81 = $1,000
This bond sells for exactly its face value. This is not a coincidence. The going interest rate in the
market is 8 percent. Considered as an interest-only loan, what interest rate does this bond have?
With an $80 coupon, this bond pays exactly 8 percent interest only when it sells for $1,000.
To illustrate what happens as interest rates change, suppose that a year has gone by.
The Xanth bond now has 9 years to maturity. If the interest rate in the market has risen to
10 percent, what will the bond be worth? To find out, we repeat the present value calcula-
tions with 9 years instead of 10, and a 10 percent yield instead of an 8 percent yield. First,
the present value of the $1,000 paid in 9 years at 10 percent is:
Present value = $1,000 / 1.10 9 = $1,000 / 2.3579 = $424.10
Second, the bond now offers $80 per year for nine years; the present value of this annu-
ity stream at 10 percent is:
Annuity present value = $80 × (1 − 1/1.109)/.10
= $80 × (1 − 1/2.3579)/.10
= $80 × 5.7590
= $460.72
We can now add the values for the two parts together to get the bond’s value:
Total bond value = $424.10 + 460.72 = $884.82
Therefore, the bond should sell for about $885. In the vernacular, we say that this bond,
with its 8 percent coupon, is priced to yield 10 percent at $885.
The Xanth Co. bond now sells for less than its $1,000 face value. Why? The market in-
terest rate is 10 percent. Considered as an interest-only loan of $1,000, this bond only pays
8 percent, its coupon rate. Because this bond pays less than the going rate, investors are only
Cash flows for Xanth Co. bond
$80
Cash flows
Year
Coupon
Face Value
0 1 2 3 4 5 6 7 8 9 10
$80 $80 $80 $80 $80 $80 $80 $80 $80
$80 $80 $80 $80 $80 $80 $80 $80
$ 80
1,000
$1,080
As shown, the Xanth bond has an annual coupon of $80 and a face, or par, value of $1,000 paid at maturity in
10 years.
FIGURE 6.1
ros13952_ch06_165-204.indd 167 12/24/18 4:46 PM
168 P A R T 4 Valuing Stocks and Bonds
willing to lend something less than the $1,000 promised repayment. Because the bond sells
for less than face value, it is said to be a discount bond.
The only way to get the interest rate up to 10 percent is to lower the price to less than
$1,000 so that the purchaser, in effect, has a built-in gain. For the Xanth bond, the price of
$885 is $115 less than the face value, so an investor who purchased and kept the bond would
get $80 per year and would have a $115 gain at maturity as well. This gain compensates the
lender for the below-market coupon rate.
Another way to see why the bond is discounted by $115 is to note that the $80 coupon
is $20 below the coupon on a newly issued par value bond, based on current market condi-
tions. The bond would be worth $1,000 only if it had a coupon of $100 per year. In a sense,
an investor who buys and keeps the bond gives up $20 per year for nine years. At 10 percent,
this annuity stream is worth:
Annuity present value = $20 × (1 − 1/1.109)/.10
= $20 × 5.7590
= $115.18
This is the amount of the discount.
What would the Xanth bond sell for if interest rates had dropped by 2 percent instead
of rising by 2 percent? As you might guess, the bond would sell for more than $1,000. Such
a bond is said to sell at a premium and is called a premium bond.
This case is the opposite of that of a discount bond. The Xanth bond has a coupon rate
of 8 percent when the market rate is now only 6 percent. Investors are willing to pay a pre-
mium to get this extra coupon amount. In this case, the relevant discount rate is 6 percent,
and there are nine years remaining. The present value of the $1,000 face amount is:
Present value = $1,000 / 1.06 9 = $1,000 / 1.6895 = $591.90
The present value of the coupon stream is:
Annuity present value = $80 × (1 − 1/1.069)/.06
= $80 × (1 − 1/1.6895)/.06
= $80 × 6.8017
= $544.14
We can now add the values for the two parts together to get the bond’s value:
Total bond value = $591.90 + 544.14 = $1,136.03
The total bond value is therefore about $136 in excess of par value. Once again, we can
verify this amount by noting that the coupon is now $20 too high, based on current market
conditions. The present value of $20 per year for nine years at 6 percent is:
Annuity present value = $20 × (1 − 1/1.069)/.06
= $20 × 6.8017
= $136.03
This is as we calculated.
Based on our examples, we can now write the general expression for the value of a
bond. If a bond has (1) a face value of F paid at maturity, (2) a coupon of C paid per period,
(3) t periods to maturity, and (4) a yield of r per period, its value is:
Bond value = C × [1 − 1/(1 + r)t ]/r + F/( 1 + r)t
Bond value = Present value + Present value [6.1]
)))))))))))))of the coupons )))))))))))))))))))))))))))))))))))))))))of the face amount
A good bond site to visit is
www.bloomberg.com
/markets/rates-bonds,
which has loads of useful
information.
ros13952_ch06_165-204.indd 168 12/24/18 4:46 PM
C H A P T E R 6 Interest Rates and Bond Valuation 169
As we have illustrated in this section, bond prices and interest rates always move in
opposite directions. When interest rates rise, a bond’s value, like any other present value,
will decline. Similarly, when interest rates fall, bond values rise. Even if we are considering
a bond that is riskless in the sense that the borrower is certain to make all the payments,
there is still risk in owning a bond. We discuss this next.
Interest Rate Risk
The risk that arises for bond owners from fluctuating interest rates is called interest rate risk.
How much interest rate risk a bond has depends on how sensitive its price is to interest rate
changes. This sensitivity directly depends on two things: the time to maturity and the cou-
pon rate. As we will see momentarily, you should keep the following in mind when looking
at a bond:
1. All other things being equal, the longer the time to maturity, the greater the interest
rate risk.
2. All other things being equal, the lower the coupon rate, the greater the interest rate
risk.
Online bond calculators
and interest rate
information are available
at money.cnn.com/data
/bonds and www
.bankrate.com.
EXAMPLE 6.1 Semiannual Coupons
In practice, bonds issued in the United States usually make coupon payments twice a year. So, if an
ordinary bond has a coupon rate of 14 percent, then the owner will get a total of $140 per year, but
this $140 will come in two payments of $70 each. Suppose we are examining such a bond. The
yield to maturity is quoted at 16 percent.
Bond yields are quoted like APRs; the quoted rate is equal to the actual rate per period multi-
plied by the number of periods. In this case, with a 16 percent quoted yield and semiannual pay-
ments, the true yield is 8 percent per six months. The bond matures in seven years. What is the
bond’s price? What is the effective annual yield on this bond?
Based on our discussion, we know that the bond will sell at a discount because it has a cou-
pon rate of 7 percent every six months when the market requires 8 percent every six months. So, if
our answer is equal to or exceeds $1,000, we know that we have made a mistake.
To get the exact price, we first calculate the present value of the bond’s face value of $1,000
paid in seven years. This seven-year period has 14 periods of six months each. At 8 percent per
period, the value is:
Present value = $1,000/1.0814 = $1,000/2.9372 = $340.46
The coupons can be viewed as a 14-period annuity of $70 per period. At an 8 percent discount rate,
the present value of such an annuity is:
Annuity present value = $70 × (1 − 1/1.0814)/.08
= $70 × (1 − .3405)/.08
= $70 × 8.2442
= $577.10
The total present value gives us what the bond should sell for:
Total present value = $340.46 + 577.10 = $917.56
To calculate the effective yield on this bond, note that 8 percent every six months is equivalent to:
Effective annual rate = (1 + .08)2 − 1 = .1664, or 16.64%
The effective yield, therefore, is 16.64 percent.
ros13952_ch06_165-204.indd 169 12/24/18 4:46 PM
170 P A R T 4 Valuing Stocks and Bonds
We illustrate the first of these two points in Figure 6.2. As shown, we compute and plot
prices under different interest rate scenarios for 10 percent coupon bonds with maturities of
1 year and 30 years. Notice how the slope of the line connecting the prices is much steeper
for the 30-year maturity bond than it is for the 1-year maturity bond. This steepness tells us
that a relatively small change in interest rates will lead to a substantial change in the bond’s
value. In comparison, the one-year bond’s price is relatively insensitive to interest rate
changes.
Intuitively, we can see that the reason that longer-term bonds have greater interest rate
sensitivity is that a large portion of a bond’s value comes from the $1,000 face amount. The
present value of this amount isn’t greatly affected by a small change in interest rates if the
amount is to be received in one year. Even a small change in the interest rate, however, once
it is compounded for 30 years, can have a significant effect on the present value. As a result,
the present value of the face amount will be much more volatile with a longer-term bond.
The other thing to know about interest rate risk is that, like most things in finance and
economics, it increases at a decreasing rate. In other words, if we compared a 10-year bond
to a 1-year bond, we would see that the 10-year bond has much greater interest rate risk.
However, if you were to compare a 20-year bond to a 30-year bond, you would find that the
30-year bond has somewhat greater interest rate risk because it has a longer maturity, but
the difference in the risk would be fairly small.
The reason that bonds with lower coupons have greater interest rate risk is easy to un-
derstand. As we discussed earlier, the value of a bond depends on the present value of its
coupons and the present value of the face amount. If two bonds with different coupon rates
have the same maturity, then the value of the one with the lower coupon is proportionately
Visit www.investorguide
.com to learn more about
bonds.
Interest rate risk and time to maturity
2,000
1,500
1,000
500
5 10 15 20
Bond
value ($)
Interest
rate (%)
$1,768.62
30-year bond
$1,047.62
1-year bond
$916.67
$502.11
Value of a Bond with a 10 Percent Coupon Rate for Different Interest Rates and Maturities
Time to Maturity
Interest Rate 1 Year 30 Years
5% $1,047.62
1,000.00
956.52
916.67
$1,768.62
1,000.00
671.70
502.11
10
15
20
FIGURE 6.2
ros13952_ch06_165-204.indd 170 12/24/18 4:46 PM
C H A P T E R 6 Interest Rates and Bond Valuation 171
more dependent on the face amount to be received at maturity. As a result, all other things
being equal, its value will fluctuate more as interest rates change. Put another way, the bond
with the higher coupon has a larger cash flow early in its life, so its value is less sensitive to
changes in the discount rate.
Bonds are usually not issued with maturities longer than 30 years. However, low interest
rates have led to the issuance of bonds with much longer maturities. In the 1990s, Walt
Disney issued “Sleeping Beauty” bonds with a 100-year maturity. Similarly, BellSouth (now
known as AT&T), Coca-Cola, and Dutch banking giant ABN AMRO all issued bonds with
100-year maturities. These companies wanted to lock in the historically low interest rates for
a long time. The current record holder for corporations appears to be Republic National
Bank, which sold bonds with 1,000 years to maturity. Before these fairly recent issues, it
appears the last time 100-year bonds were issued was in May 1954 by the Chicago and East-
ern Railroad. And low interest rates in recent years have led to more 100-year bonds. For
example, in 2017, Argentina joined Mexico, Ireland, and Belgium when it issued $2.75 bil-
lion in 100-year bonds. What made Argentina’s bond sale unique was that the country had
defaulted three times in the past 23 years.
We can illustrate the effect of interest rate risk using a 100-year BellSouth issue. The
following table provides some basic information on this issue, along with its prices on De-
cember 31, 1995; May 6, 2008; and February 1, 2018.
Percentage Percentage
Change Change in
Coupon Price on Price on in Price Price on Price
Maturity Rate 12/31/95 5/6/08 1995–2008 2/1/18 2008–2018
2095 7.00% $1,000.00 $1,008.40 + .84% $1,164.21 + 15.5%
Several things emerge from this table. First, interest rates apparently fell slightly be-
tween December 31, 1995, and May 6, 2008 (why?). After that, however, they fell even
more (why?). The bond’s price first gained .84 percent and then gained an additional
15.5 percent. These swings illustrate that longer-term bonds have significant interest
rate risk.
Finding the Yield to Maturity: More Trial and Error
Frequently, we will know a bond’s price, coupon rate, and maturity date, but not its yield to
maturity. Suppose we are interested in a six-year, 8 percent coupon bond. The coupons are
paid annually. A broker quotes a price of $955.14. What is the yield on this bond?
We’ve seen that the price of a bond can be written as the sum of its annuity and lump-
sum components. Knowing that there is an $80 coupon for six years and a $1,000 face
value, we can say that the price is:
$955.14 = $80 × [)1 − 1 / (1 + r)) 6 ] / r + $1,000 / (1 + r)) 6
where r is the unknown discount rate, or yield to maturity. We have one equation here and
one unknown, but we cannot solve for r explicitly. The only way to find the answer is to use
trial and error (or, better yet, a spreadsheet or financial calculator).
This problem is essentially identical to the one we examined in the last chapter when
we tried to find the unknown interest rate on an annuity. However, finding the rate (or
yield) on a bond is even more complicated because of the $1,000 face amount.
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172 P A R T 4 Valuing Stocks and Bonds
We can speed up the trial-and-error process by using what we know about bond prices
and yields. In this case, the bond has an $80 coupon and is selling at a discount. We thus
know that the yield is greater than 8 percent. If we compute the price at 10 percent:
Bond value = $80 × (1 − 1/1.106 )/.10 + $1,000/1.106
= $80 × 4.3553 + $1,000/1.7716
= $912.89
At 10 percent, the value we calculate is lower than the actual price, so 10 percent is too high.
The true yield must be somewhere between 8 and 10 percent. At this point, it’s “plug and
chug” to find the answer. You would probably want to try 9 percent next. If you did, you
would see that this is, in fact, the bond’s yield to maturity.
A bond’s yield to maturity should not be confused with its current yield, which is a
bond’s annual coupon divided by its price. In the example we just worked, the bond’s annual
coupon was $80 and its price was $955.14. Given these numbers, we see that the current
yield is $80/$955.14 = .0838, or 8.38 percent, which is less than the yield to maturity of 9
percent. The reason the current yield is too low is that it only considers the coupon portion
of your return; it doesn’t consider the built-in gain from the price discount. For a premium
bond, the reverse is true, meaning that current yield would be higher because it ignores the
built-in loss.
Our discussion of bond valuation is summarized in Table 6.1.
Current market rates are
available at www
.bankrate.com.
current yield
A bond’s coupon payment
divided by its closing
price.
EXAMPLE 6.2 Current Events
A bond has a quoted price of $1,080.42. It has a face value of $1,000, a semiannual coupon of $30,
and a maturity of five years. What is its current yield? What is its yield to maturity? Which is bigger?
Why?
Notice that this bond makes semiannual payments of $30, so the annual payment is $60. The
current yield is thus $60/$1,080.42 = .0555, or 5.55 percent. To calculate the yield to maturity, refer
back to Example 6.1. Now, in this case, the bond pays $30 every six months and it has 10 six-month
periods until maturity. So, we need to find r as follows:
$1,080.42 = $30 × [1 − 1/(1 + r)10]/r + $1,000/(1 + r)10
After some trial and error, we find that r is equal to 2.1 percent. But the tricky part is that this 2.1 per-
cent is the yield per six months. We have to double it to get the yield to maturity, so the yield to
maturity is 4.2 percent, which is less than the current yield. The reason is that the current yield ig-
nores the built-in loss of the premium between now and maturity.
Summary of bond
valuation
TABLE 6.1 I. Finding the value of a bond
Bond value = C × [1 − 1/(1 + r)t]/r + F/(1 + r)t
where:
C = Coupon paid each period
!!!!r = Rate per period
!!!!!t = Number of periods
F = Bond’s face value
II. Finding the yield on a bond
Given a bond value, coupon, time to maturity, and face value, it is possible to find the implicit
discount rate, or yield to maturity, by trial and error only. To do this, try different discount rates
in the preceding formula until the calculated bond value equals the given bond value.
Remember that increasing the rate decreases the bond value.
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C H A P T E R 6 Interest Rates and Bond Valuation 173
EXAMPLE 6.3 Bond Yields
You’re looking at two bonds identical in every way except for their coupons and, of course, their
prices. Both have 12 years to maturity. The first bond has a 10 percent coupon rate and sells for
$935.08. The second has a 12 percent coupon rate. What do you think it would sell for?
Because the two bonds are very similar, they will be priced to yield about the same rate. We
first need to calculate the yield on the 10 percent coupon bond. Proceeding as before, we know
that the yield must be greater than 10 percent because the bond is selling at a discount. The bond
has a fairly long maturity of 12 years. We’ve seen that long-term bond prices are relatively sensitive
to interest rate changes, so the yield is probably close to 10 percent. A little trial and error reveals
that the yield is actually 11 percent:
Bond value = $100 × (1 − 1/1.1112)/.11 + $1,000/1.1112
= $100 × 6.4924 + $1,000/3.4985
= $649.24 + 285.84
= $935.08
With an 11 percent yield, the second bond will sell at a premium because of its $120 coupon. Its
value is:
Bond value = $120 × (1 − 1/1.1112)/.11 + $1,000/1.1112
= $120 × 6.4924 + $1,000/3.4985
= $779.08 + 285.84
= $1,064.92
HOW TO CALCULATE BOND PRICES AND YIELDS USING A FINANCIAL
CALCULATOR
Many financial calculators have fairly sophisticated built-in bond valuation routines. However, these vary
quite a lot in implementation, and not all financial calculators have them. As a result, we will illustrate a
simple way to handle bond problems that will work on just about any financial calculator.
To begin, of course, we first remember to clear out the calculator! Next, for Example 6.3, we have
two bonds to consider, both with 12 years to maturity. The first one sells for $935.08 and has a 10 per-
cent coupon rate. To find its yield, we can do the following:
Enter 12 100 −935.08 1,000
I/ Y
Solve for 11
Notice that here we have entered both a future value of $1,000, representing the bond’s face value,
and a payment of 10 percent of $1,000, or $100, per year, representing the bond’s annual coupon.
Also notice that we have a negative sign on the bond’s price, which we have entered as the present
value.
For the second bond, we now know that the relevant yield is 11 percent. It has a 12 percent coupon
and 12 years to maturity, so what’s the price? To answer, we enter the relevant values and solve for the
present value of the bond’s cash flows:
Enter 12 11 120 1,000
PV
Solve for −1,064.92
CALCULATOR
HINTS
(continued)
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174 P A R T 4 Valuing Stocks and Bonds
There is an important detail that comes up here. Suppose we have a bond with a price of $902.29, 10
years to maturity, and a coupon rate of 6 percent. As we mentioned earlier, most bonds actually make
semiannual payments. Assuming that this is the case for the bond here, what’s the bond’s yield to matu-
rity? To answer, we need to enter the relevant numbers like this:
Enter 20 30 −902.29 1,000
I/ Y
Solve for 3.7
Notice that we entered $30 as the payment because the bond actually makes payments of $30 every
six months. Similarly, we entered 20 for N because there are actually 20 six-month periods. When we
solve for the yield, we get 3.7 percent, but the tricky thing to remember is that this is the yield per six
months, so we have to double it to get the right answer: 2 × 3.7% = 7.4 percent, which would be the
bond’s reported yield.
HOW TO CALCULATE BOND PRICES AND YIELDS USING A
SPREADSHEET
Like financial calculators, most spreadsheets have fairly elaborate routines available for calculating
bond values and yields; many of these routines involve details that we have not discussed. However,
setting up a simple spreadsheet to calculate prices or yields is straightforward, as our next two
spreadsheets show:
SPREADSHEET
STRATEGIES
A B C D E F G H
1
2 Using a spreadsheet to calculate bond yields
3
4 Suppose we have a bond with 22 years to maturity, a coupon rate of 8 percent, and a price of
5 $960.17. If the bond makes semiannual payments, what is its yield to maturity?
6
7 Settlement date: 1/1/00
8 Maturity date: 1/1/22
9 Annual coupon rate: .08
10 Bond price (% of par): 96.017
11 Face value (% of par): 100
12 Coupons per year: 2
13 Yield to maturity: .084
14
15 The formula entered in cell B13 is = YIELD(B7, B8, B9, B10, B11, B12); notice that face value and bond
16 price are entered as a percentage of face value.
17
(continued)
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C H A P T E R 6 Interest Rates and Bond Valuation 175
CONCEPT QUESTIONS
6.1a What are the cash flows associated with a bond?
6.1b What is the general expression for the value of a bond?
6.1c Is it true that the only risk associated with owning a bond is that the issuer will not
make all the payments? Explain.
MORE ON BOND FEATURES
In this section, we continue our discussion of corporate debt by describing in some detail
the basic terms and features that make up a typical long-term corporate bond. We discuss
additional issues associated with long-term debt in subsequent sections.
Securities issued by corporations may be classified roughly as equity securities and debt
securities. At the crudest level, a debt represents something that must be repaid; it is the re-
sult of borrowing money. When corporations borrow, they generally promise to make regu-
larly scheduled interest payments and to repay the original amount borrowed (i.e., the
principal). The person or firm making the loan is called the creditor, or lender. The corpora-
tion borrowing the money is called the debtor, or borrower.
6.2
coverage online
Excel
Master
In our spreadsheets, notice that we had to enter two dates, a settlement date and a maturity date. The
settlement date is just the date you actually pay for the bond, and the maturity date is the day the bond
actually matures. In most of our problems, we don’t explicitly have these dates, so we have to make
them up. For example, because our bond has 22 years to maturity, we just picked 1/1/2000 (January 1,
2000) as the settlement date and 1/1/2022 (January 1, 2022) as the maturity date. Any two dates would
do as long as they were exactly 22 years apart, but these are particularly easy to work with. Finally, no-
tice that we had to enter the coupon rate and yield to maturity in annual terms and then explicitly provide
the number of coupon payments per year.
A B C D E F G H
1
2 Using a spreadsheet to calculate bond values
3
4 Suppose we have a bond with 22 years to maturity, a coupon rate of 8 percent, and a yield to
5 maturity of 9 percent. If the bond makes semiannual payments, what is its price today?
6
7 Settlement date: 1/1/00
8 Maturity date: 1/1/22
9 Annual coupon rate: .08
10 Yield to maturity: .09
11 Face value (% of par): 100
12 Coupons per year: 2
13 Bond price (% of par): 90.49
14
15 The formula entered in cell B13 is = PRICE(B7, B8, B9, B10, B11, B12); notice that face value and bond
16 price are entered as a percentage of face value.
17
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176 P A R T 4 Valuing Stocks and Bonds
From a financial point of view, the main differences between debt and equity are the
following:
1. Debt is not an ownership interest in the firm. Creditors generally do not have voting
power.
2. The corporation’s payment of interest on debt is considered a cost of doing business
and is fully tax deductible. Dividends paid to stockholders are not tax deductible.
3. Unpaid debt is a liability of the firm. If it is not paid, the creditors can legally claim
the assets of the firm. This action can result in liquidation or reorganization, two of
the possible consequences of bankruptcy. Thus, one of the costs of issuing debt is the
possibility of financial failure. This possibility does not arise when equity is issued.
Is It Debt or Equity?
Sometimes it is not clear if a particular security is debt or equity. Suppose a corporation is-
sues a perpetual bond with interest payable solely from corporate income if, and only if,
earned. Whether or not this is really a debt is hard to say and is primarily a legal and seman-
tic issue. Courts and taxing authorities would have the final say.
Corporations are very adept at creating exotic, hybrid securities that have many fea-
tures of equity but are treated as debt. Obviously, the distinction between debt and equity is
very important for tax purposes. So, one reason that corporations try to create a debt secu-
rity that is really equity is to obtain the tax benefits of debt and the bankruptcy benefits of
equity.
As a general rule, equity represents an ownership interest, and it is a residual claim.
This means that equity holders are paid after debt holders. As a result, the risks and benefits
associated with owning debt and equity are different. To give one example, note that the
maximum reward for owning a debt security is ultimately fixed by the amount of the loan,
whereas there is no upper limit to the potential reward from owning an equity interest.
Long-Term Debt: The Basics
Ultimately, all long-term debt securities are promises made by the issuing firm to pay princi-
pal when due and to make timely interest payments on the unpaid balance. Beyond this,
there are a number of features that distinguish these securities from one another. We discuss
some of these features next.
The maturity of a long-term debt instrument is the length of time the debt remains
outstanding with some unpaid balance. Debt securities can be short term (with maturities
of one year or less) or long term (with maturities of more than one year).1 Short-term debt
is sometimes referred to as unfunded debt.2
Debt securities are typically called notes, debentures, or bonds. Strictly speaking, a bond
is a secured debt. However, in common usage, the word bond refers to all kinds of secured
and unsecured debt. We will, therefore, continue to use the term generically to refer to long-
term debt.
The two major forms of long-term debt are public issue and private issue. We concen-
trate on public-issue bonds. Most of what we say about them holds true for private-issue,
long-term debt as well. The main difference between public-issue and private-issue debt is
Information for bond
investors can be found at
www.investinginbonds
.com.
1There is no universally agreed-upon distinction between short-term and long-term debt. In addition, people often
refer to intermediate-term debt, which has a maturity of more than 1 year and less than 3 to 5, or even 10, years.
2The word funding is part of the jargon of finance. It generally refers to the long term. Thus, a firm planning to
“fund” its debt requirements may be replacing short-term debt with long-term debt.
ros13952_ch06_165-204.indd 176 12/24/18 4:46 PM
C H A P T E R 6 Interest Rates and Bond Valuation 177
that the latter is directly placed with a lender and not offered to the public. Because this is a
private transaction, the specific terms are up to the parties involved.
There are many other dimensions to long-term debt, including such things as security,
call features, sinking funds, ratings, and protective covenants. The following table illustrates
these features for a bond issued by the cell phone company Sprint on February 22, 2018. If
some of these terms are unfamiliar, have no fear. We discuss them all presently. Many of
these features will be detailed in the bond indenture, so we discuss this first.
Features of a Sprint Bond
Term Explanation
Amount of issue $1.5 billion The company issued $1.5 billion worth of bonds.
Date of issue 02/22/2018 The bonds were sold on 02/22/2018.
Maturity 03/01/2026 The bonds mature on 03/01/2026.
Face value $2,000 The denomination of the bonds is $2,000.
Annual coupon 7.625 Each bondholder will receive $152.50 per bond
per year (7.625% of face value).
Offer price 100 The offer price will be 100% of the $2,000 face
value, or $2,000, per bond.
Coupon payment 03/01, 09/01 Coupons of $152.50/2 = $76.25 will be paid on
dates these dates.
Security None The bonds are not secured by specific assets.
Sinking fund None The bonds have no sinking fund.
Call provision At any time The bonds do not have a deferred call.
Call price Treasury rate The bonds have a “make-whole” call price.
plus .50%.
Rating Moody’s The bonds have a “junk bond” credit rating.
B3; S&P B
The Indenture
The indenture is the written agreement between the corporation (the borrower) and its
creditors. It is sometimes referred to as the deed of trust.3 Usually, a trustee (a bank, per-
haps) is appointed by the corporation to represent the bondholders. The trust company
must (1) make sure the terms of the indenture are obeyed; (2) manage the sinking fund
(described in the following pages); and (3) represent the bondholders in default, that is, if
the company defaults on its payments to them.
The bond indenture is a legal document. It can run several hundred pages and generally
makes for very tedious reading. It is an important document, however, because it generally
includes the following provisions:
1. The basic terms of the bonds.
2. The total amount of bonds issued.
3. A description of property used as security.
4. The repayment arrangements.
5. The call provisions.
6. Details of the protective covenants.
We discuss these features next.
indenture
The written agreement
between the corporation
and the lender detailing
the terms of the debt
issue.
3The term loan agreement or loan contract is usually used for privately placed debt and term loans.
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178 P A R T 4 Valuing Stocks and Bonds
Terms of a Bond Corporate bonds have historically had a face value (i.e., a denomina-
tion) of $1,000, although par values of $2,000 like the Sprint bond have become fairly com-
mon. This is called the principal value, and it is stated on the bond certificate. So, if a
corporation wanted to borrow $1 million, 1,000 bonds with a face value of $1,000 would
have to be sold. The par value (i.e., initial accounting value) of a bond is almost always the
same as the face value, and the terms are used interchangeably in practice.
Corporate bonds are usually in registered form. For example, the indenture might read
as follows:
Interest is payable semiannually on July 1 and January 1 of each year to the person
in whose name the bond is registered at the close of business on June 15 or Decem-
ber 15, respectively.
This means that the company has a registrar who will record the ownership of each bond
and record any changes in ownership. The company will pay the interest and principal di-
rectly to the owner of record. Long ago, corporate bonds (and other types) had attached
“coupons.” To obtain an interest payment, the owner had to separate a coupon from the
bond certificate and send it to the company registrar (the paying agent).
Alternatively, the bond could be in bearer form. This means that the certificate is the
basic evidence of ownership, and the corporation will “pay the bearer.” Ownership is not
otherwise recorded, and, as with a registered bond with attached coupons, the holder of the
bond certificate detaches the coupons and sends them to the company to receive payment.
There are two drawbacks to bearer bonds. First, they are difficult to recover if they are
lost or stolen. Second, because the company does not know who owns its bonds, it cannot
notify bondholders of important events. Bearer bonds were once the dominant type, but
they are now much less common (in the United States) than registered bonds.
Security Debt securities are classified according to the collateral and mortgages used to
protect the bondholder.
Collateral is a general term that frequently means securities (e.g., bonds and stocks)
that are pledged as security for payment of debt. For example, collateral trust bonds often
involve a pledge of common stock held by the corporation. However, the term collateral is
commonly used to refer to any asset pledged on a debt.
Mortgage securities are secured by a mortgage on the real property of the borrower. The
property involved is usually real estate, for example, land or buildings. The legal document
that describes the mortgage is called a mortgage trust indenture or trust deed. A “blanket”
mortgage pledges all the real property owned by the company.4
Bonds frequently represent unsecured obligations of the company. A debenture is an
unsecured bond, for which no specific pledge of property is made. The term note is gener-
ally used for such instruments if the maturity of the unsecured bond is less than 10 or so
years from when the bond is originally issued. Debenture holders only have a claim on
property not otherwise pledged; in other words, the property that remains after mortgages
and collateral trusts are taken into account.
The terminology that we use here and elsewhere in this chapter is standard in the
United States. Outside the United States, these same terms can have different meanings.
registered form
The registrar of a
company records who
owns each bond, and
bond payments are made
directly to the owner of
record.
bearer form
A bond issued without
record of the owner’s
name; payment is made to
whomever holds the bond.
debenture
Unsecured debt, usually
with a maturity of 10 years
or more.
note
Unsecured debt, usually
with a maturity of under 10
years.
4Real property includes land and things “affixed thereto.” It does not include cash or inventories.
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C H A P T E R 6 Interest Rates and Bond Valuation 179
For example, bonds issued by the British government (“gilts”) are called treasury “stock.”
Also, in the United Kingdom, a debenture is a secured obligation.
At the current time, almost all public bonds issued in the United States by industrial
and financial companies are debentures. However, most utility and railroad bonds are se-
cured by a pledge of assets.
Seniority In general terms, seniority indicates preference in position over other lenders,
and debts are sometimes labeled as senior or junior to indicate seniority. Some debt is subor-
dinated, as in, for example, a subordinated debenture.
In the event of default, holders of subordinated debt must give preference to other speci-
fied creditors. Usually, this means that the subordinated lenders will be paid off only after the
specified creditors have been compensated. However, debt cannot be subordinated to equity.
Repayment Bonds can be repaid at maturity, at which time the bondholder will receive
the stated, or face, value of the bond, or they may be repaid in part or in entirety before
maturity. Early repayment in some form is more typical and often is handled through a
sinking fund.
A sinking fund is an account managed by the bond trustee for the purpose of repaying
the bonds. The company makes annual payments to the trustee, who then uses the funds to
retire a portion of the debt. The trustee does this by either buying up some of the bonds in
the market or calling in a fraction of the outstanding bonds. This second option is discussed
in the next section.
There are many different kinds of sinking fund arrangements, and the details would be
spelled out in the indenture. For example:
1. Some sinking funds start about 10 years after the initial issuance.
2. Some sinking funds establish equal payments over the life of the bond.
3. Some high-quality bond issues establish payments to the sinking fund that are
insufficient to redeem the entire issue. As a consequence, there is the possibility of a
large “balloon payment” at maturity.
The Call Provision A call provision allows the company to repurchase, or “call,” part
or all of the bond issue at stated prices over a specific period. Corporate bonds are usually
callable.
Generally, the call price is above the bond’s stated value (that is, the par value). The
difference between the call price and the stated value is the call premium. The amount of
the call premium usually becomes smaller over time. One arrangement is to initially set the
call premium equal to the annual coupon payment and then make it decline to zero as the
call date moves closer to the time of maturity.
Call provisions are not usually operative during the first part of a bond’s life. This
makes the call provision less of a worry for bondholders in the bond’s early years. For exam-
ple, a company might be prohibited from calling its bonds for the first 10 years. This is a
deferred call provision. During this period of prohibition, the bond is said to be
call protected.
In the last few years, use of a new type of call provision, a “make-whole” call, has be-
come very widespread in the corporate bond market. With such a feature, bondholders re-
ceive exactly what the bonds are worth if they are called. When bondholders don’t suffer a
loss in the event of a call, they are made whole.
To determine the make-whole call price, we calculate the present value of the remaining
interest and principal payments at a rate specified in the indenture. For example, looking at
The Securities Industry
and Financial Markets
Association (SIFMA)
website is www.sifma.org.
sinking fund
An account managed by
the bond trustee for early
bond redemption.
call provision
Agreement giving the
issuer the option to
repurchase a bond at a
specific price prior to
maturity.
call premium
The amount by which the
call price exceeds the par
value of the bond.
deferred call
provision
Bond call provision
prohibiting the company
from redeeming the bond
prior to a certain date.
call protected bond
Bond during period in
which it cannot be
redeemed by the issuer.
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180 P A R T 4 Valuing Stocks and Bonds
our Sprint issue, we see that the discount rate is “Treasury rate plus .50%.” What this means
is that we determine the discount rate by first finding a U.S. Treasury issue with the same
maturity. We calculate the yield to maturity on the Treasury issue and then add on an addi-
tional .50 percent to get the discount rate we use.
Notice that, with a make-whole call provision, the call price is higher when interest
rates are lower and vice versa (why?). Also notice that, as is common with a make-whole
call, the Sprint issue does not have a deferred call feature. Why might investors not be too
concerned about the absence of this feature?
Protective Covenants A protective covenant is that part of the indenture or loan
agreement that limits certain actions a company might otherwise wish to take during the
term of the loan. Protective covenants can be classified into two types: negative covenants
and positive (or affirmative) covenants.
A negative covenant is a “thou shalt not” type of covenant. It limits or prohibits actions
that the company might take. Here are some typical examples:
1. The firm must limit the amount of dividends it pays according to some formula.
2. The firm cannot pledge any assets to other lenders.
3. The firm cannot merge with another firm.
4. The firm cannot sell or lease any major assets without approval by the lender.
5. The firm cannot issue additional long-term debt.
A positive covenant is a “thou shalt” type of covenant. It specifies an action that the company
agrees to take or a condition the company must abide by. Here are some examples:
1. The company must maintain its working capital at or above some specified minimum
level.
2. The company must periodically furnish audited financial statements to the lender.
3. The firm must maintain any collateral or security in good condition.
This is only a partial list of covenants; a particular indenture may feature many different ones.
CONCEPT QUESTIONS
6.2a What are the distinguishing features of debt as compared to equity?
6.2b What is the indenture? What are protective covenants? Give some examples.
6.2c What is a sinking fund?
BOND RATINGS
Firms frequently pay to have their debt rated. The two leading bond-rating firms are
Moody’s and Standard and Poor’s (S&P). The debt ratings are an assessment of the credit-
worthiness of the corporate issuer. The definitions of creditworthiness used by Moody’s
and S&P are based on how likely the firm is to default and the protection creditors have in
the event of a default.
It is important to recognize that bond ratings are concerned only with the possibility of
default. Earlier, we discussed interest rate risk, which we defined as the risk of a change in
protective covenant
A part of the indenture
limiting certain actions
that might be taken during
the term of the loan,
usually to protect the
lender’s interest.
Want detailed information
on the amount and terms
of the debt issued by a
particular firm? Check out
the firm’s latest financial
statements by searching
SEC filings at www.sec.gov.
6.3
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C H A P T E R 6 Interest Rates and Bond Valuation 181
the value of a bond resulting from a change in interest rates. Bond ratings do not address
this issue. As a result, the price of a highly rated bond can still be quite volatile.
Bond ratings are constructed from information supplied by the corporation. The rating
classes and some information concerning them are shown in the following table.
High Grade Medium Grade Low Grade Very Low Grade
Standard & Poor’s AAA AA A BBB BB B CCC CC C D
Moody’s Aaa Aa A Baa Ba B Caa Ca C
Moody’s S&P
Aaa AAA Debt rated Aaa and AAA has the highest rating. Capacity to pay interest and principal is extremely strong.
Aa AA Debt rated Aa and AA has a very strong capacity to pay interest and repay principal. Together with the
highest rating, this group constitutes the high-grade bond class.
A A Debt rated A has a strong capacity to pay interest and repay principal, although it is somewhat more
susceptible to the adverse effects of changes in circumstances and economic conditions than debt in
higher-rated categories.
Baa BBB Debt rated Baa and BBB is regarded as having an adequate capacity to pay interest and repay
principal. Whereas it normally exhibits adequate protection parameters, adverse economic conditions
or changing circumstances are more likely to lead to a weakened capacity to pay interest and repay
principal for debt in this category than in higher-rated categories. These bonds are medium-grade
obligations.
Ba; B BB; B Debt rated in these categories is regarded, on balance, as predominantly speculative with respect to
Caa CCC capacity to pay interest and repay principal in accordance with the terms of the obligation. BB and Ba
Ca CC indicate the lowest degree of speculation, and Ca, CC, and C the highest degree of speculation.
C C Although such debt is likely to have some quality and protective characteristics, these are outweighed
by large uncertainties or major risk exposures to adverse conditions. Issues rated C by Moody’s are
typically in default.
D Debt rated D is in default, and payment of interest and/or repayment of principal is in arrears.
Note: At times, both Moody’s and S&P use adjustments (called notches) to these ratings. S&P uses plus and minus signs: A+ is the strongest A rating
and A− the weakest. Moody’s uses a 1, 2, or 3 designation, with 1 being the highest.
Investment-Quality Bond Ratings
Low-Quality, Speculative,
and/or “Junk” Bond Ratings
The highest rating a firm’s debt can have is AAA or Aaa, and such debt is judged to be
the best quality and to have the lowest degree of default risk. For example, the Sprint issue
we discussed earlier was rated B. The AAA rating is not awarded very often: As of 2018,
only two nonfinancial U.S. companies have AAA ratings, Johnson & Johnson and Micro-
soft. AA or Aa ratings indicate very good quality debt and are much more common. The
lowest rating is D, for debt that is in default.
Beginning in the 1980s, a growing part of corporate borrowing has taken the form of
low-grade, or “junk,” bonds. If these low-grade corporate bonds are rated at all, they are
rated below investment grade by the major rating agencies. Investment-grade bonds are
bonds rated at least BBB by S&P or Baa by Moody’s.
Some bonds are called “crossover” or “5B” bonds. The reason is that they are rated
triple-B (or Baa) by one rating agency and double-B (or Ba) by another, a “split rating.” For
example, in February 2016, India-based textile and chemical company Standard Industries
sold an issue of 10-year notes rated BBB– by S&P and Ba2 by Moody’s.
Want to know what
criteria are commonly
used to rate corporate
and municipal bonds? Go
to www.standardandpoors
.com, www.moodys.com,
or www.fitchinv.com.
ros13952_ch06_165-204.indd 181 12/24/18 4:46 PM
182 P A R T 4 Valuing Stocks and Bonds
A bond’s credit rating can change as the issuer’s financial strength improves or deterio-
rates. For example, in January 2018, Moody’s downgraded Teva Pharmaceuticals from in-
vestment grade to junk bond status. Bonds that drop into junk territory from above are
called “fallen angels.” Why was Teva downgraded? The reason given by Moody’s was a much
higher debt load because of an ill-timed acquisition and weakening sales of a major drug.
Executives of the company also had been accused of collaborating with contractors to pay
bribes to politicians.
Credit ratings are important because defaults really do occur, and, when they do, inves-
tors can lose heavily. For example, in 2000, AmeriServe Food Distribution, Inc., which
supplied restaurants such as Burger King with everything from burgers to giveaway toys,
defaulted on $200 million in junk bonds. After the default, the bonds traded at just 18 cents
on the dollar, leaving investors with a loss of more than $160 million.
Even worse in AmeriServe’s case, the bonds had been issued only four months earlier,
thereby making AmeriServe an NCAA champion. While that might be a good thing for a
college basketball team such as the University of Kentucky Wildcats, in the bond market it
means “No Coupon At All,” and it’s not a good thing for investors.
CONCEPT QUESTIONS
6.3a What is a junk bond?
6.3b What does a bond rating say about the risk of fluctuations in a bond’s value resulting
from interest rate changes?
SOME DIFFERENT TYPES OF BONDS
Thus far, we have considered only “plain vanilla” corporate bonds. In this section, we briefly
look at bonds issued by governments and also at bonds with unusual features.
Government Bonds
The biggest borrower in the world—by a wide margin—is everybody’s favorite family mem-
ber, Uncle Sam. In mid-2018, the total debt of the U.S. government was more than $21.5 tril-
lion, or about $64,500 per U.S. citizen (and growing rapidly). When the government wishes
to borrow money for more than one year, it sells what are known as Treasury notes and
bonds to the public (in fact, it does so every month). Treasury notes have original maturities
ranging from 2 to 10 years, while Treasury bonds have longer maturities, extending out as
far as 30 years.
Most U.S. Treasury issues are ordinary coupon bonds. There are two important things
to keep in mind, however. First, U.S. Treasury issues, unlike essentially all other bonds, have
no default risk because (we hope) the Treasury always can come up with the money to make
the payments. Second, Treasury issues are exempt from state income taxes (though not fed-
eral income taxes). In other words, the coupons you receive on a Treasury note or bond are
taxed only at the federal level.
State and local governments also borrow money by selling notes and bonds. Such issues
are called municipal notes and bonds, or “munis.” Unlike Treasury issues, munis have vary-
ing degrees of default risk, and, in fact, they are rated much like corporate issues. Also, they
6.4
If you’re nervous about
the level of debt piled up
by the U.S. government,
don’t go to www.public
debt.treas.gov or to
www.usdebtclock.org!
Learn all about
government bonds at
www.newyorkfed.org.
ros13952_ch06_165-204.indd 182 12/24/18 4:46 PM
C H A P T E R 6 Interest Rates and Bond Valuation 183
are almost always callable. The most intriguing thing about munis is that their coupons are
exempt from federal income taxes (and state income taxes in some cases), which makes
them very attractive to high-income, high-tax-bracket investors.
Because of the enormous tax break they receive, the yields on municipal bonds are
much lower than the yields on taxable bonds. For example, in the middle of 2018, long-term,
high-quality corporate bonds were yielding about 4.2 percent. At the same time, long-term,
high-quality munis were yielding about 2.8 percent. Suppose an investor was in a 30 percent
tax bracket. All else being the same, would this investor prefer an Aa corporate bond or an
Aa municipal bond?
To answer, we need to compare the aftertax yields on the two bonds. Ignoring state
and local taxes, the muni pays 2.8 percent on both a pretax and an aftertax basis. The
corporate issue pays 4.2 percent before taxes, but it only pays .042 × (1 − .30) = .029, or
2.9 percent, once we account for the 30 percent tax bite. Given this, the yields are
quite close.
EXAMPLE 6.4 Taxable versus Municipal Bonds
Suppose taxable bonds are currently yielding 8 percent, while at the same time, munis of compara-
ble risk and maturity are yielding 6 percent. Which is more attractive to an investor in a 40 percent
tax bracket? What is the break-even tax rate? How do you interpret this rate?
For an investor in a 40 percent tax bracket, a taxable bond yields 8 × (1 − .40) = 4.8 percent
after taxes, so the muni is much more attractive. The break-even tax rate is the tax rate at which an
investor would be indifferent between a taxable and a nontaxable issue. If we let t* stand for the
break-even tax rate, then we can solve for it as follows:
.08 × (1 − t*) = .06
""""1 − t* = .06/.08 = .75
"""""""t* = .25 or 25%
Thus, an investor in a 25 percent tax bracket would make 6 percent after taxes from either bond.
Zero Coupon Bonds
A bond that pays no coupons at all must be offered at a price that is much lower than its
stated value. Such bonds are called zero coupon bonds, or zeroes.5
Suppose the Eight-Inch Nails (EIN) Company issues a $1,000 face value, five-year zero
coupon bond. The initial price is set at $508.35. Even though no interest payments are
made on the bond, zero coupon bond calculations use semiannual periods to be consistent
with coupon bond calculations. Using semiannual periods, it is straightforward to verify
that, at this price, the bond yields 14 percent to maturity. The total interest paid over the life
of the bond is $1,000 − 508.35 = $491.65.
For tax purposes, the issuer of a zero coupon bond deducts interest every year even
though no interest is actually paid. Similarly, the owner must pay taxes on interest accrued
every year, even though no interest is actually received.
zero coupon bond
A bond that makes no
coupon payments, and
thus is initially priced at a
deep discount.
5A bond issued with a very low coupon rate (as opposed to a zero coupon rate) is an original-issue discount
(OID) bond.
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184 P A R T 4 Valuing Stocks and Bonds
The way in which the yearly interest on a zero coupon bond is calculated is governed
by tax law. Before 1982, corporations could calculate the interest deduction on a straight-
line basis. For EIN, the annual interest deduction would have been $491.65/5 = $98.33
per year.
Under current tax law, the implicit interest is determined by amortizing the loan. We do
this by first calculating the bond’s value at the beginning of each year. For example, after
one year, the bond will have four years until maturity, so it will be worth $1,000/1.078 =
$582.01; the value in two years will be $1,000/1.076 = $666.34; and so on. The implicit in-
terest each year is the change in the bond’s value for the year. The values and interest ex-
penses for the EIN bond are listed in Table 6.2.
Notice that under the old rules, zero coupon bonds were more attractive for corpora-
tions because the deductions for interest expense were larger in the early years (compare the
implicit interest expense with the straight-line expense).
Under current tax law, EIN could deduct $73.66 in interest paid the first year, and the
owner of the bond would pay taxes on $73.66 of taxable income (even though no interest
was actually received). This second tax feature makes taxable zero coupon bonds less attrac-
tive to individuals. However, they are still a very attractive investment for tax-exempt inves-
tors with long-term dollar-denominated liabilities, such as pension funds, because the future
dollar value is known with relative certainty.
Some bonds are zero coupon bonds for only part of their lives. For example, at one
time, General Motors had a debenture outstanding that matured on March 15, 2036.
For the first 20 years, no coupon payments were scheduled, but 20 years into the bond’s
life, it was to begin paying coupons at a rate of 7.75 percent per year, payable
semiannually.
Floating-Rate Bonds
The conventional bonds we have talked about in this chapter have fixed-dollar obligations
because the coupon rate is set as a fixed percentage of the par value. Similarly, the principal
is set equal to the par value. Under these circumstances, the coupon payment and principal
are completely fixed.
With floating-rate bonds (floaters), the coupon payments are adjustable. The adjust-
ments are tied to an interest rate index such as the Treasury bill interest rate or the
30-year Treasury bond rate. The value of a f loating-rate bond depends on exactly how
the coupon payment adjustments are defined. In most cases, the coupon adjusts with a
lag to some base rate. Suppose a coupon rate adjustment is made on June 1. The adjust-
ment might be based on the simple average of Treasury bond yields during the previous
three months.
Another good bond
market site is
money.cnn.com.
Interest expense for
EIN’s zeroes
TABLE 6.2 Beginning Ending Implicit Straight-Line
Year Value Value Interest Expense Interest Expense
1 $508.35 $ 582.01 $ 73.66 $ 98.33
2 582.01 666.34 84.33 98.33
3 666.34 762.90 96.55 98.33
4 762.90 873.44 110.54 98.33
5 873.44 1,000.00 126.56 98.33
Total $491.65 $491.65
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C H A P T E R 6 Interest Rates and Bond Valuation 185
In addition, the majority of floaters have the following features:
1. The holder has the right to redeem the note at par on the coupon payment date after
some specified amount of time. This is called a put provision, and it is discussed in the
following section.
2. The coupon rate has a floor and a ceiling, meaning that the coupon is subject to a
minimum and a maximum. In this case, the coupon rate is said to be “capped,” and
the upper and lower rates are sometimes called the collar.
A particularly interesting type of floating-rate bond is an inflation-linked bond. Such
bonds have coupons that are adjusted according to the rate of inflation (the principal
amount may be adjusted as well). The U.S. Treasury began issuing such bonds in January of
1997. The issues are sometimes called “TIPS,” or Treasury Inflation-Protected Securities.
Other countries, including Canada, Israel, and Britain, have issued similar securities.
Other Types of Bonds
Many bonds have unusual, or exotic, features. Unfortunately, there are far too many varia-
tions for us to cover in detail here. We therefore focus on only a few of the more common
types.
Structured notes are bonds that are based on stocks, bonds, commodities, or currencies.
One particular type of structured note has a return based on a stock market index. At expi-
ration, if the stock index has declined, the bond returns the principal. However, if the stock
index has increased, the bond will return a portion of the stock index return, say 80 percent.
Another type of structured note will return twice the stock index return, but with the poten-
tial for loss of principal.
A convertible bond can be swapped for a fixed number of shares of stock anytime before
maturity at the holder’s option. Convertibles are relatively common, but the number has
been decreasing in recent years.
A put bond allows the holder to force the issuer to buy the bond back at a stated price.
The put feature is therefore the reverse of the call provision and is a relatively new
development.
A given bond may have many unusual features. For example, two exotic bonds include
CoCo bonds, which have a coupon payment, and NoNo bonds, which are zero coupon
bonds. CoCo and NoNo bonds are contingent convertible, putable, callable, subordinated
bonds. The contingent convertible clause is similar to the normal conversion feature, ex-
cept the contingency feature must be met. For example, a contingency feature may require
that the company stock trade at 110 percent of the conversion price for 20 out of 30 days.
Valuing a bond of this sort can be quite complex, and the yield to maturity calculation is
often meaningless. The nearby Finance Matters box provides some more examples of ex-
otic bonds.
CONCEPT QUESTIONS
6.4a What do you think would be the effect of a call provision on a bond’s coupon? Why
might an investor want to buy a callable bond?
6.4b What do you think would be the effect of a put feature on a bond’s coupon? How
about a convertibility feature? Why?
Official information on
U.S. inflation-indexed
bonds is at www
.treasurydirect.gov.
ros13952_ch06_165-204.indd 185 12/24/18 4:46 PM
Exotic Bonds
Bonds come in many flavors. The unusual types are called “exotics” and can range from the fairly simple to the truly
esoteric. Take the case of mortgage-backed securities
(MBSs). MBSs are a type of securitized financial instrument.
In securitization, cash flows from financial assets are pooled
together into securities, and the securities are sold to inves-
tors. With an MBS, banks or mortgage brokers who originate
mortgages sell the mortgages to a trust. The trust pools the
mortgages and sells bonds to investors. Bondholders re-
ceive payments based on the mortgage payments made by
homeowners. During 2008, problems with MBSs skyrock-
eted due to the precipitous drop in real estate values and
the sharply increased default rates on the underlying
mortgages.
The reverse convertible is a relatively new type of
structured note. One type generally offers a high coupon
rate, but the redemption at maturity can be paid in cash at
par value or paid in shares of stock. For example, one recent
General Motors (GM) reverse convertible had a coupon rate
of 16 percent, which is a very high coupon rate in today’s in-
terest rate environment. However, at maturity, if GM’s stock
declined sufficiently, bondholders would receive a fixed
number of GM shares that were worth less than par value.
So, while the income portion of the bond return would be
high, the potential loss in par value easily could erode the
extra return.
CAT bonds are issued to cover insurance companies
against natural catastrophes. The type of natural catastro-
phe is outlined in the bond. For example, about 30 percent
of all CAT bonds protect against a North Atlantic hurricane.
The way these issues are structured is that the borrowers
can suspend payment temporarily (or even permanently) if
they have significant hurricane-related losses. These CAT
bonds may seem like pretty risky investments, but, to date,
only five have not been paid in full. Because of Hurricane
Katrina, CAT bondholders lost $190 million. CAT bondhold-
ers also lost $300 million due to the 2011 tsunami in Japan.
During 2011, two other CAT bond issues, each worth $100
million, were triggered due to an unusually active tornado
season, and a CAT bond was triggered due to the 2017
earthquake in Mexico. This bond was issued on August 4th
and the earthquake occurred on September 7th.
Perhaps the most unusual bond (and certainly the most
ghoulish) is the “death bond.” Companies such as Stone
Street Financial purchase life insurance policies from indi-
viduals who are expected to die within the next 10 years.
They then sell bonds that are paid off from the life insurance
proceeds received when the policyholders die. The return on
the bonds to investors depends on how long the policyhold-
ers live. A major risk is that if medical treatment advances
quickly, it will raise the life expectancy of the policyholders,
thereby decreasing the return to the bondholder.
FINANCE MATTERS
186
BOND MARKETS
Bonds are bought and sold in enormous quantities every day. You may be surprised to learn
that the trading volume in bonds on a typical day is many, many times larger than the trad-
ing volume in stocks (by trading volume, we mean the amount of money that changes
hands). Here is a finance trivia question: What is the largest securities market in the world?
Most people would guess the New York Stock Exchange. In fact, the largest securities mar-
ket in the world in terms of trading volume is the U.S. Treasury market.
How Bonds Are Bought and Sold
As we mentioned all the way back in Chapter 1, most trading in bonds takes place over the
counter, or OTC. Recall that this means that there is no particular place where buying and
selling occur. Instead, dealers around the country (and around the world) stand ready to buy
and sell. The various dealers are connected electronically.
One reason the bond markets are so big is that the number of bond issues far exceeds
the number of stock issues. There are two reasons for this. First, a corporation would typi-
cally have only one common stock issue outstanding (there are exceptions to this that we
discuss in our next chapter). However, a single large corporation could easily have a dozen
6.5
coverage online
Excel
Master
ros13952_ch06_165-204.indd 186 12/24/18 4:46 PM
C H A P T E R 6 Interest Rates and Bond Valuation 187
or more note and bond issues outstanding. Beyond this, federal, state, and local borrowing
is enormous. For example, even a small city would usually have a wide variety of notes and
bonds outstanding, representing money borrowed to pay for things like roads, sewers, and
schools. When you think about how many small cities there are in the United States, you
begin to get the picture!
Because the bond market is almost entirely OTC, it has historically had little or no
transparency. A financial market is transparent if it is possible to easily observe its prices
and trading volume. On the New York Stock Exchange, for example, it is possible to see the
price and quantity for every single transaction. In contrast, in the bond market, historically
it was not possible to observe either. Transactions are privately negotiated between parties,
and there is little or no centralized reporting of transactions.
Although the total volume of trading in bonds far exceeds that in stocks, only a very
small fraction of the total bond issues that exist actually trade on a given day. This means
that getting up-to-date prices on individual bonds is often difficult or impossible, particu-
larly for smaller corporate or municipal issues. Instead, a variety of sources of estimated
prices exist and are very commonly used.
Most of the information is self-explanatory. The Price and Yield columns show the price and yield
to maturity of the issues based on their most recent sales. If you need more information about a
particular issue, clicking on it will give you more details such as coupon dates and call dates.
QUESTIONS
1. Go to this website and find the last bond shown in the accompanying table. When was
this bond issued? What was the size of the bond issue? What were the yield to maturity
and price when the bond was issued?
2. When you search for Chevron bonds (CVX), you will find bonds for several companies
listed. Why do you think Chevron has bonds issued with different corporate names?
W R K T H E W E B
Bond quotes have become more available with the rise of the web. One site where you can find current bond prices (from TRACE) is finra-markets.morningstar.com/BondCenter. We went to
the site and entered “AZO” for AutoZone, the well-known auto parts company. We found a total of
10 bond issues outstanding. Here you see the information we pulled up.
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188 P A R T 4 Valuing Stocks and Bonds
Bond Price Reporting
In 2002, transparency in the corporate bond market began to improve dramatically. Under
new regulations, corporate bond dealers are now required to report trade information
through what is known as the Trade Reporting and Compliance Engine (TRACE). A nearby
Work the Web box shows how to get TRACE prices.
As we mentioned before, the U.S. Treasury market is the largest securities market in the
world. As with bond markets in general, it is an OTC market, so there is limited transpar-
ency. However, unlike the situation with bond markets in general, trading in Treasury issues,
particularly recently issued ones, is very heavy. Each day, representative prices for outstand-
ing Treasury issues are reported.
Figure 6.3 shows a portion of the daily Treasury note and bond listings from The Wall Street
Journal online. The only difference between a Treasury note and a Treasury bond is that notes
have 10 years or less to maturity at the time of issuance. The entry that begins “5/15/2030” is
highlighted. Reading from left to right, the “5/15/2030” tells us that the bond’s maturity is May
15, 2030. The 6.250 is the bond’s coupon rate. Treasury bonds all make semiannual payments
and have a face value of $1,000, so this bond will pay $31.25 per six months until it matures.
The next two pieces of information are the bid and asked prices. In general, in any OTC
or dealer market, the bid price represents what a dealer is willing to pay for a security, and the
asked price (or “ask” price) is what a dealer is willing to take for it. The difference between
the two prices is called the bid-ask spread (or “spread”), and it represents the dealer’s profit.
Treasury prices are quoted as a percentage of face value. The bid price, or what a dealer
is willing to pay for the bond, on the 5/15/2030 bond is 132.8984. With a $1,000 face value,
this quote represents $1,328.984. The asked price, or the price at which the dealer is willing
to sell the bond, is 132.9609, or $1,329.609.
The next number quoted is the change in the asked price from the previous day, mea-
sured as a percentage of face value, so this issue’s asked price rose by .4688 percent, or
$4.688, in value from the previous day. Finally, the last number reported is the yield to ma-
turity, based on the asked price. Notice that this is a premium bond because it sells for more
than its face value. Not surprisingly, its yield to maturity (2.949 percent) is less than its
coupon rate (6.25 percent).
The very last ordinary bond listed, in this case the 5/15/2048, is often called the “bell-
wether” bond. This bond’s yield is the one that is usually reported in the evening news. So,
for example, when you hear that long-term interest rates rose, what is really being said is that
the yield on this bond went up (and its price went down).
If you examine the yields on the various issues in Figure 6.3, you clearly see that they
vary by maturity. Why this occurs and what it might mean is one of the things we discuss in
our next section.
To learn more about
TRACE, visit www.finra
.org.
To purchase newly issued
corporate bonds, go to
www.incapital.com.
To buy Treasury bonds
directly from the
government, go to www
.treasurydirect.gov.
bid price
The price a dealer is
willing to pay for a
security.
asked price
The price a dealer is
willing to take for a
security.
bid-ask spread
The difference between
the bid price and the
asked price.
The Federal Reserve
Bank of St. Louis
maintains dozens of
online files containing
macroeconomic data as
well as rates on U.S.
Treasury issues. Go to
fred.stlouisfed.org.
EXAMPLE 6.5 Treasury Quotes
Locate the Treasury issue in Figure 6.3 maturing in February 2024. What is its coupon rate? What is
its bid price? What was the previous day’s asked price?
The bond listed as 2/29/2024 is the one we seek. Its coupon rate is 2.125 percent of face
value. The bid price is 96.1172, or 96.1172 percent of face value. The ask price is 96.1328, which is up
by .1484 from the previous day. This means that the ask price on the previous day was equal to
96.1328 − .1484 = 95.9844.
A Note on Bond Price Quotes If you buy a bond between coupon payment dates,
the price you pay is usually more than the price you are quoted. The reason is that standard
convention in the bond market is to quote prices net of “accrued interest,” meaning that
ros13952_ch06_165-204.indd 188 12/24/18 4:46 PM
C H A P T E R 6 Interest Rates and Bond Valuation 189
accrued interest is deducted to arrive at the quoted price. This quoted price is called the
clean price. The price you actually pay, however, includes the accrued interest. This price is
the dirty price, also known as the “full” or “invoice” price.
An example is the easiest way to understand these issues. Suppose you buy a bond
with a 12 percent annual coupon, payable semiannually. You actually pay $1,080 for this
bond, so $1,080 is the dirty, or invoice, price. Further, on the day you buy it, the next cou-
pon is due in four months, so you are between coupon dates. Notice that the next coupon
will be $60.
The accrued interest on a bond is calculated by taking the fraction of the coupon pe-
riod that has passed, in this case two months out of six, and multiplying this fraction by the
next coupon, $60. So, the accrued interest in this example is 2/6 × $60 = $20. The bond’s
quoted price (i.e., its clean price) would be $1,080 − 20 = $1,060.
CONCEPT QUESTIONS
6.5a Why do we say bond markets may have little or no transparency?
6.5b In general, what are bid and ask prices?
6.5c What is the difference between a bond’s clean price and dirty price?
clean price
The price of a bond net of
accrued interest; this is
the price that is typically
quoted.
dirty price
The price of a bond
including accrued interest,
also known as the full or
invoice price. This is the
price the buyer actually
pays.
Sample Wall Street
Journal U.S. Treasury
note and bond prices
FIGURE 6.3
Asked
Maturity Coupon Bid Asked Chg Yield
1/31/2019 1.500 99.5469 99.5625 −0.0078 2.205
12/31/2021 2.125 97.8906 97.9063 0.0703 2.749
1/31/2022 1.500 95.6563 95.6719 0.0547 2.762
2/28/2023 2.625 99.2109 99.2266 0.1172 2.801
9/30/2023 1.375 92.7969 92.8125 0.1172 2.847
2/29/2024 2.125 96.1172 96.1328 0.1484 2.864
7/31/2024 2.125 95.7344 95.7500 0.1172 2.887
1/31/2025 2.500 97.6328 97.6484 0.1953 2.892
4/30/2025 2.875 99.8359 99.8516 0.2109 2.899
11/15/2026 6.500 126.6406 126.6563 0.3125 2.906
2/15/2029 5.250 120.9453 121.0078 0.4063 2.941
5/15/2030 6.250 132.8984 132.9609 0.4688 2.949
2/15/2036 4.500 120.9375 121.0000 0.5625 2.964
5/15/2037 5.000 129.0938 129.1563 0.6641 2.973
11/15/2039 4.375 121.3047 121.3672 0.6953 3.014
5/15/2040 4.375 121.5313 121.5938 0.7500 3.021
8/15/2041 3.750 111.6875 111.7500 0.7500 3.040
5/15/2042 3.000 99.1875 99.2188 0.7266 3.046
2/15/2043 3.125 101.1641 101.1953 0.7344 3.056
2/15/2044 3.625 110.0313 110.0625 0.6875 3.056
8/15/2046 2.250 84.6797 84.7109 0.6016 3.064
5/15/2047 3.000 98.7578 98.7891 0.6953 3.063
5/15/2048 3.125 101.1875 101.2188 0.7422 3.062
Source: www.wsj.com, 6/14/2018.
U.S. Treasury Quotes
Treasury note and bond data are representative over-the-counter quotations as of 3 p.m. Eastern time.
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190 P A R T 4 Valuing Stocks and Bonds
INFLATION AND INTEREST RATES
So far, we haven’t considered the role of inflation in our various discussions of interest rates,
yields, and returns. Because this is an important consideration, we consider the impact of
inflation next.
Real versus Nominal Rates
In examining interest rates, or any other financial market rates such as discount rates, bond
yields, rates of return, and required returns, it is often necessary to distinguish between
real rates and nominal rates. Nominal rates are called “nominal” because they have not
been adjusted for inflation. Real rates are rates that have been adjusted for inflation.
To see the effect of inflation, suppose prices currently are rising by 5 percent per year.
In other words, the rate of inflation is 5 percent. An investment is available that will be
worth $115.50 in one year. It costs $100 today. Notice that with a present value of $100 and
a future value in one year of $115.50, this investment has a 15.5 percent rate of return. In
calculating this 15.5 percent return, we did not consider the effect of inflation, however, so
this is the nominal return.
What is the impact of inflation here? To answer, suppose pizzas cost $5 apiece at the
beginning of the year. With $100, we can buy 20 pizzas. Because the inflation rate is 5 per-
cent, pizzas will cost 5 percent more, or $5.25, at the end of the year. If we take the invest-
ment, how many pizzas can we buy at the end of the year? Measured in pizzas, what is the
rate of return on this investment?
Our $115.50 from the investment will buy us $115.50/5.25 = 22 pizzas. This is up from
20 pizzas, so our pizza rate of return is 10 percent. What this illustrates is that even though
the nominal return on our investment is 15.5 percent, our buying power goes up by only 10
percent because of inflation. Put another way, we are really only 10 percent richer. In this
case, we say that the real return is 10 percent.
Alternatively, we can say that with 5 percent inflation, each of the 115.50 nominal dol-
lars we get is worth 5 percent less in real terms, so the real dollar value of our investment in
a year is:
$115.50 / 1.05 = $110
What we have done is to deflate the $115.50 by 5 percent. Because we give up $100 in cur-
rent buying power to get the equivalent of $110, our real return is again 10 percent. Now that
we have removed the effect of future inflation, this $110 is said to be measured in current
dollars.
The difference between nominal and real rates is important and bears repeating:
The nominal rate on an investment is the percentage change in the number of dollars
you have.
The real rate on an investment is the percentage change in how much you can buy
with your dollars, in other words, the percentage change in your buying power.
The Fisher Effect
Our discussion of real and nominal returns illustrates a relationship often called the
Fisher effect (after the great economist Irving Fisher). Because investors are ultimately con-
cerned with what they can buy with their money, they require compensation for inflation.
6.6
real rates
Interest rates or rates of
return that have been
adjusted for inflation.
nominal rates
Interest rates or rates of
return that have not been
adjusted for inflation.
Fisher effect
The relationship among
nominal returns, real
returns, and inflation.
ros13952_ch06_165-204.indd 190 12/24/18 4:46 PM
C H A P T E R 6 Interest Rates and Bond Valuation 191
Let R stand for the nominal rate and r stand for the real rate. The Fisher effect tells us that
the relationship between nominal rates, real rates, and inflation can be written as:
1 + R = (1 + r) × (1 + h) [6.2]
where h is the inflation rate.
In the preceding example, the nominal rate was 15.50 percent, and the inflation rate
was 5 percent. What was the real rate? We can determine it by plugging in these numbers:
1 + .1550 = (1 + r) × (1 + .05)
1 + r = 1.1550/1.05 = 1.10
r = .10, or 10%
This real rate is the same as we had before. If we take another look at the Fisher effect, we
can rearrange things a little as follows:
1 + R = (1 + r) × (1 + h)
R = r + h + r × h [6.3]
What this tells us is that the nominal rate has three components. First, there is the real rate
on the investment, r. Next, there is the compensation for the decrease in the value of the
money originally invested because of inflation, h. The third component represents compen-
sation for the fact that the dollars earned on the investment also are worth less because of
the inflation.
This third component is usually small, so it is often dropped. The nominal rate is then
approximately equal to the real rate plus the inflation rate:
R ≈ r + h [6.4]
EXAMPLE 6.6 The Fisher Effect
If investors require a 10 percent real rate of return, and the inflation rate is 8 percent, what must the
approximate nominal rate be? The exact nominal rate?
First of all, the nominal rate is approximately equal to the sum of the real rate and the inflation
rate: 10% + 8% = 18%. From the Fisher effect, we have:
1 + R = (1 + r) × (1 + h)
= 1.10 × 1.08
= 1.1880
Therefore, the nominal rate will actually be closer to 19 percent.
It is important to note that financial rates, such as interest rates, discount rates, and
rates of return, are almost always quoted in nominal terms. To remind you of this, we will
henceforth use the symbol R instead of r in most of our discussions about such rates.
CONCEPT QUESTIONS
6.6a What is the difference between a nominal and a real return? Which is more
important to a typical investor?
6.6b What is the Fisher effect?
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192 P A R T 4 Valuing Stocks and Bonds
DETERMINANTS OF BOND YIELDS
We are now in a position to discuss the determinants of a bond’s yield. As we will see, the
yield on any particular bond is a reflection of a variety of factors, some common to all
bonds and some specific to the issue under consideration.
The Term Structure of Interest Rates
At any point in time, short-term and long-term interest rates will generally be different.
Sometimes short-term rates are higher, sometimes lower. Figure 6.4 gives us a long-range
perspective on this by showing over two centuries of short- and long-term interest rates. As
shown, through time, the difference between short- and long-term rates has ranged from es-
sentially zero to up to several percentage points, both positive and negative.
The relationship between short- and long-term interest rates is known as the
term structure of interest rates. To be a little more precise, the term structure of interest
rates tells us what nominal interest rates are on default-free, pure discount bonds of all matur-
ities. These rates are, in essence, “pure” interest rates because they involve no risk of default
and a single, lump-sum future payment. In other words, the term structure tells us the pure
time value of money for different lengths of time.
When long-term rates are higher than short-term rates, we say that the term structure is
upward sloping, and when short-term rates are higher, we say it is downward sloping. The
term structure also can be “humped.” When this occurs, it is usually because rates increase
at first, but then begin to decline as we look at longer- and longer-term rates. The most com-
mon shape of the term structure, particularly in modern times, is upward sloping, but the
degree of steepness has varied quite a bit.
6.7
coverage online
Excel
Master
term structure of
interest rates
The relationship between
nominal interest rates on
default-free, pure discount
securities and time to
maturity; that is, the pure
time value of money.
U.S. interest rates: 1800 to mid-2018
2
4
6
8
10
12
14
16
0
1800 20 40 60 80 1900 20 40 60 80 2000 2025
Year
Interest
rate (%)
Long-term rates
Short-term rates
FIGURE 6.4
Source: Siegel, Jeremy J., Stocks for the Long Run, 3rd ed., New York, NY: McGraw-Hill, 2004, as updated by the authors.
ros13952_ch06_165-204.indd 192 12/24/18 4:46 PM
C H A P T E R 6 Interest Rates and Bond Valuation 193
What determines the shape of the term structure? There are three basic components.
The first two are the ones we discussed in our previous section: the real rate of interest and
the rate of inflation. The real rate of interest is the compensation investors demand for for-
going the use of their money. You can think of it as the pure time value of money after ad-
justing for the effects of inflation.
The real rate of interest is the basic component underlying every interest rate, regard-
less of the time to maturity. When the real rate is high, all interest rates will tend to be
higher, and vice versa. Thus, the real rate doesn’t really determine the shape of the term
structure; instead, it mostly influences the overall level of interest rates.
In contrast, the prospect of future inflation very strongly influences the shape of the
term structure. Investors thinking about loaning money for various lengths of time recog-
nize that future inflation erodes the value of the dollars that will be returned. As a result,
investors demand compensation for this loss in the form of higher nominal rates. This extra
compensation is called the inflation premium.
If investors believe that the rate of inflation will be higher in the future, then long-term
nominal interest rates will tend to be higher than short-term rates. Thus, an upward-sloping term
structure may be a reflection of anticipated increases in inflation. Similarly, a downward-sloping
term structure probably reflects the belief that inflation will be falling in the future.
The third, and last, component of the term structure has to do with interest rate risk. As
we discussed earlier in the chapter, longer-term bonds have much greater risk of loss result-
ing from changes in interest rates than do shorter-term bonds. Investors recognize this risk,
and they demand extra compensation in the form of higher rates for bearing it. This extra
compensation is called the interest rate risk premium. The longer the term to maturity, the
greater is the interest rate risk, so the interest rate risk premium increases with maturity.
However, as we discussed earlier, interest rate risk increases at a decreasing rate, so the in-
terest rate risk premium does as well.6
Putting the pieces together, we see that the term structure reflects the combined effect
of the real rate of interest, the inflation premium, and the interest rate risk premium. Figure
6.5 shows how these can interact to produce an upward-sloping term structure (in the top
part of Figure 6.5) or a downward-sloping term structure (in the bottom part).
In the top part of Figure 6.5, notice how the rate of inflation is expected to rise gradually.
At the same time, the interest rate risk premium increases at a decreasing rate, so the com-
bined effect is to produce a pronounced upward-sloping term structure. In the bottom part of
Figure 6.5, the rate of inflation is expected to fall in the future, and the expected decline is
enough to offset the interest rate risk premium and produce a downward-sloping term struc-
ture. Notice that if the rate of inflation was expected to decline by only a small amount, we
could still get an upward-sloping term structure because of the interest rate risk premium.
We assumed in drawing Figure 6.5 that the real rate would remain the same. Actually,
expected future real rates could be larger or smaller than the current real rate. Also, for
simplicity, we used straight lines to show expected future inflation rates as rising or declin-
ing, but they do not necessarily have to look like this. They could, for example, rise and then
fall, leading to a humped yield curve.
Bond Yields and the Yield Curve: Putting It All Together
Going back to Figure 6.3, recall that we saw that the yields on Treasury notes and bonds of
different maturities are not the same. Each day, in addition to the Treasury prices and yields
shown in Figure 6.3, The Wall Street Journal provides a plot of Treasury yields relative to
inflation premium
The portion of a nominal
interest rate that
represents compensation
for expected future
inflation.
interest rate risk
premium
The compensation
investors demand for
bearing interest rate risk.
Online yield curve
information is available
at www.bloomberg.com
/markets.
6In days of old, the interest rate risk premium was called a “liquidity” premium. Today, the term liquidity premium has
an altogether different meaning, which we explore in our next section. Also, the interest rate risk premium is some-
times called a maturity risk premium. Our terminology is consistent with the modern view of the term structure.
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194 P A R T 4 Valuing Stocks and Bonds
The term structure of interest rates
B. Downward-sloping term structureInterest
rate
Time to
maturity
Nominal
interest
rate
Interest rate
risk premium
Inflation
premium
Real rate
Interest
rate
A. Upward-sloping term structure
Time to
maturity
Nominal
interest
rate
Interest rate
risk premium
Inflation
premium
Real rate
FIGURE 6.5
maturity. This plot is called the Treasury yield curve (or the yield curve). Figure 6.6 shows
the yield curve as of June 2018. Note, the yield curve available on the Treasury website will
display both the nominal and real yield curves.
As you probably now suspect, the shape of the yield curve is a reflection of the term
structure of interest rates. In fact, the Treasury yield curve and the term structure of interest
rates are almost the same thing. The only difference is that the term structure is based on
pure discount bonds, whereas the yield curve is based on coupon bond yields. As a result,
Treasury yields depend on the three components that underlie the term structure: the real
rate, expected future inflation, and the interest rate risk premium.
Treasury notes and bonds have three important features that we need to remind you of:
They are default-free, they are taxable, and they are highly liquid. This is not true of bonds
in general, so we need to examine what additional factors come into play when we look at
bonds issued by corporations or municipalities.
The first thing to consider is credit risk—that is, the possibility of default. Investors
recognize that issuers other than the Treasury may or may not make all the promised pay-
ments on a bond, so they demand a higher yield as compensation for this risk. This extra
compensation is called the default risk premium. Earlier in the chapter, we saw how bonds
Treasury yield curve
A plot of the yields on
Treasury notes and bonds
relative to maturity.
default risk premium
The portion of a nominal
interest rate or bond yield
that represents
compensation for the
possibility of default.
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C H A P T E R 6 Interest Rates and Bond Valuation 195
were rated based on their credit risk. What you will find if you start looking at bonds of
different ratings is that lower-rated bonds have higher yields.
An important thing to recognize about a bond’s yield is that it is calculated assuming that
all the promised payments will be made. As a result, it is really a promised yield, and it may or
may not be what you will earn. In particular, if the issuer defaults, your actual yield will be lower,
probably much lower. This fact is particularly important when it comes to junk bonds. Thanks
to a clever bit of marketing, such bonds are now commonly called high-yield bonds, which has
a much nicer ring to it; but now you recognize that these are really high-promised-yield bonds.
Next, recall that we discussed earlier how municipal bonds are free from most taxes
and, as a result, have much lower yields than taxable bonds. Investors demand the extra
yield on a taxable bond as compensation for the unfavorable tax treatment. This extra com-
pensation is the taxability premium.
Finally, bonds have varying degrees of liquidity. As we discussed earlier, there are an
enormous number of bond issues, most of which do not trade on a regular basis. As a result,
if you wanted to sell quickly, you would probably not get as good a price as you could other-
wise. Investors prefer liquid assets to illiquid ones, so they demand a liquidity premium on
top of all the other premiums we have discussed. As a result, all else being the same, less-
liquid bonds will have higher yields than more-liquid bonds.
Conclusion
If we combine all of the things we have discussed regarding bond yields, we find that bond yields
represent the combined effect of no fewer than six things. The first is the real rate of interest. On
top of the real rate are five premiums representing compensation for (1) expected future infla-
tion, (2) interest rate risk, (3) default risk, (4) taxability, and (5) lack of liquidity. As a result,
determining the appropriate yield on a bond requires careful analysis of each of these effects.
CONCEPT QUESTIONS
6.7a What is the term structure of interest rates? What determines its shape?
6.7b What is the Treasury yield curve?
6.7c What are the six components that make up a bond’s yield?
taxability premium
The portion of a nominal
interest rate or bond yield
that represents
compensation for
unfavorable tax status.
liquidity premium
The portion of a nominal
interest rate or bond yield
that represents
compensation for lack of
liquidity.
The Treasury yield
curve
June 14, 2018
FIGURE 6.6
Source: www.treasury.gov, June 14, 2018
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196 P A R T 4 Valuing Stocks and Bonds
SUMMARY AND CONCLUSIONS
This chapter has explored bonds and bond yields. We saw that:
1. Determining bond prices and yields is an application of basic discounted cash flow
principles.
2. Bond values move in the direction opposite that of interest rates, leading to potential
gains or losses for bond investors.
3. Bonds have a variety of features spelled out in a document called the indenture.
4. Bonds are rated based on their default risk. Some bonds, such as Treasury bonds, have
no risk of default, whereas so-called junk bonds have substantial default risk.
5. A wide variety of bonds exist, many of which contain exotic, or unusual, features.
6. Almost all bond trading is OTC, with little or no market transparency. As a result,
bond price and volume information can be difficult to find.
7. Bond yields reflect the effect of six different things: the real rate and five premiums
that investors demand as compensation for inflation, interest rate risk, default risk,
taxability, and lack of liquidity.
In closing, we note that bonds are a vital source of financing to governments and corpora-
tions of all types. Bond prices and yields are a rich subject, and our one chapter, necessarily,
touches on only the most important concepts and ideas. There is a great deal more we could
say, but, instead, we move on to stocks in our next chapter.
POP QUIZ!
Can you answer the following questions? If your class is using Connect, log on to
SmartBook to see if you know the answers to these and other questions, check out
the study tools, and find out what topics require additional practice!
Section 6.1 What is the coupon rate on a bond that has a par value of $1,000, a
market value of $1,100, and a coupon interest rate of $100 per year?
Section 6.2 What is the provision in the bond indenture giving the issuing company
the option to repurchase bonds prior to maturity?
Section 6.3 Do bond ratings consider default risk?
Section 6.4 What are the features of municipal bonds?
Section 6.5 What does the dirty price of a bond represent?
Section 6.6 What is the difference between a real and a nominal rate of return?
Section 6.7 What do historical data suggest about the nature of short-term and
long-term interest rates?
CHAPTER REVIEW AND SELF-TEST PROBLEMS
6.1 Bond Values A Microgates Industries bond has a 10 percent coupon rate and a
$1,000 face value. Interest is paid semiannually, and the bond has 20 years to
maturity. If investors require a 12 percent yield, what is the bond’s value? What is
the effective annual yield on the bond? (See Problem 6.)
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C H A P T E R 6 Interest Rates and Bond Valuation 197
6.2 Yields A Macrohard Corp. bond carries an 8 percent coupon, paid semiannually.
The par value is $1,000, and the bond matures in six years. If the bond currently
sells for $911.37, what is its yield to maturity? What is the effective annual yield?
(See Problem 21.)
■ Answers to Chapter Review and Self-Test Problems
6.1 Because the bond has a 10 percent coupon yield and investors require a 12 percent
return, we know that the bond must sell at a discount. Notice that, because the bond
pays interest semiannually, the coupons amount to $100/2 = $50 every six months.
The required yield is 12%/2 = 6% every six months. Finally, the bond matures in
20 years, so there are a total of 40 six-month periods.
The bond’s value thus is equal to the present value of $50 every six months for
the next 40 six-month periods, plus the present value of the $1,000 face amount:
Bond value = $50 × (1 − 1/1.0640)/.06 + 1,000/1.0640
= $50 × 15.0463 + 1,000/10.2857
= $849.54
Notice that we discounted the $1,000 back 40 periods at 6 percent per period, rather
than 20 years at 12 percent. The reason is that the effective annual yield on the bond
is 1.062 − 1 = .1236, or 12.36%, not 12 percent. We thus could have used 12.36 per-
cent per year for 20 years when we calculated the present value of the $1,000 face
amount, and the answer would have been the same.
6.2 The present value of the bond’s cash flows is its current price, $911.37. The coupon
is $40 every six months for 12 periods. The face value is $1,000. So, the bond’s yield
is the unknown discount rate in the following:
$911.37 = $40 × [1 − 1/(1 + r)12]/r + $1,000/(1 + r)12
The bond sells at a discount. Because the coupon rate is 8 percent, the yield must be
something in excess of that.
If we were to solve this by trial and error, we might try 12 percent (or 6 percent
per six months):
Bond value = $40 × (1 − 1/1.0612)/.06 + $1,000/1.0612
= $832.32
This is less than the actual value, so our discount rate is too high. We now know that
the yield is somewhere between 8 and 12 percent. With further trial and error (or a
little machine assistance), the yield works out to be 10 percent, or 5 percent every six
months.
By convention, the bond’s yield to maturity would be quoted as 2 × 5% = 10%.
The effective yield is thus 1.052 − 1 = .1025, or 10.25%.
CRITICAL THINKING AND CONCEPTS REVIEW
6.1 Treasury Bonds Is it true that a U.S. Treasury security is risk free?
LO 2 6.2 Interest Rate Risk Which has greater interest rate risk, a 30-year Treasury
bond or a 30-year BB corporate bond?
LO 1
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198 P A R T 4 Valuing Stocks and Bonds
LO 1 6.3 Treasury Pricing With regard to bid and ask prices on a Treasury bond, is
it possible for the bid price to be higher? Why or why not?
LO 2 6.4 Yield to Maturity Treasury bid and ask quotes are sometimes given in
terms of yields, so there would be a bid yield and an ask yield. Which do
you think would be larger? Explain.
LO 1 6.5 Call Provisions A company is contemplating a long-term bond issue. It is
debating whether or not to include a call provision. What are the benefits
to the company from including a call provision? What are the costs? How
do these answers change for a put provision?
LO 1 6.6 Coupon Rate How does a bond issuer decide on the appropriate coupon
rate to set on its bonds? Explain the difference between the coupon rate
and the required return on a bond.
LO 4 6.7 Real and Nominal Returns Are there any circumstances under which an
investor might be more concerned about the nominal return on an
investment than the real return?
LO 3 6.8 Bond Ratings Companies pay rating agencies such as Moody’s and S&P
to rate their bonds, and the costs can be substantial. However, companies
are not required to have their bonds rated in the first place; doing so is
strictly voluntary. Why do you think they do it?
LO 3 6.9 Bond Ratings Often, junk bonds are not rated. Why?
LO 3 6.10 Crossover Bonds Looking back at the crossover bonds we discussed in
the chapter, why do you think split ratings such as these occur?
LO 1 6.11 Municipal Bonds Why is it that municipal bonds are not taxed at the
federal level but are taxable across state lines? Why is it that U.S. Treasury
bonds are not taxable at the state level? (You may need to dust off the
history books for this one.)
LO 1 6.12 Treasury Market All Treasury bonds are relatively liquid, but some are
more liquid than others. Take a look back at Figure 6.3. Which issues
appear to be the most liquid? The least liquid?
LO 3 6.13 Rating Agencies Several years ago, a controversy erupted regarding bond-
rating agencies when some agencies began to provide unsolicited bond
ratings. Why do you think this is controversial?
LO 1 6.14 Bonds as Equity The 100-year bonds we discussed in the chapter have
something in common with junk bonds. Critics charge that, in both cases,
the issuers are really selling equity in disguise. What are the issues here?
Why would a company want to sell “equity in disguise”?
LO 2 6.15 Bond Prices versus Yields
a. What is the relationship between the price of a bond and its YTM?
b. Explain why some bonds sell at a premium over par value while
other bonds sell at a discount. What do you know about the
relationship between the coupon rate and the YTM for premium
bonds? What about for discount bonds? For bonds selling at par
value?
c. What is the relationship between the current yield and YTM for
premium bonds? For discount bonds? For bonds selling at par
value?
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C H A P T E R 6 Interest Rates and Bond Valuation 199
QUESTIONS AND PROBLEMS
Select problems are available in McGraw-Hill Connect. Please see the pack-
aging options section of the Preface for more information.
BASIC (Questions 1–17)
1. Interpreting Bond Yields Is the yield to maturity on a bond the same thing
as the required return? Is YTM the same thing as the coupon rate? Suppose
today a 10 percent coupon bond sells at par. Two years from now, the
required return on the same bond is 8 percent. What is the coupon rate on
the bond now? The YTM?
2. Interpreting Bond Yields Suppose you buy a 7 percent coupon, 20-year
bond today when it’s first issued. If interest rates suddenly rise to 15 percent,
what happens to the value of your bond? Why?
3. Bond Prices Vulcan, Inc., has 7 percent coupon bonds on the market that
have 13 years left to maturity. The bonds make annual payments and have a
par value of $1,000. If the YTM on these bonds is 8.4 percent, what is the
current bond price?
4. Bond Yields The Petit Chef Co. has 7 percent coupon bonds on the market
with nine years left to maturity. The bonds make annual payments and have a
par value of $1,000. If the bonds currently sell for $1,038.50, what is the YTM?
5. Coupon Rates Big Canyon Enterprises has bonds on the market making
annual payments, with 12 years to maturity, a par value of $1,000, and a
price of $1,030. At this price, the bonds yield 6.14 percent. What must the
coupon rate be on the bonds?
6. Bond Prices Dufner Co. issued 15-year bonds one year ago at a coupon rate of
4.8 percent. The bonds make semiannual payments. If the YTM on these bonds
is 5.3 percent, what is the current dollar price assuming a $1,000 par value?
7. Bond Yields Parkway Void Co. issued 15-year bonds two years ago at a
coupon rate of 5.4 percent. The bonds make semiannual payments. If these
bonds currently sell for 106 percent of par value, what is the YTM?
8. Coupon Rates Henley Corporation has bonds on the market with 10.5
years to maturity, a YTM of 5.7 percent, a par value of $1,000, and a current
price of $945. The bonds make semiannual payments. What must the
coupon rate be on the bonds?
9. Calculating Real Rates of Return If Treasury bills are currently paying 4.7
percent and the inflation rate is 1.9 percent, what is the approximate real rate
of interest? The exact real rate?
10. Inflation and Nominal Returns Suppose the real rate is 1.8 percent and the
inflation rate is 3.7 percent. What rate would you expect to see on a Treasury bill?
11. Nominal and Real Returns An investment offers a total return of 12 percent
over the coming year. Alex Hamilton thinks the total real return on this
investment will be only 9 percent. What does Alex believe the inflation rate
will be over the next year?
12. Nominal versus Real Returns Say you own an asset that had a total return
last year of 12.1 percent. If the inflation rate last year was 3.4 percent, what
was your real return?
LO 2
LO 2
LO 2
LO 2
LO 2
LO 2
LO 2
LO 2
LO 4
LO 4
LO 4
LO 4
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200 P A R T 4 Valuing Stocks and Bonds
13. Using Treasury Quotes Locate the Treasury issue in Figure 6.3 maturing
in February 2029. What is its coupon rate? What is the dollar bid price for a
$1,000 par value bond? What was the previous day’s asked price for a $1,000
par value bond?
14. Using Treasury Quotes Locate the Treasury bond in Figure 6.3 maturing in
May 2037. Is this a premium or a discount bond? What is its current yield?
What is its yield to maturity? What is the bid-ask spread for a $1,000 par
value bond?
15. Zero Coupon Bonds You find a zero coupon bond with a par value of
$10,000 and 13 years to maturity. If the yield to maturity on this bond is 4.7
percent, what is the price of the bond? Assume semiannual compounding
periods.
16. Valuing Bonds Lion Corp. has a $2,000 par value bond outstanding with a
coupon rate of 3.8 percent paid semiannually and 13 years to maturity. The
yield to maturity of the bond is 4.9 percent. What is the dollar price of the
bond?
17. Valuing Bonds Union Local School District has bonds outstanding with a
coupon rate of 3.2 percent paid semiannually and 16 years to maturity. The
yield to maturity on these bonds is 3.7 percent and the bonds have a par
value of $5,000. What is the dollar price of the bonds?
INTERMEDIATE (Questions 18–33)
18. Bond Price Movements Bond X is a premium bond making semiannual
payments. The bond has a coupon rate of 7.5 percent, a YTM of 6 percent,
and 13 years to maturity. Bond Y is a discount bond making semiannual
payments. This bond has a coupon rate of 6 percent, a YTM of 7.5 percent,
and also 13 years to maturity. What are the prices of these bonds today
assuming both bonds have a $1,000 par value? If interest rates remain
unchanged, what do you expect the prices of these bonds to be in 1 year?
In 3 years? In 8 years? In 12 years? In 13 years? What’s going on here?
Illustrate your answers by graphing bond prices versus time to maturity.
19. Interest Rate Risk Both Bond Bill and Bond Ted have 5.8 percent coupons,
make semiannual payments, and are priced at par value. Bond Bill has 5
years to maturity, whereas Bond Ted has 25 years to maturity. If interest
rates suddenly rise by 2 percent, what is the percentage change in the price
of Bond Bill? Of Bond Ted? Both bonds have a par value of $1,000. If rates
were to suddenly fall by 2 percent instead, what would the percentage change
in the price of Bond Bill be then? Of Bond Ted? Illustrate your answers by
graphing bond prices versus YTM. What does this problem tell you about
the interest rate risk of longer-term bonds?
20. Interest Rate Risk Bond J has a coupon rate of 4 percent. Bond K has a
coupon rate of 14 percent. Both bonds have 17 years to maturity, a par value
of $1,000, and a YTM of 8 percent, and both make semiannual payments. If
interest rates suddenly rise by 2 percent, what is the percentage price change
of these bonds? What if rates suddenly fall by 2 percent instead? What does
this problem tell you about the interest rate risk of lower-coupon bonds?
LO 2
LO 2
LO 2
LO 2
LO 2
LO 2
LO 2
LO 2
ros13952_ch06_165-204.indd 200 12/24/18 4:46 PM
C H A P T E R 6 Interest Rates and Bond Valuation 201
21. Bond Yields Bart Software has 5.7 percent coupon bonds on the market
with 22 years to maturity. The bonds make semiannual payments and
currently sell for 97 percent of par. What is the current yield? The YTM?
The effective annual yield?
22. Bond Yields BDJ Co. wants to issue new 25-year bonds for some
much-needed expansion projects. The company currently has 4.8 percent
coupon bonds on the market that sell for $1,028, make semiannual
payments, have a $1,000 par value, and mature in 25 years. What coupon
rate should the company set on its new bonds if it wants them to sell at
par?
23. Accrued Interest You purchase a bond with an invoice price of $1,043. The
bond has a coupon rate of 4.7 percent, semiannual coupons, and a $1,000
par value, and there are five months to the next coupon date. What is the
clean price of the bond?
24. Accrued Interest You purchase a bond with a coupon rate of 5.2 percent,
semiannual coupons, and a clean price of $993. If the next coupon payment
is due in two months, what is the invoice price?
25. Using Bond Quotes Suppose the following bond quote for IOU
Corporation appears in the financial page of today’s newspaper. Assume the
bond has a face value of $1,000, and the current date is April 15, 2019. What
is the yield to maturity of the bond? What is the current yield?
Company
(Ticker) Coupon Maturity
Last
Price
Last
Yield
EST Vol
(000s)
IOU (IOU) 7.60 Apr 15, 2031 91.645 ?? 1,827
26. Zero Coupon Bonds Suppose your company needs to raise $40 million
and you want to issue 20-year bonds for this purpose. Assume the required
return on your bond issue will be 5.7 percent, and you’re evaluating two issue
alternatives: a 5.7 percent semiannual coupon bond and a zero coupon bond.
Your company’s tax rate is 21 percent.
a. How many of the coupon bonds would you need to issue to raise the $40
million? How many of the zeroes would you need to issue?
b. In 20 years, what will your company’s repayment be if you issue the
coupon bonds? What if you issue the zeroes?
c. Based on your answers in parts (a) and (b), why would you ever want to
issue the zeroes? To answer, calculate the firm’s aftertax cash outflows
for the first year under the two different scenarios. Assume that the IRS
amortization rules apply for the zero coupon bonds.
27. Finding the Maturity You’ve just found a 10 percent coupon bond on the
market that sells for par value. What is the maturity on this bond? (Warning:
possible trick question.)
Use the following Treasury bond quotes to answer Questions 28–30: To calculate the
number of years until maturity, assume that it is currently May 2019. All of the
bonds have a $1,000 par value and pay semiannual coupons.
LO 2
LO 2
LO 2
LO 2
LO 2
LO 2
LO 2
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202 P A R T 4 Valuing Stocks and Bonds
Rate
Maturity
Mo/Yr Bid Asked Chg
Ask
Yld
?? May 25 103.5362 103.8235 +.3204 2.18
5.850 May 27 103.1840 103.3215 +.4513 ??
6.125 May 36 ?? ?? +.6821 3.87
28. Bond Yields In the table, find the Treasury bond that matures in May 2027.
What is your yield to maturity if you buy this bond?
29. Bond Prices In the table, find the Treasury bond that matures in May 2036.
What is the asked price of this bond in dollars? If the bid-ask spread for this
bond is .0628, what is the bid price in dollars?
30. Coupon Rates Find the Treasury bond that matures in May 2025. What is
the coupon rate for this bond?
Use the following corporate bond quotes to answer Questions 31–33: To calculate the
number of years until maturity, assume that it is currently January 15, 2019. All of
the bonds have a $2,000 par value and pay semiannual coupons.
Company
(Ticker) Coupon Maturity Last Price Last Yield
EST $ Vol
(000’s)
Xenon, Inc. (XIC) 5.400 Jan 15, 2024 96.153 ?? 57,362
Kenny Corp. (KCC) 7.125 Jan 15, 2026 ?? 6.02 48,941
Williams Co. (WICO) ?? Jan 15, 2028 95.165 6.85 43,802
31. Bond Yields What is the yield to maturity for the bond issued by Xenon, Inc.?
32. Bond Prices What price would you expect to pay for the Kenny Corp.
bond? What is the bond’s current yield?
33. Coupon Rates What is the coupon rate for the Williams Co. bond?
CHALLENGE (Question 34–35)
34. Components of Bond Returns Bond P is a premium bond with a coupon rate
of 8.2 percent. Bond D is a discount bond with a coupon rate of 5.9 percent.
Both bonds make annual payments and have a YTM of 7 percent, a par value
of $1,000, and five years to maturity. What is the current yield for Bond P? For
Bond D? If interest rates remain unchanged, what is the expected capital gains
yield over the next year for Bond P? For Bond D? Explain your answers and the
interrelationships among the various types of yields.
35. Holding Period Yield The YTM on a bond is the interest rate you earn on your
investment if interest rates don’t change. If you actually sell the bond before it
matures, your realized return is known as the holding period yield (HPY).
a. Suppose that today you buy an annual coupon bond with a coupon rate
of 6 percent for $915. The bond has 10 years to maturity and a par value
of $1,000. What rate of return do you expect to earn on your investment?
b. Two years from now, the YTM on your bond has declined by one
percentage point, and you decide to sell. What price will your bond sell
for? What is the HPY on your investment? Compare this yield to the
YTM when you first bought the bond. Why are they different?
LO 2
LO 2
LO 2
LO 2
LO 2
LO 2
LO 2
LO 2
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C H A P T E R 6 Interest Rates and Bond Valuation 203
EXCEL MASTER IT! PROBLEM
coverage online
Excel
Master
In an earlier worksheet, we discussed the difference between yield to maturity and yield to call.
There is another yield that is commonly quoted, the yield to worst. The yield to worst is the
lowest potential yield that can be received on a bond without the issuer actually defaulting.
Yield to worst is calculated on all possible call dates. It is assumed that prepayment occurs if
the bond has a call provision. The yield to worst will be the lower of yield to maturity or yield
to call. The yield to worst may be the same as yield to maturity but never higher. Of course, with
a traditional callable bond that has a call premium, the call premium can decline over time.
A company has the following bond outstanding. The bond is callable every year on May 1,
the anniversary date of the bond. The bond has a deferred call with 3 years left. The call
premium on the first call date is 1 year’s interest. The call premium will decline by 10 percent
of the original call premium for 10 years. Thirteen years from today, the call premium will be
zero. Given the following information, what is the yield to worst for this bond?
Current date: 5/1/2019
Maturity date: 5/1/2039
Price (percent of par): 98.5%
Coupon rate: 10.00%
Par value (percent of par): 100%
Coupons per year: 2
Call date Call premium
5/1/2022 $100
5/1/2023 <<<<90
5/1/2024 <<<<80
5/1/2025 <<<<70
5/1/2026 <<<<60
5/1/2027 <<<<50
5/1/2028 <<<<40
5/1/2029 <<<<30
5/1/2030 <<<<20
5/1/2031 10
6.1 Bond Quotes You can find current bond prices at finra-markets.morningstar.com/
BondCenter. You want to find the bond prices and yields for bonds issued by Pfizer. Enter
the ticker symbol “PFE” to do a search. What is the shortest-maturity bond issued by
Pfizer that is outstanding? What is the longest-maturity bond? What is the credit rating for
Pfizer’s bonds? Do all of the bonds have the same credit rating? Why do you think this is?
6.2 Yield Curves You can find information regarding the most current bond yields at
money.cnn.com. Go there and graph the yield curve for U.S. Treasury bonds. What is
the general shape of the yield curve? What does this imply about expected future
inflation? Now graph the yield curve for AAA-, AA-, and A-rated corporate bonds. Is the
corporate yield curve the same shape as the Treasury yield curve? Why or why not?
6.3 Default Premiums The Federal Reserve Bank of St. Louis has files listing historical
interest rates on its website www.stlouisfed.org. Find your way to the “FRED®” data,
then “Interest Rates.” You will find listings for Moody’s Seasoned Aaa Corporate Bond
Yield and Moody’s Seasoned Baa Corporate Bond Yield. A default premium can be
calculated as the difference between the Aaa bond yield and the Baa bond yield.
Calculate the default premium using these two bond indexes for the most recent 36
months. Is the default premium the same for every month? Why do you think this is?
WHAT’S ON
THE WEB?
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204 P A R T 4 Valuing Stocks and Bonds
Although Chris is aware of the bond features, he is
uncertain as to the costs and benefits of some features,
so he isn’t clear on how each feature would affect the
coupon rate of the bond issue. You are Renata’s assis-
tant, and she has asked you to prepare a memo to Chris
describing the effect of each of the following bond fea-
tures on the coupon rate of the bond. She also would like
you to list any advantages or disadvantages of each
feature.
Mark Sexton and Todd Story, the owners of S&S Air, have decided to expand their operations. They in-
structed their newly hired financial analyst, Chris Guthrie,
to enlist an underwriter to help sell $20 million in new
10-year bonds to finance construction. Chris has entered
into discussions with Renata Harper, an underwriter from
the firm of Crowe & Mallard, about which bond features
S&S Air should consider and what coupon rate the issue
will likely have.
CHAPTER CASE
Financing S&S Air’s Expansion Plans with a Bond Issue
1. The security of the bond—that is, whether the
bond has collateral.
2. The seniority of the bond.
3. The presence of a sinking fund.
4. A call provision with specified call dates and call
prices.
5. A deferred call accompanying the preceding call
provision.
6. A make-whole call provision.
7. Any positive covenants. Also, discuss several
possible positive covenants S&S Air might
consider.
8. Any negative covenants. Also, discuss several
possible negative covenants S&S Air might
consider.
9. A conversion feature (note that S&S Air is not a
publicly traded company).
10. A floating-rate coupon.
Q U E S T I O N S
ros13952_ch06_165-204.indd 204 12/24/18 4:46 PM
Please visit us at essentialsofcorporatefinance.blogspot.com for the latest developments in the world of corporate finance.
205
When the stock market closed on June 15, 2018, the common stock of biopharmaceutical company Gilead Sciences was
selling for $70.23 per share. On that same day, well-known credit
rating provider TransUnion closed at $71.16 per share, while oil and
natural gas company PrimeEnergy closed at $70.00. Because the
stock prices of these three companies were so similar, you might
expect they would be offering similar dividends to their stockhold-
ers, but you would be wrong. In fact, Gilead Science’s annual divi-
dend was $2.28 per share, TransUnion’s was $.30 per share, and
PrimeEnergy was paying no dividend at all!
As we will see in this chapter, the dividends currently being
paid are one of the primary factors we look at when we attempt to
value common stocks. However, it is obvious from looking at Prime-
Energy that current dividends are not the end of the story, so this chapter explores divi-
dends, stock values, and the connection between the two.
Going back to Chapter 1, we see that the goal of financial management is to maximize
stock prices, so an understanding of what determines share values is obviously a key con-
cern. When a corporation has publicly held stock, its shares often will be bought and sold
on one or more of the major stock exchanges, so we will examine how stocks are traded.
We also will see that the shareholders in a corporation have certain rights, and that how
these rights are allocated can have a significant impact on corporate control and
governance.
Equity Markets and
Stock Valuation7
LEARNING OBJECTIVES
After studying this chapter, you should be
able to:
LO 1 Assess how stock prices depend
on future dividends and dividend
growth.
LO 2 Identify the different ways
corporate directors are elected to
office.
LO 3 Explain how the stock markets
work.
Please visit us at essentialsofcorporatefinance.blogspot.com for the latest developments in the world of corporate finance.
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206 P A R T 4 Valuing Stocks and Bonds
In our previous chapter, we introduced you to bonds and bond valuation. In this chapter, we turn to the other major source of financing for corporations, common and preferred
stock. We first describe the cash flows associated with a share of stock and then go on to
develop a very famous result, the dividend growth model. From there, we move on to exam-
ine various important features of common and preferred stock, focusing on shareholder
rights. We close out the chapter with a discussion of how shares of stock are traded and how
stock prices and other important information are reported in the financial press.
COMMON STOCK VALUATION
A share of common stock is more difficult to value in practice than a bond, for at least three
reasons. First, with common stock, not even the promised cash flows are known in advance.
Second, the life of the investment is essentially forever because common stock has no matu-
rity. Third, there is no way to easily observe the rate of return that the market requires.
Nonetheless, as we will see, there are cases in which we can come up with the present value
of the future cash flows for a share of stock and thus determine its value.
Cash Flows
Imagine that you are considering buying a share of stock today. You plan to sell the stock in
one year. You somehow know that the stock will be worth $70 at that time. You predict that
the stock also will pay a $10 per share dividend at the end of the year. If you require a 25
percent return on your investment, what is the most you would pay for the stock? In other
words, what is the present value of the $10 dividend along with the $70 ending value at 25
percent?
If you buy the stock today and sell it at the end of the year, you will have a total of $80
in cash. At 25 percent:
Present value = ( $10 + 70 ) / 1.25 = $64
Therefore, $64 is the value you would assign to the stock today.
More generally, let P0 be the current price of the stock, and assign P1 to be the price in
one period. If D1 is the cash dividend paid at the end of the period, then:
P0 = (D1 + P1)/(1 + R) [7.1]
where R is the required return in the market on this investment.
Notice that we really haven’t said much so far. If we wanted to determine the value of a
share of stock today (P0), we would first have to come up with the value in one year (P1).
This is even harder to do, so we’ve only made the problem more complicated.
What is the price in one period, P1? We don’t know in general. Instead, suppose we
somehow knew the price in two periods, P2. Given a predicted dividend in two periods, D2,
the stock price in one period would be:
P1 = (D2 + P2)/(1 + R)
If we were to substitute this expression for P1 into our expression for P0, we would have:
P0 =
D1 + %P1 _____ 1 + R =
D1+
D2 + P2 ______ 1 + R ________ 1 + R
=
D1 ______ (1 + R%)1 +
D2 _____ (1 + R%)2 +
P2 ______ (1 + R%)2
7.1
coverage online
Excel
Master
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C H A P T E R 7 Equity Markets and Stock Valuation 207
Now we need to get a price in two periods. We don’t know this either, so we can procrasti-
nate again and write:
P2 = (D3 + P3)/(1 + R)
If we substitute this back in for P2, we have:
P0 =
D1 ______ (1 + R%)1 +
D2 _____ (1 + R%)2 +
P2 ______ (1 + R%)2
=
D1 ______ (1 + R%)1 +
D2 ______ (1 + R!)2 +
D3 + P3 ______ 1 + R ______ (1 + R%)2
=
D1 ______ (1 + R!)1 +
D2 ______ (1 + R%)2 +
D3 ______ (1 + R%)3 +
P3 ______ (1 + R%)3
You should start to notice that we can push the problem of coming up with the stock
price off into the future forever. It is important to note that no matter what the stock price
is, the present value is essentially zero if we push the sale of the stock far enough away.
What we are eventually left with is the result that the current price of the stock can be
written as the present value of the dividends beginning in one period and extending out
forever:
P 0 =
D 1 ______ (1 + R%) 1 % + %
D 2 ______ (1 + R%) 2 % + %
D 3 ______ (1 + R%) 3 % + %
D 4 ______ (1 + R%) 4 % + %
D 5 ______ (1 + R%) 5 % + …
We have illustrated here that the price of the stock today is equal to the present value of
all of the future dividends. How many future dividends are there? In principle, there can
be an infinite number. This means that we still can’t compute a value for the stock be-
cause we would have to forecast an infinite number of dividends and then discount them
all. In the next section, we consider some special cases in which we can get around this
problem.
EXAMPLE 7.1 Growth Stocks
You might be wondering about shares of stock in companies such as eBay that currently pay no
dividends. Small, growing companies frequently plow back everything and thus pay no dividends.
Are such shares worth nothing? It depends. When we say that the value of the stock is equal to the
present value of the future dividends, we don’t rule out the possibility that some number of those
dividends are zero. They just can’t all be zero.
Imagine a company that has a provision in its corporate charter that prohibits the paying of
dividends now or ever. The corporation never borrows any money, never pays out any money to
stockholders in any form whatsoever, and never sells any assets. Such a corporation couldn’t really
exist because the IRS wouldn’t like it, and the stockholders could always vote to amend the charter
if they wanted to. If it did exist, however, what would the stock be worth?
The stock would be worth absolutely nothing. Such a company is a financial “black hole.”
Money goes in, but nothing valuable ever comes out. Because nobody would ever get any return
on this investment, the investment has no value. This example is a little absurd, but it illustrates that
when we speak of companies that don’t pay dividends, what we really mean is that they are not
currently paying dividends.
Some Special Cases
There are a few very useful special circumstances under which we can come up with a value
for the stock. What we have to do is make some simplifying assumptions about the pattern
ros13952_ch07_205-236.indd 207 12/24/18 4:50 PM
208 P A R T 4 Valuing Stocks and Bonds
of future dividends. The cases we consider are the following: (1) the dividend has a zero
growth rate, (2) the dividend grows at a constant rate, and (3) the dividend grows at a non-
constant rate. Finally, we examine stock pricing using comparables.
Zero Growth The case of zero growth is one we’ve already seen. A share of common
stock in a company with a constant dividend is much like a share of preferred stock. From
Chapter 5 (Example 5.7), we know that the dividend on a share of preferred stock has zero
growth and thus is constant through time. For a zero-growth share of common stock, this
implies that:
D 1 = D 2 = D 3 = D = constant
So, the value of the stock is:
P 0 =
D ______ (1 + R%) 1 % + %
D ______ (1 + R%) 2 % + %
D ______ (1 + R%) 3 % + %
D ______ (1 + R%) 4 % + %
D ______ (1 + R%) 5 % + …
Because the dividend is always the same, the stock can be viewed as an ordinary perpetuity
with a cash flow equal to D every period. The per-share value is thus given by:
P0 = D/R [7.2]
where R is the required return.
For example, suppose the Paradise Prototyping Company has a policy of paying a
$10 per-share dividend every year. If this policy is to be continued indefinitely, what is the
value of a share of stock if the required return is 20 percent? The stock in this case amounts
to an ordinary perpetuity, so the stock is worth $10/.20 = $50 per share.
Constant Growth Suppose we know that the dividend for some company always
grows at a steady rate. Call this growth rate g. If we let D0 be the dividend just paid, then the
next dividend, D1, is:
D1 = D0 × (1 + g)
The dividend in two periods is:
D2 = D1 × (1 + g)
= [D0 × (1 + g)] × (1 + g)
= D0 × (1 + g)2
We could repeat this process to come up with the dividend at any point in the future. In
general, from our discussion of compound growth in Chapter 4, we know that the dividend
t periods into the future, Dt, is given by:
Dt = D0 × (1 + g)
t
An asset with cash flows that grow at a constant rate forever is called a growing perpetuity.
As we will see momentarily, there is a simple expression for determining the value of such
an asset.
The assumption of steady dividend growth might strike you as peculiar. Why would the
dividend grow at a constant rate? The reason is that, for many companies, steady growth in
dividends is an explicit goal. This subject falls under the general heading of dividend policy,
so we defer further discussion of it to a later chapter.
Students who are
interested in equity
valuation techniques
should check out
the Motley Fool at
www.fool.com.
ros13952_ch07_205-236.indd 208 12/24/18 4:50 PM
C H A P T E R 7 Equity Markets and Stock Valuation 209
If the dividend grows at a steady rate, then we have replaced the problem of fore-
casting an infinite number of future dividends with the problem of coming up with a
single growth rate, a considerable simplification. In this case, if we take D0 to be the
dividend just paid and g to be the constant growth rate, the value of a share of stock can
be written as:
P0 =
D1 _____ (1 + R%)1 +
D2 ______ (1 + R%)2% +
D3 ______ (1 + R%)3 + …
=
D0 (1 + g%)
1
_______ (1 + R%)1 +
D0(1 + g%)
2
_______ (1 + R%)2 +
D0(1 + g%)
3
_______ (1 + R%)3 + …
As long as the growth rate, g, is less than the discount rate, R, the present value of this series
of cash flows can be written as:
P 0 =
D 0 %% × (1% + %g%) ________ R − g =
D 1 ____ R − g [7.3]
This elegant result goes by a lot of different names. We will call it the dividend
growth model. By any name, it is very easy to use. To illustrate, suppose D0 is $2.30, R is
13 percent, and g is 5 percent. The price per share in this case is:
P0 = D0 × (1 + g)/(R − g)
= $2.30 × 1.05/(.13 − .05)
= $2.415/.08
= $30.19
We can actually use the dividend growth model to get the stock price at any point in time,
not just today. In general, the price of the stock as of Time t is:
P t =
D t %% × (1 + g%) ________ R − g =
D t!+ 1 ____ R − g [7.4]
In our example, suppose we are interested in the price of the stock in five years, P5. We first
need the dividend at Time 5, D5. Because the dividend just paid is $2.30 and the growth rate
is 5 percent per year, D5 is:
D5 = $2.30 × 1.05
5 = $2.30 × 1.2763 = $2.935
From the dividend growth model, we get that the price of the stock in five years is:
P 5 =
D 5 × (1 + g%) _________ R − g =
$2.935 × 1.05 ___________ .13 − .05 =
$3.0822 ______ .08 = $38.53
dividend growth
model
A model that determines
the current price of a
stock as its dividend next
period divided by the
discount rate less the
dividend growth rate.
EXAMPLE 7.2 Dividend Growth
The Hedless Corporation has just paid a dividend of $3 per share. The dividend of this company
grows at a steady rate of 8 percent per year. Based on this information, what will the dividend be in
five years?
Here we have a $3 current amount that grows at 8 percent per year for five years. The future
amount is thus:
$3 × " 1.08 5 = $3 × 1.4693 = $4.41
The dividend, therefore, will increase by $4.41 − 3 = $1.41 over the coming five years.
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210 P A R T 4 Valuing Stocks and Bonds
You might wonder what would happen with the dividend growth model if the growth
rate, g, were greater than the discount rate, R. It looks like we would get a negative stock
price because R − g would be less than zero. This is not what would happen.
Instead, if the constant growth rate exceeds the discount rate, then the stock price is
infinitely large. Why? If the growth rate is bigger than the discount rate, then the present
value of the dividends keeps on getting bigger and bigger. Essentially, the same is true if the
growth rate and the discount rate are equal. In both cases, the simplification that allows us
to replace the infinite stream of dividends with the dividend growth model is “illegal,” so the
answers we get from the dividend growth model are nonsense unless the growth rate is less
than the discount rate.
Finally, the expression we came up with for the constant growth case will work for any
growing perpetuity, not just dividends on common stock. If C1 is the next cash flow on a
growing perpetuity, then the present value of the cash flows is given by:
Present value = C1/(R − g) = C0(1 + g)/(R − g)
EXAMPLE 7.3 Gordon Growth Company
The next dividend for the Gordon Growth Company will be $4 per share. Investors require a 16
percent return on companies such as Gordon. Gordon’s dividend increases by 6 percent every year.
Based on the dividend growth model, what is the value of Gordon’s stock today? What is the value
in four years?
The only tricky thing here is that the next dividend, D1, is given as $4, so we won’t multiply this
by (1 + g). With this in mind, the price per share is given by:
P0 = D1 / (R − g)
= $4/(.16 − .06)
= $4/.10
= $40
Because we already have the dividend in one year, we know that the dividend in four years is equal
to D1 × (1 + g)
3 = $4 × 1.063 = $4.764. The price in four years is therefore:
P4 = D4 × (1 + g)/(R − g)
= $4.764 × 1.06/(.16 − .06)
= $5.05/.10
= $50.50
Notice in this example that P4 is equal to P0 × (1 + g)
4:
P4 = $50.50 = $40 × 1.06
4 = P0 × (1 + g)
4
To see why this is so, notice first that:
P4 = D5 / (R − g)
However, D5 is equal to D1 × (1 + g)
4, so we can write P4 as:
P4 = D1 × (1 + g)
4/(R − g)
= [D1 / (R − g)] × (1 + g)4
= P0 × (1 + g)4
This last example illustrates that the dividend growth model makes the implicit assumption that the
stock price will grow at the same constant rate as the dividend. This really isn’t too surprising. What
it tells us is that if the cash flows on an investment grow at a constant rate through time, so does the
value of that investment.
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C H A P T E R 7 Equity Markets and Stock Valuation 211
Notice that this expression looks like the result for an ordinary perpetuity except that
we have R − g on the bottom instead of only R.
Nonconstant Growth The last case we consider is nonconstant growth. The
main reason to consider this case is to allow for “supernormal” growth rates over some
finite length of time. As we discussed earlier, the growth rate cannot exceed the re-
quired return indefinitely, but it certainly could do so for some number of years. To
avoid the problem of having to forecast and discount an infinite number of dividends,
we will require that the dividends start growing at a constant rate sometime in the
future.
For a simple example of nonconstant growth, consider the case of a company that is
currently not paying dividends. You predict that, in five years, the company will pay a divi-
dend for the first time. The dividend will be $.50 per share. You expect that this dividend
will then grow at a rate of 10 percent per year indefinitely. The required return on compa-
nies such as this one is 20 percent. What is the price of the stock today?
To see what the stock is worth today, we first find out what it will be worth once divi-
dends are paid. We can then calculate the present value of that future price to get today’s
price. The first dividend will be paid in five years, and the dividend will grow steadily
from then on. Using the dividend growth model, we can say that the price in four years
will be:
P4 = D4 × (1 + g)/(R − g)
= D5/(R − g)
= $.50/(.20 − .10)
= $5
If the stock will be worth $5 in four years, then we can get the current value by discounting
this price back four years at 20 percent:
P 0 = $5 / 1.20
4 = $5 / 2.0736 = $2.41
The stock is therefore worth $2.41 today.
The problem of nonconstant growth is only slightly more complicated if the dividends
are not zero for the first several years. Suppose that you have come up with the following
dividend forecasts for the next three years:
Year Expected Dividend
1 $1.00
2 $2.00
3 $2.50
After the third year, the dividend will grow at a constant rate of 5 percent per year. The re-
quired return is 10 percent. What is the value of the stock today?
In dealing with nonconstant growth, a time line can be very helpful. Figure 7.1
illustrates one for this problem. The important thing to notice is when constant growth
starts. As we’ve shown, for this problem, constant growth starts at Time 3. This means
that we can use our constant growth model to determine the stock price at Time 3,
P3. By far the most common mistake in this situation is to incorrectly identify the start
of the constant growth phase and, as a result, calculate the future stock price at the
wrong time.
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212 P A R T 4 Valuing Stocks and Bonds
As always, the value of the stock is the present value of all the future dividends. To cal-
culate this present value, we first have to compute the present value of the stock price three
years down the road, as we did before. We then have to add in the present value of the divi-
dends that will be paid between now and then. So, the price in three years is:
P3 = D3 × (1 + g)/(R − g)
= $2.50 × 1.05/(.10 − .05)
= $52.50
We can now calculate the total value of the stock as the present value of the first three divi-
dends plus the present value of the price at Time 3, P3:
P0 =
D1 ______ (1 + R!)1 +
D2 ______ (1 + R%)2 +
D3 ______ (1 + R%)3 +
P3 ______ (1 + R%)3
= $1 ___ 1.10 +
2 ____ 1.102 +
2.50 ____ 1.103 +
52.50 _____ 1.103
= $.91 + 1.65 + 1.88 + 39.44
= $43.88
The value of the stock today is thus $43.88.
0 1 2 3 4 5
$1 $2 $2.50 $2.50
X 1.05
Time
Dividends $2.50
X 1.052
Nonconstant growth Constant growth @ 5%
Nonconstant growth
FIGURE 7.1
EXAMPLE 7.4 Supernormal Growth
Chain Reaction, Inc., has been growing at a phenomenal rate of 30 percent per year because of its
rapid expansion and explosive sales. You believe that this growth rate will last for three more years
and that the rate will then drop to 10 percent per year. If the growth rate then remains at 10 percent
indefinitely, what is the total value of the stock? Total dividends just paid were $5 million, and the
required return is 20 percent.
Chain Reaction’s situation is an example of supernormal growth. It is unlikely that a 30 percent
growth rate can be sustained for any extended length of time. To value the equity in this company,
we first need to calculate the total dividends over the supernormal growth period:
Year Total Dividends (in millions)
1
2
3
$5.00 × 1.3 = $ 6.500
6.50 × 1.3 = 8.450
00008.45 × 1.3 = 10.985
The price at Time 3 can be calculated as:
P3 = D3 × (1 + g)/(R − g)
(continued!)
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C H A P T E R 7 Equity Markets and Stock Valuation 213
Components of the Required Return
Thus far, we have taken the required return, or discount rate, R, as given. We will have quite
a bit to say on this subject in Chapters 10 and 11. For now, we want to examine the implica-
tions of the dividend growth model for this required return. Earlier, we calculated P0 as:
P0 = D1 / (R − g)
If we rearrange this to solve for R, we get:
R − g = D1 / P0
R = D1 / P0 + g [7.5]
This tells us that the total return, R, has two components. The first of these, D1/P0, is called
the dividend yield. Because this is calculated as the expected cash dividend divided by the
current price, it is conceptually similar to the current yield on a bond.
The second part of the total return is the growth rate, g. We know that the dividend
growth rate is also the rate at which the stock price grows (see Example 7.3). Thus, this
growth rate can be interpreted as the capital gains yield, that is, the rate at which the value
of the investment grows.1
To illustrate the components of the required return, suppose we observe a stock selling
for $20 per share. The next dividend will be $1 per share. You think that the dividend will
grow by 10 percent per year more or less indefinitely. What return does this stock offer you
if this is correct?
The dividend growth model calculates the total return as:
R = Dividend yield + Capital gains yield
R = D1 / P0 + g
In this case, the total return works out to be:
R = $1/$20 + .10
= .05 + .10
= .15, or 15%
This stock, therefore, has a required return of 15 percent.
dividend yield
A stock’s expected cash
dividend divided by its
current price.
capital gains yield
The dividend growth rate,
or the rate at which the
value of an investment
grows.
where g is the long-run growth rate. So we have:
P3 = $10.985 × 1.10/(.20 − .10) = $120.835
To determine the value today, we need the present value of this amount plus the present value of
the total dividends:
P0 =
D1 _____ (1 + R)1 +
D2 _____ (1 + R)2 +
D3 _____ (1 + R)3 +
P3 _____ (1 + R)3
= $6.50 _____ 1.20 +
8.45 ____ 1.202 +
10.985 _____ 1.203 +
120.835 ______ 1.203
= $5.42 + 5.87 + 6.36 + 69.93
= $87.57
The total value of the stock today is thus $87.57 million. If there were 20 million shares, then the
stock would be worth $87.57/20 = $4.38 per share.
1Here and elsewhere, we use the term capital gains a little loosely. For the record, a capital gain (or loss) is, strictly
speaking, something defined by the IRS. For our purposes, it would be more accurate (but less common) to use the
term price appreciation instead of capital gain.
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214 P A R T 4 Valuing Stocks and Bonds
We can verify this answer by calculating the price in one year, P1, using 15 percent as
the required return. Based on the dividend growth model, this price is:
P1 = D1 × (1 + g)/(R − g)
= $1 × 1.10/(.15 − .10)
= $1.10/.05
= $22
Notice that this $22 is $20 × 1.1, so the stock price has grown by 10 percent, as it should. If
you pay $20 for the stock today, you will get a $1 dividend at the end of the year, and you
will have a $22 − 20 = $2 gain. Your dividend yield is thus $1/$20 = .05, or 5 percent.
Your capital gains yield is $2/$20 = .10, or 10 percent, so your total return would be 5% +
10% = 15%.
To get a feel for actual numbers in this context, consider that, according to the 2018
Value Line Investment Survey, The Hershey Company’s dividends were expected to grow by
5.5 percent over the next 5 or so years, compared to a historical growth rate of 9 percent
over the preceding 10 years. In 2018, the projected dividend for the coming year was given
as $2.85. The stock price at that time was about $94 per share. What is the return investors
require on Hershey? Here, the dividend yield is about 3 percent and the capital gains yield
is 5.5 percent, giving a total required return of 8.5 percent on Hershey stock.
Stock Valuation Using Comparables, or Comps
An obvious problem with our dividend-based approach to stock valuation is that many com-
panies don’t pay dividends. What do we do in such cases? A common approach is to make
use of the PE ratio, which we defined in Chapter 3 as the ratio of a stock’s price per share
to its earnings per share (EPS) over the previous year. The idea here is to have some sort of
benchmark or reference PE ratio, which we then multiply by earnings to come up with a
price:
Price at Time t = Pt = Benchmark PE ratio × EPSt [7.6]
The benchmark PE ratio could come from one of several possible sources. It could be based
on similar companies (perhaps an industry average or median), or it could be based on a
company’s own historical values. Suppose we are trying to value Inactivision, Inc., a video
game developer known for its hit Slack Ops series. Inactivision does not pay dividends, but
after studying the industry, you feel that a PE ratio of 20 is appropriate for a company like
this one. Total earnings over the four most recent quarters combined are $2 per share, so
you think the stock should sell for 20 × $2 = $40. You might view it as an attractive pur-
chase if it is going for less than $40, but not attractive if it sells for more than $40.
Security analysts spend a lot of time forecasting future earnings, particularly for the
coming year. A PE ratio that is based on estimated future earnings is called a forward PE
ratio. Suppose you felt that Inactivision’s earnings for the coming year were going to be
$2.50, reflecting the growing popularity of the company’s World of Slackcraft massively mul-
tiplayer online role-playing game (MMORPG). In this case, if the current stock price is $40,
the forward PE ratio is $40/$2.50 = 16.
Finally, notice that your benchmark PE of 20 applies to earnings over the previous year. If
earnings over the coming year turn out to be $2.50, then the stock price one year from today
should be 20 × $2.50 = $50. Forecast prices such as this one often are called target prices.
Often we will be interested in valuing newer companies that both don’t pay dividends and
are not yet profitable, meaning that earnings are negative. What do we do then? One answer is
to use the price-sales ratio, which we also introduced in Chapter 3. As the name suggests, this
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C H A P T E R 7 Equity Markets and Stock Valuation 215
ratio is the price per share on the stock divided by sales per share. You use this ratio like you
use the PE ratio, except you use sales per share instead of earnings per share. As with PE ra-
tios, price-sales ratios vary depending on company age and industry. Typical values are in the
.8–2.0 range, but they can be much higher for younger, faster-growing companies.
For future reference, our discussion of stock valuation techniques is summarized in
Table 7.1.
CONCEPT QUESTIONS
7.1a What are the relevant cash flows for valuing a share of common stock?
7.1b Does the value of a share of stock depend on how long you expect to keep it?
7.1c What is the value of a share of stock when the dividend grows at a constant rate?
7.1d What is a “target price” on a stock? How is it determined?
Summary of stock
valuation
I. The general case
In general, the price today of a share of stock, P0, is the present value of all of its future
dividends, D1, D2, D3, … :
P 0 =
D 1 ______ (1 + R0) 1 0 + 0
D 2 ______ (1 + R0) 2 0 + 0
D 3 ______ (1 + R0) 3 0 + …
where R is the required return.
II. Constant growth case
If the dividend is constant and equal to D, then the price can be written as:
P 0 =
D __ R
If the dividend grows at a steady rate g, then the price can be written as:
P 0 =
D 1 ____ R − g
This result is called the dividend growth model.
III. Nonconstant Growth
If the dividend grows steadily after t periods, then the price can be written as:
P 0 =
D 1 ______ (1 + R0) 1 0 + 0
D 2 ______ (1 + R0) 2 0 + … + 0
D t ______ (1 + R0) t 0 +
P t ______ (1 + R0) t
where:
P t =
D t ! × (1 + g!) _________ (R − g!)
IV. The required return, R, can be written as the sum of two things:
R = D 1 / P 0 ! + g
where D1/P0 is the dividend yield and g is the capital gains yield (which is the same thing
as the growth rate in dividends for the steady growth case).
V. Valuation Using Comparables
For stocks that don’t pay dividends (or have erratic dividend growth rates), we can value
them using the PE ratio and/or the price-sales ratio:
Pt = Benchmark PE ratio × EPSt
Pt = Benchmark price–sales ratio × Sales per sharet
TABLE 7.1
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216 P A R T 4 Valuing Stocks and Bonds
SOME FEATURES OF COMMON AND
PREFERRED STOCK
In discussing common stock features, we focus on shareholder rights and dividend pay-
ments. For preferred stock, we explain what “preferred” means, and we also debate whether
preferred stock is really debt or equity.
Common Stock Features
The term common stock means different things to different people, but it is usually applied
to stock that has no special preference either in paying dividends or in bankruptcy.
Shareholder Rights The conceptual structure of the corporation assumes that share-
holders elect directors who, in turn, hire management to carry out their directives. Sharehold-
ers, therefore, control the corporation through the right to elect the directors. Generally, only
shareholders have this right.
Directors are elected each year at an annual meeting. Although there are exceptions
(discussed in a moment), the general idea is “one share, one vote” (not one shareholder, one
vote). Corporate democracy is thus very different from our political democracy. With cor-
porate democracy, the “golden rule” prevails absolutely.2
Directors are elected at an annual shareholders’ meeting by a vote of the holders of a
majority of shares who are present and entitled to vote. However, the exact mechanism for
electing directors differs across companies. The most important difference is whether shares
must be voted cumulatively or voted straight.
To illustrate the two different voting procedures, imagine that a corporation has two share-
holders: Smith with 20 shares and Jones with 80 shares. Both want to be a director. Jones does
not want Smith, however. We assume that there are a total of four directors to be elected.
The effect of cumulative voting is to permit minority participation.3 If cumulative vot-
ing is permitted, the total number of votes that each shareholder may cast is determined
first. This is usually calculated as the number of shares (owned or controlled) multiplied by
the number of directors to be elected.
With cumulative voting, the directors are elected all at once. In our example, this means
that the top four vote-getters will be the new directors. Individual shareholders can distrib-
ute votes however they wish.
Will Smith get a seat on the board? If we ignore the possibility of a five-way tie, then the
answer is yes. Smith will cast 20 × 4 = 80 votes, and Jones will cast 80 × 4 = 320 votes. If
Smith gives all his votes to himself, he is assured of a directorship. The reason is that Jones
can’t divide 320 votes among four candidates in such a way as to give all of them more than
80 votes, so Smith will finish fourth at worst.
In general, if there are N directors up for election, then 1/(N + 1) percent of the stock
plus one share will guarantee you a seat. In our current example, this is 1/(4 + 1) = .20, or
20 percent (plus one share). So, the more seats that are up for election at one time, the
easier (and cheaper) it is to win one.
With straight voting the directors are elected one at a time. Each time, Smith can cast
20 votes and Jones can cast 80. As a consequence, Jones will elect all of the candidates. The
only way to guarantee a seat is to own 50 percent plus one share. This also guarantees that
you will win every seat, so it’s really all or nothing.
7.2
common stock
Equity without priority for
dividends or in
bankruptcy.
cumulative voting
A procedure in which a
shareholder may cast all
votes for one member of
the board of directors.
straight voting
A procedure in which a
shareholder may cast all
votes for each member of
the board of directors.
2The golden rule: Whoever has the gold makes the rules.
3By minority participation, we mean participation by shareholders with relatively small amounts of stock.
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C H A P T E R 7 Equity Markets and Stock Valuation 217
As we’ve illustrated, straight voting can “freeze out” minority shareholders; that is the
reason many states have mandatory cumulative voting. In states where cumulative voting is
mandatory, devices have been worked out to minimize its impact.
Many companies have staggered elections for directors. With staggered elections, only
a fraction of the directorships are up for election at a particular time. Thus, if only two
directors are up for election at any one time, it will take 1/(2 + 1) = .3333, or 33.33 per-
cent of the stock plus one share to guarantee a seat. Staggered boards are often called
“classified” boards because directors are placed into different classes with terms that ex-
pire at different times. In recent years, corporations have come under pressure to “declas-
sify” their boards, meaning that all directors would stand for election every year, and many
have done so.
Overall, staggering has two basic effects:
1. Staggering makes it more difficult for a minority shareholder to elect a director
when there is cumulative voting because there are fewer directors to be elected at
one time.
2. Staggering makes takeover attempts less likely to be successful because it makes it
more difficult to vote in a majority of new directors.
We should note that staggering may serve a beneficial purpose. It provides “institu-
tional memory,” that is, continuity on the board of directors. This may be important for
corporations with significant long-range plans and projects.
Proxy Voting A proxy is the grant of authority by a shareholder to someone else to
vote that shareholder’s shares. For convenience, much of the voting in large public corpora-
tions is actually done by proxy.
As we have seen, with straight voting, each share of stock has one vote. The owner of
10,000 shares has 10,000 votes. Large companies have hundreds of thousands or even mil-
lions of shareholders. Shareholders can come to the annual meeting and vote in person, or
they can transfer their right to vote to another party.
Obviously, management always tries to get as many proxies as possible transferred to it.
However, if shareholders are not satisfied with management, an “outside” group of share-
holders can try to obtain votes via proxy. They can vote by proxy in an attempt to replace
management by electing enough directors. The resulting battle is called a proxy fight.
Classes of Stock Some firms have more than one class of common stock. Often, the
classes are created with unequal voting rights. The Ford Motor Company, for example, has
Class B common stock, which is not publicly traded (it is held by Ford family interests and
proxy
A grant of authority by a
shareholder allowing
another individual to vote
his or her shares.
EXAMPLE 7.5 Buying the Election
Stock in JRJ Corporation sells for $20 per share and features cumulative voting. There are 10,000
shares outstanding. If three directors are up for election, how much does it cost to ensure yourself
a seat on the board?
The question here is how many shares of stock it will take to get a seat. The answer is 2,501,
so the cost is 2,501 × $20 = $50,020. Why 2,501? Because there is no way the remaining 7,499
votes can be divided among three people to give all of them more than 2,501 votes. For example,
suppose two people receive 2,502 votes and the first two seats. A third person can receive at most
10,000 − 2,502 − 2,502 − 2,501 = 2,495, so the third seat is yours. Verify that we arrived at 2,501
using the formula described earlier.
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218 P A R T 4 Valuing Stocks and Bonds
trusts). This class has about 40 percent of the voting power, even though it represents less
than 10 percent of the total number of shares outstanding.
There are many other cases of corporations with different classes of stock. For exam-
ple, Google, the web search company, has three publicly traded classes of common stock,
A, B, and C. The Class A shares are held by the public, and each share has one vote. The
Class B shares are held by company insiders, and each Class B share has 10 votes. Then, in
2014, the company had a stock split of its Class B shares, creating Class C shares, which
have no vote at all. As a result, Google’s founders and managers control the company. The
CEO of cable TV giant Comcast, Brian Roberts, owns about .04 percent of the company’s
equity, but he has a third of all the votes thanks to the creation of a special class of stock.
In principle, the New York Stock Exchange does not allow companies to create classes
of publicly traded common stock with unequal voting rights. Exceptions (e.g., Ford) appear
to have been made. In addition, many non-NYSE companies have dual classes of common
stock.
A primary reason for creating dual or multiple classes of stock has to do with control of
the firm. If such stock exists, management of a firm can raise equity capital by issuing non-
voting or limited-voting stock while maintaining control.
The subject of unequal voting rights is controversial in the United States, and the idea
of one share, one vote has a strong following and a long history. Interestingly, however,
shares with unequal voting rights are quite common in the United Kingdom and elsewhere
around the world.
Other Rights The value of a share of common stock in a corporation is directly related
to the general rights of shareholders. In addition to the right to vote for directors, sharehold-
ers usually have the following rights:
1. The right to share proportionally in dividends paid.
2. The right to share proportionally in assets remaining after liabilities have been paid in
a liquidation.
3. The right to vote on stockholder matters of great importance, such as a merger. Voting
is usually done at the annual meeting or a special meeting.
In addition, shareholders sometimes have the right to share proportionally in any new stock
sold. This is called the preemptive right.
Essentially, a preemptive right means that a company that wishes to sell stock must first
offer it to the existing stockholders before offering it to the general public. The purpose is to
give stockholders the opportunity to protect their proportionate ownership in the
corporation.
Dividends A distinctive feature of corporations is that they have shares of stock on
which they are authorized by law to pay dividends to their shareholders. Dividends paid to
shareholders represent a return on the capital directly or indirectly contributed to the cor-
poration by the shareholders. The payment of dividends is at the discretion of the board of
directors.
Some important characteristics of dividends include the following:
1. Unless a dividend is declared by the board of directors of a corporation, it is not a
liability of the corporation. A corporation cannot default on an undeclared dividend.
As a consequence, corporations cannot become bankrupt because of nonpayment of
dividends. The amount of the dividend and even whether it is paid are decisions based
on the business judgment of the board of directors.
dividend
Payments by a
corporation to
shareholders, made in
either cash or stock.
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C H A P T E R 7 Equity Markets and Stock Valuation 219
2. The payment of dividends by the corporation is not a business expense. Dividends are
not deductible for corporate tax purposes. In short, dividends are paid out of the
corporation’s aftertax profits.
3. Dividends received by individual shareholders are taxable. In 2018, the tax rate was
15 to 20 percent. However, corporations that own stock in other corporations are
permit ted to exclude 50 percent of the dividend amounts they receive and are taxed
on only the remaining 50 percent (the 50 percent exclusion was reduced from 70
percent by the Tax Cuts and Jobs Act of 2017).4
Preferred Stock Features
Preferred stock differs from common stock because it has preference over common stock in
the payment of dividends and in the distribution of corporation assets in the event of liqui-
dation. Preference means only that the holders of the preferred shares must receive a divi-
dend (in the case of an ongoing firm) before holders of common shares are entitled to
anything.
Preferred stock is a form of equity from a legal and tax standpoint. It is important to
note, however, that holders of preferred stock sometimes have no voting privileges.
Stated Value Preferred shares have a stated liquidating value, usually $100 per share.
The cash dividend is described in terms of dollars per share. For example, General Motors
“$5 preferred” easily translates into a dividend yield of 5 percent of stated value.
Cumulative and Noncumulative Dividends A preferred dividend is not like in-
terest on a bond. The board of directors may decide not to pay the dividends on preferred
shares, and their decision may have nothing to do with the current net income of the
corporation.
Dividends payable on preferred stock are either cumulative or noncumulative; most are
cumulative. If preferred dividends are cumulative and are not paid in a particular year, they
will be carried forward as an arrearage. Usually, both the accumulated (past) preferred divi-
dends and the current preferred dividends must be paid before the common shareholders
can receive anything.
Unpaid preferred dividends are not debts of the firm. Directors elected by the common
shareholders can defer preferred dividends indefinitely. However, in such cases, common
shareholders also must forgo dividends. In addition, holders of preferred shares are often
granted voting and other rights if preferred dividends have not been paid for some time. For
example, at one point, US Airways had failed to pay dividends on one of its preferred stock
issues for six quarters. As a consequence, the holders of the shares were allowed to nomi-
nate two people to represent their interests on the airline’s board. Because preferred stock-
holders receive no interest on the accumulated dividends, some have argued that firms have
an incentive to delay paying preferred dividends, but, as we have seen, this may mean shar-
ing control with preferred stockholders.
Is Preferred Stock Really Debt? A good case can be made that preferred stock is
really debt in disguise, a kind of equity bond. Preferred shareholders are only entitled to re-
ceive a stated dividend, and, if the corporation is liquidated, preferred shareholders are only
preferred stock
Stock with dividend
priority over common
stock, normally with a
fixed dividend rate,
sometimes without voting
rights.
4For the record, the 50 percent exclusion applies when the recipient owns less than 20 percent of the outstanding
stock in a corporation. If a corporation owns more than 20 percent but less than 65 percent, the exclusion is 65
percent. If more than 65 percent is owned, the corporation can file a single “consolidated” return, and the exclu-
sion is effectively 100 percent.
ros13952_ch07_205-236.indd 219 12/24/18 4:50 PM
220 P A R T 4 Valuing Stocks and Bonds
entitled to the stated value of their preferred shares. Often, preferred stocks carry credit
ratings much like those of bonds. Furthermore, preferred stock is sometimes convertible
into common stock, and preferred stocks are often callable.
In addition, in recent years, many new issues of preferred stock have had obligatory
sinking funds. The existence of such a sinking fund effectively creates a final maturity be-
cause it means that the entire issue ultimately will be retired. For these reasons, preferred
stock seems to be a lot like debt. However, for tax purposes, preferred dividends are treated
like common stock dividends.
CONCEPT QUESTIONS
7.2a What is a proxy?
7.2b What rights do stockholders have?
7.2c Why is preferred stock called preferred?
THE STOCK MARKETS
Back in Chapter 1, we very briefly mentioned that shares of stock are bought and sold on
various stock exchanges, the two most important of which are the New York Stock Ex-
change and the NASDAQ. From our earlier discussion, recall that the stock market consists
of a primary market and a secondary market. In the primary, or new-issue, market, shares
of stock are first brought to the market and sold to investors. In the secondary market, exist-
ing shares are traded among investors.
In the primary market, companies sell securities to raise money. We will discuss this
process in detail in a later chapter. We therefore focus mainly on secondary market activity
in this section. We conclude with a discussion of how stock prices are quoted in the finan-
cial press.
Dealers and Brokers
Because most securities transactions involve dealers and brokers, it is important to under-
stand exactly what is meant by the terms dealer and broker. A dealer maintains an inventory
and stands ready to buy and sell at any time. In contrast, a broker brings buyers and sellers
together but does not maintain an inventory. Thus, when we speak of used car dealers and
real estate brokers, we recognize that the used car dealer maintains an inventory, whereas
the real estate broker does not.
In the securities markets, a dealer stands ready to buy securities from investors wishing
to sell them and sell securities to investors wishing to buy them. Recall from our previous
chapter that the price the dealer is willing to pay is called the bid price. The price at which
the dealer will sell is called the ask price (sometimes called the asked, offered, or offering
price). The difference between the bid and ask prices is called the spread, and it is the basic
source of dealer profits.
Dealers exist in all areas of the economy, not just the stock markets. For example, your
local college bookstore is probably both a primary and a secondary market textbook dealer.
If you buy a new book, this is a primary market transaction. If you buy a used book, this is a
secondary market transaction, and you pay the store’s ask price. If you sell the book back,
you receive the store’s bid price, often half of the ask price. The bookstore’s spread is the
difference between the two prices.
7.3
coverage online
Excel
Master
primary market
The market in which new
securities are originally
sold to investors.
secondary market
The market in which
previously issued
securities are traded
among investors.
dealer
An agent who buys and
sells securities from
inventory.
broker
An agent who arranges
security transactions
among investors.
ros13952_ch07_205-236.indd 220 12/24/18 4:50 PM
C H A P T E R 7 Equity Markets and Stock Valuation 221
In contrast, a securities broker arranges transactions between investors, matching inves-
tors wishing to buy securities with investors wishing to sell securities. The distinctive char-
acteristic of security brokers is that they do not buy or sell securities for their own accounts.
Facilitating trades by others is their business.
Organization of the NYSE
The New York Stock Exchange, or NYSE, popularly known as the Big Board, was founded
in 1792. It has occupied its current location on Wall Street since the turn of the twentieth
century. Measured in terms of dollar volume of activity and the total value of shares listed,
it is the largest stock market in the world.
Members Historically, the NYSE had 1,366 exchange members. Prior to 2006, the
exchange members were said to own “seats” on the exchange, and, collectively, the mem-
bers of the exchange were also the owners. For this and other reasons, seats were valuable
and were bought and sold fairly regularly. Seat prices reached a record $4 million
in 2005.
In 2006, all of this changed when the NYSE became a publicly owned corporation
called NYSE Group, Inc. Naturally, its stock is listed on the NYSE. Now, instead of pur-
chasing seats, exchange members must purchase trading licenses, the number of which is
limited to 1,366. In 2018, a license would set you back a cool $50,000—per year. Having a
license entitles you to buy and sell securities on the floor of the exchange. Different mem-
bers play different roles in this regard.
On April 4, 2007, the NYSE grew even larger when it merged with Euronext to form
NYSE Euronext. Euronext was a stock exchange in Amsterdam, with subsidiaries in Bel-
gium, France, Portugal, and the United Kingdom. With the merger, NYSE Euronext be-
came the world’s “first global exchange.” Further expansion occurred in 2008 when NYSE
Euronext merged with the American Stock Exchange. Then, in November 2013, the acquisi-
tion of the NYSE by the Intercontinental Exchange (ICE) was completed. ICE, which was
founded in May 2000, was originally a commodities exchange, but its rapid growth gave it
the necessary $8.2 billion to acquire the NYSE.
As we briefly describe how the NYSE operates, keep in mind that other markets owned
by NYSE Euronext and ICE may function differently. What makes the NYSE somewhat
unique is that it is a hybrid market. In a hybrid market, trading takes place both electroni-
cally and face-to-face.
With electronic trading, orders to buy and orders to sell are submitted to the
exchange. Orders are compared by a computer and whenever there is a match, the orders
are executed with no human intervention. Most trades on the NYSE occur this way. For
orders that are not handled electronically, the NYSE relies on its license holders. There
are three different types of license holders, designated market makers (DMMs),
floor brokers, and supplemental liquidity providers (SLPs), and we now discuss the role
played by each.
The DMMs, formerly known as “specialists,” act as dealers in particular stocks. Typi-
cally, each stock on the NYSE is assigned to a single DMM. As a dealer, a DMM maintains
a two-sided market, meaning that the DMM continually posts and updates bid and ask
prices. By doing so, the DMM ensures that there is always a buyer or seller available, thereby
promoting market liquidity.
The job of a floor broker is to execute trades for customers, with an emphasis on getting
the best price possible. Floor brokers are generally employees of large brokerage firms such
as Merrill Lynch, the wealth management division of Bank of America. The interaction
member
As of 2006, a member is
the owner of a trading
license on the NYSE.
designated market
makers (DMMs)
NYSE members who act
as dealers in particular
stocks. Formerly known
as “specialists.”
floor brokers
NYSE members who
execute customer buy and
sell orders.
supplemental
liquidity providers
(SLPs)
Investment firms that are
active participants in
stocks assigned to them.
Their job is to make a one-
sided market (i.e., offering
to either buy or sell). They
trade purely for their own
accounts.
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222 P A R T 4 Valuing Stocks and Bonds
between floor brokers and DMMs is the key to nonelectronic trading on the NYSE. We
discuss this interaction in detail in just a moment.
The SLPs are essentially investment firms that agree to be active participants in stocks
assigned to them. Their job is to regularly make a one-sided market (i.e., offering to either
buy or sell). They trade purely for their own accounts (using their own money), so they do
not represent customers. They are given a small rebate on their buys and sells, thereby en-
couraging them to be more aggressive. The NYSE’s goal is to generate as much liquidity as
possible, which makes it easier for ordinary investors to quickly buy and sell at prevailing
prices. Unlike DMMs and floor brokers, SLPs do not operate on the floor of the stock
exchange.
In recent years, floor brokers have become less important on the exchange floor be-
cause of the efficient Pillar system, which allows orders to be transmitted electronically di-
rectly to the DMM. Additionally, the NYSE has an electronic platform called Arca, which
accounts for a substantial percentage of all trading on the NYSE, particularly for smaller
orders. The average time for a trade on the NYSE Arca is less than 1 second.
Finally, a small number of NYSE members are floor traders who independently trade
for their own accounts. Floor traders try to anticipate temporary price fluctuations and
profit from them by buying low and selling high. In recent decades, the number of floor
traders has declined substantially, suggesting that it has become increasingly difficult to
profit from short-term trading on the exchange floor.
Operations Now that we have a basic idea of how the NYSE is organized and who the
major players are, we turn to the question of how trading actually takes place. Fundamen-
tally, the business of the NYSE is to attract and process order flow. The term order flow
means the flow of customer orders to buy and sell stocks. The customers of the NYSE are
the millions of individual investors and tens of thousands of institutional investors who
place their orders to buy and sell shares in NYSE-listed companies. The NYSE has been
quite successful in attracting order flow. Currently, it is common for more than one billion
shares to change hands in a single day.
Floor Activity It is quite likely that you have seen footage of the NYSE trading floor
on television, or you may have visited the NYSE and viewed exchange floor activity from
the visitors’ gallery (it’s worth the trip). Either way, you would have seen a big room,
about the size of a basketball gym. This big room is called, technically, “the Big Room.”
There are a couple of other, smaller rooms that you normally don’t see, one of which is
called “the Garage” because that is literally what it was before it was taken over for
trading.
On the floor of the exchange are a number of stations. These stations have multiple
counters with numerous terminal screens above and on the sides. People operate behind
and in front of the counters in relatively stationary positions.
Other people move around on the exchange floor. In all, you may be reminded of
worker ants moving around an ant colony. It is natural to wonder: What are all those people
doing down there (and why are so many wearing funny-looking coats)?
As an overview of exchange floor activity, here is a quick look at what goes on. Each
of the counters is a DMM’s post. DMMs normally operate in front of their posts to
monitor and manage trading in the stocks assigned to them. Clerical employees working
for the DMMs operate behind the counter. Moving from the many workstations lining
the walls of the exchange out to the exchange floor and back again are swarms of floor
order flow
The flow of customer
orders to buy and sell
securities.
DMM’s post
A fixed place on the
exchange floor where the
DMM operates.
ros13952_ch07_205-236.indd 222 12/24/18 4:50 PM
C H A P T E R 7 Equity Markets and Stock Valuation 223
brokers, receiving customer orders, walking out to DMMs’ posts where the orders can
be executed, and returning to confirm order executions and receive new customer
orders.
To better understand activity on the NYSE trading floor, imagine yourself as a floor
broker. Your clerk has just handed you an order to sell 2,000 shares of Walmart for a cus-
tomer of the brokerage company that employs you. The customer wants to sell the stock at
the best possible price as soon as possible. You immediately walk (running violates
exchange rules) to the DMM’s post where Walmart stock is traded.
As you approach the DMM’s post where Walmart is traded, you check the terminal
screen for information on the current market price. The screen reveals that the last executed
trade was at $25.63 and that the DMM is bidding $25.50 per share. You could immediately
sell to the DMM at $25.50, but that would be too easy.
Instead, as the customer’s representative, you are obligated to get the best possible
price. It is your job to “work” the order, and your job depends on providing satisfactory or-
der execution service. So, you look around for another broker who represents a customer
who wants to buy Walmart stock. Luckily, you quickly find another broker at the DMM’s
post with an order to buy 2,000 shares. Noticing that the dealer is asking $25.76 per share,
you both agree to execute your orders with each other at a price of $25.63. This price is
halfway between the DMM’s bid and ask prices, and it saves each of your customers $.13 ×
2,000 = $260 as compared to dealing at the posted prices.
For a very actively traded stock, there may be many buyers and sellers around the
DMM’s post, and most of the trading will be done directly between brokers. This is called
trading in the “crowd.” In such cases, the DMM’s responsibility is to maintain order and to
make sure that all buyers and sellers receive a fair price. In other words, the DMM essen-
tially functions as a referee.
More often, however, there will be no crowd at the DMM’s post. Going back to our
Walmart example, suppose you are unable to quickly find another broker with an order to
buy 2,000 shares. Because you have an order to sell immediately, you may have no choice
but to sell to the DMM at the bid price of $25.50. In this case, the need to execute an order
quickly takes priority, and the DMM provides the liquidity necessary to allow immediate
order execution.
Finally, note that colored coats are worn by many of the people on the floor of the ex-
change. The color of the coat indicates the person’s job or position. Clerks, runners, visi-
tors, exchange officials, and so on wear particular colors to identify themselves. Also, things
can get a little hectic on a busy day, with the result that good clothing doesn’t last long; the
cheap coats offer some protection.
NASDAQ Operations
In terms of the number of companies listed and, on many days, the number of shares traded,
the NASDAQ (say “Naz-dak”) is even bigger than the NYSE. As we mentioned in Chapter
1, the somewhat odd name is derived from the acronym NASDAQ, which stood for National
Association of Securities Dealers Automated Quotations system; but NASDAQ is now a
name in its own right.
Introduced in 1971, the NASDAQ market is a computer network of securities dealers
who disseminate timely security price quotes to NASDAQ subscribers. These dealers act as
market makers for securities listed on the NASDAQ. As market makers, NASDAQ dealers
post bid and asked prices at which they accept sell and buy orders, respectively. With each
Take a virtual field trip to
the New York Stock
Exchange at
www.nyse.com.
How big is the bid-ask
spread on your favorite
NASDAQ stock? Check
out the latest quotes at
money.cnn.com!
ros13952_ch07_205-236.indd 223 12/24/18 4:50 PM
224 P A R T 4 Valuing Stocks and Bonds
price quote, they also post the number of stock shares that they obligate themselves to trade
at their quoted prices.
Not to be outdone by the NYSE, the NASDAQ completed a merger in May 2007 when
it finalized its deal to buy the OMX, which controlled seven Nordic and Baltic stock ex-
changes. Since the merger, the NASDAQ is officially the NASDAQ OMX Group, although
it is still often referred to as NASDAQ.
Unlike the NYSE DMM system, NASDAQ relies on multiple market makers for
actively traded stocks. Thus, there are two key differences between the NYSE and NAS-
DAQ: (1) NASDAQ is a computer network and has no physical location where trading
takes place and (2) NASDAQ has a multiple market maker system rather than a DMM
system. Notice that there is no direct trading in the crowd as there may be on the
NYSE.
About 3,400 companies are listed on the NASDAQ system, with an average of about
a dozen market makers for each security. Traditionally, shares of stock in smaller com-
panies were listed on the NASDAQ, and there was a tendency for companies to move
from the NASDAQ to the NYSE once they became large enough. Today, however, giant
companies such as Amazon, Microsoft, and Intel have chosen to remain on the
NASDAQ.
The NASDAQ network operates with three levels of information access. Level 1 is de-
signed to provide a timely, accurate source of price quotations. These prices are freely avail-
able over the Internet.
Level 2 allows users to view price quotes from all NASDAQ market makers. In
particular, this level allows access to inside quotes. Inside quotes are the highest bid
quotes and the lowest asked quotes for a NASDAQ-listed security. Level 2 is now avail-
able on the web, sometimes for a small fee. Level 3 is for the use of market makers
only. This access level allows NASDAQ dealers to enter or change their price quote
information.
The NASDAQ is actually made up of three separate markets: the NASDAQ Global
Select Market, the NASDAQ Global Market, and the NASDAQ Capital Market. As the
market for NASDAQ’s larger and more actively traded securities, the Global Select Market
lists about 1,600 companies (as of 2018), including some of the best-known companies in
the world, such as Microsoft and Intel. The Global Market companies are somewhat smaller
in size, and NASDAQ lists about 860 of these companies. Finally, the smallest companies
listed on NASDAQ are in the NASDAQ Capital Market; about 940 are currently listed. Of
course, as Capital Market companies become more established, they may move up to the
Global Market or Global Select Market.
ECNs In a very important development in the late 1990s, the NASDAQ system was
opened to so-called electronic communications networks (ECNs). ECNs are basically web-
sites that allow investors to trade directly with one another. Investor buy and sell orders
placed on ECNs are transmitted to the NASDAQ and displayed along with market maker
bid and ask prices. Thus, the ECNs open up the NASDAQ by essentially allowing individual
investors, not just market makers, to enter orders. As a result, the ECNs act to increase li-
quidity and competition. Our nearby Work the Web box describes one ECN, the
CBOE Global Markets (markets.cboe.com/us/equities), and contains important informa-
tion about ECN “order books.” Be sure to read it.
NASDAQ
(www.nasdaq.com) has a
great website; check it
out!
inside quotes
The highest bid quotes
and the lowest ask
quotes for a security.
electronic
communications
networks (ECNs)
Websites that allow
investors to trade directly
with one another.
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C H A P T E R 7 Equity Markets and Stock Valuation 225
You can actually watch trading taking place on the web by visiting markets.cboe.com/us/equi-ties. This stock market was originally the BATS Exchange until it was purchased by the CBOE
in 2016. This market is somewhat unique in that the “order book,” meaning the list of all buy and
sell orders, is public in real time. As shown, we have captured a sample of the order book for Intel
(INTC). On the top in blue are sell orders (asks); buy orders (bids) are in green on the bottom. All
orders are “limit” orders, which means the customer has specified the most he or she will pay (for
buy orders) or the least he or she will accept (for sell orders). The inside quotes (the highest bid,
or buy, and the lowest ask, or sell) in the market are shown in bold face.
W R K T H E W E B
QUESTIONS
1. Go to markets.cboe.com/us/equities and look up the order book for Microsoft (MSFT).
What are the inside quotes for Microsoft?
2. Go to markets.cboe.com/us/equities. This website shows the 25 most active
stocks. Looking down through this list, what are the bid-ask spreads for these
stocks?
If you visit the site, you can see trading take place as orders are entered and executed. No-
tice that on this particular day, about 2.8 million shares of Intel had traded on the CBOE Market. At
that time, the inside quotes for Intel were 1,500 shares bid at $52.32 and 800 shares offered at
$52.33. This is not the entire order book for Intel as there are more buy orders below $52.28 and
more sell orders above $52.37.
Source: markets.cboe.com
Of course, the NYSE and NASDAQ are not the only places stocks are traded. See our
nearby Finance Matters box for a discussion of somewhat wilder markets.
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The Wild, Wild West of Stock Trading
W """"""""here do companies go when they can’t (or don’t want to) meet the listing requirements of the larger stock
markets? Two options are the Over-the-Counter Bulletin
Board (OTCBB) and the OTC Markets, formerly Pink Sheets.
These two electronic markets are part of the Wild, Wild West
of stock trading. The somewhat odd names have simple ex-
planations. The OTCBB began as an electronic bulletin board
that was created to facilitate OTC trading in nonlisted stocks.
The name “Pink Sheets” reflects the fact that, at one time,
prices for such stocks were quoted on pink sheets of paper.
The well-known markets such as the NASDAQ and the
NYSE have relatively strict listing requirements. If a company
fails to meet these requirements, it can be delisted. The
OTCBB and the Pink Sheets, on the other hand, have no list-
ing requirements. The OTCBB does require that companies
file financial statements with the SEC (or other relevant
agency), but the Pink Sheets does not.
Stocks traded on these markets often have very low
prices and are frequently referred to as “penny stocks,” “mi-
crocaps,” or even “nanocaps.” Relatively few brokers do any
research on these companies, so information is often spread
through word of mouth or the internet, not the most reliable
of sources. In fact, for many stocks, these markets often look
like big electronic rumor mills and gossip factories. To get a
feel for what trading looks like, we captured a typical screen
from the OTCBB website (finra-markets.morningstar.com/
MarketData/EquityOptions/default.jsp).
First, let’s look at the returns. Intelligent Highway So-
lutions, Inc. (IHSI), had a return on this day of 100 percent!
Of course, the gain occurred because the stock price
jumped by $.0001. The stock price of Sky440, Inc. (SKYF),
fell about 43 percent, as its price dropped by $.0003.
Stocks on the OTCBB tend to have large trading volumes
when they do trade, but the dollar amount is quite a bit
FINANCE MATTERS
lower than seen on the larger exchanges. For example,
by the end of this same trading day, Advance Micro De-
vices (AMD) was the most active stock on the NYSE, with
about 94 million shares changing hands. Sky440 (SKYF)
traded about 632 million shares. However, the total dollar
volume for the day was a whopping $340,000 or so. In
contrast, about $1.48 billion worth of AMD stock was
traded.
The OTC Markets (www.otcmarkets.com) is a publicly
traded company. To be listed on the OTC Markets, a com-
pany just has to find a market maker willing to trade in the
company’s stock. Companies list on the OTC Markets for
various reasons. Small companies that do not wish to meet
listing requirements are one type. Foreign companies often
list on the OTC Markets because they do not prepare their
financial statements according to GAAP, a requirement for
listing on U.S. stock exchanges. There are many companies
that were formerly listed on bigger stock markets that were
either delisted involuntarily or chose to “go dark” for various
reasons, including, as we discussed in Chapter 1, the costs
associated with Sarbox compliance.
All in all, the OTCBB and OTC Markets can be pretty
wild places to trade. Low stock prices allow huge percent-
age returns on small stock price movements. Be advised,
however, that attempts at manipulation and fraud are com-
monplace. Also, stocks on these markets are often very
thinly traded, meaning there is little volume. It is not unusual
for a stock listed on either market to have no trades on a
given day. Even two or three days in a row without a trade in
a particular stock is not uncommon.
Source: finra-markets.morningstar.com
226
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C H A P T E R 7 Equity Markets and Stock Valuation 227
Stock Market Reporting
Like so many other things, stock price reporting has largely migrated to the web. You can
get up-to-the-minute prices on stocks from many online servers, along with plenty of infor-
mation about a stock. The following is a stock quote from finance.yahoo.com for famed
motorcycle manufacturer Harley-Davidson (HOG) from June 21, 2018.
In the upper left, we have a recent trade price of $45.61. Based on that price, the stock had
fallen by $.07 during the day, or .15 percent. In the box below, more information is provided. For
example, the “Previous Close” is the closing price from the previous trading day, and “Open” is
the first price of the current day. The high price for this day so far, shown in “Day’s Range,” was
$45.84, and the low price was $45.10. About 1.33 million shares of Harley-Davidson had traded,
relative to an average volume over the last three months of 2.16 million shares. As always, the
bid and ask are the highest price someone was willing to pay and the lowest price someone was
willing to take. For example, 45.57 × 1,200 tells you that someone was willing to pay $45.57 for
1,200 shares. The “×” is read as “by.” You also can see the number of shares at the ask price.
The “52 Week Range” gives the highest and lowest stock prices over the past 52 weeks.
And there is even more information in the quote. “Beta” is an important number. We
will have lots more to say about it in a later chapter. Harley-Davidson, like most dividend-
paying companies, actually pays dividends quarterly. However, the dividend shown of $1.48
is the expected dividend for the coming year. The dividend yield is the annual dividend di-
vided by the stock price. Harley-Davidson’s EPS for the past year was $2.99. The PE ratio
shown is calculated using the current stock price divided by the last 12 months’ earnings. The
“1y Target Est” is the projected price next year based on analysts’ estimates. Finally, we are
shown the “Market Cap” (market capitalization, or total value of Harley-Davidson’s stock).
CONCEPT QUESTIONS
7.3a What is the difference between a securities broker and a securities dealer?
7.3b Which is bigger, the bid price or the ask price? Why?
7.3c What are the three types of license holders of the New York Stock Exchange, or NYSE?
7.3d How does NASDAQ differ from the NYSE?
You can get real-time
stock quotes on the web.
See finance.yahoo.com
for details.
Source: finance.yahoo.com, 2018
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228 P A R T 4 Valuing Stocks and Bonds
SUMMARY AND CONCLUSIONS
This chapter has covered the basics of stocks and stock valuation. The key points include:
1. The cash flows from owning a share of stock come in the form of future dividends.
We saw that in certain special cases it is possible to calculate the present value of all
the future dividends and thus come up with a value for the stock.
2. As the owner of shares of common stock in a corporation, you have various rights,
including the right to vote to elect corporate directors. Voting in corporate elections
can be either cumulative or straight. Most voting actually is done by proxy, and a
proxy battle breaks out when competing sides try to gain enough votes to have their
candidates for the board elected.
3. In addition to common stock, some corporations have issued preferred stock. The
name stems from the fact that preferred stockholders must be paid first, before
common stockholders can receive anything. Preferred stock has a fixed dividend.
4. The two biggest stock markets in the United States are the NYSE and the NASDAQ.
We discussed the organization and operation of these two markets, and we saw how
stock price information is reported.
This chapter completes Part Four of our book. By now, you should have a good grasp of
what we mean by present value. You also should be familiar with how to calculate present
values, loan payments, and so on. In Part Five, we cover capital budgeting decisions. As you
will see, the techniques you have learned in Chapters 4–7 form the basis for our approach to
evaluating business investment decisions.
POP QUIZ!
Can you answer the following questions? If your class is using Connect, log on to
SmartBook to see if you know the answers to these and other questions, check out
the study tools, and find out what topics require additional practice!
Section 7.1 What is the total return for a stock that currently sells for $50, just paid
a $1.75 dividend, and has a constant growth rate of 8 percent?
Section 7.2 True or false: For tax purposes, preferred stock is considered a form of
equity.
CHAPTER REVIEW AND SELF-TEST PROBLEMS
7.1. Dividend Growth and Stock Valuation The Brigapenski Co. has just paid a cash
dividend of $2 per share. Investors require a 16 percent return from investments
such as this. If the dividend is expected to grow at a steady 8 percent per year, what
is the current value of the stock? What will the stock be worth in five years? (See
Problem 1.)
7.2. Required Returns Suppose we observe a stock selling for $40 per share. The next
dividend will be $1 per share, and you think the dividend will grow at 12 percent per
year forever. What is the dividend yield in this case? The capital gains yield? The
total required return? (See Problem 3.)
ros13952_ch07_205-236.indd 228 12/24/18 4:50 PM
C H A P T E R 7 Equity Markets and Stock Valuation 229
■ Answers to Chapter Review and Self-Test Problems
7.1 The last dividend, D0, was $2. The dividend is expected to grow steadily at 8 percent.
The required return is 16 percent. Based on the dividend growth model, we can say
that the current price is:
P0 = D1/(R − g)
= D0 × (1 + g)/(R − g)
= $2 × 1.08/(.16 − .08)
= $2.16/.08
= $27
We could calculate the price in five years by calculating the dividend in five years
and then using the growth model again. Alternatively, we could recognize that the
stock price will increase by 8 percent per year and calculate the future price directly.
We’ll do both. First, the dividend in five years will be:
D5 = D0 × (1 + g)5
= $2 × 1.085
= $2.9387
The price in five years therefore would be:
P5 = D5 × (1 + g)/(R − g)
= $2.9387 × 1.08/.08
= $3.1738/.08
= $39.67
Once we understand the dividend model, however, it’s easier to notice that:
P5 = P0 × (1 + g)5
= $27 × 1.085
= $27 × 1.4693
= $39.67
Notice that both approaches yield the same price in five years.
7.2 The dividend yield is the next dividend, D1, divided by the current price, P0, or
$1/$40 = .025, or 2.5%. The capital gains yield is the same as the dividend growth
rate, 12 percent. The total required return is the sum of the two, 2.5% + 12% =
14.5%.
CRITICAL THINKING AND CONCEPTS REVIEW
LO 1 7.1 Stock Valuation Why does the value of a share of stock depend on
dividends?
LO 1 7.2 Stock Valuation A substantial percentage of the companies listed on the
NYSE and the NASDAQ don’t pay dividends, but investors are nonetheless
willing to buy shares in them. How is this possible given your answer to the
previous question?
LO 1 7.3 Dividend Policy Referring to the previous questions, under what
circumstances might a company choose not to pay dividends?
ros13952_ch07_205-236.indd 229 12/24/18 4:50 PM
230 P A R T 4 Valuing Stocks and Bonds
LO 1 7.4 Dividend Growth Model Under what two assumptions can we use the
dividend growth model presented in the chapter to determine the value of a
share of stock? Comment on the reasonableness of these assumptions.
LO 1 7.5 Common versus Preferred Stock Suppose a company has a preferred
stock issue and a common stock issue. Both have just paid a $2 dividend.
Which do you think will have a higher price, a share of the preferred or a
share of the common?
LO 1 7.6 Dividend Growth Model Based on the dividend growth model, what are
the two components of the total return on a share of stock? Which do you
think is typically larger?
LO 1 7.7 Growth Rate In the context of the dividend growth model, is it true that
the growth rate in dividends and the growth rate in the price of the stock
are identical?
LO 1 7.8 Dividends and Earnings Is it possible for a company to pay dividends
when it has a negative net income for the year? Could this happen for
longer periods?
LO 2 7.9 Corporate Ethics Is it unfair or unethical for corporations to create
classes of stock with unequal voting rights?
LO 2 7.10 Voting Rights Some companies, such as Google, have created classes of
stock with little or no voting rights at all. Why would investors buy such
stock?
LO 2 7.11 Stock Valuation Evaluate the following statement: Managers should not
focus on the current stock value because doing so will lead to an
overemphasis on short-term profits at the expense of long-term profits.
LO 1 7.12 Constant Dividend Growth Model In the constant dividend growth
model, what is the highest reasonable growth rate for a stock’s dividend?
LO 2 7.13 Voting Rights In the chapter, we mentioned that many companies have
been under pressure to declassify their boards of directors. Why would
investors want a board to be declassified? What are the advantages of a
classified board?
LO 1 7.14 Price Ratio Valuation What are the difficulties in using the PE ratio to
value stock?
QUESTIONS AND PROBLEMS
BASIC (Questions 1–14)
1. Stock Values Fowler, Inc., just paid a dividend of $2.55 per share on its
stock. The dividends are expected to grow at a constant rate of 3.9 percent
per year, indefinitely. If investors require a return of 10.4 percent on this
stock, what is the current price? What will the price be in 3 years? In
15 years?
2. Stock Values The next dividend payment by Hoffman, Inc., will be $2.65
per share. The dividends are anticipated to maintain a growth rate of
LO 1
LO 1
Select problems are available in McGraw-Hill Connect. Please see the pack-
aging options section of the Preface for more information.
ros13952_ch07_205-236.indd 230 12/24/18 4:50 PM
C H A P T E R 7 Equity Markets and Stock Valuation 231
4.5 percent forever. If the stock currently sells for $43.15 per share, what is
the required return?
3. Stock Values For the company in the previous problem, what is the
dividend yield? What is the expected capital gains yield?
4. Stock Values Poulter Corporation will pay a dividend of $3.25 per share
next year. The company pledges to increase its dividend by 5.1 percent per
year, indefinitely. If you require a return of 11 percent on your investment,
how much will you pay for the company’s stock today?
5. Stock Valuation Redan, Inc., is expected to maintain a constant 4.3 percent
growth rate in its dividends, indefinitely. If the company has a dividend yield
of 5.6 percent, what is the required return on the company’s stock?
6. Stock Valuation Suppose you know that a company’s stock currently sells
for $67 per share and the required return on the stock is 10.8 percent. You
also know that the total return on the stock is evenly divided between capital
gains yield and dividend yield. If it’s the company’s policy to always maintain
a constant growth rate in its dividends, what is the current dividend per
share?
7. Stock Valuation Burkhardt Corp. pays a constant $15.25 dividend on its
stock. The company will maintain this dividend for the next nine years and
will then cease paying dividends forever. If the required return on this stock
is 9.2 percent, what is the current share price?
8. Valuing Preferred Stock Smiling Elephant, Inc., has an issue of preferred
stock outstanding that pays a $2.85 dividend every year, in perpetuity. If this
issue currently sells for $77.32 per share, what is the required return?
9. Voting Rights After successfully completing your corporate finance class,
you feel the next challenge ahead is to serve on the board of directors of
Schenkel Enterprises. Unfortunately, you will be the only individual voting
for you. If the company has 525,000 shares outstanding and the stock
currently sells for $38, how much will it cost you to buy a seat if the company
uses straight voting? Assume that the company uses cumulative voting and
there are four seats in the current election; how much will it cost you to buy
a seat now?
10. Growth Rates The stock price of Alps Co. is $67. Investors require a return
of 10.5 percent on similar stocks. If the company plans to pay a dividend of
$4.25 next year, what growth rate is expected for the company’s stock price?
11. Valuing Preferred Stock E-Eyes.com has a new issue of preferred stock it
calls 20/20 preferred. The stock will pay a $20 dividend per year, but the
first dividend will not be paid until 20 years from today. If you require a
return of 7.3 percent on this stock, how much should you pay today?
12. Stock Valuation Cape Corp. will pay a dividend of $2.64 next year. The
company has stated that it will maintain a constant growth rate of 4.5
percent a year forever. If you want a return of 12 percent, how much will you
pay for the stock? What if you want a return of 8 percent? What does this
tell you about the relationship between the required return and the stock
price?
13. Stock Valuation and PE Ratio The Blooming Flower Co. has earnings of
$3.68 per share. The benchmark PE for the company is 18. What stock price
would you consider appropriate? What if the benchmark PE were 21?
LO 1
LO 1
LO 1
LO 1
LO 1
LO 1
LO 2
LO 1
LO 1
LO 1
LO 2
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232 P A R T 4 Valuing Stocks and Bonds
14. Stock Valuation and PS Ratio TwitterMe, Inc., is a new company and
currently has negative earnings. The company’s sales are $1.45 million and
there are 130,000 shares outstanding. If the benchmark price-sales ratio is
3.9, what is your estimate of an appropriate stock price? What if the price-
sales ratio were 3.2?
INTERMEDIATE (Questions 15–30)
15. Nonconstant Growth Metallica Bearings, Inc., is a young start-up company.
No dividends will be paid on the stock over the next 9 years because the firm
needs to plow back its earnings to fuel growth. The company will then pay a
dividend of $23 per share 10 years from today and will increase the dividend
by 5 percent per year thereafter. If the required return on this stock is 12 percent,
what is the current share price?
16. Nonconstant Dividends Bon Chance, Inc., has an odd dividend policy. The
company has just paid a dividend of $3 per share and has announced that it
will increase the dividend by $5 per share for each of the next four years, and
then never pay another dividend. If you require a return of 9.7 percent on the
company’s stock, how much will you pay for a share today?
17. Nonconstant Dividends Synovec Corporation is expected to pay the
following dividends over the next four years: $7, $13, $18, and $3.25.
Afterward, the company pledges to maintain a constant 5 percent growth
rate in dividends forever. If the required return on the stock is 10.4 percent,
what is the current share price?
18. Supernormal Growth Biarritz Corp. is growing quickly. Dividends are
expected to grow at a rate of 25 percent for the next three years, with the
growth rate falling off to a constant 4.5 percent thereafter. If the required
return is 10.5 percent and the company just paid a dividend of $2.85, what is
the current share price?
19. Negative Growth Antiques ‘R’ Us is a mature manufacturing firm. The
company just paid a dividend of $16.30, but management expects to reduce
the payout by 3.5 percent per year, indefinitely. If you require a return of 8
percent on this stock, what will you pay for a share today?
20. Finding the Dividend Dropshot Corporation stock currently sells for
$68.98 per share. The market requires a return of 10.3 percent on the firm’s
stock. If the company maintains a constant 4.9 percent growth rate in
dividends, what was the most recent dividend per share paid on the stock?
You’ve collected the following information from your favorite financial website.
Use it to answer Questions 21–25 (the 52-week Hi and Lo are the highest and
lowest stock prices over the previous 52 weeks).
LO 2
LO 1
LO 1
LO 1
LO 1
LO 1
LO 2
52-Week Price
Hi Lo Stock (Div)
Div
Yld %
PE
Ratio
Close
Price
Net
Chg
64.60 47.80 Abbott 1.12 1.9 235.6 62.91 −.05
145.94 70.28 Ralph Lauren 2.50 1.8 70.9 139.71 −.62
171.13 139.13 IBM 6.30 4.3 23.8 145.39 .19
91.80 71.96 Duke Energy 3.56 4.9 17.6 74.30 .84
113.19 96.20 Disney 1.68 1.7 15.5 ?? .10
ros13952_ch07_205-236.indd 232 12/24/18 4:50 PM
C H A P T E R 7 Equity Markets and Stock Valuation 233
21. Dividend Yield Find the quote for Duke Energy. Assume that the dividend
is constant. What was the highest dividend yield over the past year? What
was the lowest dividend yield over the past year?
22. Stock Valuation According to the 2018 Value Line Investment Survey, the
growth rate in dividends for IBM for the next five years is expected to be 5
percent. Suppose IBM meets this growth rate in dividends for the next five
years and then the dividend growth rate falls to 3.5 percent indefinitely.
Assume investors require a return of 10 percent on IBM stock. Is the stock
priced correctly? What factors could affect your answer?
23. Stock Valuation According to the 2018 Value Line Investment Survey, the
growth rate in dividends for Ralph Lauren for the next five years will be .5
percent. If investors feel this growth rate will continue, what is the required
return for the company’s stock?
24. Negative Growth According to the 2018 Value Line Investment Survey, the
growth rate in dividends for Abbott Laboratories for the previous five years
has been negative 11.5 percent. If investors feel this growth rate will continue,
what is the required return for the company’s stock? Does this number make
sense? What are some of the potential reasons for the negative growth in
dividends?
25. Stock Quotes Using the dividend yield, calculate the closing price for
Walt Disney on this day. The actual closing price for Walt Disney was
$108.85. Why is your closing price different? The Value Line Investment
Survey projects a 4 percent dividend growth rate for Walt Disney. What is
the required return for the stock using the dividend discount model and the
actual stock price?
26. Stock Valuation and PE Sunset Corp. currently has an EPS of $3.85, and
the benchmark PE for the company is 19. Earnings are expected to grow at 6
percent per year.
a. What is your estimate of the current stock price?
b. What is the target stock price in one year?
c. Assuming the company pays no dividends, what is the implied return
on the company’s stock over the next year? What does this tell you
about the implied stock return using PE valuation?
27. Stock Valuation and PE You have found the following historical
information for the Daniela Company:
Year 1 Year 2 Year 3 Year 4
Stock price $63.25 $71.94 $83.43 $88.27
EPS 3.15 3.35 3.60 3.85
Earnings are expected to grow at 7 percent for the next year. Using the compa-
ny’s historical average PE as a benchmark, what is the target stock price in
one year?
28. Stock Valuation and PE In the previous problem, we assumed that the
stock had a single stock price for the year. However, if you look at stock
prices over any year, you will find a high and low stock price for the year.
Instead of a single benchmark PE ratio, we now have a high and low PE
LO 3
LO 1
LO 1
LO 1
LO 1
LO 1
LO 1
LO 1
ros13952_ch07_205-236.indd 233 12/24/18 4:50 PM
234 P A R T 4 Valuing Stocks and Bonds
ratio for each year. We can use these ratios to calculate a high and a low
stock price for the next year. Suppose we have the following information on a
particular company:
Year 1 Year 2 Year 3 Year 4
High price $48.60 $57.34 $69.46 $74.85
Low price 37.25 42.18 55.85 63.18
EPS 2.02 2.31 2.45 3.05
Earnings are projected to grow at 9 percent over the next year. What are your
high and low target stock prices over the next year?
29. Stock Valuation and PE Berta, Inc., currently has an EPS of $3.85 and an
earnings growth rate of 7 percent. If the benchmark PE ratio is 21, what is
the target share price five years from now?
30. PE and Terminal Stock Price In practice, a common way to value a share
of stock when a company pays dividends is to value the dividends over the
next five years or so, then find the “terminal” stock price using a benchmark
PE ratio. Suppose a company just paid a dividend of $1.15. The dividends
are expected to grow at 10 percent over the next five years. The company has
a payout ratio of 40 percent and a benchmark PE of 19. What is the target
stock price in five years? What is the stock price today assuming a required
return of 11 percent on this stock?
CHALLENGE (Questions 31–32)
31. Capital Gains versus Income Consider four different stocks, all of which
have a required return of 19 percent and a most recent dividend of $2.40 per
share. Stocks W, X, and Y are expected to maintain constant growth rates in
dividends for the foreseeable future of 8 percent, 0 percent, and −5 percent
per year, respectively. Stock Z is a growth stock that will increase its dividend
by 20 percent for the next two years and then maintain a constant 12 percent
growth rate, thereafter. What is the dividend yield for each of these four
stocks? What is the expected capital gains yield? Discuss the relationship
among the various returns that you find for each of these stocks.
32. Stock Valuation Most corporations pay quarterly dividends on their
common stock rather than annual dividends. Barring any unusual
circumstances during the year, the board raises, lowers, or maintains the
current dividend once a year and then pays this dividend out in equal
quarterly installments to its shareholders.
a. Suppose a company currently pays an annual dividend of $2.80 on its
common stock in a single annual installment, and management plans on
raising this dividend by 6 percent per year indefinitely. If the required
return on this stock is 12 percent, what is the current share price?
b. Now suppose the company in part (a) actually pays its annual dividend
in equal quarterly installments; thus, the company has just paid a
dividend of $.70 per share, as it has for the previous three quarters.
What is your value for the current share price now? (Hint: Find the
equivalent annual end-of-year dividend for each year.) Comment on
whether you think this model of stock valuation is appropriate.
LO 1
LO 1
LO 1
LO 1
ros13952_ch07_205-236.indd 234 12/24/18 4:50 PM
C H A P T E R 7 Equity Markets and Stock Valuation 235
In practice, the use of the dividend discount model is refined from the method we presented
in the textbook. Many analysts will estimate the dividend for the next 5 years and then esti-
mate a perpetual growth rate at some point in the future, typically 10 years. Rather than
have the dividend growth fall dramatically from the fast growth period to the perpetual
growth period, linear interpolation is applied. That is, the dividend growth is projected to
fall by an equal amount each year. For example, if the high growth period is 15 percent for
the next 5 years and the dividends are expected to fall to a 5 percent perpetual growth rate
5 years later, the dividend growth rate would decline by 2 percent each year.
The Value Line Investment Survey provides information for investors. Below, you will
find information for Microsoft (MSFT) found in the 2018 edition of Value Line:
2018 dividend: $1.56
Five-year dividend growth rate: 12.0%
a. Assume that a perpetual growth rate of 5 percent begins 10 years from now and
use linear interpolation between the high growth rate and perpetual growth rate.
Construct a table that shows the dividend growth rate and dividend each year. What is
the stock price at Year 10? What is the stock price today?
b. Instead of applying the constant dividend growth model to find the stock price in
the future, analysts will often combine the dividend discount method with price ratio
valuation, often with the PE ratio. Remember that the PE ratio is the price per share
divided by the earnings per share. So, if we know what the PE ratio is, we can solve for
the stock price. Suppose we also have the following information about MSFT:
Payout ratio: 20%
PE at constant growth rate: 15
Use the PE ratio to calculate the stock price when MSFT reaches a perpetual growth
rate in dividends. Now supply the value of the stock today by finding the present value
of the dividends during the supernormal growth rate and the price you calculated
using the PE ratio.
c. How sensitive is the current stock price to changes in PE ratio when the stock reaches
the perpetual growth rate? Graph the current stock price against the PE ratio in 10
years to find out.
WHAT’S ON
THE WEB?
7.1 Dividend Discount Model According to the 2018 Value Line Investment Survey, the
dividend growth rate for ExxonMobil (XOM) is 3 percent. Find the current stock price
quote and dividend information at finance.yahoo.com. If this dividend growth rate is
correct, what is the required return for ExxonMobil? Does this number make sense to you?
7.2 Stock Quotes What is the most expensive publicly traded stock in the United States?
Go to finance.yahoo.com and enter BRKA (for Berkshire Hathaway Class A). What is
the current price per share? What are the 52-week high and low? How many shares trade
on an average day? How many shares have traded today?
7.3 Supernormal Growth You are interested in buying stock in Coca-Cola (KO). You
believe that the dividends will grow at 15 percent for the next four years and level off at 6
percent thereafter. Using the most recent dividend on finance.yahoo.com, if you want a
12 percent return, how much should you be willing to pay for a share of stock?
7.4 Market Operations How does a stock trade take place? Go to www.nyse.com to find
out. Describe the process of a trade on the NYSE.
EXCEL MASTER IT! PROBLEM
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Excel
Master
ros13952_ch07_205-236.indd 235 12/24/18 4:50 PM
236 P A R T 4 Valuing Stocks and Bonds
Ragan, Inc. — Competitors
EPS Div.
Stock
Price ROE R
Arctic Cooling,
Inc.
$1.30 $.16 $25.34 8.50% 10.00%
National
Heating &
Cooling
1.95 .23 29.85 10.50 13.00
Expert HVAC
Corp.
−.37 .14 22.13 9.78 12.00
Industry
average
$.96 $.18 $25.77 9.59% 11.67
Expert HVAC Corporation’s negative earnings per
share were the result of an accounting write-off last year.
Without the write-off, earnings per share for the com-
pany would have been $1.10.
Last year, Ragan, Inc., had an EPS of $3.15 and paid
a dividend to Carrington and Genevieve of $45,000
each. The company also had a return on equity of
17 percent. The siblings believe that 14 percent is an
appropriate required return for the company.
Ragan, Inc., was founded nine years ago by brother and sister Carrington and Genevieve Ragan. The
company manufactures and installs commercial heat-
ing, ventilation, and cooling (HVAC) units. Ragan, Inc.,
has experienced rapid growth because of a proprietary
technology that increases the energy efficiency of its
units. The company is equally owned by Carrington
and Genevieve. The original partnership agreement
between the siblings gave each 50,000 shares of
stock. In the event either wished to sell stock, the
shares first had to be offered to the other at a dis-
counted price.
Although neither sibling wants to sell, they have de-
cided they should value their holdings in the company.
To get started, they have gathered the following infor-
mation about their main competitors:
CHAPTER CASE
Stock Valuation at Ragan, Inc.
1. Assuming the company continues its current
growth rate, what is the value per share of the
company’s stock?
2. To verify their calculations, Carrington and Gene-
vieve have hired Josh Schlessman as a consultant.
Josh was previously an equity analyst and cov-
ered the HVAC industry. Josh has examined the
company’s financial statements, as well as those
of its competitors. Although Ragan, Inc., cur-
rently has a technological advantage, his re-
search indicates that other companies are
investigating methods to improve efficiency.
Given this, Josh believes that the company’s
technological advantage will last only for the
next five years. After that period, the company’s
growth will likely slow to the industry growth av-
erage. Additionally, Josh believes that the re-
quired return used by the company is too high.
He believes the industry average required re-
turn is more appropriate. Under this growth rate
assumption, what is your estimate of the stock
price?
Q U E S T I O N S
ros13952_ch07_205-236.indd 236 12/24/18 4:50 PM
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237
PART FIVE Capital Budgeting
Please visit us at essentialsofcorporatefinance.blogspot.com for the latest developments in the world of corporate finance.
Is there green in green? General Electric (GE) thinks so. Through its “Ecomagination” program, the company planned to double re-
search and development spending on green products. In fact, by
2016, GE already had invested more than $20 billion in its Ecomag-
ination program, with plans to invest another $5 billion by 2020.
With products such as a hybrid railroad locomotive (described
as a 200-ton, 6,000-horsepower “Prius on rails”), GE’s green initia-
tive seems to be paying off. Revenue from the company’s green
products was more than $200 billion from 2005 to 2016. Further,
revenues from Ecomagination products were growing twice as fast
as the company’s other revenues. GE’s internal commitment to re-
duced energy consumption through green “Treasure Hunts” saved
it more than $100 million, and, by 2016, the company had reduced
water consumption by 53 percent relative to its 2006 baseline, an-
other considerable cost savings.
While GE was in part motivated by the desire to go green, from
a financial perspective the decision only makes sense if the com-
pany makes some green. Given that GE plans to spend about
$2 billion per year on such undertakings, it is obviously a major
financial decision, and the risks and rewards must be carefully weighed. In this chapter, we
discuss the basic tools used in making such decisions.
This chapter introduces you to the practice of capital budgeting. Back in Chapter 1, we
saw that increasing the value of the stock in a company is the goal of financial management.
Thus, what we need to learn is how to tell whether a particular investment will achieve that
or not. This chapter considers a variety of techniques that are actually used in practice. More
importantly, it shows how many of these techniques can be misleading, and it explains why
the net present value approach is the right one.
Net Present Value and
Other Investment Criteria8
LEARNING OBJECTIVES
After studying this chapter, you should
be able to:
LO 1 Summarize the payback rule and
some of its shortcomings.
LO 2 Discuss accounting rates of return
and some of the problems with
them.
LO 3 Explain the internal rate of return
criterion and its associated
strengths and weaknesses.
LO 4 Evaluate proposed investments by
using the net present value
criterion.
LO 5 Apply the modified internal rate of
return.
LO 6 Calculate the profitability index
and understand its relation to net
present value.
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238 P A R T 5 Capital Budgeting
In Chapter 1, we identified the three key areas of concern to the financial manager. The first of these was the following: What long-term investments should we make? We called
this the capital budgeting decision. In this chapter, we begin to deal with the issues that arise
in answering this question.
The process of allocating, or budgeting, capital is usually more involved than just decid-
ing whether or not to buy a particular fixed asset. We frequently will face broader issues like
whether or not we should launch a new product or enter a new market. Decisions such as
these will determine the nature of a firm’s operations and products for years to come, pri-
marily because fixed asset investments are generally long-lived and not easily reversed once
they are made.
For these reasons, the capital budgeting question is probably the most important issue
in corporate finance. How a firm chooses to finance its operations (the capital structure
question) and how a firm manages its short-term operating activities (the working capital
question) are certainly issues of concern, but it is the fixed assets that define the business of
the firm. Airlines, for example, are airlines because they operate airplanes, regardless of how
they finance them.
Any firm possesses a huge number of possible investments. Each possible investment is
an option available to the firm. Some options are valuable and some are not. The essence of
successful financial management, of course, is learning to identify which are which. With
this in mind, our goal in this chapter is to introduce you to the techniques used to analyze
potential business ventures to decide which are worth undertaking.
We present and compare several different procedures used in practice. Our primary
goal is to acquaint you with the advantages and disadvantages of the various approaches. As
we shall see, the most important concept in this area is the idea of net present value. We
consider this next.
NET PRESENT VALUE
In Chapter 1, we argued that the goal of financial management is to create value for the
stockholders. The financial manager must therefore examine a potential investment in light
of its likely effect on the price of the firm’s shares. In this section, we describe a widely used
procedure for doing this, the net present value approach.
The Basic Idea
An investment is worth undertaking if it creates value for its owners. In the most general
sense, we create value by identifying an investment worth more in the marketplace than it
costs us to acquire. How can something be worth more than it costs? It’s a case of the whole
being worth more than the cost of the parts.
Suppose you buy a run-down house for $75,000 and spend another $75,000 on painters,
plumbers, and so on to get it fixed up. Your total investment is $150,000. When the work is
completed, you place the house back on the market and find that it’s worth $170,000. The
market value ($170,000) exceeds the cost ($150,000) by $20,000. What you have done here
is to act as a manager and bring together some fixed assets (a house), some labor (plumbers,
carpenters, and others), and some materials (carpeting, paint, and so on). The net result is
that you have created $20,000 in value. Put another way, this $20,000 is the value added by
management.
With our house example, it turned out after the fact that $20,000 in value was created.
Things thus worked out very nicely. The real challenge, of course, would have been to
8.1
coverage online
Excel
Master
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C H A P T E R 8 Net Present Value and Other Investment Criteria 239
somehow identify ahead of time whether or not investing the necessary $150,000 was a good
idea in the first place. This is what capital budgeting is all about, namely, trying to determine
whether a proposed investment or project will be worth more than it costs once it is in place.
For reasons that will be obvious in a moment, the difference between an investment’s
market value and its cost is called the net present value, or NPV, of the investment. In other
words, net present value is a measure of how much value is created or added today by under-
taking an investment. Given our goal of creating value for the stockholders, the capital budget-
ing process can be viewed as a search for investments with positive net present values.
With our run-down house, you probably can imagine how we would go about making
the capital budgeting decision. We first would look at what comparable, fixed-up properties
were selling for in the market. We then would get estimates of the cost of buying a particular
property, fixing it up, and bringing it to market. At this point, we have an estimated total
cost and an estimated market value. If the difference is positive, then this investment is
worth undertaking because it has a positive estimated net present value. There is risk, of
course, because there is no guarantee that our estimates will turn out to be correct.
As our example illustrates, investment decisions are greatly simplified when there is a
market for assets similar to the investment we are considering. Capital budgeting becomes
much more difficult when we cannot observe the market price for at least roughly compara-
ble investments. The reason is that we are then faced with the problem of estimating the
value of an investment using only indirect market information. Unfortunately, this is pre-
cisely the situation the financial manager usually encounters. We examine this issue next.
Estimating Net Present Value
Imagine we are thinking of starting a business to produce and sell a new product, say, organic
fertilizer. We can estimate the start-up costs with reasonable accuracy because we know what
we will need to buy to begin production. Would this be a good investment? Based on our dis-
cussion, you know that the answer depends on whether or not the value of the new business
exceeds the cost of starting it. In other words, does this investment have a positive NPV?
This problem is much more difficult than our “fixer-upper” house example because en-
tire fertilizer companies are not routinely bought and sold in the marketplace; so it is essen-
tially impossible to observe the market value of a similar investment. As a result, we must
somehow estimate this value by other means.
Based on our work in Chapters 4 and 5, you may be able to guess how we will go about
estimating the value of our fertilizer business. We first will try to estimate the future cash
flows we expect the new business to produce. We then will apply our basic discounted cash
flow procedure to estimate the present value of those cash flows. Once we have this esti-
mate, we then estimate NPV as the difference between the present value of the future cash
flows and the cost of the investment. As we mentioned in Chapter 5, this procedure is often
called discounted cash flow, or DCF, valuation.
To see how we might go about estimating NPV, suppose we believe the cash revenues
from our fertilizer business will be $20,000 per year, assuming everything goes as expected.
Cash costs (including taxes) will be $14,000 per year. We will wind down the business in
eight years. The plant, property, and equipment will be worth $2,000 as salvage at that time.
The project costs $30,000 to launch. We use a 15 percent discount rate on new projects such
as this one. Is this a good investment? If there are 1,000 shares of stock outstanding, what
will be the effect on the price per share from taking the investment?
From a purely mechanical perspective, we need to calculate the present value of the
future cash flows at 15 percent. The net cash inflow will be $20,000 cash income less
$14,000 in costs per year for eight years. These cash flows are illustrated in Figure 8.1.
net present value
(NPV)
The difference between
an investment’s market
value and its cost.
discounted cash
flow (DCF) valuation
(a) Calculating the present
value of a future cash flow
to determine its value
today. (b) The process of
valuing an investment by
discounting its future cash
flows.
ros13952_ch08_237-274.indd 239 12/22/18 5:54 PM
240 P A R T 5 Capital Budgeting
As Figure 8.1 suggests, we effectively have an eight-year annuity of $20,000 − 14,000 =
$6,000 per year along with a single lump-sum inflow of $2,000 in eight years. Calculating
the present value of the future cash flows thus comes down to the same type of problem we
considered in Chapter 5. The total present value is:
Present value = $6,000 × (1 − 1/1.158)/.15 + 2,000/1.158
= $6,000 × 4.4873 + 2,000/3.0590
= $26,924 + 654
= $27,578
When we compare this to the $30,000 estimated cost, the NPV is:
NPV = −$30,000 + 27,578 = −$2,422
Therefore, this is not a good investment. Based on our estimates, taking it would decrease
the total value of the stock by $2,422. With 1,000 shares outstanding, our best estimate of the
impact of taking this project is a loss of value of $2,422/1,000 = $2.422 per share.
Our fertilizer example illustrates how NPV estimates can be used to determine whether
or not an investment is desirable. From our example, notice that if the NPV is negative, the
effect on share value will be unfavorable. If the NPV were positive, the effect would be fa-
vorable. As a consequence, all we need to know about a particular proposal for the purpose
of making an accept-reject decision is whether the NPV is positive or negative.
Given that the goal of financial management is to increase share value, our discussion
in this section leads us to the net present value rule:
An investment should be accepted if the net present value is positive and rejected if
it is negative.
In the unlikely event that the net present value turned out to be exactly zero, we would
be indifferent between taking the investment and not taking it.
Two comments about our example are in order. First and foremost, it is not the rather
mechanical process of discounting the cash flows that is important. Once we have the cash
flows and the appropriate discount rate, the required calculations are fairly straightforward.
The task of coming up with the cash flows and the discount rate in the first place is much
more challenging. We will have much more to say about this in our next chapter. For the
remainder of this chapter, we take it as given that we have estimates of the cash revenues
and costs and, where needed, an appropriate discount rate.
The second thing to keep in mind about our example is that the −$2,422 NPV is an esti-
mate. Like any estimate, it can be high or low. The only way to find out the true NPV would be
to place the investment up for sale and see what we could get for it. We generally won’t be do-
ing this, so it is important that our estimates be reliable. Once again, we will have more to say
about this later. For the rest of this chapter, we will assume that the estimates are accurate.
$20
− 14
$ 6
$ 6
0 1 2 3 4 5 6 7 8Time
(years)
−$30
−$30
Initial cost
Inflows
Outflows
Net inflow
Salvage
Net cash flow
$20
− 14
$ 6
$ 6
$20
− 14
$ 6
$ 6
$20
− 14
$ 6
$ 6
$20
− 14
$ 6
$ 6
$20
− 14
$ 6
$ 6
$20
− 14
$ 6
$ 6
$20
− 14
$ 6
2
$ 8
Project cash flows
($000)
FIGURE 8.1
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C H A P T E R 8 Net Present Value and Other Investment Criteria 241
EXAMPLE 8.1 Using the NPV Rule
Suppose we are asked to decide whether or not a new consumer product should be launched.
Based on projected sales and costs, we expect that the cash flows over the five-year life of the
project will be $2,000 in the first two years, $4,000 in the next two, and $5,000 in the last year. It
will cost about $10,000 to begin production. We use a 10 percent discount rate to evaluate new
products. What should we do here?
Given the cash flows and discount rate, we can calculate the total value of the product by
discounting the cash flows back to the present:
Present value = $2,000/1.1 + 2,000/1.12 + 4,000/1.13 + 4,000/1.14 + 5,000/1.15
= $1,818 + 1,653 + 3,005 + 2,732 + 3,105
= $12,313
The present value of the expected cash flows is $12,313, but the cost of getting those cash flows
is only $10,000, so the NPV is $12,313 − 10,000 = $2,313. This is positive; so, based on the net
present value rule, we should take on the project.
Calculating NPVs with a Spreadsheet
Spreadsheets and financial calculators are commonly used to calculate NPVs. The procedures used by
various financial calculators are too different for us to illustrate here, so we will focus on using a spread-
sheet (financial calculators are covered in Appendix D). Examining the use of spreadsheets in this con-
text also allows us to issue an important warning. Let’s rework Example 8.1:
SPREADSHEET
STRATEGIES
A B C D E F G H
1
2 Using a spreadsheet to calculate net present values
3
4 From Example 8.1, the project’s cost is $10,000. The cash flows are $2,000 per year for the first two
5 years, $4,000 per year for the next two, and $5,000 in the last year. The discount rate is
6 10 percent; what’s the NPV?
7
8 Year Cash flow
9 0 −$10,000 Discount rate = 10%
10 1 2,000
11 2 2,000 NPV = $2,102.72 (wrong answer)
12 3 4,000 NPV = $2,312.99 (right answer)
13 4 4,000
14 5 5,000
15
16 The formula entered in cell F11 is = NPV(F9,C9:C14). This gives the wrong answer because the
17 NPV function actually calculates present values, not net present values.
18
19 The formula entered in cell F12 is = NPV(F9,C10:C14) + C9. This gives the right answer because the
20 NPV function is used to calculate the present value of the cash flows and then the initial cost is
21 subtracted to calculate the answer. Notice that we added cell C9 because it is already negative.
ros13952_ch08_237-274.indd 241 12/22/18 5:54 PM
242 P A R T 5 Capital Budgeting
As we have seen in this section, estimating NPV is one way of assessing the profitability
of a proposed investment. It is certainly not the only way profitability is assessed, and we
now turn to some alternatives. As we will see, when compared to NPV, each of the ways of
assessing profitability that we examine is flawed in some key way; so, NPV is the preferred
approach in principle, if not always in practice.
In our nearby Spreadsheet Strategies box, we rework Example 8.1. Notice that we have
provided two answers. By comparing the answers to that found in Example 8.1, we see that
the first answer is wrong even though we used the spreadsheet’s NPV formula. What hap-
pened is that the “NPV” function in our spreadsheet is actually a PV function; unfortu-
nately, one of the original spreadsheet programs many years ago got the definition wrong,
and subsequent spreadsheets have copied it! Our second answer shows how to use the for-
mula properly.
The example here illustrates the danger of blindly using calculators or computers with-
out understanding what is going on; we shudder to think of how many capital budgeting
decisions in the real world are based on incorrect use of this particular function. We see
another example of something that can go wrong with a spreadsheet later in the chapter.
CONCEPT QUESTIONS
8.1a What is the net present value rule?
8.1b If we say an investment has an NPV of $1,000, what exactly do we mean?
THE PAYBACK RULE
It is very common in practice to talk of the payback on a proposed investment. Loosely, the
payback is the length of time it takes to recover our initial investment, or “get our bait back.”
Because this idea is widely understood and used, we examine it in some detail.
Defining the Rule
We can illustrate how to calculate a payback with an example. Figure 8.2 shows the cash
flows from a proposed investment. How many years do we have to wait until the accumu-
lated cash flows from this investment equal or exceed the cost of the investment? As Figure
8.2 indicates, the initial investment is $50,000. After the first year, the firm has recovered
$30,000, leaving $20,000 outstanding. The cash flow in the second year is exactly $20,000,
so this investment “pays for itself” in exactly two years. Put another way, the payback period
(or just payback) is two years. If we require a payback of, say, three years or less, then this
investment is acceptable. This illustrates the payback period rule:
Based on the payback rule, an investment is acceptable if its calculated payback
period is less than some prespecified number of years.
8.2
coverage online
Excel
Master
payback period
The amount of time
required for an investment
to generate cash flows
sufficient to recover its
initial cost.
0 1 2 3 4
$30,000 $20,000 $10,000 $5,000
Year
−$50,000
Net project cash
flows
FIGURE 8.2
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C H A P T E R 8 Net Present Value and Other Investment Criteria 243
In our example, the payback works out to be exactly two years. This usually won’t hap-
pen, of course. When the numbers don’t work out exactly, it is customary to work with
fractional years. Suppose the initial investment is $60,000, and the cash flows are $20,000
in the first year and $90,000 in the second. The cash flows over the first two years are
$110,000, so the project obviously pays back sometime in the second year. After the first
year, the project has paid back $20,000, leaving $40,000 to be recovered. To figure out the
fractional year, note that this $40,000 is $40,000/$90,000 = 4/9 of the second year’s cash
flow. Assuming that the $90,000 cash flow is paid uniformly throughout the year, the pay-
back would thus be 14/9 years.
EXAMPLE 8.2 Calculating Payback
The projected cash flows from a proposed investment are:
Year Cash Flow
1 $100
2 200
3 500
This project costs $500. What is the payback period for this investment?
The initial cost is $500. After the first two years, the cash flows total $300. After the third year, the
total cash flow is $800, so the project pays back sometime between the end of Year 2 and the end of
Year 3. Because the accumulated cash flows for the first two years are $300, we need to recover
$200 in the third year. The third-year cash flow is $500, so we will have to wait $200/$500 = .40 year
to do this. The payback period is thus 2.4 years, or about two years and five months.
Now that we know how to calculate the payback period on an investment, using the
payback period rule for making decisions is straightforward. A particular cutoff time is se-
lected, say, two years, and all investment projects that have payback periods of two years or
less are accepted, and all of those that pay back in more than two years are rejected.
Table 8.1 illustrates cash flows for five different projects. The figures shown as the Year
0 cash flows are the cost of the investment. We examine these to indicate some peculiarities
that can, in principle, arise with payback periods.
The payback for the first project, A, is easily calculated. The sum of the cash flows for
the first two years is $70, leaving us with $100 − 70 = $30 to go. The cash flow in the third
year is $50, so the payback occurs sometime in that year. When we compare the $30 we
need to the $50 that will be coming in, we get $30/$50 = .60; so, payback will occur 60
percent of the way into the year. The payback period is thus 2.6 years.
Project B’s payback also is easy to calculate: It never pays back because the cash flows
never total up to the original investment. Project C has a payback of exactly four years be-
cause it supplies the $130 that B is missing in Year 4. Project D is a little strange. Because of
Year A B C D E
0 −$100 −$200 −$200 −$200 −$ 50
1 30 40 40 100 100
2 40 20 20 100 − 50,000,000
3 50 10 10 − 200
4 60 130 200
Expected cash flows
for Projects A
through E
TABLE 8.1
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244 P A R T 5 Capital Budgeting
the negative cash flow in Year 3, you can easily verify that it has two different payback peri-
ods, two years and four years. Which of these is correct? Both of them; the way the payback
period is calculated doesn’t guarantee a single answer. Finally, Project E is obviously unreal-
istic, but it does pay back in six months, thereby illustrating the point that a rapid payback
does not guarantee a good investment.
Analyzing the Rule
When compared to the NPV rule, the payback period rule has some rather severe shortcom-
ings. First, the payback period is calculated by adding up the future cash flows. There is no
discounting involved, so the time value of money is completely ignored. The payback rule
also fails to consider risk differences. The payback would be calculated the same way for
both very risky and very safe projects.
Perhaps the biggest problem with the payback period rule is coming up with the right
cutoff period because we don’t really have an objective basis for choosing a particular num-
ber. Put another way, there is no economic rationale for looking at payback in the first
place, so we have no guide as to how to pick the cutoff. As a result, we end up using a num-
ber that is arbitrarily chosen.
Suppose we have somehow decided on an appropriate payback period, say, two years or
less. As we have seen, the payback period rule ignores the time value of money for the first two
years. More seriously, cash flows after the second year are ignored entirely. To see this, con-
sider the two investments, Long and Short, in Table 8.2. Both projects cost $250. Based on our
discussion, the payback on Long is 2 + $50/$100 = 2.5 years, and the payback on Short is
1 + $150/$200 = 1.75 years. With a cutoff of two years, Short is acceptable and Long is not.
Is the payback period rule giving us the right decisions? Maybe not. Suppose again that
we require a 15 percent return on this type of investment. We can calculate the NPVs for
these two investments as:
NPV (Short) = −$250 + 100/1.15 + 200/1.152 = −$11.81
NPV (Long) = −$250 + 100 × (1 − 1/1.154)/.15 = $35.50
Now we have a problem. The NPV of the shorter-term investment is actually negative,
meaning that taking it diminishes the value of the shareholders’ equity. The opposite is true
for the longer-term investment—it increases share value.
Our example illustrates two primary shortcomings of the payback period rule. First, by
ignoring time value, we may be led to take investments (like Short) that actually are worth
less than they cost. Second, by ignoring cash flows beyond the cutoff, we may be led to re-
ject profitable long-term investments (like Long). More generally, using a payback period
rule will tend to bias us toward shorter-term investments.
Redeeming Qualities of the Rule
Despite its shortcomings, the payback period rule is often used by large and sophisticated
companies when they are making relatively minor decisions. There are several reasons for
Investment projected
cash flows
TABLE 8.2 Year Long Short
0 −$250 −$250
1 100 100
2 100 200
3 100 0
4 100 0
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C H A P T E R 8 Net Present Value and Other Investment Criteria 245
this. The primary reason is that many decisions do not warrant detailed analysis because the
cost of the analysis would exceed the possible loss from a mistake. As a practical matter, an
investment that pays back rapidly and has benefits extending beyond the cutoff period prob-
ably has a positive NPV.
Small investment decisions are made by the hundreds every day in large organizations.
Moreover, they are made at all levels. As a result, it would not be uncommon for a corpora-
tion to require, for example, a two-year payback on all investments of less than $10,000. In-
vestments larger than this are subjected to greater scrutiny. The requirement of a two-year
payback is not perfect for reasons we have seen, but it does exercise some control over ex-
penditures and thus has the effect of limiting possible losses.
In addition to its simplicity, the payback rule has two other positive features. First,
because it is biased toward short-term projects, it is biased toward liquidity. In other
words, a payback rule tends to favor investments that free up cash for other uses more
quickly. This could be very important for a small business; it would be less so for a
large corporation. Second, the cash flows that are expected to occur later in a project’s
life are probably more uncertain. Arguably, a payback period rule adjusts for the extra
riskiness of later cash f lows, but it does so in a rather draconian fashion—by ignoring
them altogether.
We should note here that some of the apparent simplicity of the payback rule is
an illusion. The reason is that we still must come up with the cash f lows first, and, as
we discuss above, this is not at all easy to do. Thus, it would probably be more accu-
rate to say that the concept of a payback period is both intuitive and easy to
understand.
Summary of the Rule
To summarize, the payback period is a kind of “break-even” measure. Because time value is
ignored, you can think of the payback period as the length of time it takes to break even in
an accounting sense, but not in an economic sense. The biggest drawback to the payback
period rule is that it doesn’t ask the right question. The relevant issue is the impact an invest-
ment will have on the value of our stock, not how long it takes to recover the initial
investment.
Nevertheless, because it is so simple, companies often use it as a screen for dealing
with the myriad of minor investment decisions they have to make. There is certainly noth-
ing wrong with this practice. Like any rule of thumb, there will be some errors in using it,
but it wouldn’t have survived all this time if it weren’t useful. Now that you understand the
rule, you can be on the alert for those circumstances under which it might lead to prob-
lems. To help you remember, the following table lists the pros and cons of the payback
period rule:
Advantages and Disadvantages of the Payback Period Rule
Advantages Disadvantages
1. Easy to understand.
2. Adjusts for uncertainty of later cash flows.
3. Biased toward liquidity.
1. Ignores the time value of money.
2. Requires an arbitrary cutoff point.
3. Ignores cash flows beyond the cutoff date.
4. Biased against long-term projects, such as
research and development, and new
projects.
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246 P A R T 5 Capital Budgeting
CONCEPT QUESTIONS
8.2a In words, what is the payback period? The payback period rule?
8.2b Why do we say that the payback period is, in a sense, an accounting break-even
measure?
THE AVERAGE ACCOUNTING RETURN
Another attractive, but flawed, approach to making capital budgeting decisions involves the
average accounting return (AAR). There are many different definitions of the AAR.
However, in one form or another, the AAR is always defined as:
Some measure of average accounting profit
_______________________________
Some measure of average accounting value
The specific definition we will use is:
Average net income
______________
Average book value
To see how we might calculate this number, suppose we are deciding whether or not to open
a store in a new shopping mall. The required investment in improvements is $500,000. The
store would have a five-year life because everything reverts to the mall owners after that
time. The required investment would be 100 percent depreciated (straight-line) over five
years, so the depreciation would be $500,000/5 = $100,000 per year. The tax rate is 25
percent. Table 8.3 contains the projected revenues and expenses. Based on these figures, net
income in each year also is shown.
To calculate the average book value for this investment, we note that we started out with
a book value of $500,000 (the initial cost) and ended up at $0. The average book value dur-
ing the life of the investment is thus ($500,000 + 0)/2 = $250,000. As long as we use
straight-line depreciation and a zero salvage value, the average investment will always be
one-half of the initial investment.1
8.3
coverage online
Excel
Master
average accounting
return (AAR)
An investment’s average
net income divided by its
average book value.
Year 1 Year 2 Year 3 Year 4 Year 5
Revenue $433,333 $450,000 $266,667 $200,000 $133,333
Expenses 200,000 150,000 100,000 100,000 100,000
Earnings before
depreciation $233,333 $300,000 $166,667 $100,000 $ 33,333
Depreciation 100,000 100,000 100,000 100,000 100,000
Earnings before taxes $133,333 $200,000 $ 66,667 $ 0 −$ 66,667
Taxes (25%) 33,333 50,000 16,667 0 − 16,667
Net income $100,000 $150,000 $ 50,000 $ 0 −$ 50,000
Average net income =
($100,000 + 150,000 + 50,000 + 0 − 50,000)
_______________________________________
5
= $50,000
Average book value =
$500,000 + 0
____________
2
;= $250,000
Projected yearly
revenues and costs
for average
accounting return
TABLE 8.3
1We could, of course, calculate the average of the six book values directly. In thousands, we would have
($500 + 400 + 300 + 200 + 100 + 0)/6 = $250.
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C H A P T E R 8 Net Present Value and Other Investment Criteria 247
Looking at Table 8.3, we see that net income is $100,000 in the first year, $150,000 in
the second year, $50,000 in the third year, $0 in Year 4, and −$50,000 in Year 5. The aver-
age net income, then, is:
[$100,000 + 150,000 + 50,000 + 0 + (−50,000)]/5 = $50,000
The average accounting return is:
AAR =
Average net income
______________
Average book value
=
$50,000
_______
$250,000
= .-20, or 20%
If the firm has a target AAR less than 20 percent, then this investment is acceptable; other-
wise, it is not. The average accounting return rule is thus:
Based on the average accounting return rule, a project is acceptable if its average
accounting return exceeds a target average accounting return.
As we will see next, this rule has a number of problems.
You should recognize the chief drawback to the AAR immediately. Above all else, the AAR
is not a rate of return in any meaningful economic sense. Instead, it is the ratio of two accounting
numbers, and it is not comparable to the returns offered, for example, in financial markets.2
One of the reasons the AAR is not a true rate of return is that it ignores time value.
When we average figures that occur at different times, we are treating the near future and
the more distant future the same way. There was no discounting involved when we com-
puted the average net income, for example.
The second problem with the AAR is similar to the problem we had with the payback
period rule concerning the lack of an objective cutoff period. A calculated AAR is really not
comparable to a market return, so the target AAR must somehow be specified. There is no
generally agreed-upon way to do this. One way of doing it is to calculate the AAR for the
firm as a whole and use this as a benchmark, but there are lots of other ways as well.
The third, and perhaps worst, flaw in the AAR is that it doesn’t even look at the right
things. Instead of cash flow and market value, it uses net income and book value. These are
both poor substitutes. As a result, an AAR doesn’t tell us what the effect on share price will
be from taking an investment, so it doesn’t tell us what we really want to know.
Does the AAR have any redeeming features? About the only one is that it almost always
can be computed. The reason is that accounting information almost always will be available,
both for the project under consideration and for the firm as a whole. We hasten to add that
once the accounting information is available, we always can convert it to cash flows, so even
this is not a particularly important fact. The AAR is summarized in the table that follows:
Advantages and Disadvantages of the Average Accounting Return
Advantages Disadvantages
1. Easy to calculate.
2. Needed information will usually
be available.
1. Not a true rate of return; time value of money
is ignored.
2. Uses an arbitrary benchmark cutoff rate.
3. Based on accounting net income and book
values, not cash flows and market values.
2The AAR is closely related to the return on assets, or ROA, discussed in Chapter 3. In practice, the AAR is some-
times computed by first calculating the ROA for each year and then averaging the results. This produces a number
that is similar, but not identical, to the one we computed.
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248 P A R T 5 Capital Budgeting
CONCEPT QUESTIONS
8.3a What is an average accounting rate of return, or AAR?
8.3b What are the weaknesses of the AAR rule?
THE INTERNAL RATE OF RETURN
We now come to the most important alternative to NPV, the internal rate of return, or IRR.
As we will see, the IRR is closely related to NPV. With the IRR, we try to find a single rate
of return that summarizes the merits of a project. Furthermore, we want this rate to be an
“internal” rate in the sense that it only depends on the cash flows of a particular investment,
not on rates offered elsewhere.
To illustrate the idea behind the IRR, consider a project that costs $100 today and pays
$110 in one year. Suppose you were asked, “What is the return on this investment?” What
would you say? It seems both natural and obvious to say that the return is 10 percent be-
cause, for every dollar we put in, we get $1.10 back. In fact, as we will see in a moment,
10 percent is the internal rate of return, or IRR, on this investment.
Is this project with its 10 percent IRR a good investment? Once again, it would seem
apparent that this is a good investment only if our required return is less than 10 percent.
This intuition is also correct and illustrates the IRR rule:
Based on the IRR rule, an investment is acceptable if the IRR exceeds the required
return. It should be rejected otherwise.
Imagine that we wanted to calculate the NPV for our simple investment. At a discount
rate of R, the NPV is:
NPV = −$100 + 110/(1 + R)
Now, suppose we didn’t know the discount rate. This presents a problem, but we could still
ask how high the discount rate would have to be before this project was unacceptable. We
know that we are indifferent between taking and not taking this investment when its NPV is
just equal to zero. In other words, this investment is economically a break-even proposition
when the NPV is zero because value is neither created nor destroyed. To find the break-even
discount rate, we set NPV equal to zero and solve for R:
NPV = 0 = −$100 + 110/(1 + R)
$100 = $110/(1 + R)
1 + R = $110/100 = 1.10
R = .10, or 10%
This 10 percent is what we already have called the return on this investment. What we
have now illustrated is that the internal rate of return on an investment (or “return” for
short) is the discount rate that makes the NPV equal to zero. This is an important observa-
tion, so it bears repeating:
The IRR on an investment is the required return that results in a zero NPV when it is
used as the discount rate.
8.4
coverage online
Excel
Master
internal rate of
return (IRR)
The discount rate that
makes the net present
value of an investment
zero.
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C H A P T E R 8 Net Present Value and Other Investment Criteria 249
The fact that the IRR is the discount rate that makes the NPV equal to zero is im-
portant because it tells us how to calculate the returns on more complicated invest-
ments. As we have seen, finding the IRR turns out to be relatively easy for a single-period
investment. However, suppose you were now looking at an investment with the cash
f lows shown in Figure 8.3. As illustrated, this investment costs $100 and has a cash
flow of $60 per year for two years, so it’s only slightly more complicated than our sin-
gle-period example. However, if you were asked for the return on this investment, what
would you say? There doesn’t seem to be any obvious answer (at least to us). However,
based on what we now know, we can set the NPV equal to zero and solve for the dis-
count rate:
NPV = 0 = −$100 + 60/(1 + IRR) + 60/(1 + IRR)2
Unfortunately, the only way to find the IRR in general is by trial and error, either by hand or
by calculator. This is precisely the same problem that came up in Chapter 5 when we found
the unknown rate for an annuity and in Chapter 6 when we found the yield to maturity on a
bond. In fact, we now see that, in both of those cases, we were finding an IRR.
In this particular case, the cash flows form a two-period, $60 annuity. To find the un-
known rate, we can try some different rates until we get the answer. If we were to start with
a 0 percent rate, the NPV would obviously be $120 − 100 = $20. At a 10 percent discount
rate, we would have:
NPV = −$100 + 60/1.1 + 60/1.12 = $4.13
Now, we’re getting close. We can summarize these and some other possibilities as
shown in Table 8.4. From our calculations, the NPV appears to be zero between 10
percent and 15 percent, so the IRR is somewhere in that range. With a little more effort,
we can find that the IRR is about 13.1 percent. So, if our required return is less than
13.1 percent, we would take this investment. If our required return exceeds 13.1 percent,
we would reject it.
By now, you have probably noticed that the IRR rule and the NPV rule appear to
be quite similar. In fact, the IRR is sometimes called the discounted cash flow, or DCF,
return. The easiest way to illustrate the relationship between NPV and IRR is to plot
the numbers we calculated in Table 8.4. We put the different NPVs on the vertical
axis, or y-axis, and the discount rates on the horizontal axis, or x-axis. If we had a very
large number of points, the resulting picture would be a smooth curve called a
Project cash flows
FIGURE 8.30 1 2
+ $60 + $60
Year
−$100
NPV at different
discount rates
TABLE 8.4Discount Rate NPV
0% $20.00
5 11.56
10 4.13
15 − 2.46
20 − 8.33
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250 P A R T 5 Capital Budgeting
net present value profile. Figure 8.4 illustrates the NPV profile for this project. Begin-
ning with a 0 percent discount rate, we have $20 plotted directly on the y-axis. As the
discount rate increases, the NPV declines smoothly. Where will the curve cut through
the x-axis? This will occur where the NPV is equal to zero, so it will happen right at
the IRR of 13.1 percent.
In our example, the NPV rule and the IRR rule lead to identical accept-reject decisions.
We will accept an investment using the IRR rule if the required return is less than 13.1 per-
cent. As Figure 8.4 illustrates, however, the NPV is positive at any discount rate less than
13.1 percent, so we would accept the investment using the NPV rule as well. The two rules
are equivalent in this case.
net present value
profile
A graphical representation
of the relationship
between an investment’s
net present value and
various discount rates.
An NPV profile
FIGURE 8.4
20
NPV ($)
R (% )
15
10
5
0
−5
−10
5 1 0 1 5 20 25 30
IRR = 13.1%NPV > 0
NPV < 0
EXAMPLE 8.3 Calculating the IRR
A project has a total up-front cost of $435.44. The cash flows are $100 in the first year, $200 in the
second year, and $300 in the third year. What’s the IRR? If we require an 18 percent return, should
we take this investment?
We’ll describe the NPV profile and find the IRR by calculating some NPVs at different discount
rates. You should check our answers for practice. Beginning with 0 percent, we have:
Discount Rate NPV
0% $164.56
5 100.36
10 46.15
15 .00
20 − 39.61
The NPV is zero at 15 percent, so 15 percent is the IRR. If we require an 18 percent return, then we
should not take the investment. The reason is that the NPV is negative at 18 percent (verify that it is
–$24.47). The IRR rule tells us the same thing in this case. We shouldn’t take this investment be-
cause its 15 percent return is below our required 18 percent return.
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C H A P T E R 8 Net Present Value and Other Investment Criteria 251
At this point, you may be wondering whether the IRR and NPV rules always lead to
identical decisions. The answer is yes as long as two very important conditions are met.
First, the project’s cash flows must be conventional, meaning that the first cash flow (the ini-
tial investment) is negative and all the rest are positive. Second, the project must be inde-
pendent, meaning that the decision to accept or reject this project does not affect the
decision to accept or reject any other. The first of these conditions is typically met, but the
second often is not. In any case, when one or both of these conditions are not met, prob-
lems can arise. We discuss some of these in a moment.
CALCULATING IRRS WITH A SPREADSHEET
Because IRRs are so tedious to calculate by hand, financial calculators and, especially, spreadsheets
are generally used. The procedures used by various financial calculators are too different for us to illus-
trate here, so we will focus on using a spreadsheet (financial calculators are covered in Appendix D). As
the following example illustrates, using a spreadsheet is very easy:
SPREADSHEET
STRATEGIES
A B C D E F G H
1
2 Using a spreadsheet to calculate internal rates of return
3
4 Suppose we have a four-year project that costs $500. The cash flows over the four-year life will be
5 $100, $200, $300, and $400. What is the IRR?
6
7 Year Cash flow
8 0 –$500
9 1 100 IRR = 27.3%
10 2 200
11 3 300
12 4 400
13
14
15 The formula entered in cell F9 is = IRR(C8:C12). Notice that the Year 0 cash flow has a negative sign,
16 representing the initial cost of the project.
17
Problems with the IRR
The problems with the IRR come about when the cash flows are not conventional or when
we are trying to compare two or more investments to see which is best. In the first case,
surprisingly, the simple question “What’s the return?” can become very difficult to answer.
In the second case, the IRR can be a misleading guide.
Nonconventional Cash Flows Suppose we have a strip-mining project that requires
a $60 investment. Our cash flow in the first year will be $155. In the second year, the mine
is depleted, but we have to spend $100 to restore the terrain. As Figure 8.5 illustrates, both
the first and third cash flows are negative.
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252 P A R T 5 Capital Budgeting
To find the IRR on this project, we can calculate the NPV at various rates:
Discount Rate NPV
0% −$5.00
10 − 1.74
20 − .28
30 .06
40 − .31
The NPV appears to be behaving in a very peculiar fashion here. First, as the discount
rate increases from 0 percent to 30 percent, the NPV starts out negative and becomes posi-
tive. This seems backward because the NPV is rising as the discount rate rises. It then starts
getting smaller and becomes negative again. What’s the IRR? To find out, we draw the NPV
profile in Figure 8.6.
0 1 2
+ $155 −$100
Year
−$60
Project cash flows
FIGURE 8.5
NPV profile
FIGURE 8.6
2
1
0
−1
−2
−3
−4
−5
10 20 30 40 50
IRR = 25% IRR = 33 % 1
3
R (% )
NPV ($)
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C H A P T E R 8 Net Present Value and Other Investment Criteria 253
In Figure 8.6, notice that the NPV is zero when the discount rate is 25 percent, so this
is the IRR. Or is it? The NPV is also zero at 33 ⅓ percent. Which of these is correct? The
answer is both or neither; more precisely, there is no unambiguously correct answer. This is
the multiple rates of return problem. Many computer spreadsheet packages aren’t aware of
this problem and just report the first IRR that is found. Others report only the smallest posi-
tive IRR, even though this answer is no better than any other. For example, if you enter this
problem in our spreadsheet example, it will report that the IRR is 25 percent.
In our current example, the IRR rule breaks down completely. Suppose our required
return was 10 percent. Should we take this investment? Both IRRs are greater than 10 per-
cent, so, by the IRR rule, maybe we should. However, as Figure 8.6 shows, the NPV is nega-
tive at any discount rate less than 25 percent, so this is not a good investment. When should
we take it? Looking at Figure 8.6 one last time, we see that the NPV is positive only if our
required return is between 25 percent and 33 ⅓ percent.
The moral of the story is that when the cash flows aren’t conventional, strange things
can start to happen to the IRR. This is not anything to get upset about, however, because the
NPV rule, as always, works fine. This illustrates that, oddly enough, the obvious question
“What’s the rate of return?” may not always have a good answer.
multiple rates of
return
The possibility that more
than one discount rate will
make the net present
value of an investment
zero.
EXAMPLE 8.4 What’s the IRR?
You are looking at an investment that requires you to invest $51 today. You’ll get $100 in one year,
but you must pay out $50 in two years. What is the IRR on this investment?
You’re on the alert now to the nonconventional cash flow problem, so you probably wouldn’t
be surprised to see more than one IRR. However, if you start looking for an IRR by trial and error, it
will take you a long time. The reason is that there is no IRR. The NPV is negative at every discount
rate, so we shouldn’t take this investment under any circumstances. What’s the return on this invest-
ment? Your guess is as good as ours.
Mutually Exclusive Investments Even if there is a single IRR, another problem
can arise concerning mutually exclusive investment decisions. If two investments, X and Y,
are mutually exclusive, then taking one of them means that we cannot take the other. Two
projects that are not mutually exclusive are said to be independent. For example, if we own
one corner lot, then we can build a gas station or an apartment building, but not both. These
are mutually exclusive alternatives.
Thus far, we have asked whether or not a given investment is worth undertaking. There
is a related question that comes up very often: Given two or more mutually exclusive invest-
ments, which one is the best? The answer is simple enough: The best one is the one with the
largest NPV. Can we also say that the best one has the highest return? As we show, the an-
swer is no.
To illustrate the problem with the IRR rule and mutually exclusive investments, con-
sider the cash flows from the following two mutually exclusive investments:
Year Investment A Investment B
0 −$100 −$100
1 50 20
2 40 40
3 40 50
4 30 60
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254 P A R T 5 Capital Budgeting
The IRR for A is 24 percent, and the IRR for B is 21 percent. Because these invest-
ments are mutually exclusive, we only can take one of them. Simple intuition suggests that
Investment A is better because of its higher return. Unfortunately, simple intuition is not
always correct.
To see why Investment A is not necessarily the better of the two investments, we’ve
calculated the NPV of these investments for different required returns:
Discount Rate NPV (A) NPV (B)
0% $60.00 $70.00
5 43.13 47.88
10 29.06 29.79
15 17.18 14.82
20 7.06 2.31
25 − 1.63 − 8.22
The IRR for A (24 percent) is larger than the IRR for B (21 percent). However, if you
compare the NPVs, you’ll see that which investment has the higher NPV depends on our
required return. B has greater total cash flow, but it pays back more slowly than A. As a re-
sult, it has a higher NPV at lower discount rates.
In our example, the NPV and IRR rankings conflict for some discount rates. If our re-
quired return is 10 percent, for instance, then B has the higher NPV and is thus the better of
the two, even though A has the higher IRR. If our required return is 15 percent, then there
is no ranking conflict: A is better.
The conflict between the IRR and NPV for mutually exclusive investments can be il-
lustrated by plotting their NPV profiles as we have done in Figure 8.7. In Figure 8.7, notice
NPV profiles for
mutually exclusive
investments
FIGURE 8.7
70
60
50
40
30
20
10
0
−10
5
26.34
10 15
11.1%
20
IR R B = 21%
25 30
IR R A = 24%
Crossover point
Investment
B
Investment
A
NPVB > NPVA
NPVA > NPVB
NPV ($)
R (% )
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C H A P T E R 8 Net Present Value and Other Investment Criteria 255
that the NPV profiles cross at about 11.1 percent. Notice also that at any discount rate less
than 11.1 percent, the NPV for B is higher. In this range, taking B benefits us more than tak-
ing A, even though A’s IRR is higher. At any rate greater than 11.1 percent, Investment A
has the greater NPV.
This example illustrates that whenever we have mutually exclusive projects, we shouldn’t
rank them based on their returns. More generally, any time we are comparing investments to
determine which is best, IRRs can be misleading. Instead, we need to look at the relative
NPVs to avoid the possibility of choosing incorrectly. Remember, we’re ultimately inter-
ested in creating value for the shareholders, so the option with the higher NPV is preferred,
regardless of the relative returns.
If this seems counterintuitive, think of it this way. Suppose you have two investments.
One has a 10 percent return and makes you $100 richer immediately. The other has a
20 percent return and makes you $50 richer immediately. Which one do you like better?
We would rather have $100 than $50, regardless of the returns, so we like the first one
better.
As we saw from Figure 8.7, the crossover rate for Investment A and Investment B is
11.1 percent. You might be wondering how we got this number. Actually, the calculation
is fairly easy. We begin by subtracting the cash flows from one project from the cash flows
of the second project. In this case, we will subtract Investment B from Investment A. Do-
ing so, we get:
Year Investment A Investment B Cash Flow Difference (A – B)
0 −$100 −$100 $ 0
1 50 20 30
2 40 40 0
3 40 50 − 10
4 30 60 − 30
Now all we have to do is calculate the IRR for these differential cash flows, which
works out to be 11.1 percent. Verify for yourself that if you subtract Investment A’s cash
flows from Investment B’s cash flows, the crossover rate is still 11.1 percent, so it doesn’t
matter which one you subtract from which.
Redeeming Qualities of the IRR
Despite its flaws, the IRR is very popular in practice, more so than even the NPV. It proba-
bly survives because it fills a need that the NPV does not. In analyzing investments, people
in general, and financial analysts in particular, seem to prefer talking about rates of return
rather than dollar values.
In a similar vein, the IRR also appears to provide a simple way of communicating infor-
mation about a proposal. One manager might say to another, “Remodeling the clerical wing
has a 20 percent return.” This may somehow be simpler than saying, “At a 10 percent dis-
count rate, the net present value is $4,000.”
Finally, under certain circumstances, the IRR may have a practical advantage
over the NPV. We can’t estimate the NPV unless we know the appropriate discount
rate, but we can still estimate the IRR. Suppose we didn’t know the required return on
an investment, but we found, for example, that it had a 40 percent return. We would
probably be inclined to take it because it is very unlikely that the required return
would be that high. The advantages and disadvantages of the IRR are summarized in
the following table.
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256 P A R T 5 Capital Budgeting
Advantages and Disadvantages of the Internal Rate of Return
Advantages Disadvantages
1. Closely related to NPV, often leading to
identical decisions.
2. Easy to understand and communicate.
1. May result in multiple answers with
nonconventional cash flows.
2. May lead to incorrect decisions in comparisons
of mutually exclusive investments.
The Modified Internal Rate of Return (MIRR)
To address some of the problems that can crop up with the standard IRR, it is often pro-
posed that a modified version be used. As we will see, there are several different ways of
calculating a modified IRR, or MIRR, but the idea is to modify the cash flows first and then
calculate IRR using the modified cash flows.
To illustrate, let’s go back to the cash flows in Figure 8.5: −$60, +$155, and −$100.
As we saw, there are two IRRs, 25 percent and 33 ⅓ percent. We next illustrate three differ-
ent MIRRs, all of which have the property that only one answer will result, thereby eliminat-
ing the multiple IRR problem.
Method 1: The Discounting Approach With the discounting approach, the idea
is to discount all negative cash flows back to the present at the required return and add them
to the initial cost. Then, calculate the IRR. Because only the first modified cash flow is
negative, there will be only one IRR. The discount rate used might be the required return, or
it might be some other externally supplied rate. We use the project’s required return.
If the required return on the project is 20 percent, then the modified cash flows look
like this:
Time 0: − $60 + − $100 _____
1.20 2
= − $129.44
Time 1: +$155
Time 2: +$0
If you calculate the MIRR now, you should get 19.74 percent.
Method 2: The Reinvestment Approach With the reinvestment approach, we
compound all cash flows (positive and negative) except the first out to the end of the proj-
ect’s life and then calculate the IRR. In a sense, we are “reinvesting” the cash flows and not
taking them out of the project until the very end. The rate we use could be the required re-
turn on the project, or it could be a separately specified “reinvestment rate.” We use the
project’s required return. When we do, here are the modified cash flows:
Time 0: −$60
Time 1: +0
Time 2: −$100 + ($155 × 1.2) = $86
The MIRR on this set of cash flows is 19.72 percent, or a little lower than we got using
the discounting approach.
Method 3: The Combination Approach As the name suggests, the combination
approach blends our first two methods. Negative cash flows are discounted back to the pres-
ent, and positive cash flows are compounded to the end of the project. In practice,
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C H A P T E R 8 Net Present Value and Other Investment Criteria 257
different discount or compounding rates might be used, but we again stick with the project’s
required return.
With the combination approach, the modified cash flows are as follows:
Time 0: − $60 + − $100 _____
1.20 2
= − $129.44
Time 1: +0
Time 2: $155 × 1.2 = $186
See if you don’t agree that the MIRR is 19.87, the highest of the three.
MIRR or IRR: Which Is Better? MIRRs are controversial. At one extreme are those
who claim that MIRRs are superior to IRRs, period. For example, by design, they clearly
don’t suffer from the multiple rate of return problem.
At the other end, detractors say that MIRR should stand for “meaningless internal rate
of return.” As our example makes clear, one problem with MIRRs is that there are different
ways of calculating them, and there is no clear reason to say one of our three methods is
better than any other. The differences are small with our simple cash flows, but they could
be much larger for a more complex project. Further, it’s unclear how to interpret an MIRR.
It may look like a rate of return; but it’s a rate of return on a modified set of cash flows, not
the project’s actual cash flows.
We’re not going to take sides. However, notice that calculating an MIRR requires discount-
ing, compounding, or both, which leads to two obvious observations. First, if we have the rele-
vant discount rate, why not calculate the NPV and be done with it? Second, because an MIRR
depends on an externally supplied discount (or compounding) rate, the answer you get is not
truly an “internal” rate of return, which, by definition, depends on only the project’s cash flows.
We will take a stand on one issue that frequently comes up in this context. The value of a
project does not depend on what the firm does with the cash flows generated by that project. A
firm might use a project’s cash flows to fund other projects, to pay dividends, or to buy an execu-
tive jet. It doesn’t matter: How the cash flows are spent in the future does not affect their value
today. As a result, there is generally no need to consider reinvestment of interim cash flows.
CONCEPT QUESTIONS
8.4a Under what circumstances will the IRR and NPV rules lead to the same accept-reject
decisions? When might they conflict?
8.4b Is it generally true that an advantage of the IRR rule over the NPV rule is that we
don’t need to know the required return to use the IRR rule?
THE PROFITABILITY INDEX
Another method used to evaluate projects involves the profitability index (PI), or benefit-
cost ratio. This index is defined as the present value of the future cash flows divided by the
initial investment. So, if a project costs $200 and the present value of its future cash flows is
$220, the profitability index value would be $220/$200 = 1.10. Notice that the NPV for this
investment is $20, so it is a desirable investment.
More generally, if a project has a positive NPV, then the present value of the future cash
flows must be bigger than the initial investment. The profitability index thus would be bigger
than 1.00 for a positive NPV investment and less than 1.00 for a negative NPV investment.
8.5
profitability index
(PI)
The present value of an
investment’s future cash
flows divided by its initial
cost. Also benefit-cost ratio.
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258 P A R T 5 Capital Budgeting
How do we interpret the profitability index? In our example, the PI was 1.10. This tells
us that, per dollar invested, $1.10 in value, or $.10 in NPV, results. The profitability index
thus measures “bang for the buck,” that is, the value created per dollar invested. For this
reason, it is often proposed as a measure of performance for government or other not-
for-profit investments. Also, when capital is scarce, it may make sense to allocate it to those
projects with the highest PIs.
The PI is obviously very similar to the NPV. However, consider an investment that costs
$5 and has a $10 present value and an investment that costs $100 with a $150 present value.
The first of these investments has an NPV of $5 and a PI of 2. The second has an NPV of
$50 and a PI of 1.50. If these are mutually exclusive investments, then the second one is
preferred, even though it has a lower PI. This ranking problem is very similar to the IRR
ranking problem we saw in the previous section. In all, there seems to be little reason to rely
on the PI instead of the NPV. Our discussion of the PI is summarized here:
Advantages and Disadvantages of the Profitability Index
Advantages Disadvantages
1. Closely related to NPV, generally leading to
identical decisions.
2. Easy to understand and communicate.
3. May be useful when available investment
funds are limited.
1. May lead to incorrect decisions in comparisons
of mutually exclusive investments.
CONCEPT QUESTIONS
8.5a What does the profitability index measure?
8.5b How would you state the profitability index rule?
THE PRACTICE OF CAPITAL BUDGETING
Given that NPV seems to be telling us directly what we want to know, you might be wonder-
ing why there are so many other procedures and why alternative procedures are commonly
used. Recall that we are trying to make an investment decision and that we are frequently
operating under considerable uncertainty about the future. We can only estimate the NPV of
an investment in this case. The resulting estimate can be very “soft,” meaning that the true
NPV might be quite different.
Because the true NPV is unknown, the astute financial manager seeks clues to assess
whether the estimated NPV is reliable. For this reason, firms would typically use multiple
criteria for evaluating a proposal. Suppose we have an investment with a positive estimated
NPV. Based on our experience with other projects, this one appears to have a short payback
and a very high AAR. In this case, the different indicators seem to agree that it’s “all sys-
tems go.” Put another way, the payback and the AAR are consistent with the conclusion
that the NPV is positive.
On the other hand, suppose we had a positive estimated NPV, a long payback, and a low
AAR. This still could be a good investment, but it looks like we need to be much more careful
in making the decision because we are getting conflicting signals. If the estimated NPV is
based on projections in which we have little confidence, then further analysis is probably in
order. We consider how to go about this analysis in more detail in the next chapter.
8.6
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C H A P T E R 8 Net Present Value and Other Investment Criteria 259
Capital expenditures by individual corporations can add up to enormous sums for the
economy as a whole. For example, for 2018, ExxonMobil announced that it expected to have
about $25 billion in capital outlays during the year, down from its record $42.5 billion in
2013. About the same time, competitor Chevron announced that it would decrease its capi-
tal spending for 2018 to $18.3 billion, down from about $19.1 billion in 2017. Other compa-
nies with large capital spending budgets included Walmart, which projected capital spending
of about $6.9 billion for 2018, and Apple, which projected capital spending of about $16
billion for 2018.
Large-scale capital spending is often an industrywide occurrence. For example, in 2018,
capital spending in the semiconductor industry was expected to reach $77.4 billion. This
tidy sum also was spent by the industry in 2017.
According to information released by the Census Bureau in 2018, capital investment for
the economy as a whole was $1.576 trillion in 2016, $1.642 trillion in 2015, and $1.507 tril-
lion in 2014. The totals for the three years therefore exceeded $4.7 trillion! Given the sums
at stake, it is not too surprising that careful analysis of capital expenditures is something at
which successful businesses seek to become adept.
There have been a number of surveys conducted asking firms what types of invest-
ment criteria they actually use. Table 8.5 summarizes the results of several of these. The
first part of the table is a historical comparison looking at the primary capital budget-
ing techniques used by large firms through time. In 1959, only 19 percent of the firms
surveyed used either IRR or NPV, and 68 percent used either payback periods or ac-
counting returns. It is clear that, by the 1980s, IRR and NPV had become the dominant
criteria.
A. Historical Comparison of the Primary Use of Various Capital Budgeting Techniques
1959 1964 1970 1975 1977 1979 1981
Payback period 34% 24% 12% 15% 9% 10% 5.0%
Average accounting return (AAR) 34 30 26 10 25 14 10.7
Internal rate of return (IRR) 19 38 57 37 54 60 65.3
Net present value (NPV) — — — 26 10 14 16.5
IRR or NPV 19 38 57 63 64 74 81.8
B. Percentage of CFOs Who Always or Almost Always Use a Given Technique in 1999
Capital Budgeting
Technique
Percentage
Always or Almost
Always Use Overall
Average Score
Scale Is 4 (always) to 0 (never)
Large Firms Small Firms
Internal rate of return 76% 3.09 3.41 2.87
Net present value 75 3.08 3.42 2.83
Payback period 57 2.53 2.25 2.72
Accounting rate of return 20 1.34 1.25 1.41
Profitability index 12 .83 .75 .88
Sources: Graham, J.R. and Harvey, C.R., “The Theory and Practice of Corporate Finance: Evidence from the Field,” Journal of Financial Economics,
May–June 2001, pp. 187–244; Moore, J.S. and Reichert, A.K., “An Analysis of the Financial Management Techniques Currently Employed by Large
U.S. Corporations,” Journal of Business Finance and Accounting, Winter 1983, pp. 623–45; Stanley, M.T. and Block, S.B., “A Survey of Multinational
Capital Budgeting,” The Financial Review, March 1984, pp. 36–51.
Capital budgeting techniques in practiceTABLE 8.5
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260 P A R T 5 Capital Budgeting
Panel B of Table 8.5 summarizes the results of a 1999 survey of chief financial officers
(CFOs) at both large and small firms in the United States. A total of 392 CFOs responded.
What is shown is the percentage of CFOs who always or almost always use the various capi-
tal budgeting techniques we described in this chapter. Not surprisingly, IRR and NPV are
the two most widely used techniques, particularly at larger firms. However, over half of the
respondents always, or almost always, use the payback criterion as well. In fact, among
smaller firms, payback is used about as much as NPV and IRR. Less commonly used are
accounting rate of return and the profitability index. For quick reference, these criteria are
briefly summarized in Table 8.6.
CONCEPT QUESTIONS
8.6a What are the most commonly used capital budgeting procedures?
8.6b If NPV is conceptually the best tool for capital budgeting, why do you think multiple
measures are used in practice?
Summary of
investment criteria
TABLE 8.6
I. Discounted cash flow criteria
A. Net present value (NPV). The NPV of an investment is the difference between its market
value and its cost. The NPV rule is to take a project if its NPV is positive. NPV is
frequently estimated by calculating the present value of the future cash flows (to
estimate market value) and then subtracting the cost. NPV has no serious flaws; it is the
preferred decision criterion.
B. Internal rate of return (IRR). The IRR is the discount rate that makes the estimated NPV of
an investment equal to zero; it is sometimes called the discounted cash flow (DCF)
return. The IRR rule is to take a project when its IRR exceeds the required return. IRR is
closely related to NPV, and it leads to exactly the same decisions as NPV for
conventional, independent projects. When project cash flows are unconventional there
may be no IRR or there may be more than one. More seriously, the IRR cannot be used to
rank mutually exclusive projects; the project with the highest IRR is not necessarily the
preferred investment.
C. Modified internal rate of return (MIRR). The MIRR is a modification to the IRR. A project’s
cash flows are modified by (1) discounting the negative cash flows back to the present;
(2) compounding all cash flows to the end of the project’s life; or (3) combining (1) and
(2). An IRR is then computed on the modified cash flows. MIRRs are guaranteed to avoid
the multiple rate of return problem. But, it is unclear how to interpret them, and they are
not truly “internal” because they depend on externally supplied discounting or
compounding rates.
D. Profitability index (PI). The PI, also called the benefit-cost ratio, is the ratio of present
value to cost. The PI rule is to take an investment if the index exceeds 1. The PI
measures the present value of an investment per dollar invested. It is quite similar to
NPV, but, like IRR, it cannot be used to rank mutually exclusive projects. However, it is
sometimes used to rank projects when a firm has more positive NPV investments than it
can currently finance.
II. Payback criteria
Payback period. The payback period is the length of time until the sum of an investment’s
cash flows equals its cost. The payback period rule is to take a project if its payback is less
than some cutoff. The payback period is a flawed criterion primarily because it ignores risk,
the time value of money, and cash flows beyond the cutoff point.
III. Accounting criteria
Average accounting return (AAR). The AAR is a measure of accounting profit relative to book
value. It is not related to the IRR, but it is similar to the accounting return on assets (ROA)
measure in Chapter 3. The AAR rule is to take an investment if its AAR exceeds a benchmark
AAR. The AAR is seriously flawed for a variety of reasons, and it has little to recommend it.
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C H A P T E R 8 Net Present Value and Other Investment Criteria 261
SUMMARY AND CONCLUSIONS
This chapter has covered the different criteria used to evaluate proposed investments. The
criteria, in the order in which we discussed them, are:
1. Net present value (NPV)
2. Payback period
3. Average accounting return (AAR)
4. Internal rate of return (IRR)
5. Modified internal rate of return (MIRR)
6. Profitability index (PI)
We illustrated how to calculate each of these and discussed the interpretation of the
results. We also described the advantages and disadvantages of each of them. Ultimately, a
good capital budgeting criterion must tell us two things. First, is a particular project a good
investment? Second, if we have more than one good project, but we can only take one of
them, which one should we take? The main point of this chapter is that only the NPV crite-
rion can always provide the correct answer to both questions.
For this reason, NPV is one of the two or three most important concepts in finance,
and we refer to it many times in the chapters ahead. When we do, keep two things in mind:
(1) NPV is always the difference between the market value of an asset or project and its cost
and (2) the financial manager acts in the shareholders’ best interests by identifying and
taking positive NPV projects.
Finally, we noted that NPVs can’t normally be observed in the market; instead, they
must be estimated. Because there is always the possibility of a poor estimate, financial man-
agers use multiple criteria for examining projects. These other criteria provide additional
information about whether a project truly has a positive NPV.
POP QUIZ!
Can you answer the following questions? If your class is using Connect, log on to
SmartBook to see if you know the answers to these and other questions, check out
the study tools, and find out what topics require additional practice!
Section 8.1 Describe the basic NPV investment rule.
Section 8.2 What are the advantages of the payback period method for management?
Section 8.3 How would you define the average accounting return rule?
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262 P A R T 5 Capital Budgeting
8.1 Investment Criteria This problem will give you some practice calculating NPVs
and paybacks. A proposed overseas expansion has the following cash flows:
Year Cash Flow
0 −$100
1 50
2 40
3 40
4 15
Calculate the payback and NPV at a required return of 15 percent. (See Problem 21.)
8.2 Mutually Exclusive Investments Consider the following two mutually exclusive
investments. Calculate the IRR for each. Under what circumstances will the IRR and
NPV criteria rank the two projects differently? (See Problem 10.)
Year Investment A Investment B
0 −$100 −$100
1 ;50 ;;70
2 ;70 ;;75
3 ;;40 ;;10
8.3 Average Accounting Return You are looking at a three-year project with a
projected net income of $1,000 in Year 1, $2,000 in Year 2, and $4,000 in Year 3.
The cost is $9,000, which will be depreciated straight-line to zero over the three-year
life of the project. What is the average accounting return, or AAR? (See Problem 4.)
■ Answers to Chapter Review and Self-Test Problems
8.1 In the following table, we have listed the cash flows and their discounted values
(at 15 percent).
Cash Flow
Year Undiscounted Discounted (at 15%)
1 $ ;;50 $ 43.48
2 ;;;40 30.25
3 ;;;40 26.30
4 ;;;15 8.58
Total $145 $108.60
Recall that the initial investment is $100. Examining the undiscounted cash flows, we
see that the payback occurs between Years 2 and 3. The cash flows for the first two
years are $90 total, so, going into the third year, we are short by $10. The total cash
flow in Year 3 is $40, so the payback is 2 + $10/$40 = 2.25 years.
CHAPTER REVIEW AND SELF-TEST PROBLEMS
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C H A P T E R 8 Net Present Value and Other Investment Criteria 263
Looking at the discounted cash flows, we see that the sum is $108.60, so the
NPV is $8.60.
8.2 To calculate the IRR, we might try some guesses as in the following table:
Discount Rate NPV(A) NPV(B)
0% $60.00 $55.00
10 33.36 33.13
20 13.43 16.20
30 − 1.91 2.78
40 −;;; 13.99 − 8.09
Several things are immediately apparent from our guesses. First, the IRR on A must
be just a little less than 30 percent (why?). With some more effort, we find that it’s
28.61 percent. For B, the IRR must be a little more than 30 percent (again, why?); it
works out to be 32.37 percent. Also, notice that at 10 percent, the NPVs are very
close, indicating that the NPV profiles cross in that vicinity. Verify that the NPVs
are the same at 10.61 percent.
Now, the IRR for B is always higher. As we’ve seen, A has the larger NPV
for any discount rate less than 10.61 percent, so the NPV and IRR rankings will
conflict in that range. Remember, if there’s a conflict, we will go with the
higher NPV. Our decision rule is thus very simple: Take A if the required return
is less than 10.61 percent, take B if the required return is between 10.61 percent
and 32.37 percent (the IRR on B), and take neither if the required return is
more than 32.37 percent.
8.3 Here we need to calculate the ratio of average net income to average book value to
get the AAR. Average net income is:
Average net income = ($1,000 + 2,000 + 4,000)/3
= $2,333.33
Average book value is:
Average book value = $9,000/2 = $4,500
So, the average accounting return is:
AAR = $2,333.33/$4,500 = .5185, or 51.85%
This is an impressive return. Remember, however, that it isn’t really a rate of return
like an interest rate or an IRR, so the size doesn’t tell us a lot. In particular, our money
is probably not going to grow at 51.85 percent per year, sorry to say.
CRITICAL THINKING AND CONCEPTS REVIEW
LO 4 8.1 Payback Period and Net Present Value If a project with conventional
cash flows has a payback period less than its life, can you definitively state
the algebraic sign of the NPV? Why or why not?
LO 4 8.2 Net Present Value Suppose a project has conventional cash flows and a
positive NPV. What do you know about its payback? Its profitability index?
Its IRR? Explain.
LO 1
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264 P A R T 5 Capital Budgeting
LO 1 8.3 Payback Period Concerning payback:
a. Describe how the payback period is calculated and describe the
information this measure provides about a sequence of cash flows.
What is the payback criterion decision rule?
b. What are the problems associated with using the payback period as a
means of evaluating cash flows?
c. What are the advantages of using the payback period to evaluate cash
flows? Are there any circumstances under which using payback might
be appropriate? Explain.
LO 2 8.4 Average Accounting Return Concerning AAR:
a. Describe how the average accounting return is usually calculated and
describe the information this measure provides about a sequence of
cash flows. What is the AAR criterion decision rule?
b. What are the problems associated with using the AAR as a means of
evaluating a project’s cash flows? What underlying feature of AAR is
most troubling to you from a financial perspective? Does the AAR
have any redeeming qualities?
LO 4 8.5 Net Present Value Concerning NPV:
a. Describe how NPV is calculated and describe the information this
measure provides about a sequence of cash flows. What is the NPV
criterion decision rule?
b. Why is NPV considered to be a superior method of evaluating the cash
flows from a project? Suppose the NPV for a project’s cash flows is
computed to be $2,500. What does this number represent with respect
to the firm’s shareholders?
LO 3 8.6 Internal Rate of Return Concerning IRR:
a. Describe how the IRR is calculated, and describe the information this
measure provides about a sequence of cash flows. What is the IRR
criterion decision rule?
b. What is the relationship between IRR and NPV? Are there any situations
in which you might prefer one method over the other? Explain.
c. Despite its shortcomings in some situations, why do most financial
managers use IRR along with NPV when evaluating projects? Can you
think of a situation in which IRR might be a more appropriate measure
to use than NPV? Explain.
LO 6 8.7 Profitability Index Concerning the profitability index:
a. Describe how the profitability index is calculated and describe the
information this measure provides about a sequence of cash flows.
What is the profitability index decision rule?
b. What is the relationship between the profitability index and the NPV?
Are there any situations in which you might prefer one method over
the other? Explain.
LO 3 8.8 Payback and Internal Rate of Return A project has perpetual cash flows
of C per period, a cost of I, and a required return of R. What is the
relationship between the project’s payback and its IRR? What implications
does your answer have for long-lived projects with relatively constant cash
flows?
LO 1
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C H A P T E R 8 Net Present Value and Other Investment Criteria 265
LO 4 8.9 International Investment Projects In June 2017, automobile manufacturer
BMW announced plans to invest $600 million to expand production at its
South Carolina plant. BMW apparently felt that it would better be able to
compete and create value with a U.S.-based facility. In fact, BMW expected
to export 70 percent of the vehicles produced in South Carolina. Also in
2017, noted Taiwanese iPhone supplier Foxconn announced plans to build a
$10 billion plant in Wisconsin, and Chinese tire manufacturer Wanli Tire
Corp. announced plans to build a $1 billion plant in South Carolina. What
are some of the reasons that foreign manufacturers of products as diverse as
automobiles, cell phones, and tires might arrive at this same conclusion?
LO 4 8.10 Capital Budgeting Problems What are some of the difficulties that might
come up in actual applications of the various criteria we discussed in this
chapter? Which one would be the easiest to implement in actual
applications? The most difficult?
LO 4 8.11 Capital Budgeting in Not-for-Profit Entities Are the capital budgeting
criteria we discussed applicable to not-for-profit corporations? How should
such entities make capital budgeting decisions? What about the U.S.
government? Should it evaluate spending proposals using these techniques?
LO 3 8.12 Internal Rate of Return In a previous chapter, we discussed the yield to
maturity (YTM) of a bond. In what ways are the IRR and the YTM
similar? How are they different?
LO 5 8.13 Modified Internal Rate of Return One of the less flattering interpretations
of the acronym MIRR is “meaningless internal rate of return.” Why do you
think this term is applied to MIRR?
LO 4 8.14 Net Present Value It is sometimes stated that “the net present value
approach assumes reinvestment of the intermediate cash flows at the
required return.” Is this claim correct? To answer, suppose you calculate the
NPV of a project in the usual way. Next, suppose you do the following:
a. Calculate the future value (as of the end of the project) of all the cash
flows other than the initial outlay assuming they are reinvested at the
required return, producing a single future value figure for the project.
b. Calculate the NPV of the project using the single future value
calculated in the previous step and the initial outlay. It is easy to verify
that you will get the same NPV as in your original calculation only if
you use the required return as the reinvestment rate in the previous
step.
LO 3 8.15 Internal Rate of Return It is sometimes stated that “the internal rate of
return approach assumes reinvestment of the intermediate cash flows at the
internal rate of return.” Is this claim correct? To answer, suppose you
calculate the IRR of a project in the usual way. Next, suppose you do the
following:
a. Calculate the future value (as of the end of the project) of all the cash
flows other than the initial outlay assuming they are reinvested at the
IRR, producing a single future value figure for the project.
b. Calculate the IRR of the project using the single future value
calculated in the previous step and the initial outlay. It is easy to verify
that you will get the same IRR as in your original calculation only if
you use the IRR as the reinvestment rate in the previous step.
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266 P A R T 5 Capital Budgeting
QUESTIONS AND PROBLEMS
BASIC (Questions 1–22)
1. Calculating Payback What is the payback period for the following set of
cash flows?
Year Cash Flow
0 −$7,800
1 3,100
2 3,200
3 2,200
4 1,400
2. Calculating Payback An investment project provides cash inflows of $865
per year for eight years. What is the project payback period if the initial cost
is $3,100? What if the initial cost is $4,300? What if it is $7,900?
3. Calculating Payback Stenson, Inc., imposes a payback cutoff of three years
for its international investment projects. If the company has the following
two projects available, should it accept either of them?
Year Cash Flow (A) Cash Flow (B)
0 −$75,000 −$125,000
1 33,000 29,000
2 36,000 32,000
3 19,000 35,000
4 9,000 240,000
4. Calculating AAR You’re trying to determine whether or not to expand your
business by building a new manufacturing plant. The plant has an installation
cost of $10.8 million, which will be depreciated straight-line to zero over
its four-year life. If the plant has projected net income of $1,293,000,
$1,725,000, $1,548,000, and $1,310,000 over these four years, what is the
project’s average accounting return (AAR)?
5. Calculating IRR A firm evaluates all of its projects by applying the IRR rule.
If the required return is 11 percent, should the firm accept the following project?
Year Cash Flow
0 −$157,300
1 74,000
2 87,000
3 46,000
6. Calculating NPV For the cash flows in the previous problem, suppose the
firm uses the NPV decision rule. At a required return of 9 percent, should
the firm accept this project? What if the required return was 21 percent?
LO 1
LO 1
LO 1
LO 2
LO 3
LO 4
Select problems are available in McGraw-Hill Connect. Please see the pack-
aging options section of the Preface for more information.
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C H A P T E R 8 Net Present Value and Other Investment Criteria 267
7. Calculating NPV and IRR A project that provides annual cash f lows of
$2,620 for eight years costs $9,430 today. Is this a good project if the
required return is 8 percent? What if it’s 24 percent? At what discount
rate would you be indifferent between accepting the project and
rejecting it?
8. Calculating IRR What is the IRR of the following set of cash flows?
Year Cash Flow
0 −$19,400
1 10,400
2 9,320
3 6,900
9. Calculating NPV For the cash flows in the previous problem, what is the
NPV at a discount rate of 0 percent? What if the discount rate is 10 percent?
If it is 20 percent? If it is 30 percent?
10. NPV versus IRR Piercy, LLC, has identified the following two mutually
exclusive projects:
Year Cash Flow (A) Cash Flow (B)
0 −$77,500 −$77,500
1 43,000 21,000
2 29,000 28,000
3 23,000 34,000
4 21,000 41,000
a. What is the IRR for each of these projects? If you apply the IRR
decision rule, which project should the company accept? Is this decision
necessarily correct?
b. If the required return is 11 percent, what is the NPV for each of these
projects? Which project will you choose if you apply the NPV decision
rule?
c. Over what range of discount rates would you choose Project A? Project
B? At what discount rate would you be indifferent between these two
projects? Explain.
11. NPV versus IRR Consider the following two mutually exclusive projects:
Year Cash Flow (X) Cash Flow (Y)
0 −$23,900 −$23,900
1 13,100 9,300
2 9,480 10,620
3 7,890 11,180
Sketch the NPV profiles for X and Y over a range of discount rates from 0 to
25 percent. What is the crossover rate for these two projects?
LO 3
LO 4
LO 3
LO 4
LO 3
LO 4
LO 3
LO 4
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268 P A R T 5 Capital Budgeting
12. Problems with IRR Howell Petroleum, Inc., is trying to evaluate a
generation project with the following cash flows:
Year Cash Flow
0 −$38,000,000
1 56,000,000
2 − ;;;;9,000,000
a. If the company requires a return of 10 percent on its investments, should
it accept this project? Why?
b. Compute the IRR for this project. How many IRRs are there? If you
apply the IRR decision rule, should you accept the project or not?
What’s going on here?
13. Calculating Profitability Index What is the profitability index for the
following set of cash flows if the relevant discount rate is 10 percent? What if
the discount rate is 15 percent? If it is 22 percent?
Year Cash Flow
0 −$29,500
1 16,900
2 13,600
3 8,300
14. Problems with Profitability Index The Whenworth Corporation is trying to
choose between the following two mutually exclusive design projects:
Year Cash Flow (I) Cash Flow (II)
0 −$84,000 −$29,800
1 30,600 10,500
2 36,900 17,400
3 43,700 15,600
a. If the required return is 11 percent and the company applies the
profitability index decision rule, which project should the firm accept?
b. If the company applies the NPV decision rule, which project should it
take?
c. Explain why your answers in parts (a) and (b) are different.
15. Comparing Investment Criteria Consider the following two mutually
exclusive projects:
Year Cash Flow (A) Cash Flow (B)
0 −$245,000 −$53,000
1 34,000 31,900
2 49,000 21,800
3 51,000 17,300
4 325,000 16,200
LO 3
LO 6
LO 4
LO 6
LO 1
LO 6
LO 3
LO 4
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C H A P T E R 8 Net Present Value and Other Investment Criteria 269
Whichever project you choose, if any, you require a return of 13 percent on
your investment.
a. If you apply the payback criterion, which investment will you choose?
Why?
b. If you apply the NPV criterion, which investment will you choose? Why?
c. If you apply the IRR criterion, which investment will you choose? Why?
d. If you apply the profitability index criterion, which investment will you
choose? Why?
e. Based on your answers in parts (a) through (d), which project will you finally
choose? Why?
16. NPV and IRR Bausch Company is presented with the following two mutually
exclusive projects. The required return for both projects is 15 percent.
Year Project M Project N
0 −$140,000 −$359,000
1 61,500 159,300
2 73,400 168,400
3 68,100 154,800
4 40,500 110,400
a. What is the IRR for each project?
b. What is the NPV for each project?
c. Which, if either, of the projects should the company accept?
17. NPV and Profitability Index Coore Manufacturing has the following two
possible projects. The required return is 12 percent.
Year Project Y Project Z
0 −$47,600 −$81,000
1 23,900 34,000
2 18,600 32,800
3 20,700 30,500
4 14,600 27,300
a. What is the profitability index for each project?
b. What is the NPV for each project?
c. Which, if either, of the projects should the company accept?
18. Crossover Point Crenshaw Enterprises has gathered projected cash flows
for two projects. At what interest rate would the company be indifferent
between the two projects? Which project is better if the required return is
above this interest rate? Why?
Year Project I Project J
0 −$189,000 −$189,000
1 93,500 73,600
2 84,600 72,800
3 63,200 76,800
4 57,800 84,000
LO 3
LO 4
LO 4
LO 6
LO 3
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270 P A R T 5 Capital Budgeting
19. Payback Period and IRR Suppose you have a project with a payback period
exactly equal to the life of the project. What do you know about the IRR of
the project? Suppose that the payback period is never. What do you know
about the IRR of the project now?
20. NPV and Discount Rates An investment has an installed cost of $787,350.
The cash flows over the four-year life of the investment are projected to be
$312,615, $304,172, $245,367, and $229,431. If the discount rate is zero,
what is the NPV? If the discount rate is infinite, what is the NPV? At what
discount rate is the NPV equal to zero? Sketch the NPV profile for this
investment based on these three points.
21. NPV and Payback Period Kaleb Konstruction, Inc., has the following
mutually exclusive projects available. The company has historically used a
three-year cutoff for projects. The required return is 10 percent.
Year Project F Project G
0 −$195,000 −$298,000
1 ;;98,400 ;;71,600
2 ;;86,300 ;;94,500
3 ;;81,600 123,600
4 ;;72,000 166,800
5 ;;64,800 187,200
a. Calculate the payback period for both projects.
b. Calculate the NPV for both projects.
c. Which project, if any, should the company accept?
22. MIRR Doak Corp. is evaluating a project with the following cash flows:
Year Cash Flow
0 −$32,600
1 11,520
2 14,670
3 11,270
4 10,940
5 − 4,230
The company uses an interest rate of 10 percent on all of its projects. Calcu-
late the MIRR of the project using all three methods.
INTERMEDIATE (Questions 23–27)
23. MIRR Suppose the company in the previous problem uses a discount rate
of 11 percent and a reinvestment rate of 8 percent on all of its projects.
Calculate the MIRR of the project using all three methods with these rates.
24. Crossover and NPV Hanse, Inc., has the following two mutually exclusive
projects available.
Year Project R Project S
0 −$51,000 −$76,000
1 19,000 20,000
2 19,000 20,000
3 24,000 35,000
4 11,000 30,000
5 7,000 10,000
LO 1
LO 3
LO 4
LO 1
LO 4
LO 5
LO 5
LO 4
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C H A P T E R 8 Net Present Value and Other Investment Criteria 271
What is the crossover rate for these two projects? What is the NPV of each
project at the crossover rate?
25. Calculating IRR A project has the following cash flows:
Year Cash Flow
0 $112,000
1 − 67,000
2 − 57,000
What is the IRR for this project? If the required return is 10 percent, should
the firm accept the project? What is the NPV of this project? What is the
NPV of the project if the required return is 0 percent? 24 percent? What is
going on here? Sketch the NPV profile to help you with your answer.
26. NPV and the Profitability Index If we define the NPV index as the ratio of
NPV to cost, what is the relationship between this index and the profitability
index?
27. Cash Flow Intuition A project has an initial cost of I, has a required return
of R, and pays C annually for N years.
a. Find C in terms of I and N such that the project has a payback period
equal to its life.
b. Find C in terms of I, N, and R such that this is a profitable project
according to the NPV decision rule.
c. Find C in terms of I, N, and R such that the project has a benefit-cost
ratio of 2.
CHALLENGE (Questions 28–30)
28. NPV Valuation The Yurdone Corporation wants to set up a private
cemetery business. According to the CFO, Barry M. Deep, business is
“looking up.” As a result, the cemetery project will provide a net cash
inflow of $164,000 for the firm during the first year, and the cash flows
are projected to grow at a rate of 4.7 percent per year forever. The project
requires an initial investment of $1,825,000.
a. If the company requires a return of 12 percent on such undertakings,
should the cemetery business be started?
b. The company is somewhat unsure about the assumption of a 4.7 percent
growth rate in its cash flows. At what constant growth rate would the
company just break even if it still required a return of 12 percent on its
investment?
29. Problems with IRR Koepka Corp. has a project with the following cash
flows:
Year Cash Flow
0 $35,000
1 − 27,000
2 29,000
What is the IRR of the project? What is happening here?
LO 3
LO 4
LO 4
LO 6
LO 1
LO 4
LO 6
LO 4
LO 3
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272 P A R T 5 Capital Budgeting
30. NPV and IRR Anderson International Limited is evaluating a project in
Erewhon. The project will create the following cash flows:
Year Cash Flow
0 −$875,000
1 306,900
2 287,600
3 285,300
4 259,300
All cash flows will occur in Erewhon and are expressed in dollars. In an at-
tempt to improve its economy, the Erewhonian government has declared that
all cash flows created by a foreign company are “blocked” and must be rein-
vested with the government for one year. The reinvestment rate for these
funds is 4 percent. If Anderson uses a required return of 10 percent on this
project, what are the NPV and IRR of the project? Is the IRR you calculated
the MIRR of the project? Why or why not?
LO 3
LO 4
WHAT’S ON
THE WEB?
8.1 Net Present Value You have a project that has an initial cash outflow of −$20,000
and cash inflows of $6,000, $5,000, $4,000, and $3,000, respectively, for the next four
years. Go to www.vindeep.com and find the IRR calculator. Enter the cash flows. If the
required return is 12 percent, what is the IRR of the project? The NPV?
8.2 Internal Rate of Return Using the online calculator from the previous problem, find
the IRR for a project with cash flows of −$500, $1,200, and −$400. What is going on
here?
As you have already seen, Excel does not have a function to calculate the payback period.
We have shown three ways to calculate the payback period, but there are numerous other
methods as well. Below, the cash flows for a project are shown. You need to calculate the
payback period using two different methods.
a. Calculate the payback period in a table. The first three columns of the table will be
the year, the cash flow for that year, and the cumulative cash flow. The fourth column
will show the whole year for the payback. In other words, if the payback period is
3+ years, this column will have a 3, otherwise it will be a zero. The next column will
calculate the fractional part of the payback period, or else it will display zero. The
last column will add the previous two columns and display the final payback period
calculation. You should also have a cell that displays the final payback period by itself,
and a cell that returns the correct accept or reject decision based on the payback
criteria.
b. Write a nested IF statement that calculates the payback period using only the project
cash flow column. The IF statement should return a value of “Never” if the project
has no payback period. In contrast to the example we showed previously, the nested
IF function should test for the payback period starting with shorter payback periods
coverage online
Excel
Master
EXCEL MASTER IT! PROBLEM
ros13952_ch08_237-274.indd 272 12/22/18 5:54 PM
C H A P T E R 8 Net Present Value and Other Investment Criteria 273
and working toward longer payback periods. Another cell should display the correct
accept or reject decision based on the payback criteria.
Year Cash Flow
0 −$250,000
1 41,000
2 48,000
3 63,000
4 79,000
5 88,000
6 64,000
7 41,000
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274 P A R T 5 Capital Budgeting
Alma has used the estimates provided by Dan to
determine the revenues that could be expected from
the mine. She also has projected the expense of open-
ing the mine and the annual operating expenses. If the
company opens the mine, it will cost $625 million today,
and it will have a cash outflow of $90 million nine years
from today in costs associated with closing the mine and
reclaiming the area surrounding it. The expected cash
flows each year from the mine are shown in the nearby
table. Bullock Gold Mining has a 12 percent required re-
turn on all of its gold mines.
Year Cash Flow
0 −$625,000,000
1 70,000,000
2 129,000,000
3 183,000,000
4 235,000,000
5 210,000,000
6 164,000,000
7 108,000,000
8 86,000,000
9 − 90,000,000
Seth Bullock, the owner of Bullock Gold Mining, is evaluating a new gold mine in South Dakota. Dan
Dority, the company’s geologist, has just finished his
analysis of the mine site. He has estimated that the
mine would be productive for eight years, after which
the gold would be completely mined. Dan has taken an
estimate of the gold deposits to Alma Garrett, the com-
pany’s financial officer. Alma has been asked by Seth
to perform an analysis of the new mine and present her
recommendation on whether the company should
open the new mine.
CHAPTER CASE
Bullock Gold Mining
1. Construct a spreadsheet to calculate the payback
period, internal rate of return, modified internal
rate of return, and net present value of the pro-
posed mine.
2. Based on your analysis, should the company open
the mine?
3. Bonus question: Most spreadsheets do not have a
built-in formula to calculate the payback period.
Write a VBA script that calculates the payback pe-
riod for a project.
Q U E S T I O N S
ros13952_ch08_237-274.indd 274 12/22/18 5:54 PM
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275
Even having a major star is no guarantee of success for a movie re-lease. In 2018, the film Gotti, which starred John Travolta, slept with
the fishes as it debuted with a 0.0 rating on Rotten Tomatoes. The crit-
ics all said, “fugeddaboudit!” Fortunately for the production company,
Oasis Films, the film didn’t lose a lot of money (it only cost $10 million to
make). Not all films are as lucky. Take Monster Trucks, the children’s film
about the monsters that live in trucks. According to critics, just watching
the movie amounted to a crushing experience. One called it a “clueless
family caper.” Another was even more harsh, saying “Monster Trucks is
a wreck, fueled by the crazy belief that noise and repetition can dis-
guise the lack of credible writing, directing, acting and FX.”
Looking at the numbers, Paramount Pictures spent close to $125 million making the
movie, plus millions more for marketing and distribution. Paramount was so negative about
movie ticket sales that it wrote off $115 million before the movie was released! And the movie
subsequently crashed, pulling in only $64.5 million worldwide. Of course, there are movies
that do quite well. Also in 2018, the superhero hit Black Panther raked in about $1.4 billion
worldwide at a production cost of about $200 million.
Obviously, Paramount didn’t plan to lose $60 or so million on Monster Trucks, but it hap-
pened. As that movie’s box office crack-up shows, projects don’t always go as companies
think they will. This chapter explores how this can happen and what companies can do to
analyze and possibly avoid these situations.
In broader terms, this chapter follows up on our previous one by delving more deeply into
capital budgeting. We have two main tasks. First, recall that in the last chapter, we saw that cash
flow estimates are the critical input into a net present value analysis, but we didn’t say very much
about where these cash flows come from; so, we will now examine this question in some detail.
Our second goal is to learn how to critically examine NPV estimates and, in particular, how to
evaluate the sensitivity of NPV estimates to assumptions made about the uncertain future.
Making Capital Investment
Decisions9
LEARNING OBJECTIVES
After studying this chapter, you should be
able to:
LO 1 Determine the relevant cash flows
for a proposed investment.
LO 2 Analyze a project’s expected cash
flows.
LO 3 Evaluate an estimated NPV.
Please visit us at essentialsofcorporatefinance.blogspot.com for the latest developments in the world of corporate finance.
ros13952_ch09_275-309.indd 275 12/24/18 5:00 PM
276 P A R T 5 Capital Budgeting
So far, we’ve covered various parts of the capital budgeting decision. Our task in this chapter is to start bringing these pieces together. In particular, we will show you how to
“spread the numbers” for a proposed investment or project and, based on those numbers,
make an initial assessment about whether or not the project should be undertaken.
In the discussion that follows, we focus on the process of setting up a discounted cash
flow analysis. From the last chapter, we know that the projected future cash flows are the
key element in such an evaluation. Accordingly, we emphasize working with financial and
accounting information to come up with these figures.
In evaluating a proposed investment, we pay special attention to deciding what informa-
tion is relevant to the decision at hand and what information is not. As we shall see, it is
easy to overlook important pieces of the capital budgeting puzzle. We also describe how to
go about evaluating the results of our discounted cash flow analysis.
PROJECT CASH FLOWS: A FIRST LOOK
The effect of taking a project is to change the firm’s overall cash flows today and in the fu-
ture. To evaluate a proposed investment, we must consider these changes in the firm’s cash
flows and then decide whether or not they add value to the firm. The first (and most impor-
tant) step, therefore, is to decide which cash flows are relevant and which are not.
Relevant Cash Flows
What is a relevant cash flow for a project? The general principle is simple enough: A rele-
vant cash flow for a project is a change in the firm’s overall future cash flow that comes
about as a direct consequence of the decision to take that project. Because the relevant cash
flows are defined in terms of changes in, or increments to, the firm’s existing cash flow, they
are called the incremental cash flows associated with the project.
The concept of incremental cash flow is central to our analysis, so we will state a gen-
eral definition and refer back to it as needed:
The incremental cash flows for project evaluation consist of any and all changes in
the firm’s future cash flows that are a direct consequence of taking the project.
This definition of incremental cash flows has an obvious and important corollary: Any
cash flow that exists regardless of whether or not a project is undertaken is not relevant.
The Stand-Alone Principle
In practice, it would be very cumbersome to actually calculate the future total cash flows to
the firm with and without a project, especially for a large firm. Fortunately, it is not really
necessary to do so. Once we identify the effect of undertaking the proposed project on the
firm’s cash flows, we need only focus on the project’s resulting incremental cash flows. This
is called the stand-alone principle.
What the stand-alone principle says is that, once we have determined the incremental
cash flows from undertaking a project, we can view that project as a kind of “minifirm” with
its own future revenues and costs, its own assets, and, of course, its own cash flows. We will
then be primarily interested in comparing the cash flows from this minifirm to the cost of
acquiring it. An important consequence of this approach is that we will be evaluating the
proposed project purely on its own merits, in isolation from any other activities or projects.
9.1
incremental cash
flows
The difference between a
firm’s future cash flows
with a project and those
without the project.
stand-alone
principle
The assumption that
evaluation of a project
may be based on the
project’s incremental cash
flows.
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C H A P T E R 9 Making Capital Investment Decisions 277
INCREMENTAL CASH FLOWS
We are concerned here only with those cash flows that are incremental and that result
from a project. Looking back at our general definition, it seems easy enough to decide
whether or not a cash flow is incremental. Even so, there are a few situations where mis-
takes are easy to make. In this section, we describe some of these common pitfalls and how
to avoid them.
Sunk Costs
A sunk cost, by definition, is a cost we have already paid or have already incurred the liabil-
ity to pay. Such a cost cannot be changed by the decision today to accept or reject a project.
Put another way, the firm will have to pay this cost no matter what. Based on our general
definition of incremental cash flow, such a cost is clearly irrelevant to the decision at hand.
So, we will always be careful to exclude sunk costs from our analysis.
That a sunk cost is irrelevant seems obvious given our discussion. Nonetheless, it’s
easy to fall prey to the sunk cost fallacy. Suppose General Milk Company hires a finan-
cial consultant to help evaluate whether or not a line of chocolate milk should be
launched. When the consultant turns in the report, General Milk objects to the analysis
because the consultant did not include the hefty consulting fee as a cost of the chocolate
milk project.
Who is correct? By now, we know that the consulting fee is a sunk cost because the
consulting fee must be paid whether or not the chocolate milk line is actually launched (this
is an attractive feature of the consulting business).
Opportunity Costs
When we think of costs, we normally think of out-of-pocket costs, namely, those that require
us to actually spend some amount of cash. An opportunity cost is slightly different; it re-
quires us to give up a benefit. A common situation arises where a firm already owns some of
the assets a proposed project will be using. For example, we might be thinking of converting
an old rustic cotton mill we bought years ago for $100,000 into “upmarket”
condominiums.
If we undertake this project, there will be no direct cash outflow associated with buy-
ing the old mill since we already own it. For purposes of evaluating the condo project,
should we then treat the mill as “free”? The answer is no. The mill is a valuable resource
used by the project. If we didn’t use it here, we could do something else with it. Like what?
The obvious answer is that, at a minimum, we could sell it. Using the mill for the condo
complex thus has an opportunity cost: We give up the valuable opportunity to do some-
thing else with it.1
9.2
sunk cost
A cost that has already
been incurred and cannot
be recouped and
therefore should not be
considered in an
investment decision.
opportunity cost
The most valuable
alternative that is given up
if a particular investment
is undertaken.
CONCEPT QUESTIONS
9.1a What are the relevant incremental cash flows for project evaluation?
9.1b What is the stand-alone principle?
1Economists sometimes use the acronym TANSTAAFL, which is short for “There ain’t no such thing as a free
lunch,” to describe the fact that only very rarely is something truly free.
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278 P A R T 5 Capital Budgeting
There is another issue here. Once we agree that the use of the mill has an opportunity
cost, how much should the condo project be charged? Given that we paid $100,000, it might
seem that we should charge this amount to the condo project. Is this correct? The answer is
no, and the reason is based on our discussion concerning sunk costs.
The fact that we paid $100,000 some years ago is irrelevant. That cost is sunk. At a
minimum, the opportunity cost that we charge the project is what the mill would sell for
today (net of any selling costs) because this is the amount that we give up by using it instead
of selling it.
Side Effects
Remember that the incremental cash flows for a project include all the changes in the firm’s
future cash flows. It would not be unusual for a project to have side, or spillover, effects,
both good and bad. For example, if the Innovative Motors Company (IMC) introduces a
new car, some of the sales might come at the expense of other IMC cars. This is called
erosion, and the same general problem could occur for any multiline producer or seller.2 In
this case, the cash flows from the new line should be adjusted downward to reflect lost prof-
its on other lines.
In accounting for erosion, it is important to recognize that any sales lost as a result of
our launching a new product might be lost anyway because of future competition. Erosion is
only relevant when the sales would not otherwise be lost.
Net Working Capital
Normally, a project will require that the firm invest in net working capital in addition to
long-term assets. For example, a project will generally need some amount of cash on hand
to pay any expenses that arise. In addition, a project will need an initial investment in inven-
tories and accounts receivable (to cover credit sales). Some of this financing will be in the
form of amounts owed to suppliers (accounts payable), but the firm will have to supply the
balance. This balance represents the investment in net working capital.
It’s easy to overlook an important feature of net working capital in capital budgeting.
As a project winds down, inventories are sold, receivables are collected, bills are paid,
and cash balances can be drawn down. These activities free up the net working capital
originally invested. So, the firm’s investment in project net working capital closely resem-
bles a loan. The firm supplies working capital at the beginning and recovers it toward
the end.
Financing Costs
In analyzing a proposed investment, we will not include interest paid or any other financing
costs such as dividends or principal repaid because we are interested in the cash flow gener-
ated by the assets of the project. As we mentioned in Chapter 2, interest paid, for example,
is a component of cash flow to creditors, not cash flow from assets.
More generally, our goal in project evaluation is to compare the cash flow from a proj-
ect to the cost of acquiring that project in order to estimate NPV. The particular mixture of
debt and equity a firm actually chooses to use in financing a project is a managerial variable
and primarily determines how project cash flow is divided between owners and creditors.
This is not to say that financing arrangements are unimportant. They are something to be
analyzed separately. We will cover this in later chapters.
erosion
The cash flows of a new
project that come at the
expense of a firm’s
existing projects.
2More colorfully, erosion is sometimes called piracy or cannibalism.
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C H A P T E R 9 Making Capital Investment Decisions 279
Other Issues
There are some other things to watch out for. First, we are only interested in measuring cash
flow. Moreover, we are interested in measuring it when it actually occurs, not when it
accrues in an accounting sense. Second, we are always interested in aftertax cash flow be-
cause taxes are definitely a cash outflow. In fact, whenever we write “incremental cash
flows,” we mean aftertax incremental cash flows. Remember, however, that aftertax cash
flow and accounting profit, or net income, are entirely different things.
CONCEPT QUESTIONS
9.2a What is a sunk cost? An opportunity cost?
9.2b Explain what erosion is, and why it is relevant.
9.2c Explain why interest paid is not a relevant cash flow for project evaluation.
PRO FORMA FINANCIAL STATEMENTS AND
PROJECT CASH FLOWS
The first thing we need when we begin evaluating a proposed investment is a set of pro
forma, or projected, financial statements. Given these, we can develop the projected cash
flows from the project. Once we have the cash flows, we can estimate the value of the
project using the techniques we described in the previous chapter.
Getting Started: Pro Forma Financial Statements
Pro forma financial statements are a convenient and easily understood means of summariz-
ing much of the relevant information for a project. To prepare these statements, we will need
estimates of quantities such as unit sales, the selling price per unit, the variable cost per unit,
and total fixed costs. We also will need to know the total investment required, including any
investment in net working capital.
To illustrate, suppose we think we can sell 50,000 cans of shark attractant per year at a
price of $4.00 per can. It costs us about $2.50 per can to make the attractant, and a new
product such as this one typically has only a three-year life (perhaps because the customer
base dwindles rapidly). We require a 20 percent return on new products.
Fixed costs for the project, including such things as rent on the production facility, will
run $17,430 per year. Further, we will need to invest a total of $90,000 in manufacturing
equipment. For simplicity, we will assume that this $90,000 will be 100 percent depreciated
over the three-year life of the project. Furthermore, the cost of removing the equipment will
roughly equal its actual value in three years, so it will be essentially worthless on a market
value basis as well. Finally, the project will require an initial $20,000 investment in net work-
ing capital, and the tax rate is 21 percent.
In Table 9.1, we organize these initial projections by first preparing the pro forma in-
come statement for each of the three years. Once again, notice that we have not deducted
any interest expense. This will always be so. As we described earlier, interest paid is a financ-
ing expense, not a component of operating cash flow.
We also can prepare a series of abbreviated balance sheets that show the capital require-
ments for the project. as we’ve done in Table 9.2. Here we have net working capital of
9.3
coverage online
Excel
Master
pro forma financial
statements
Financial statements
projecting future years’
operations.
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280 P A R T 5 Capital Budgeting
$20,000 in each year. Fixed assets are $90,000 at the start of the project’s life (Year 0), and
they decline by the $30,000 in depreciation each year, ending up at zero. Notice that the
total investment given here for future years is the total book, or accounting, value, not mar-
ket value.
At this point, we need to start converting this accounting information into cash flows.
We consider how to do this next.
Project Cash Flows
To develop the cash flows from a project, we need to recall (from Chapter 2) that cash flow
from assets has three components: operating cash flow, capital spending, and additions to
net working capital. To evaluate a project, or minifirm, we need to arrive at estimates for
each of these.
Once we have estimates of the components of cash flow, we will calculate cash flow for
our minifirm as we did in Chapter 2 for an entire firm:
Project cash flow = Project operating cash flow
− Project change in net working capital
− Project capital spending
We consider these components next.
Project Operating Cash Flow To determine the operating cash flow associated
with a project, we first need to recall the definition of operating cash flow:
Operating cash flow = Earnings before interest and taxes
+ Depreciation
− Taxes
To illustrate the calculation of operating cash flow, we will use the projected information
from the shark attractant project. For ease of reference, Table 9.3 repeats the income
statement.
Sales (50,000 units at $4.00/unit) $200,000
Variable costs ($2.50/unit) 125,000
Fixed costs 17,430
Depreciation (= $90,000/3) 30,000
EBIT $ 27,570
Taxes (21%) 5,790
Net income $ 21,780
Projected income
statement, shark
attractant project,
Years 1–3
TABLE 9.1
Projected capital
requirements, shark
attractant project
TABLE 9.2 Year
0 1 2 3
Net working capital $ 20,000 $20,000 $20,000 $20,000
Net fixed assets 90,000 60,000 30,000 0
Total investment $110,000 $80,000 $50,000 $20,000
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C H A P T E R 9 Making Capital Investment Decisions 281
Given the income statement in Table 9.3, calculating the operating cash flow is straight-
forward. As we see in Table 9.4, projected operating cash flow for the shark attractant
project is $51,780.
Project Net Working Capital and Capital Spending We next need to take
care of the fixed asset and net working capital requirements. Based on our balance sheets
above, the firm must spend $90,000 up front for fixed assets and invest an additional
$20,000 in net working capital. The immediate outflow is thus $110,000. At the end of the
project’s life, the fixed assets will be worthless (the salvage value will be zero), but the firm
will recover the $20,000 that was tied up in working capital. This will lead to a $20,000 cash
inflow in the last year.
On a purely mechanical level, notice that whenever we have an investment in net work-
ing capital, that same investment has to be recovered; in other words, the same number
needs to appear at some time in the future with the opposite sign.
Projected Total Cash Flow and Value
Given the information we’ve accumulated, we can finish the preliminary cash flow analysis
as illustrated in Table 9.5.
Now that we have cash flow projections, we are ready to apply the various criteria we
discussed in the last chapter. First, the NPV at the 20 percent required return is:
NPV = −$110,000 + 51,780/1.2 + 51,780/1.22 + 71,780/1.23
= $10,648
Sales $200,000
Variable costs 125,000
Fixed costs 17,430
Depreciation 30,000
EBIT $ 27,570
Taxes (21%) 5,790
Net income $ 21,780
Projected income
statement, shark
attractant project,
Years 1–3
TABLE 9.3
Projected operating
cash flow, shark
attractant project
TABLE 9.4EBIT $27,570
Depreciation +30,000
Taxes −5,790
Operating cash flow $ 51,780
Projected total cash
flows, shark
attractant project
TABLE 9.5Year
0 1 2 3
Operating cash flow $51,780 $51,780 $51,780
Change in NWC − $ 20,000 +20,000
Capital spending − 90,000
Total project cash flow −$110,000 $51,780 $51,780 $71,780
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282 P A R T 5 Capital Budgeting
So, based on these projections, the project creates more than $10,000 in value and
should be accepted. Also, the return on this investment obviously exceeds 20 percent
(because the NPV is positive at 20 percent). After some trial and error, we find that the IRR
works out to be about 25.76 percent.
In addition, if required, we could go ahead and calculate the payback and the average
accounting return, or AAR. Inspection of the cash flows shows that the payback on this
project is a little over two years (verify that it’s about 2.1 years).
From the last chapter, we know that the AAR is average net income divided by aver-
age book value. The net income each year is $21,780. The average of the four book val-
ues (from Table 9.2) is ($110,000 + 80,000 + 50,000 + 20,000)/4 = $65,000, so the
AAR is $21,780/$65,000 = .3351, or 33.51 percent. We’ve already seen that the return
on this investment (the IRR) is about 26 percent. The fact that the AAR is larger illus-
trates again why the AAR cannot be meaningfully interpreted as the return on a
project.
The Tax Shield Approach
A useful variation on our basic definition of operating cash flow (OCF) is the tax shield
approach. The tax shield definition of OCF is:
OCF = (Sales − Costs) × (1 − Tc) + Depreciation × Tc
where Tc is the corporate tax rate. Assuming that Tc = 21%, the OCF works out to be:
OCF = ($200,000 − 142,430) × .79 + 30,000 × .21
= $45,480 + 6,300
= $51,780
This is as we had before.
This approach views OCF as having two components. The first part is what the
project’s cash flow would be if there were no depreciation expense. In this case, this would-
have-been cash flow is $45,480.
The second part of OCF in this approach is the depreciation deduction multiplied by
the tax rate. This is called the depreciation tax shield. We know that depreciation is a non-
cash expense. The only cash flow effect of deducting depreciation is to reduce our taxes, a
benefit to us. At the current 21 percent corporate tax rate, every dollar in depreciation ex-
pense saves us 21 cents in taxes. In our example, the $30,000 depreciation deduction saves
us $30,000 × .21 = $6,300 in taxes.
The tax shield approach will always give the same answer as our basic approach, so you
might wonder why we bother. The answer is that it is sometimes a little simpler to use, par-
ticularly for projects that involve cost-cutting.
CONCEPT QUESTIONS
9.3a What is the definition of project operating cash flow? How does this differ from net
income?
9.3b In the shark attractant project, why did we add back the firm’s net working capital
investment in the final year?
9.3c What is the “depreciation tax shield”?
depreciation tax
shield
The tax saving that results
from the depreciation
deduction, calculated as
depreciation multiplied by
the corporate tax rate.
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C H A P T E R 9 Making Capital Investment Decisions 283
MORE ON PROJECT CASH FLOW
In this section, we take a closer look at some aspects of project cash flow. In particular, we
discuss project net working capital in more detail. We then examine current tax laws regard-
ing depreciation.
A Closer Look at Net Working Capital
In calculating operating cash flow, we did not explicitly consider the fact that some of our
sales might be on credit. Also, we may not actually have paid some of the costs shown. In
either case, the cash flow has not yet occurred. We show here that these possibilities are not
a problem as long as we don’t forget to include additions to net working capital in our analy-
sis. This discussion thus emphasizes the importance and the effect of doing so.
Suppose during a particular year of a project we have the following simplified income
statement:
Sales $500
Costs 310
Net income $190
Depreciation and taxes are zero. No fixed assets are purchased during the year. Also, to il-
lustrate a point, we assume that the only components of net working capital are accounts
receivable and payable. The beginning and ending amounts for these accounts are:
Beginning of Year End of Year Change
Accounts receivable $880 $910 +$30
Accounts payable 550 605 + 55
Net working capital $330 $305 −$25
Based on this information, what is total cash flow for the year? We first can mechanically
apply what we have been discussing to come up with the answer. Operating cash flow in this
particular case is the same as EBIT because there are no taxes or depreciation, and thus
equals $190. Also, notice that net working capital actually declined by $25, so the change in
net working capital is negative. This means that $25 was freed up during the year. There was
no capital spending, so the total cash flow for the year is:
Total cash flow = Operating cash flow − Change in NWC − Capital spending
= $190 − (−25) − 0
= $215
Now, we know that this $215 total cash flow has to be “dollars in” less “dollars out” for
the year. We, therefore, could ask a different question: What were cash revenues for the
year? Also, what were cash costs?
To determine cash revenues, we need to look more closely at net working capital. Dur-
ing the year, we had sales of $500. However, accounts receivable rose by $30 over the same
time period. What does this mean? The $30 increase tells us that sales exceeded collections
by $30. In other words, we haven’t yet received the cash from $30 of the $500 in sales. As a
result, our cash inflow is $500 − 30 = $470. In general, cash inflow is sales minus the in-
crease in accounts receivable.
9.4
coverage online
Excel
Master
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284 P A R T 5 Capital Budgeting
Cash outflows can be determined similarly. We show costs of $310 on the income state-
ment, but accounts payable increased by $55 during the year. This means that we have not
yet paid $55 of the $310, so cash costs for the period are $310 − 55 = $255. In other words,
in this case, cash costs equal costs less the increase in accounts payable.
Putting this information together, cash inflows less cash outflows is $470 − 255 =
$215, as we had before. Notice that:
Cash flow = Cash inflow − Cash outflow
= ($500 − 30) − (310 − 55)
= ($500 − 310) − (30 − 55)
= Operating cash flow − Change in NWC
= $190 − (−25)
= $215
More generally, this example illustrates that including net working capital changes in our
calculations has the effect of adjusting for the discrepancy between accounting sales and
costs and actual cash receipts and payments.
EXAMPLE 9.1 Cash Collections and Costs
For the year just completed, the Combat Wombat Telestat Co. (CWT) reports sales of $998 and
costs of $734. You have collected the following beginning and ending balance sheet information:
Beginning Ending
Accounts receivable $100 $110
Inventory 100 80
Accounts payable 100 70
Net working capital $100 $120
Based on these figures, what are cash inflows? Cash outflows? What happened to each account?
What is net cash flow?
Sales were $998, but receivables rose by $10. So, cash collections were $10 less than sales,
or $988. Costs were $734, but inventories fell by $20. This means that we didn’t replace $20 worth
of inventory, so costs are actually overstated by this amount. Also, payables fell by $30. This means
that, on a net basis, we actually paid our suppliers $30 more than we received from them, resulting
in a $30 understatement of costs. Adjusting for these events, cash costs are $734 – 20 + 30 =
$744. Net cash flow is $988 – 744 = $244.
Finally, notice that net working capital increased by $20 overall. We can check our answer by
noting that the original accounting sales less costs of $998 – 734 is $264. In addition, CWT spent
$20 on net working capital, so the net result is a cash flow of $264 – 20 = $244, as we calculated.
Depreciation
As we note elsewhere, accounting depreciation is a noncash deduction. As a result, de-
preciation has cash flow consequences only because it influences the tax bill. The way
that depreciation is computed for tax purposes is thus the relevant method for capital
investment decisions. Not surprisingly, the procedures are governed by tax law. We now
discuss some specifics of the depreciation system enacted by the Tax Reform Act of
1986. This system is a modification of the Accelerated Cost Recovery System (ACRS)
instituted in 1981.
Accelerated Cost
Recovery System
(ACRS)
Depreciation method
under U.S. tax law
allowing for the
accelerated write-off of
property under various
classifications.
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C H A P T E R 9 Making Capital Investment Decisions 285
Modified ACRS (MACRS) Depreciation Calculating depreciation is normally
very mechanical. While there are a number of ifs, ands, and buts involved, the basic idea is
that every asset is assigned to a particular class. An asset’s class establishes its life for tax
purposes. Once an asset’s tax life is determined, we compute the depreciation for each year
by multiplying the cost of the asset by a fixed percentage. The expected salvage value (what
we think the asset will be worth when we dispose of it) and the actual expected economic
life (how long we expect the asset to be in service) are not explicitly considered in the calcu-
lation of depreciation.
Some typical depreciation classes are described in Table 9.6, and associated percent-
ages (rounded to two decimal places) are shown in Table 9.7. Remember that land cannot
be depreciated.
To illustrate how depreciation is calculated, we consider an automobile costing $35,000.
Autos are normally classified as five-year property. Looking at Table 9.7, we see that the
relevant figure for the first year of a five-year asset is 20 percent. The depreciation in
the first year is thus $35,000 × .20 = $7,000. The relevant percentage in the second year is
32 percent, so the depreciation in the second year is $35,000 × .32 = $11,200, and so on.
We can summarize these calculations as follows:
Year MACRS Percentage Depreciation
1 20.00% .2000 × $35,000 = $ 7,000
2 32.00 .3200 × 35,000 = 11,200
3 19.20 .1920 × 35,000 = 6,720
4 11.52 .1152 × 35,000 = 4,032
5 11.52 .1152 × 35,000 = 4,032
6 5.76 .0576 × 35,000 = 2,016
100.00% $35,000
Class Examples
3-year Equipment used in research
5-year Autos, computers
7-year Most industrial equipment
Modified ACRS
property classes
TABLE 9.6
Property Class
Year 3-Year 5-Year 7-Year
1 33.33% 20.00% 14.29%
2 44.45 32.00 24.49
3 14.81 19.20 17.49
4 7.41 11.52 12.49
5 11.52 8.93
6 5.76 8.92
7 8.93
8 4.46
Modified ACRS
depreciation
allowances
TABLE 9.7
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286 P A R T 5 Capital Budgeting
Notice that the MACRS percentages sum up to 100 percent. As a result, we write off
100 percent of the cost of the asset, or $35,000 in this case.
Bonus Depreciation For a number of years prior to 2018, various tax rules and regu-
lations were enacted that allowed “bonus” depreciation. Based on the Protecting Americans
from Tax Hikes (PATH) Act of 2015, the size of the bonus in 2017 was 50 percent. What
this meant is that a firm could take a depreciation deduction of 50 percent of the cost on an
eligible asset in the first year and then depreciate the remaining 50 percent using the
MACRS schedules as we have just described. Significantly, in late 2017, Congress passed
the Tax Cuts and Jobs Act, which increased the bonus depreciation to 100 percent for 2018,
lasting until the end of 2022. After that, it drops by 20 percent per year until it reaches zero
after 2026. The implication is that most firms will not use the MACRS schedules until 2023
unless they wish to (taking the bonus depreciation is optional). Of course, future legislation
may change things.
Book Value versus Market Value In calculating depreciation under current tax
law, the economic life and future market value of the asset are not an issue. As a result, the
book value of an asset can differ substantially from its actual market value. For example,
with our $35,000 car, book value after the first year is $35,000 less the first year’s deprecia-
tion of $7,000, or $28,000. The remaining book values are summarized in Table 9.8. After
six years, the book value of the car is zero.
Suppose we wanted to sell the car after five years. Based on historical averages, it will
be worth, say, 25 percent of the purchase price, or .25 × $35,000 = $8,750. If we actually
sold it for this, then we would have to pay taxes at the ordinary income tax rate on the
difference between the sale price of $8,750 and the book value of $2,016. For a corporation
in the 21 percent bracket, the tax liability is .21 × $6,734 = $1,414.14.
The reason that taxes must be paid in this case is that the difference in market value
and book value is “excess” depreciation, and it must be “recaptured” when the asset is sold.
What this means is that, as it turns out, we overdepreciated the asset by $8,750 − 2,016 =
$6,734. Because we deducted $6,734 too much in depreciation, we paid $1,414.14 too little
in taxes, and we have to make up the difference.
Notice that this is not a tax on a capital gain. As a general (albeit rough) rule, a capital
gain only occurs if the market price exceeds the original cost. However, what is and what is
not a capital gain is ultimately up to taxing authorities, and the specific rules can be very
complex. We will ignore capital gains taxes for the most part.
Finally, if the book value exceeds the market value, then the difference is treated as a
loss for tax purposes. For example, if we sell the car after two years for $15,000, then the
book value exceeds the market value by $1,800. In this case, a tax savings of .21 × $1,800 =
$378 occurs.
Year Beginning Book Value Depreciation Ending Book Value
1 $35,000 $ 7,000 $28,000
2 928,000 11,200 16,800
3 16,800 6,720 10,080
4 10,080 4,032 6,048
5 96,048 4,032 2,016
6 92,016 2,016 0
MACRS book values
TABLE 9.8
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C H A P T E R 9 Making Capital Investment Decisions 287
An Example: The Majestic Mulch
and Compost Company (MMCC)
At this point, we want to go through a somewhat more involved capital budgeting analysis.
Keep in mind as you read that the basic approach here is exactly the same as that in our
earlier shark attractant example. We have only added some more “real-world” detail (and a
lot more numbers).
MMCC is investigating the feasibility of a new line of power mulching tools aimed at
the growing number of home composters. Based on exploratory conversations with buyers
for large garden shops, it projects unit sales as follows:
Year Unit Sales
1 3,000
2 5,000
3 6,000
4 6,500
5 6,000
6 5,000
7 4,000
8 3,000
The new power mulcher will be priced to sell at $120 per unit to start. When the competi-
tion catches up after three years, however, MMCC anticipates that the price will drop
to $110.
EXAMPLE 9.2 MACRS Depreciation
The Staple Supply Co. has just purchased a new computerized information system with an installed
cost of $160,000. The computer is treated as five-year property. What are the yearly depreciation
allowances? Based on historical experience, we think that the system will be worth only $10,000
when we get rid of it in four years. What are the tax consequences of the sale? What is the total
aftertax cash flow from the sale?
The yearly depreciation allowances are calculated by multiplying $160,000 by the five-year
percentages in Table 9.7:
Year MACRS Percentage Depreciation Ending Book Value
1 20.00% .2000 × $160,000 = $ 32,000 $128,000
2 32.00 .3200 × 160,000 = 51,200 76,800
3 19.20 .1920 × 160,000 = 30,720 46,080
4 11.52 .1152 × 160,000 = 18,432 27,648
5 11.52 .1152 × 160,000 = 18,432 9,216
6 5.76 .0576 × 160,000 = 9,216 0
100.00% $160,000
Notice that we also have computed the book value of the system as of the end of each year.
The book value at the end of Year 4 is $27,648. If we sell the system for $10,000 at that time, we will
have a loss of $17,648 (the difference) for tax purposes. This loss, of course, is like depreciation
because it isn’t a cash expense.
What really happens? Two things. First: We get $10,000 from the buyer. Second: We save .21 ×
$17,648 = $3,706 in taxes. So, the total aftertax cash flow from the sale is a $13,706 cash inflow.
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288 P A R T 5 Capital Budgeting
The power mulcher project will require $20,000 in net working capital at the start.
Subsequently, total net working capital at the end of each year will be about 15 percent
of sales for that year. The variable cost per unit is $60, and total fixed costs are $25,000
per year.
It will cost about $800,000 to buy the equipment necessary to begin production. This
investment is primarily in industrial equipment and thus qualifies as seven-year MACRS
property. The equipment actually will be worth about 20 percent of its cost in eight years, or
.20 × $800,000 = $160,000. The relevant tax rate is 21 percent, and the required return is
15 percent. Based on this information, should MMCC proceed?
Operating Cash Flows There is a lot of information here that we need to organize.
The first thing we can do is calculate projected sales. Sales in the first year are projected
at 3,000 units at $120 apiece, or $360,000 total. The remaining figures are shown in
Table 9.9.
Next, we compute the depreciation on the $800,000 investment in Table 9.10. With this
information, we can prepare the pro forma income statements, as shown in Table 9.11. From
here, computing the operating cash flows is straightforward. The results are illustrated in the
first part of Table 9.13.
Changes in NWC Now that we have the operating cash flows, we need to determine
the changes in NWC. By assumption, net working capital requirements change as sales
change. In each year, we generally will either add to or recover some of our project net work-
ing capital. Recalling that NWC starts out at $20,000 and then rises to 15 percent of sales,
we can calculate the amount of NWC for each year as illustrated in Table 9.12.
Year Unit Price Unit Sales Revenues
1 $120 3,000 $360,000
2 120 5,000 600,000
3 120 6,000 720,000
4 110 6,500 715,000
5 110 6,000 660,000
6 110 5,000 550,000
7 110 4,000 440,000
8 110 3,000 330,000
Projected revenues,
power mulcher
project
TABLE 9.9
Year MACRS Percentage Depreciation Ending Book Value
1 14.29% .1429 × $800,000 = $114,320 $685,680
2 24.49 .2449 × 800,000 = 195,920 489,760
3 17.49 .1749 × 800,000 = 139,920 349,840
4 12.49 .1249 × 800,000 = 99,920 249,920
5 8.93 .0893 × 800,000 = 71,440 178,480
6 8.92 .0892 × 800,000 = 71,360 107,120
7 8.93 .0893 × 800,000 = 71,440 35,680
8 4.46 .0446 × 800,000 = 35,680 0
100.00% 9 $800,000
Annual depreciation,
power mulcher
project
TABLE 9.10
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C H A P T E R 9 Making Capital Investment Decisions 289
Year
1 2 3 4 5 6 7 8
Unit price $ 120 $ 120 $ 120 $ 110 $ 110 $ 110 $ 110 $ 110
Unit sales 3,000 5,000 6,000 6,500 6,000 5,000 4,000 3,000
Revenues $360,000 $600,000 $720,000 $715,000 $660,000 $550,000 $440,000 $330,000
Variable costs 180,000 300,000 360,000 390,000 360,000 300,000 240,000 180,000
Fixed costs 25,000 25,000 25,000 25,000 25,000 25,000 25,000 25,000
Depreciation 114,320 195,920 139,920 99,920 71,440 71,360 71,440 35,680
EBIT $ 40,680 $ 79,080 $ 195,080 $200,080 $203,560 $153,640 $103,560 $ 89,320
Taxes (21%) 9 9 8,543 16,607 99 40,967 42,017 42,748 32,264 21,748 18,757
Net income $ 932,137 $9 9 62,473 $154,113 $ 158,063 $160,812 $121,376 $ 81,812 $ 70,563
Pro forma income statements, power mulcher projectTABLE 9.11
Year Revenues Net Working Capital Cash Flow
0 $ 20,000 −$20,000
1 $360,000 54,000 − 34,000
2 600,000 90,000 − 36,000
3 720,000 108,000 − 18,000
4 715,000 107,250 750
5 660,000 99,000 8,250
6 550,000 82,500 16,500
7 440,000 66,000 16,500
8 330,000 49,500 16,500
Changes in net
working capital,
power mulcher
project
TABLE 9.12
As illustrated, during the first year, net working capital grows from $20,000 to .15 ×
$360,000 = $54,000. The increase in net working capital for the year is thus $54,000 −
20,000 = $34,000. The remaining figures are calculated the same way.
Remember that an increase in net working capital is a cash outflow, so we use a nega-
tive sign in this table to indicate an additional investment that the firm makes in net working
capital. A positive sign represents net working capital returning to the firm. Thus, for exam-
ple, $16,500 in NWC flows back to the firm in Year 6. Over the project’s life, net working
capital builds to a peak of $108,000 and declines from there as sales begin to drop off.
We show the result for changes in net working capital in the second part of Table 9.13.
Notice that at the end of the project’s life, there is $49,500 in net working capital still to be
recovered. Therefore, in the last year, the project returns $16,500 of NWC during the year
and then returns the remaining $49,500 at the end of the year for a total of $66,000.
Capital Spending Finally, we have to account for the long-term capital invested in the
project. In this case, we invest $800,000 at Year 0. By assumption, this equipment will be
worth $160,000 at the end of the project. It will have a book value of zero at that time. As
we discussed above, this $160,000 excess of market value over book value is taxable, so the
aftertax proceeds will be $160,000 × (1 − .21) = $126,400. These figures are shown in the
third part of Table 9.13.
Total Cash Flow and Value We now have all the cash flow pieces, and we put them
together in Table 9.14. In addition to the total project cash flows, we have calculated the
ros13952_ch09_275-309.indd 289 12/24/18 5:00 PM
290
Year
0 1 2 3 4 5 6 7 8
I. Operating Cash Flow
EBIT $ 40,680 $ 79,080 $195,080 $200,080 $203,560 $153,640 $103,560 $ 89,320
Depreciation 114,320 195,920 139,920 99,920 71,440 71,360 71,440 35,680
Taxes − 8,543 − 16,607 − 40,967 − 42,017 − 42,748 − 32,264 − 21,748 − 18,757
Operating cash flow $146,457 $258,393 $294,033 $257,983 $232,252 $192,736 $153,252 $106,243
II. Net Working Capital
Initial NWC −$ 20,000
Increases in NWC −$ 34,000 −$ 36,000 −$ 18,000 $ 750 $ 8,250 $ 16,500 $ 16,500 $ 16,500
NWC recovery 49,500
Changes in NWC −$ 20,000 −$ 34,000 −$ 36,000 −$ 18,000 $ 750 $ 8,250 $ 16,500 $ 16,500 $ 66,000
III. Capital Spending
Initial outlay −$800,000
Aftertax salvage $126,400
Capital spending −$800,000 $126,400
Projected cash flows, power mulcher projectTABLE 9.13
Year
0 1 2 3 4 5 6 7 8
Operating cash flow $999146,457 $258,393 $294,033 $257,983 $232,252 $192,736 $153,252 $ 106,243
Changes in NWC −$ 20,000 − 34,000 − 36,000 − 18,000 750 8,250 16,500 16,500 66,000
Capital spending − 800,000 126,400
Total project cash flow −$820,000 $999112,457 $222,393 $276,033 $258,733 $240,502 $209,236 $169,752 $298,643
Cumulative cash flow −$820,000 −$707,543 −$485,150 −$209,116 $ 49,617 $290,119 $499,355 $669,107 $967,750
Net present value (15%) = $146,852
Internal rate of return = 19.86%
Payback = 3.81 years
Projected total cash flows, power mulcher projectTABLE 9.14
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12/24/18 5:00 P
M
C H A P T E R 9 Making Capital Investment Decisions 291
cumulative cash flows. At this point, it’s essentially plug-and-chug to calculate the net present
value, internal rate of return, and payback.
If we sum the discounted cash flows and the initial investment, the net present value (at
15 percent) works out to be $146,852. This is positive; so, based on these preliminary pro-
jections, the power mulcher project is acceptable. The internal, or DCF, rate of return is
greater than 15 percent because the NPV is positive. It works out to be 19.86 percent,
again indicating that the project is acceptable.
Looking at the cumulative cash flows, we see that the project has been paid back some-
where between three and four years because the cumulative cash flow is almost zero at that
time. As indicated, the fractional year works out to be $209,116/$258,733 = .81, so the
payback is 3.81 years. We can’t say whether or not this is good because we don’t have a
benchmark for MMCC. This is the usual problem with payback periods.
Conclusion
This completes our preliminary DCF analysis. Where do we go from here? If we have a
great deal of confidence in our projections, then there is no further analysis to be done. We
should begin production and marketing immediately. It is unlikely that this will be the case.
It is important to remember that the result of our analysis is an estimate of NPV, and we
usually will have less than complete confidence in our projections. This means we have
more work to do. In particular, we almost surely will want to spend some time evaluating the
quality of our estimates. We take up this subject in the next several sections.
CONCEPT QUESTIONS
9.4a Why is it important to consider changes in net working capital in developing cash
flows? What is the effect of doing so?
9.4b How is depreciation calculated for fixed assets under current tax law? What effect do
expected salvage value and estimated economic life have on the calculated
depreciation deduction?
EVALUATING NPV ESTIMATES
As we discussed in Chapter 8, an investment has a positive net present value if its market
value exceeds its cost. Such an investment is desirable because it creates value for its owner.
The primary problem in identifying such opportunities is that, most of the time, we can’t
actually observe the relevant market value. Instead, we estimate it. Having done so, it is only
natural to wonder whether or not our estimates are at least close to the true values. We con-
sider this question next.
The Basic Problem
Suppose we are working on a preliminary DCF analysis along the lines we described in
previous sections. We carefully identify the relevant cash flows, avoiding such things as sunk
costs, and we remember to consider working capital requirements. We add back any depre-
ciation, we account for possible erosion, and we pay attention to opportunity costs. Finally,
we double-check our calculations, and, when all is said and done, the bottom line is that the
estimated NPV is positive.
9.5
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Now what? Do we stop here and move on to the next proposal? Probably not. The fact
that the estimated NPV is positive is definitely a good sign, but, more than anything, this
tells us that we need to take a closer look.
If you think about it, there are two circumstances under which a discounted cash flow
analysis could lead us to conclude that a project has a positive NPV. The first possibility is
that the project really does have a positive NPV. That’s the good news. The bad news is the
second possibility: A project may appear to have a positive NPV because our estimate is
inaccurate.
Notice that we also could err in the opposite way. If we conclude that a project has a
negative NPV when the true NPV is positive, then we lose a valuable opportunity.
Forecasting Risk
The key inputs into a DCF analysis are projected future cash flows. If these projections are
seriously in error, then we have a classic GIGO, or garbage-in, garbage-out, system. In this
case, no matter how carefully we arrange the numbers and manipulate them, the resulting
answer still can be grossly misleading. This is the danger in using a relatively sophisticated
technique like DCF. It is sometimes easy to get caught up in number crunching and forget
the underlying nuts-and-bolts economic reality.
The possibility that we will make a bad decision because of errors in the projected
cash flows is called forecasting risk (or estimation risk). Because of forecasting risk, there
is the danger that we will think a project has a positive NPV when it really does not. How
is this possible? It occurs if we are overly optimistic about the future, and, as a result, our
projected cash flows don’t realistically reflect the possible future cash flows. Our nearby
Finance Matters box shows what can happen in such cases.
forecasting risk
The possibility that errors
in projected cash flows
will lead to incorrect
decisions. Also estimation
risk.
When Things Go Wrong . . .
If you think about it, the decision by a company to acquire another company is a capital budgeting decision. One im-
portant difference, however, is that an acquisition may be
more expensive than a typical project and, possibly, much
more expensive. Of course, as with any other project, acqui-
sitions can fail. When they do, the losses can be huge.
For example, in April 2014, Microsoft announced it was
acquiring Nokia for $7.2 billion. The acquisition of Nokia was
supposed to give Microsoft the hardware necessary to boost
the company’s mobile operating system. Of course, the ac-
quisition did not go as planned. In July 2015, Microsoft an-
nounced that it was writing off $7.6 billion due to the
acquisition, which was more than the acquisition price.
In another example, in early 2018, Teva Pharmeceutical
announced it would write off $17 billion in assets. Much of
the write-off was due to the company’s 2016 acquisition of
Allergan’s generic drug business. Teva spent $40 billion on
the acquisition but soon found it couldn’t charge as much as
expected for new generic drugs because of competition and
price pressure.
One of the largest acquisitions in U.S. history was
America Online’s (AOL’s) purchase of Time Warner in 2001.
AOL purchased Time Warner under the assumption that AOL
was part of the “new economy” and primed for fast growth.
Time Warner was the “old” communications company,
owning cable stations and a music label, among other
things. But things didn’t work as well as planned. Infighting
among employees from the two companies hurt production
and morale. In 2002, accounting irregularities were uncov-
ered at AOL, and, as a result of the acquisition costs,
the company was saddled with massive debt. To make mat-
ters worse, AOL began to lose customers and money.
Although AOL was the acquirer, and the once-dominant
partner, things got so bad at AOL that the company changed
its name back to Time Warner. To cap things off, in 2002,
Time Warner wrote off a stunning $54 billion in assets
associated with the acquisition, which was, at the time,
the largest such write-off in history. Finally, in 2016, Time
Warner was acquired by Charter Communications for about
$79 billion.
FINANCE MATTERS
292
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C H A P T E R 9 Making Capital Investment Decisions 293
So far, we have not explicitly considered what to do about the possibility of errors in
our forecasts, so our goal is to develop some tools that will be useful in identifying areas
where potential errors exist and where they might be especially damaging. In one form or
another, we will be trying to assess the economic “reasonableness” of our estimates. We
also will be wondering how much damage will be done by errors in those estimates.
Sources of Value
The first line of defense against forecasting risk is to ask: What is it about this investment
that leads to a positive NPV? We should be able to point to something specific as the source
of value. For example, if the proposal under consideration involved a new product, then we
might ask questions such as the following: Are we certain that our new product is signifi-
cantly better than that of the competition? Can we truly manufacture at lower cost, or dis-
tribute more effectively, or identify undeveloped market niches, or gain control of a
market?
These are just a few of the potential sources of value. There are many others. A key fac-
tor to keep in mind is the degree of competition in the market. It is a basic principle of
economics that positive NPV investments will be rare in a highly competitive environment.
Therefore, proposals that appear to show significant value in the face of stiff competition
are particularly troublesome, and the likely reaction of the competition to any innovations
must be closely examined.
The point to remember is that positive NPV investments are probably not all that com-
mon, and the number of positive NPV projects is almost certainly limited for any given firm.
If we can’t articulate some sound economic basis for thinking ahead of time that we have
found something special, then the conclusion that our project has a positive NPV should be
viewed with some suspicion.
CONCEPT QUESTIONS
9.5a What is forecasting risk? Why is it a concern for the financial manager?
9.5b What are some potential sources of value in a new project?
SCENARIO AND OTHER WHAT-IF ANALYSES
Our basic approach to evaluating cash flow and NPV estimates involves asking what-if ques-
tions. Accordingly, we discuss some organized ways of going about a what-if analysis. Our
goal in doing so is to assess the degree of forecasting risk and to identify those components
most critical to the success or failure of an investment.
Getting Started
We are investigating a new project. Naturally, the first thing we do is estimate NPV based on
our projected cash flows. We will call this the base case. Now, however, we recognize the
possibility of error in those cash flow projections. After completing the base case, we thus
wish to investigate the impact of different assumptions about the future on our estimates.
One way to organize this investigation is to put an upper and lower bound on the various
components of the project. Suppose we forecast sales at 100 units per year. We know this
estimate may be high or low, but we are relatively certain it is not off by more than 10 units
9.6
coverage online
Excel
Master
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294 P A R T 5 Capital Budgeting
in either direction. We thus would pick a lower bound of 90 and an upper bound of 110.
We go on to assign such bounds to any other cash flow components we are unsure about.
When we pick these upper and lower bounds, we are not ruling out the possibility that
the actual values could be outside this range. What we are saying, loosely speaking, is that it
is unlikely that the true average (as opposed to our estimated average) of the possible values
is outside this range.
An example is useful to illustrate the idea here. The project under consideration costs
$200,000, has a five-year life, and has no salvage value. Depreciation is straight-line to zero.
The required return is 12 percent, and the tax rate is 21 percent. In addition, we have com-
piled the following information:
Base Case Lower Bound Upper Bound
Unit sales 6,000 5,500 6,500
Price per unit $80 $75 $85
Variable cost per unit $60 $58 $62
Fixed costs per year $50,000 $45,000 $55,000
With this information, we can calculate the base-case NPV by first calculating net
income:
Sales $480,000
Variable costs 360,000
Fixed costs 50,000
Depreciation 40,000
EBIT $ 30,000
Taxes (21%) 6,300
Net income $ 23,700
Operating cash flow is thus $30,000 + 40,000 − 6,300 = $63,700 per year. At 12 percent,
the five-year annuity factor is 3.6048, so the base-case NPV is:
Base-case NPV = −$200,000 + 63,700 × 3.6048
= $29,624
Thus, the project looks good so far.
Scenario Analysis
The basic form of what-if analysis is called scenario analysis. What we do is investigate the
changes in our NPV estimates that result from asking questions like: “What if unit sales
realistically should be projected at 5,500 units instead of 6,000?”
Once we start looking at alternative scenarios, we might find that most of the plausible
ones result in positive NPVs. In this case, we have some confidence in proceeding with the
project. If a substantial percentage of the scenarios look bad, then the degree of forecasting
risk is high and further investigation is in order.
There are a number of possible scenarios we could consider. A good place to start is
with the worst-case scenario. This will tell us the minimum NPV of the project. If this is
positive, we will be in good shape. While we are at it, we will go ahead and determine the
other extreme, the best case. This puts an upper bound on our NPV.
To get the worst case, we assign the least favorable value to each item. This means low
values for items such as units sold and price per unit and high values for costs. We do the
reverse for the best case. For our project, these values would be:
scenario analysis
The determination of what
happens to net present
value estimates when we
ask what-if questions.
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C H A P T E R 9 Making Capital Investment Decisions 295
Worst Case Best Case
Unit sales 5,500 6,500
Price per unit $75 $85
Variable cost per unit $62 $58
Fixed costs $55,000 $45,000
With this information, we can calculate the net income and cash flows under each
scenario (check these for yourself):
Scenario Net Income Cash Flow Net Present Value IRR
Base case $23,700 $63,700 $ 29,624 17.8%
Worst case* − 18,565 21,435 − 122,732 −17.7
Best case 71,495 111,495 201,915 47.9
* We assume a tax credit is created in our worst-case scenario.
What we learn is that under the worst scenario, the cash flow is still positive at $21,435.
That’s good news. The bad news is that the return is −17.7 percent in this case, and the
NPV is −$122,732. Because the project costs $200,000, we stand to lose more than half of
the original investment under the worst possible scenario. The best case offers an attractive
47.9 percent return.
The terms best case and worst case are very commonly used, and we will stick with
them, but we should note that they are somewhat misleading. The absolute best thing
that could happen would be something absurdly unlikely, such as launching a new diet
soda and subsequently learning that our (patented) formulation also happens to cure
the common cold. Of course, on rare occasions, things do go very, very wrong. For
example, in April 2010, BP’s Gulf of Mexico oil rig Deepwater Horizon caught fire and
sank following an explosion, leading to a massive oil spill. The leak was finally stopped
in July after releasing more than 200 million gallons of crude oil into the Gulf. In 2018,
BP took a charge of $1.7 billion related to closing claims from the accident, raising the
total costs associated with the disaster to about $65 billion, not including opportunity
costs such as lost government contracts. And the company noted that there were
numerous claims yet to be settled. Nonetheless, our point is that in assessing the rea-
sonableness of an NPV estimate, we need to stick to cases that are reasonably likely
to occur.
Instead of best and worst, then, it is probably more accurate to say optimistic and pessi-
mistic. In broad terms, if we were thinking about a reasonable range for, say, unit sales, then
what we call the best case would correspond to something near the upper end of that range.
The worst case would correspond to the lower end.
As we have mentioned, there are an unlimited number of different scenarios that we
could examine. At a minimum, we might want to investigate two intermediate cases by going
halfway between the base amounts and the extreme amounts. This would give us five sce-
narios in all, including the base case.
Beyond this point, it is hard to know when to stop. As we generate more and more pos-
sibilities, we run the risk of “paralysis of analysis.” The difficulty is that no matter how many
scenarios we run, all we can learn are possibilities, some good and some bad. Beyond that,
we don’t get any guidance as to what to do. Scenario analysis is thus useful in telling us what
can happen and in helping us gauge the potential for disaster, but it does not tell us whether
or not to take the project.
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296 P A R T 5 Capital Budgeting
Sensitivity Analysis
Sensitivity analysis is a variation on scenario analysis that is useful in pinpointing the areas
where forecasting risk is especially severe. The basic idea with a sensitivity analysis is to
freeze all of the variables except one and then see how sensitive our estimate of NPV is to
changes in that one variable. If our NPV estimate turns out to be very sensitive to relatively
small changes in the projected value of some component of project cash flow, then the fore-
casting risk associated with that variable is high.
To illustrate how sensitivity analysis works, we go back to our base case for every item
except unit sales. We then can calculate cash flow and NPV using the largest and smallest
unit sales figures.
Scenario Unit Sales Cash Flow Net Present Value IRR
Base case 6,000 $63,700 $29,624 17.8%
Worst case 5,500 55,800 1,147 12.2
Best case 6,500 71,600 58,102 23.2
The results of our sensitivity analysis for unit sales can be illustrated graphically as in
Figure 9.1. Here we place NPV on the vertical axis and unit sales on the horizontal axis.
When we plot the combinations of unit sales versus NPV, we see that all possible combina-
tions fall on a straight line. The steeper the resulting line is, the greater is the sensitivity of
the estimated NPV to the projected value of the variable being investigated.
By way of comparison, we now freeze everything except fixed costs and repeat the
analysis:
Scenario Fixed Costs Cash Flow Net Present Value IRR
Base case $50,000 $63,700 $29,624 17.8%
Worst case 55,000 59,750 15,385 15.1
Best case 45,000 67,650 43,863 20.5
sensitivity analysis
Investigation of what
happens to net present
value when only one
variable is changed.
50
60
40
30
20
10
0
(Worst
case)
(Base
case)
6,000
(Best
case)
6,5005,500
NPV = $1,147
NPV = $29,624
NPV = $58,102
Net present
value ($000)
Unit
sales
FIGURE 9.1
Sensitivity analysis
for unit sales
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C H A P T E R 9 Making Capital Investment Decisions 297
What we see here is that, given our ranges, the estimated NPV of this project is more sensi-
tive to projected unit sales than it is to projected fixed costs. In fact, under the worst case for
fixed costs, the NPV is still positive.
As we have illustrated, sensitivity analysis is useful in pinpointing those variables that
deserve the most attention. If we find that our estimated NPV is especially sensitive to a
variable that is difficult to forecast (such as unit sales), then the degree of forecasting risk is
high. We might decide that further market research would be a good idea in this case.
Because sensitivity analysis is a form of scenario analysis, it suffers from the same draw-
backs. Sensitivity analysis is useful for pointing out where forecasting errors will do the most
damage, but it does not tell us what to do about possible errors.
CONCEPT QUESTIONS
9.6a What are scenario and sensitivity analyses?
9.6b What are the drawbacks to what-if analyses?
ADDITIONAL CONSIDERATIONS
IN CAPITAL BUDGETING
Our final task for this chapter is a brief discussion of two additional considerations in capi-
tal budgeting: managerial options and capital rationing. Both of these can be very important
in practice, but, as we will see, explicitly dealing with either of them is difficult.
Managerial Options and Capital Budgeting
In our capital budgeting analysis thus far, we have more or less ignored the possibility of
future managerial actions. Implicitly, we have assumed that once a project is launched,
its basic features cannot be changed. For this reason, we say that our analysis is static
(as opposed to dynamic).
In reality, depending on what actually happens in the future, there always will be ways
to modify a project. We will call these opportunities managerial options. Because they
involve real (as opposed to financial) assets, such options are often called “real” options.
There are a great number of these options. The way a product is priced, manufactured,
advertised, and produced all can be changed, and these are just a few of the possibilities. We
discuss some of the most important managerial options in the next few sections.
Contingency Planning The various what-if procedures in this chapter have another
use. We also can view them as primitive ways of exploring the dynamics of a project and
investigating managerial options. What we think about in this case are some of the possible
futures that could come about and what actions we might take if they do.
For example, we might find that a project fails to break even when sales drop below
10,000 units. This is a fact that is interesting to know, but the more important thing is
then to go on and ask, “What actions are we going to take if this actually occurs?” This is
called contingency planning, and it amounts to an investigation of some of the managerial
options implicit in a project.
There is no limit to the number of possible futures, or contingencies, that we could in-
vestigate. However, there are some broad classes, and we consider these next.
9.7
managerial options
Opportunities that
managers can exploit if
certain things happen in
the future. Also known as
“real” options.
contingency
planning
Taking into account the
managerial options
implicit in a project.
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298 P A R T 5 Capital Budgeting
The Option to Expand One particularly important option we have not explicitly addressed
is the option to expand. If we truly find a positive NPV project, then there is an obvious
consideration: Can we expand the project or repeat it to get an even larger NPV? Our static
analysis implicitly assumes that the scale of the project is fixed.
For example, if the sales demand for a particular product were to greatly exceed expec-
tations, we might investigate increasing production. If this were not feasible for some rea-
son, then we could always increase cash flow by raising the price. Either way, the potential
cash flow is higher than we have indicated because we have implicitly assumed that no
expansion or price increase is possible. Overall, because we ignore the option to expand in
our analysis, we underestimate NPV (all other things being equal).
The Option to Abandon At the other extreme, the option to scale back or even abandon a
project is also quite valuable. For example, if a project does not even cover its own expenses,
we might be better off if we abandoned it. Our DCF analysis implicitly assumes that we
would keep operating even in this case.
In reality, if sales demand were significantly below expectations, we might be able to
sell off some capacity or put it to another use. Maybe the product or service could be rede-
signed or otherwise improved. Regardless of the specifics, we once again underestimate NPV
if we assume that the project must last for some fixed number of years, no matter what hap-
pens in the future.
The Option to Wait Implicitly, we have treated proposed investments as if they were “go or
no-go” decisions. Actually, there is a third possibility. The project can be postponed, perhaps
in hope of more favorable conditions. We call this the option to wait.
For example, suppose an investment costs $120 and has a perpetual cash flow of $10
per year. If the discount rate is 10 percent, then the NPV is $10/.10 − $120 = −$20, so the
project should not be undertaken now. However, this does not mean that we should forget
about the project forever because in the next period, the appropriate discount rate could be
different. If it fell to, say, 5 percent, then the NPV would be $10/.05 − $120 = $80, and we
would take the project.
More generally, as long as there is some possible future scenario under which a project
has a positive NPV, then the option to wait is valuable.
To illustrate some of these ideas, consider the case of Euro Disney (known today as
Disneyland Paris). The deal to open Euro Disney occurred in 1987, and the park opened its
doors outside of Paris in 1992. Disney’s management thought Europeans would go goofy
over the new park, but trouble soon began. The number of visitors never met expectations,
in part because the company priced tickets too high. Disney also decided not to serve alco-
hol in a country that was accustomed to wine with meals. French labor inspectors fought
Disney’s strict dress codes, and so on.
After several years of operations, the park began serving wine in its restaurants, lowered
ticket prices, and made other adjustments. In other words, management exercised its option
to reformulate the product. The park began to make a small profit. Then, the company exer-
cised the option to expand by adding a “second gate,” which was another theme park next
to Euro Disney named Walt Disney Studios. The second gate was intended to encourage
visitors to extend their stays. But the new park flopped. The reasons ranged from high ticket
prices, attractions geared toward Hollywood rather than European filmmaking, labor strikes
in Paris, and a summer heat wave.
By the summer of 2003, Euro Disney was close to bankruptcy again. Executives
discussed a variety of options. These options ranged from letting the company go broke
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C H A P T E R 9 Making Capital Investment Decisions 299
(the option to abandon) to pulling the Disney name from the park. In 2005, the company
finally agreed to a restructuring with the help of the French government.
After all the changes made at Euro Disney, the park gained momentum for several
years, almost breaking even in 2008. In 2017, the resort posted revenues of $6.5 billion and
a net income of $1.8 billion. And then, in 2018, Walt Disney announced plans to invest
€2 billion in Disneyland Paris.
Disney hopes to leverage the lessons learned in its other theme parks around the world.
For example, in 2014, Hong Kong Disneyland had a total of 7.5 million visitors for the year,
resulting in a record revenue of $5.5 billion and a record net income of $332 million. And
in April 2011, the groundbreaking occurred on a new $4.4 billion theme park in Shanghai
that opened in the spring of 2016.
The whole idea of managerial options was summed up aptly by Jay Rasulo, the overseer
of Disney’s theme parks, when he said: “One thing we know for sure is that you never get it
100 percent right the first time. We open every one of our parks with the notion that we’re
going to add content.”
Strategic Options Companies sometimes undertake new projects just to explore pos-
sibilities and evaluate potential future business strategies. This is a little like testing the water
by sticking a toe in before diving. Such projects are difficult to analyze using conventional
DCF methods because most of the benefits come in the form of strategic options, that is,
options for future, related business moves. Projects that create such options may be very
valuable, but that value is difficult to measure. Research and development, for example, is
an important and valuable activity for many firms precisely because it creates options for
new products and procedures.
To give another example, a large manufacturer might decide to open a retail outlet as a
pilot study. The primary goal is to gain some market insight. Because of the high start-up
costs, this one operation won’t break even. However, based on the sales experience from the
pilot, we can then evaluate whether or not to open more outlets, change the product mix,
enter new markets, and so on. The information gained and the resulting options for actions
are all valuable, but coming up with a reliable dollar figure is probably not feasible.
Conclusion We have seen that incorporating options into capital budgeting analysis is
not easy. What can we do about them in practice? The answer is that we can only keep them
in the back of our minds as we work with the projected cash flows. We will tend to underes-
timate NPV by ignoring options. The damage might be small for a highly structured, very
specific proposal, but it might be great for an exploratory one.
Capital Rationing
Capital rationing is said to exist when we have profitable (positive NPV) investments avail-
able but we can’t get the needed funds to undertake them. For example, as division manag-
ers for a large corporation, we might identify $5 million in excellent projects but find that,
for whatever reason, we can spend only $2 million. Now what? Unfortunately, for reasons
we will discuss, there may be no truly satisfactory answer.
Soft Rationing The situation we have just described is soft rationing. This occurs when,
for example, different units in a business are allocated some fixed amount of money each year
for capital spending. Such an allocation is primarily a means of controlling and keeping track
of overall spending. The important thing about soft rationing is that the corporation as a
whole isn’t short of capital; more can be raised on ordinary terms if management so desires.
strategic options
Options for future, related
business products or
strategies.
capital rationing
The situation that exists if
a firm has positive net
present value projects but
cannot obtain the
necessary financing.
soft rationing
The situation that occurs
when units in a business
are allocated a certain
amount of financing for
capital budgeting.
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300 P A R T 5 Capital Budgeting
If we face soft rationing, the first thing to do is try and get a larger allocation. Failing
that, one common suggestion is to generate as large a net present value as possible within
the existing budget. This amounts to choosing those projects with the largest benefit-cost
ratio (profitability index).
Strictly speaking, this is the correct thing to do only if the soft rationing is a one-time
event; that is, it won’t exist next year. If the soft rationing is a chronic problem, then some-
thing is amiss. The reason goes all the way back to Chapter 1. Ongoing soft rationing means
we are constantly bypassing positive NPV investments. This contradicts our goal of the
firm. If we are not trying to maximize value, then the question of which projects to take be-
comes ambiguous because we no longer have an objective goal in the first place.
Hard Rationing With hard rationing, a business cannot raise capital for a project un-
der any circumstances. For large, healthy corporations, this situation probably does not oc-
cur very often. This is fortunate because with hard rationing, our DCF analysis breaks
down, and the best course of action is ambiguous.
The reason DCF analysis breaks down has to do with the required return. Suppose we
say that our required return is 20 percent. Implicitly, we are saying that we will take a project
with a return that exceeds this. However, if we face hard rationing, then we are not going to
take a new project no matter what the return on that project is, so the whole concept of a
required return is ambiguous. About the only interpretation we can give this situation is that
the required return is so large that no project has a positive NPV in the first place.
Hard rationing can occur when a company experiences financial distress, meaning that
bankruptcy is a possibility. Also, a firm may not be able to raise capital without violating a pre-
existing contractual agreement. We discuss these situations in greater detail in a later chapter.
CONCEPT QUESTIONS
9.7a Why do we say that our standard discounted cash flow analysis is static?
9.7b What are managerial options in capital budgeting? Give some examples.
9.7c What is capital rationing? What types are there? What problems does capital
rationing create for discounted cash flow analysis?
hard rationing
The situation that occurs
when a business cannot
raise financing for a
project under any
circumstances.
SUMMARY AND CONCLUSIONS
This chapter has described how to go about putting together a discounted cash flow analysis
and evaluating the results. In it, we covered:
1. The identification of relevant project cash flows. We discussed project cash flows and
described how to handle some issues that often come up, including sunk costs,
opportunity costs, financing costs, net working capital, and erosion.
2. Preparing and using pro forma, or projected, financial statements. We showed how
pro forma financial statement information is useful in coming up with projected cash
flows.
3. The use of scenario and sensitivity analysis. These tools are widely used to evaluate
the impact of assumptions made about future cash flows and NPV estimates.
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C H A P T E R 9 Making Capital Investment Decisions 301
4. Additional issues in capital budgeting. We examined the managerial options implicit
in many capital budgeting situations. We also discussed the capital rationing
problem.
The discounted cash flow analysis we’ve covered here is a standard tool in the business
world. It is a very powerful tool, so care should be taken in its use. The most important thing
is to get the cash flows identified in a way that makes economic sense. This chapter gives
you a good start on learning to do this.
POP QUIZ!
Can you answer the following questions? If your class is using Connect, log on to
SmartBook to see if you know the answers to these and other questions, check out
the study tools, and find out what topics require additional practice!
Section 9.1 What is the first step in estimating cash flow?
Section 9.2 What are sunk costs?
Section 9.3 What investment criteria can be applied to estimated cash flows?
Section 9.4 If a firm’s current assets are $150,000, its total assets are $320,000,
and its current liabilities are $80,000, what is its net working capital?
Section 9.5 A project has a positive NPV. What could drive this result?
Section 9.6 If a firm’s variable cost per unit estimate used in its base case analysis
is $50 per unit and it anticipates the upper and lower bounds to be ±10 percent,
what is the “worst case” for variable cost per unit?
Section 9.7 Capital rationing exists when a company has identified positive NPV
projects but can’t or won’t find what?
CHAPTER REVIEW AND SELF-TEST PROBLEMS
9.1 Calculating Operating Cash Flow Mater Pasta, Inc., has projected a sales
volume of $1,432 for the second year of a proposed expansion project. Costs
normally run 70 percent of sales, or about $1,002 in this case. The depreciation
expense will be $80, and the tax rate is 22 percent. What is the operating cash
flow? (See Problem 9.)
9.2 Scenario Analysis A project under consideration costs $500,000, has a five-year
life, and has no salvage value. Depreciation is straight-line to zero. The required
return is 15 percent, and the tax rate is 21 percent. Sales are projected at 400
units per year. Price per unit is $3,000, variable cost per unit is $1,900, and fixed
costs are $250,000 per year. No net working capital is required.
Suppose you think the unit sales, price, variable cost, and fixed cost projections
are accurate to within 5 percent. What are the upper and lower bounds for these pro-
jections? What is the base-case NPV? What are the best- and worst-case scenario
NPVs? (See Problem 21.)
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302 P A R T 5 Capital Budgeting
■ Answers to Chapter Review and Self-Test Problems
9.1 First, we can calculate the project’s EBIT, its tax bill, and its net income.
EBIT = $1,432 − 1,002 − 80 = $350
Taxes = $350 × .22 = $77
Net income = $350 − 77 = $273
With these numbers, operating cash flow is:
OCF = EBIT + Depreciation − Taxes
= $350 + 80 − 77
= $353
9.2 We can summarize the relevant information as follows:
Base Case Lower Bound Upper Bound
Unit sales 400 380 420
Price per unit $3,000 $2,850 $3,150
Variable cost per unit $1,900 $1,805 $1,995
Fixed costs $250,000 $237,500 $262,500
The depreciation is $100,000 per year, and the tax rate is 21 percent, so we can
calculate the cash flows under each scenario. Remember that we assign high costs
and low prices and volume under the worst case and the opposite for the best case.
Scenario Unit Sales Price Variable Costs Fixed Costs Cash Flow
Base case 400 $3,000 $1,900 $250,000 $171,100
Best case 420 3,150 1,805 237,500 279,646
Worst case 380 2,850 1,995 262,500 70,296
At 15 percent, the five-year annuity factor is 3.35216, so the NPVs are:
Base-case NPV = −$500,000 + 171,100 × 3.35216 = $73,554
Best-case NPV = −$500,000 + 279,646 × 3.35216 = $437,417
Worst-case NPV = −$500,000 + 70,296 × 3.35216 = −$264,357
CRITICAL THINKING AND CONCEPTS REVIEW
LO 1 9.1 Opportunity Cost In the context of capital budgeting, what is an
opportunity cost?
LO 1 9.2 Depreciation Given the choice, would a firm prefer to use MACRS
depreciation or straight-line depreciation? Why?
LO 1 9.3 Net Working Capital In our capital budgeting examples, we assumed that
a firm would recover all of the working capital it invested in a project. Is
this a reasonable assumption? When might it not be valid?
LO 1 9.4 Stand-Alone Principle Suppose a financial manager is quoted as saying,
“Our firm uses the stand-alone principle. Because we treat projects like
minifirms in our evaluation process, we include financing costs because
they are relevant at the firm level.” Critically evaluate this statement.
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C H A P T E R 9 Making Capital Investment Decisions 303
LO 1 9.5 Cash Flow and Depreciation “When evaluating projects, we’re only
concerned with the relevant incremental aftertax cash flows. Therefore,
because depreciation is a noncash expense, we should ignore its effects
when evaluating projects.” Critically evaluate this statement.
LO 1 9.6 Capital Budgeting Considerations A major college textbook publisher
has an existing finance textbook. The publisher is debating whether or not
to produce an “essentialized” version, meaning a shorter (and lower-priced)
book. What are some of the considerations that should come into play?
To answer the next three questions, refer to the following example. In 2003, Porsche un-
veiled its new sports-utility vehicle (SUV), the Cayenne. With a price tag of more than
$40,000, the Cayenne went from zero to 62 mph in 9.7 seconds. Porsche’s decision to
enter the SUV market was in response to the runaway success of other high-priced SUVs
such as the Mercedes-Benz M-class. Vehicles in this class had generated years of very
high profits. The Cayenne certainly spiced up the market, and Porsche subsequently in-
troduced the Cayenne Turbo S, which goes from zero to 60 mph in 4.8 seconds and has a
top speed of 168 mph. The price tag for the Cayenne Turbo S? The price started at
$124,600 in 2018.
Some analysts questioned Porsche’s entry into the luxury SUV market. The analysts
were concerned not only that Porsche was a late entry into the market, but also that the
introduction of the Cayenne would damage Porsche’s reputation as a maker of high-
performance automobiles.
LO 1 9.7 Erosion In evaluating the Cayenne, would you consider the possible
damage to Porsche’s reputation?
LO 1 9.8 Capital Budgeting Porsche was one of the last manufacturers to enter the
sports-utility vehicle market. Why would one company decide to proceed
with a product when other companies, at least initially, decide not to enter
the market?
LO 1 9.9 Capital Budgeting In evaluating the Cayenne, what do you think Porsche
needs to assume regarding the substantial profit margins that exist in this
market? Is it likely they will be maintained as the market becomes more
competitive, or will Porsche be able to maintain the profit margin because
of its image and the performance of the Cayenne?
LO 2 9.10 Sensitivity Analysis and Scenario Analysis What is the essential
difference between sensitivity analysis and scenario analysis?
LO 1 9.11 Marginal Cash Flows A co-worker claims that looking at all this marginal
this and incremental that is a bunch of nonsense and states: “Listen, if our
average revenue doesn’t exceed our average cost, then we will have a
negative cash flow, and we will go broke!” How do you respond?
LO 1 9.12 Capital Rationing Going all the way back to Chapter 1, recall that we saw
that partnerships and proprietorships can face difficulties when it comes to
raising capital. In the context of this chapter, the implication is that small
businesses will generally face what problem?
LO 2 9.13 Forecasting Risk What is forecasting risk? In general, would the degree of
forecasting risk be greater for a new product or a cost-cutting proposal?
Why?
LO 2 9.14 Options and NPV What is the option to abandon? The option to expand?
Explain why we tend to underestimate NPV when we ignore these options.
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304 P A R T 5 Capital Budgeting
BASIC (Questions 1–22)
1. Relevant Cash Flows Kenny, Inc., is looking at setting up a new
manufacturing plant in South Park. The company bought some land six
years ago for $5.3 million in anticipation of using it as a warehouse and
distribution site, but the company has since decided to rent facilities
elsewhere. The land would net $7.7 million if it were sold today. The
company now wants to build its new manufacturing plant on this land; the
plant will cost $29.3 million to build, and the site requires $1.41 million
worth of grading before it is suitable for construction. What is the proper
cash flow amount to use as the initial investment in fixed assets when
evaluating this project? Why?
2. Relevant Cash Flows Winnebagel Corp. currently sells 28,000 motor
homes per year at $84,000 each and 7,000 luxury motor coaches per year
at $135,000 each. The company wants to introduce a new portable camper
to fill out its product line; it hopes to sell 29,000 of these campers per year
at $24,700 each. An independent consultant has determined that if the
company introduces the new campers, it could boost the sales of its existing
motor homes by 2,500 units per year and reduce the sales of its motor
coaches by 750 units per year. What is the amount to use as the annual sales
figure when evaluating this project? Why?
3. Calculating Projected Net Income A proposed new investment has projected
sales of $635,000. Variable costs are 40 percent of sales, and fixed costs are
$168,000; depreciation is $83,000. Prepare a pro forma income statement
assuming a tax rate of 23 percent. What is the projected net income?
4. Calculating OCF Consider the following income statement:
Sales $537,200
Costs 346,800
Depreciation 94,500
EBIT
Taxes (21%)
Net income
Fill in the missing numbers and then calculate the OCF. What is the depreci-
ation tax shield?
5. Calculating Depreciation A piece of newly purchased industrial equipment
costs $745,000 and is classified as seven-year property under MACRS.
Calculate the annual depreciation allowances and end-of-the-year book values
for this equipment.
6. Calculating Salvage Value Consider an asset that costs $635,000 and is
depreciated straight-line to zero over its eight-year tax life. The asset is to be
used in a five-year project; at the end of the project, the asset can be sold for
$105,000. If the relevant tax rate is 22 percent, what is the aftertax cash flow
from the sale of this asset?
LO 1
LO 1
LO 2
LO 2
?
?
?
LO 2
LO 2
QUESTIONS AND PROBLEMS
Select problems are available in McGraw-Hill Connect. Please see the pack-
aging options section of the Preface for more information.
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C H A P T E R 9 Making Capital Investment Decisions 305
7. Calculating Salvage Value An asset used in a four-year project falls in the
five-year MACRS class for tax purposes. The asset has an acquisition cost of
$6.8 million and will be sold for $1.46 million at the end of the project. If the
tax rate is 23 percent, what is the aftertax salvage value of the asset?
8. Calculating Project OCF Cusic Music Company is considering the sale
of a new sound board used in recording studios. The new board would sell
for $26,400, and the company expects to sell 1,500 per year. The company
currently sells 1,850 units of its existing model per year. If the new model
is introduced, sales of the existing model will fall to 1,520 units per year.
The old board retails for $24,900. Variable costs are 55 percent of sales,
depreciation on the equipment to produce the new board will be $1.875
million per year, and fixed costs are $2.9 million per year. If the tax rate is
22 percent, what is the annual OCF for the project?
9. Calculating Project OCF H. Cochran, Inc., is considering a new three-year
expansion project that requires an initial fixed asset investment of $2.15
million. The fixed asset will be depreciated straight-line to zero over its three-
year tax life, after which time it will be worthless. The project is estimated to
generate $2.23 million in annual sales, with costs of $1.25 million. If the tax
rate is 23 percent, what is the OCF for this project?
10. Calculating Project NPV In the previous problem, suppose the required
return on the project is 14 percent. What is the project’s NPV?
11. Calculating Project Cash Flow from Assets In the previous problem,
suppose the project requires an initial investment in net working capital of
$150,000, and the fixed asset will have a market value of $185,000 at the end
of the project. What is the project’s Year 0 net cash flow? Year 1? Year 2?
Year 3? What is the new NPV?
12. NPV and Modified ACRS In the previous problem, suppose the fixed asset
actually falls into the three-year MACRS class. All the other facts are the
same. What is the project’s Year 1 net cash flow now? Year 2? Year 3? What
is the new NPV?
13. NPV and Bonus Depreciation In the previous problem, suppose the fixed
asset actually qualifies for 100 percent bonus depreciation. All the other facts
are the same. What is the project’s Year 1 net cash flow now? Year 2? Year
3? What is the new NPV?
14. Project Evaluation Kolby’s Korndogs is looking at a new sausage system
with an installed cost of $655,000. This cost will be depreciated straight-
line to zero over the project’s five-year life, at the end of which the sausage
system can be scrapped for $85,000. The sausage system will save the firm
$183,000 per year in pretax operating costs, and the system requires an initial
investment in net working capital of $35,000. If the tax rate is 22 percent and
the discount rate is 8 percent, what is the NPV of this project?
15. NPV and Bonus Depreciation In the previous problem, suppose the fixed
asset actually qualifies for 100 percent bonus depreciation. All the other facts
are the same. What is the new NPV?
16. Project Evaluation Your firm is contemplating the purchase of a new
$395,000 computer-based order entry system. The system will be depreciated
straight-line to zero over its five-year life. It will be worth $30,000 at the end
of that time. You will save $125,000 before taxes per year in order processing
costs, and you will be able to reduce working capital by $35,000 at the
LO 2
LO 2
LO 2
LO 2
LO 2
LO 2
LO 2
LO 2
LO 2
LO 2
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306 P A R T 5 Capital Budgeting
beginning of the project. Working capital will revert back to normal at the end
of the project. If the tax rate is 21 percent, what is the IRR for this project?
17. Project Evaluation In the previous problem, suppose your required return
on the project is 10 percent and your pretax cost savings are $135,000 per
year. Will you accept the project? What if the pretax cost savings are only
$95,000 per year?
18. Scenario Analysis Automatic Transmissions, Inc., has the following estimates
for its new gear assembly project: price = $940 per unit; variable cost = $340
per unit; fixed costs = $3.4 million; quantity = 53,000 units. Suppose the
company believes all of its estimates are accurate only to within ±15 percent.
What values should the company use for the four variables given here when it
performs its best-case scenario analysis? What about the worst-case scenario?
19. Sensitivity Analysis For the company in the previous problem, suppose
management is most concerned about the impact of its price estimate on the
project’s profitability. How could you address this concern for Automatic
Transmissions? Describe how you would calculate your answer. What values
would you use for the other forecast variables?
20. Sensitivity Analysis We are evaluating a project that costs $1.68 million,
has a six-year life, and has no salvage value. Assume that depreciation is
straight-line to zero over the life of the project. Sales are projected at 90,000
units per year. Price per unit is $37.95, variable cost per unit is $23.20, and
fixed costs are $815,000 per year. The tax rate is 21 percent, and we require a
return of 11 percent on this project.
a. Calculate the base-case cash flow and NPV. What is the sensitivity of
NPV to changes in the sales figure? Explain what your answer tells you
about a 500-unit decrease in projected sales.
b. What is the sensitivity of OCF to changes in the variable cost figure?
Explain what your answer tells you about a $1 decrease in estimated
variable costs.
21. Scenario Analysis In the previous problem, suppose the projections given
for price, quantity, variable costs, and fixed costs are all accurate to within
±10 percent. Calculate the best-case and worst-case NPV figures.
22. Calculating Project Cash Flows and NPV Pappy’s Potato has come up with
a new product, the Potato Pet (they are freeze-dried to last longer). Pappy’s
paid $120,000 for a marketing survey to determine the viability of the
product. It is felt that Potato Pet will generate sales of $835,000 per year. The
fixed costs associated with this will be $204,000 per year, and variable costs
will amount to 20 percent of sales. The equipment necessary for production
of the Potato Pet will cost $865,000 and will be depreciated in a straight-
line manner for the four years of the product life (as with all fads, it is felt
the sales will end quickly). This is the only initial cost for the production.
Pappy’s has a tax rate of 23 percent and a required return of 13 percent.
Calculate the payback period, NPV, and IRR.
INTERMEDIATE (Questions 23–28)
23. Cost-Cutting Proposals CSM Machine Shop is considering a four-year
project to improve its production efficiency. Buying a new machine press for
$395,000 is estimated to result in $144,000 in annual pretax cost savings.
The press falls in the MACRS five-year class, and it will have a salvage
LO 2
LO 3
LO 3
LO 3
LO 3
LO 2
LO 2
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C H A P T E R 9 Making Capital Investment Decisions 307
value at the end of the project of $45,000. The press also requires an initial
investment in spare parts inventory of $15,000, along with an additional
$2,000 in inventory for each succeeding year of the project. If the shop’s tax
rate is 22 percent and its discount rate is 11 percent, should the company buy
and install the machine press?
24. NPV and Bonus Depreciation In the previous problem, suppose the fixed
asset actually qualifies for 100 percent bonus depreciation. All the other facts
are the same. What is the new NPV?
25. NPV and Bonus Depreciation Eggz, Inc., is considering the purchase of
new equipment that will allow the company to collect loose hen feathers for
sale. The equipment will cost $425,000 and will be eligible for 100 percent
bonus depreciation. The equipment can be sold for $45,000 at the end of
the project in five years. Sales would be $275,000 per year, with annual fixed
costs of $47,000 and variable costs equal to 35 percent of sales. The project
would require an investment of $25,000 in NWC that would be returned at
the end of the project. The tax rate is 22 percent, and the required return is
9 percent. What is the project’s NPV?
26. Sensitivity Analysis Consider a three-year project with the following
information: initial fixed asset investment = $665,000; straight-line
depreciation to zero over the five-year life; zero salvage value; price = $39.20;
variable costs = $29.85; fixed costs = $315,000; quantity sold = 85,000 units;
tax rate = 23 percent. How sensitive is OCF to changes in quantity sold?
27. Project Analysis You are considering a new product launch. The project
will cost $780,000, have a four-year life, and have no salvage value;
depreciation is straight-line to zero. Sales are projected at 170 units per year,
price per unit will be $16,300, variable cost per unit will be $11,100, and
fixed costs will be $535,000 per year. The required return on the project is
11 percent, and the relevant tax rate is 21 percent.
a. Based on your experience, you think the unit sales, variable cost, and fixed
cost projections given here are probably accurate to within ±10 percent.
What are the best and worst cases for these projections? What is the base-
case NPV? What are the best-case and worst-case scenarios?
b. Evaluate the sensitivity of your base-case NPV to changes in fixed costs.
28. Project Analysis McGilla Golf has decided to sell a new line of golf
clubs. The clubs will sell for $925 per set and have a variable cost of
$480 per set. The company has spent $150,000 for a marketing study that
determined the company will sell 75,000 sets per year for seven years. The
marketing study also determined that the company will lose sales of 8,800
sets per year of its high-priced clubs. The high-priced clubs sell at $1,325
and have variable costs of $640. The company also will increase sales
of its cheap clubs by 11,000 sets per year. The cheap clubs sell for $385
and have variable costs of $160 per set. The fixed costs each year will be
$14.65 million. The company also has spent $1 million on research and
development for the new clubs. The plant and equipment required will
cost $30.1 million and will be depreciated on a straight-line basis. The new
clubs also will require an increase in net working capital of $3.5 million
that will be returned at the end of the project. The tax rate is 23 percent,
and the cost of capital is 14 percent. Calculate the payback period, the
NPV, and the IRR.
LO 2
LO 2
LO 2
LO 2
LO 2
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308 P A R T 5 Capital Budgeting
CHALLENGE (Questions 29–30)
29. Project Evaluation Aria Acoustics, Inc. (AAI), projects unit sales for a new
seven-octave voice emulation implant as follows:
Year Unit Sales
1 71,500
2 87,800
3 104,300
4 89,200
5 75,300
Production of the implants will require $1.5 million in net working capital to
start and additional net working capital investments each year equal to
15 percent of the projected sales increase for the following year. Total fixed
costs are $2.15 million per year, variable production costs are $230 per unit,
and the units are priced at $375 each. The equipment needed to begin produc-
tion has an installed cost of $20.5 million. Because the implants are intended
for professional singers, this equipment is considered industrial machinery
and thus qualifies as seven-year MACRS property. In five years, this equip-
ment can be sold for about 20 percent of its acquisition cost. AAI has a
21 percent tax rate and a required return on all its projects of 15 percent.
Based on these preliminary project estimates, what is the NPV of the project?
What is the IRR?
30. Calculating Required Savings A proposed cost-saving device has an
installed cost of $565,000. The device will be used in a five-year project but
is classified as three-year MACRS property for tax purposes. The required
initial net working capital investment is $40,000, the tax rate is 23 percent,
and the project discount rate is 12 percent. The device has an estimated Year
5 salvage value of $55,000. What level of pretax cost savings do we require
for this project to be profitable?
LO 2
LO 2
For this Master It! assignment, refer to the Conch Republic Electronics case at the end of
Chapter 9. For your convenience, we have entered the relevant values in the case, such as
the price and variable cost, already. For this project, answer the following questions.
a. What is the profitability index of the project?
b. What is the IRR of the project?
c. What is the NPV of the project?
d. How sensitive is the NPV to changes in the price of the new smartphone? Construct a
one-way data table to help you.
e. How sensitive is the NPV to changes in the quantity sold?
coverage online
Excel
Master
EXCEL MASTER IT! PROBLEM
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C H A P T E R 9 Making Capital Investment Decisions 309
company has spent a further $250,000 for a marketing
study to determine the expected sales figures for the
new smartphone.
Conch Republic can manufacture the new smart-
phone for $210 each in variable costs. Fixed costs for
the operation are estimated to run $5.3 million per
year. The estimated sales volumes are 64,000, 106,000,
87,000, 78,000, and 54,000 per year for each of the
next five years, respectively. The unit price of the new
smartphone will be $515. The necessary equipment
can be purchased for $38.5 million and will be depreci-
ated on a seven-year MACRS schedule. It is believed
the value of the equipment in five years will be $5.8
million.
Net working capital for the smartphones will be
20 percent of sales and will occur with the timing of the
cash flows for the year (i.e., there is no initial outlay for
NWC). Changes in NWC thus will occur first in Year 1 with
the first year’s sales. Conch Republic has a 22 percent
corporate tax rate and a required return of 12 percent.
Shelly has asked Jay to prepare a report that
answers the following questions:
Conch Republic Electronics is a midsized electronics manufacturer located in Key West, Florida. The com-
pany president is Shelly Couts, who inherited the com-
pany. The company originally repaired radios and other
household appliances when it was founded more than
70 years ago. Over the years, the company has ex-
panded, and it is now a reputable manufacturer of vari-
ous specialty electronic items. Jay McCanless, a recent
MBA graduate, has been hired by the company in its fi-
nance department.
One of the major revenue-producing items manu-
factured by Conch Republic is a smartphone. Conch Re-
public currently has one smartphone model on the
market and sales have been excellent. The smartphone
is a unique item in that it comes in a variety of tropical
colors and is preprogrammed to play Jimmy Buffett mu-
sic. However, as with any electronic item, technology
changes rapidly, and the current smartphone has limited
features in comparison with newer models. Conch Re-
public spent $1.2 million to develop a prototype for a
new smartphone that has all the features of the existing
one but adds new features such as Wifi tethering. The
CHAPTER CASE
Conch Republic Electronics
1. What is the payback period of the project?
2. What is the profitability index of the project?
3. What is the IRR of the project?
4. What is the NPV of the project?
5. How sensitive is the NPV to changes in the price
of the new smartphone?
6. How sensitive is the NPV to changes in the quan-
tity sold?
7. Should Conch Republic produce the new
smartphone?
8. Suppose Conch Republic loses sales on other
models because of the introduction of the new
model. How would this affect your analysis?
Q U E S T I O N S
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310
PART SIX Risk and Return
Please visit us at essentialsofcorporatefinance.blogspot.com for the latest developments in the world of corporate finance.
With the S&P 500 Index returning about 19 percent and the NASDAQ Composite Index up about 28 percent in 2017,
stock market performance overall was very good. In particular, in-
vestors in biopharmaceutical company Madrigal Pharmaceuticals,
Inc., had to be happy about the 516 percent gain in that stock, and
investors in genomic therapy company Sangamo Therapeutics
had to feel pretty good following that company’s 438 percent gain.
Of course, not all stocks increased in value during the year. Stock
in Sears Holdings fell 61 percent, and stock in Under Armour
dropped 48 percent. These examples show that there were tre-
mendous potential profits to be made during 2017, but there was
also the risk of losing money—and lots of it. So what should you, as
a stock market investor, expect when you invest your own money?
In this chapter, we study more than eight decades of market his-
tory to find out.
This chapter and the next take us into new territory: the relation between risk and
return. As you will see, this chapter has a lot of very practical information for anyone
thinking of investing in financial assets such as stocks and bonds. For example, suppose
you were to start investing in stocks today. Do you think your money would grow at an
average rate of 5 percent per year? Or 10 percent? Or 20 percent? This chapter gives
you an idea of what to expect (the answer may surprise you). The chapter also shows
how risky certain investments can be, and it gives you the tools to think about risk in an
objective way.
Some Lessons from Capital
Market History 10
LEARNING OBJECTIVES
After studying this chapter, you should
be able to:
LO 1 Calculate the return on an
investment.
LO 2 Discuss the historical returns on
various important types of
investments.
LO 3 Explain the historical risks on
various important types of
investments.
LO 4 Assess the implications of market
efficiency.
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C H A P T E R 1 0 Some Lessons from Capital Market History 311
Thus far, we haven’t had much to say about what determines the required return on an investment. In one sense, the answer is very simple: The required return depends on the
risk of the investment. The greater the risk, the greater is the required return.
Having said this, we are left with a somewhat more difficult problem. How can we
measure the amount of risk present in an investment? Put another way, what does it mean
to say that one investment is riskier than another? Obviously, we need to define what we
mean by risk if we are going to answer these questions. This is our task in the next two
chapters.
From the last several chapters, we know that one of the responsibilities of the financial
manager is to assess the value of proposed investments. In doing this, it is important that we
first look at what financial investments have to offer. At a minimum, the return we require
from a proposed nonfinancial investment must be at least as large as what we can get from
buying financial assets of similar risk.
Our goal in this chapter is to provide a perspective on what capital market history can
tell us about risk and return. The most important thing to get out of this chapter is a feel for
the numbers. What is a high return? What is a low one? More generally, what returns should
we expect from financial assets and what are the risks from such investments? This perspec-
tive is essential for understanding how to analyze and value risky investment projects.
We start our discussion of risk and return by describing the historical experience of in-
vestors in the U.S. financial markets. In 1931, for example, the stock market lost 43 percent
of its value. Just two years later, the stock market gained 54 percent. In more recent mem-
ory, the market lost about 25 percent of its value on October 19, 1987, alone, and stocks lost
almost 40 percent in 2008. What lessons, if any, can financial managers learn from such
shifts in the stock market? We will explore the last half century (and then some) of market
history to find out.
Not everyone agrees on the value of studying history. On the one hand, there is philoso-
pher George Santayana’s famous comment: “Those who cannot remember the past are con-
demned to repeat it.” On the other hand, there is industrialist Henry Ford’s equally famous
comment: “History is more or less bunk.” Nonetheless, perhaps everyone would agree with
the following observation from Mark Twain: “October. This is one of the peculiarly danger-
ous months to speculate in stocks. The others are July, January, September, April, Novem-
ber, May, March, June, December, August, and February.”
There are two central lessons that emerge from our study of market history. First: There
is a reward for bearing risk. Second: The greater the potential reward, the greater is the risk.
To understand these facts about market returns, we devote much of this chapter to reporting
the statistics and numbers that make up the modern capital market history of the United
States. In the next chapter, these facts provide the foundation for our study of how financial
markets put a price on risk.
RETURNS
We wish to discuss historical returns on different types of financial assets. The first thing we
need to do, then, is to briefly discuss how to calculate the return from investing.
Dollar Returns
If you buy an asset of any sort, your gain (or loss) from that investment is called your return
on investment. This return will usually have two components. First: You may receive some
cash directly while you own the investment. This is called the income component of
10.1
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Excel
Master
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312 P A R T 6 Risk and Return
your return. Second: The value of the asset you purchase often will change. In this case, you
have a capital gain or capital loss on your investment.1
To illustrate, suppose the Video Concept Company has several thousand shares of
stock outstanding. You purchased some of these shares of stock in the company at the be-
ginning of the year. It is now year-end, and you want to determine how well you have done
on your investment.
First, over the year, a company may pay cash dividends to its shareholders. As a stock-
holder in Video Concept Company, you are a part owner of the company. If the company is
profitable, it may choose to distribute some of its profits to shareholders (we discuss the
details of dividend policy in a later chapter). So, as the owner of some stock, you will receive
some cash. This cash is the income component from owning the stock.
In addition to the dividend, the other part of your return is the capital gain or capital
loss on the stock. This part arises from changes in the value of your investment. For exam-
ple, consider the cash flows illustrated in Figure 10.1. At the beginning of the year, the stock
is selling for $37 per share. If you buy 100 shares, you have a total outlay of $3,700. Suppose,
over the year, the stock pays a dividend of $1.85 per share. By the end of the year, then, you
will have received income of:
Dividend = $1.85 × 100 = $185
Also, the value of the stock rises to $40.33 per share by the end of the year. Your 100
shares are worth $4,033, so you have a capital gain of:
Capital gain = ($40.33 − 37) × 100 = $333
On the other hand, if the price had dropped to, say, $34.78, you would have had a capi-
tal loss of:
Capital loss = ($34.78 − 37) × 100 = −$222
Notice that a capital loss is the same thing as a negative capital gain.
How did the market do
today? Find out at
finance.yahoo.com.
1As we mentioned in an earlier chapter, strictly speaking, what is and what is not a capital gain (or loss) is deter-
mined by the IRS. We thus use the terms loosely.
$4,218
$185
$4,033
Total
Dividends
Ending
market
value
Initial
investment
−$3,700
Time
Outflows
Inflows
0 1
Dollar returns
FIGURE 10.1
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C H A P T E R 1 0 Some Lessons from Capital Market History 313
The total dollar return on your investment is the sum of the dividend and the capital
gain:
Total dollar return = Dividend income + Capital gain (or loss) [10.1]
In our first example, the total dollar return is thus given by:
Total dollar return = $185 + 333 = $518
Notice that, if you sold the stock at the end of the year, the total amount of cash you would
have would be your initial investment plus the total return. In the preceding example, then:
Total cash if stock is sold = Initial investment + Total return [10.2]
= $3,700 + 518
= $4,218
As a check, notice that this is the same as the proceeds from the sale of the stock plus
the dividends:
Proceeds from stock sale + Dividends = $40.33 × 100 + 185
= $4,033 + 185
= $4,218
Suppose you hold on to your Video Concept stock and don’t sell it at the end of the
year. Should you still consider the capital gain as part of your return? Isn’t this only a
“paper” gain and not really a return if you don’t sell the stock?
The answer to the first question is a strong yes, and the answer to the second is an
equally strong no. The capital gain is every bit as much a part of your return as the dividend,
and you should certainly count it as part of your return. That you actually decided to keep
the stock and not sell (you don’t “realize” the gain) is irrelevant because you could have
converted it to cash if you had wanted to. Whether you choose to do so or not is up to you.
After all, if you insisted on converting your gain to cash, you could always sell the stock
at year-end and immediately reinvest by buying the stock back. There is no net difference
between doing this and not selling (assuming, of course, that there are no tax consequences
from selling the stock). Again, the point is that whether you actually cash out and buy sodas
(or whatever) or reinvest by not selling doesn’t affect the return you earn.
Percentage Returns
It is usually more convenient to summarize information about returns in percentage terms,
rather than dollar terms, because that way your return doesn’t depend on how much you
actually invest. The question we want to answer is this: How much do we get for each dollar
we invest?
To answer this question, let Pt be the price of the stock at the beginning of the year and
let Dt+1 be the dividend paid on the stock during the year. Consider the cash flows in
Figure 10.2. These are the same as those in Figure 10.1, except that we have now expressed
everything on a per-share basis.
In our example, the price at the beginning of the year was $37 per share and the divi-
dend paid during the year on each share was $1.85. As we discussed in Chapter 7, express-
ing the dividend as a percentage of the beginning stock price results in the dividend yield:
Dividend yield = Dt+1/Pt
= $1.85/$37 = .05, or 5%
This says that, for each dollar we invest, we get five cents in dividends.
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314 P A R T 6 Risk and Return
The second component of our percentage return is the capital gains yield. Recall (from
Chapter 7) that this is calculated as the change in the price during the year (the capital
gain) divided by the beginning price:
Capital gains yield = (Pt+1 − Pt)/Pt
= ($40.33 − 37)/$37
= $3.33/$37
= .09, or 9%
So, per dollar invested, we get nine cents in capital gains.
Putting it together, per dollar invested, we get 5 cents in dividends and 9 cents in capital
gains; so, we get a total of 14 cents. Our percentage return is 14 cents on the dollar, or 14
percent.
To check this, notice that we invested $3,700 and ended up with $4,218. By what per-
centage did our $3,700 increase? As we saw, we picked up $4,218 − 3,700 = $518. This is a
$518/$3,700 = .14, or 14 percent increase.
To give a more concrete example, stock in Microsoft began 2017 at $62.14 per share.
Microsoft paid dividends of $1.59 during 2017 and the stock price at the end of the year was
$85.54. What was the return on Microsoft for the year? For practice, see if you agree that
the answer is 40.22 percent. Of course, negative returns occur as well. For example, again in
2017, GameStop’s stock price at the end of the year was $17.95 per share and dividends of
$1.52 were paid. The stock began the year at $25.26 per share. Verify that the loss was 22.92
percent for the year.
$42.18
$1.85
$40.33
Total
Dividends
Ending
market
value
−$37
Time
Outflows
Inflows
t t+ 1
Dollar returns per
share
FIGURE 10.2
EXAMPLE 10.1 Calculating Returns
Suppose you buy some stock for $25 per share. At the end of the year, the price is $35 per share.
During the year, you get a $2 dividend per share. This is the situation illustrated in Figure 10.3. What
is the dividend yield? The capital gains yield? The percentage return? If your total investment was
$1,000, how much do you have at the end of the year?
Your $2 dividend per share works out to a dividend yield of:
Dividend yield = Dt+1/Pt
= $2/$25 = .08, or 8%
ros13952_ch10_310-349.indd 314 12/24/18 5:11 PM
C H A P T E R 1 0 Some Lessons from Capital Market History 315
CONCEPT QUESTIONS
10.1a What are the two parts of total return?
10.1b Why are unrealized capital gains or losses included in the calculation of returns?
10.1c What is the difference between a dollar return and a percentage return? Why are
percentage returns more convenient?
THE HISTORICAL RECORD
Roger Ibbotson and Rex Sinquefield conducted a famous set of studies dealing with rates of
return in U.S. financial markets.2 They presented year-to-year historical rates of return on
five important types of financial investments. The returns can be interpreted as what you
would have earned if you had held portfolios of the following:
1. Large-company stocks. The large-company stock portfolio is based on the Standard &
Poor’s 500 index, which contains 500 of the largest companies (in terms of total
market value of outstanding stock) in the United States.
10.2
coverage online
Excel
Master
The per-share capital gain is $10, so the capital gains yield is:
Capital gains yield = (Pt+1 − Pt)/Pt
= ($35 − 25)/$25
= $10/$25
= .40, or 40%
The total percentage return is thus 48 percent.
If you had invested $1,000, you would have had $1,480 at the end of the year, representing a
48 percent increase. To check this, note that your $1,000 would have bought you $1,000/$25 =
40 shares. Your 40 shares would then have paid you a total of 40 × $2 = $80 in cash dividends.
Your $10 per share gain would have given you a total capital gain of $10 × 40 = $400. Add these
together, and you get the $480 increase.
Cash flow: An
investment example
FIGURE 10.3$37
$2
$35
Total
Dividends
(D1)
Ending
price per
share (P1)
−$25 (P0)
Time
Outflows
Inflows
0 1
2R. G. Ibbotson and R. A. Sinquefield, Stocks, Bonds, Bills, and Inflation [SBBI] (Charlottesville, VA: Financial
Analysis Research Foundation, 1982).
ros13952_ch10_310-349.indd 315 12/24/18 5:11 PM
316 P A R T 6 Risk and Return
2. Small-company stocks. This is a stock portfolio composed of smaller companies,
where “small” corresponds to the smallest 20 percent of the companies listed on
the New York Stock Exchange, again as measured by market value of outstanding
stock.
3. Long-term corporate bonds. This is a portfolio of high-quality bonds with 20 years to
maturity.
4. Long-term U.S. government bonds. This is a portfolio of U.S. government bonds with 20
years to maturity.
5. U.S. Treasury bills. This is based on Treasury bills (T-bills for short) with a one-month
maturity.
These returns are not adjusted for inflation or taxes; thus, they are nominal, pretax
returns.
In addition to the year-to-year returns on these financial instruments, the year-to-
year percentage change in the consumer price index (CPI) also is computed. This is a
commonly used measure of inflation, so we can calculate real returns using this as the
inflation rate.
A First Look
Before looking closely at the different portfolio returns, we take a look at the big pic-
ture. Figure 10.4 shows what happened to $1 invested in these different portfolios at
the beginning of 1926. The growth in value for each of the different portfolios over the
92-year period ending in 2017 is given separately (the long-term corporate bonds are
omitted). Notice that to get everything on a single graph, some modification in scal-
ing is used. As is commonly done with financial series, the vertical axis is scaled such
that equal distances measure equal percentage (as opposed to dollar) changes in
values.
Looking at Figure 10.4, we see that the small-company, or “small-cap” (short for small-
capitalization), investment did the best overall. Every dollar invested grew to a remarkable
$36,931.00 over the 92 years. The larger common stock portfolio did less well; a dollar in-
vested in it grew to $7,346.15.
At the other end, the T-bill portfolio grew to only $20.78. This is even less impressive
when we consider the inflation over this period. As illustrated, the increase in the price level
was such that $13.78 is needed just to replace the original $1.
Given the historical record, why would anybody buy anything other than small-cap
stocks? If you look closely at Figure 10.4, you will probably see the answer. The T-bill port-
folio and the long-term government bond portfolio grew more slowly than did the stock
portfolios, but they also grew much more steadily. The small stocks ended up on top, but, as
you can see, they grew quite erratically at times. For example, small stocks were the worst
performers for about the first 10 years and had a smaller return than long-term government
bonds for almost 15 years.
A Closer Look
To illustrate the variability of the different investments, Figures 10.5 through 10.8 plot
the year-to-year percentage returns in the form of vertical bars drawn from the horizontal
axis. The height of the bar tells us the return for the particular year. Looking at the long-
term government bonds (Figure 10.7), we see that the largest historical return
(40.35 percent) occurred in 1982. This was a good year for bonds. In comparing these
charts, notice the differences in the vertical axis scales. With these differences in mind,
For more on market
history, visit
www.globalfinancialdata
.com, where you can
download free sample
data.
Go to www.bigcharts.com
to see both intraday and
long-term charts.
ros13952_ch10_310-349.indd 316 12/24/18 5:11 PM
C H A P T E R 1 0 Some Lessons from Capital Market History 317
A $1 investment in different types of portfolios: 1925–2017 (year-end 1925 = $1)FIGURE 10.4
$0
$1
$10
$100
$1,000
$10,000
$100,000
1925 1930 1935 1940 1945 1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010 2015
$36,931.00
$7,346.15
$142.35
$20.78
$13.78
Inflation
Treasury bills
Long-term
government bonds
Large-company stocks
Small-company stocks
Source: Morningstar, 2018, author calculations.
Year-to-year total
returns on large-
company stocks:
1926–2017
FIGURE 10.5
−60
−40
−20
0
20
40
60
19
25
19
30
19
35
19
40
19
45
19
50
19
55
19
60
19
65 19
70
19
75
19
80
19
85
19
90
19
95
20
00
20
05
20
10
20
15
Source: Morningstar, 2018, author calculations.
ros13952_ch10_310-349.indd 317 12/24/18 5:11 PM
318 P A R T 6 Risk and Return
Year-to-year total
returns on small-
company stocks:
1926–2017
FIGURE 10.6
−100
−50
0
50
100
150
200
19
25
19
30
19
35
19
40
19
45
19
50
19
55
19
60
19
65 19
70
19
75
19
80
19
85
19
90
19
95
20
00
20
05
20
10
20
15
Source: Morningstar, 2018, author calculations.
you can see how predictably the Treasury bills (Figure 10.7) behaved compared to the
small stocks (Figure 10.6).
The returns shown in these bar graphs are sometimes very large. Looking at the graphs,
we see, for example, that the largest single-year return was a remarkable 143 percent for the
small-cap stocks in 1933. In the same year, the large-company stocks “only” returned 53
percent. In contrast, the largest Treasury bill return was 15 percent in 1981. For future refer-
ence, the actual year-to-year returns for the S&P 500, long-term government bonds, Treasury
bills, and the CPI are shown in Table 10.1.
Year-to-year total
returns on bonds
and bills: 1926–2017
FIGURE 10.7
−20
−10
0
10
20
30
40
50
Long-term government bonds
19
25
19
30
19
35
19
40
19
45
19
50
19
55
19
60
19
65 19
70
19
75
19
80
19
85
19
90
19
95
20
00
20
05
20
10
20
15
(continued)
ros13952_ch10_310-349.indd 318 12/24/18 5:11 PM
C H A P T E R 1 0 Some Lessons from Capital Market History 319
Source: Morningstar, 2018, author calculations.
−2
0
2
4
6
8
10
12
14
16
19
25
19
30
19
35
19
40
19
45
19
50
19
55
19
60
19
65 19
70
19
75
19
80
19
85
19
90
19
95
20
00
20
05
20
10
20
15
Treasury bills
Year-to-year
inflation: 1926–2017
FIGURE 10.8
−15
−10
−5
0
5
10
15
20
19
25
19
30
19
35
19
40
19
45
19
50
19
55
19
60
19
65 19
70
19
75
19
80
19
85
19
90
19
95
20
00
20
05
20
10
20
15
Source: Morningstar, 2018, author calculations.
CONCEPT QUESTIONS
10.2a With 20-20 hindsight, what was the best investment for the period 1926–1935?
10.2b Why doesn’t everyone buy only small stocks as investments?
10.2c What was the smallest return observed over the 92 years for each of these
investments? Approximately when did it occur?
10.2d About how many times did large stocks (common stocks) return more than 30
percent? How many times did they return less than −20 percent?
10.2e What was the longest “winning streak” (years without a negative return) for large
stocks? For long-term government bonds?
10.2f How often did the T-bill portfolio have a negative return?
ros13952_ch10_310-349.indd 319 12/24/18 5:11 PM
Year
Large-Company
Stocks
Long-Term
Government Bonds
U.S. Treasury
Bills
Consumer
Price Index
1926 11.14% 7.90% 3.30% − 1.12%
1927 37.13 10.36 3.15 − 2.26
1928 43.31 − 1.37 4.05 − 1.16
1929 − 8.91 5.23 4.47 .58
1930 −25.26 5.80 2.27 − 6.40
1931 −43.86 − 8.04 1.15 − 9.32
1932 − 8.85 14.11 .88 −10.27
1933 52.88 .31 .52 .76
1934 − 2.34 12.98 .27 1.52
1935 47.22 5.88 .17 2.99
1936 32.80 8.22 .17 1.45
1937 −35.26 − .13 .27 2.86
1938 33.20 6.26 .06 − 2.78
1939 − .91 5.71 .04 .00
1940 −10.08 10.34 .04 .71
1941 −11.77 − 8.66 .14 9.93
1942 21.07 2.67 .34 9.03
1943 25.76 2.50 .38 2.96
1944 19.69 2.88 .38 2.30
1945 36.46 5.17 .38 2.25
1946 − 8.18 4.07 .38 18.13
1947 5.24 − 1.15 .62 8.84
1948 5.10 2.10 1.06 2.99
1949 18.06 7.02 1.12 − 2.07
1950 30.58 − 1.44 1.22 5.93
1951 24.55 − 3.53 1.56 6.00
1952 18.50 1.82 1.75 .75
1953 − 1.10 − .88 1.87 .75
1954 52.40 7.89 .93 − .74
1955 31.43 − 1.03 1.80 .37
1956 6.63 − 3.14 2.66 2.99
1957 −10.85 5.25 3.28 2.90
1958 43.34 − 6.70 1.71 1.76
1959 11.90 − 1.35 3.48 1.73
1960 .48 7.74 2.81 1.36
1961 26.81 3.02 2.40 .67
1962 − 8.78 4.63 2.82 1.33
1963 22.69 1.37 3.23 1.64
1964 16.36 4.43 3.62 .97
1965 12.36 1.40 4.06 1.92
1966 −10.10 − 1.61 4.94 3.46
1967 23.94 − 6.38 4.39 3.04
1968 11.00 5.33 5.49 4.72
1969 − 8.47 − 7.45 6.90 6.20
1970 3.94 12.24 6.50 5.57
1971 14.30 12.67 4.36 3.27
Year
Large-Company
Stocks
Long-Term
Government Bonds
U.S. Treasury
Bills
Consumer
Price Index
1972 18.99 9.15 4.23 3.41
1973 −14.69 −12.66 7.29 8.71
1974 −26.47 − 3.28 7.99 12.34
1975 37.23 4.67 5.87 6.94
1976 23.93 18.34 5.07 4.86
1977 − 7.16 2.31 5.45 6.70
1978 6.57 − 2.07 7.64 9.02
1979 18.61 − 2.76 10.56 13.29
1980 32.50 − 5.91 12.10 12.52
1981 − 4.92 − .16 14.60 8.92
1982 21.55 49.99 10.94 3.83
1983 22.56 − 2.11 8.99 3.79
1984 6.27 16.53 9.90 3.95
1985 31.73 39.03 7.71 3.80
1986 18.67 32.51 6.09 1.10
1987 5.25 − 8.09 5.88 4.43
1988 16.61 8.71 6.94 4.42
1989 31.69 22.15 8.44 4.65
1990 − 3.10 5.44 7.69 6.11
1991 30.46 20.04 5.43 3.06
1992 7.62 8.09 3.48 2.90
1993 10.08 22.32 3.03 2.75
1994 1.32 −11.46 4.39 2.67
1995 37.58 37.28 5.61 2.54
1996 22.96 − 2.59 5.14 3.32
1997 33.36 17.70 5.19 1.70
1998 28.58 19.22 4.86 1.61
1999 21.04 −12.76 4.80 2.68
2000 − 9.10 22.16 5.98 3.39
2001 −11.89 5.30 3.33 1.55
2002 −22.10 14.08 1.61 2.38
2003 28.68 1.62 1.03 1.88
2004 10.88 10.34 1.43 3.26
2005 4.91 10.35 3.30 3.42
2006 15.79 .28 4.97 2.54
2007 5.49 10.85 4.52 4.08
2008 −37.00 39.46 1.24 .09
2009 26.46 −25.61 .15 2.72
2010 15.06 7.73 .14 1.50
2011 2.11 35.75 .06 2.96
2012 16.00 1.80 .08 1.74
2013 32.39 −14.69 .05 1.50
2014 13.69 22.60 .03 .76
2015 1.41 −.64 .04 .74
2016 11.98 1.76 .21 2.11
2017 19.57 5.78 .75 1.58
Year-to-year total returns: 1926–2017
Source: Author calculations based on data from Global Financial Data and other sources.
TABLE 10.1
320
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12/24/18 5:11 P
M
C H A P T E R 1 0 Some Lessons from Capital Market History 321
AVERAGE RETURNS: THE FIRST LESSON
As you’ve probably begun to notice, the history of capital market returns is too complicated
to be of much use in its undigested form. We need to begin summarizing all these numbers.
Accordingly, we discuss how to go about condensing the detailed data. We start out by cal-
culating average returns.
Calculating Average Returns
The obvious way to calculate the average returns on the different investments in Table 10.1
is to add up the yearly returns and divide by 92. The result is the historical average of the
individual values.
If you add up the returns for the large-company common stocks for the 92 years, you
will get about 11.09. The average annual return is thus 11.09/92 = .121, or 12.1%. You inter-
pret this 12.1 percent like any other average. If you picked a year at random from the 92-year
history and you had to guess the return in that year, the best guess would be 12.1 percent.
Average Returns: The Historical Record
Table 10.2 shows the average returns for the investments we have discussed. As shown, in a
typical year, the small stocks increased in value by 16.5 percent. Notice also how much
larger the stock returns are than the bond returns.
These averages are, of course, nominal since we haven’t worried about inflation. Notice
that the average inflation rate was 3.0 percent per year over this 92-year span. The nominal
return on U.S. Treasury bills was 3.4 percent per year. The average real return on Treasury
bills was thus approximately .4 percent per year; so, the real return on T-bills has been quite
low historically.
At the other extreme, small stocks had an average real return of about 16.5% − 3.0% =
13.5%, which is relatively large. If you remember the Rule of 72 (Chapter 4), then you recall
that a quick back-of-the-envelope calculation tells us that 13.5 percent real growth doubles
your buying power about every five years. Notice also that the real value of the large stock
portfolio increased by 9.1 percent in a typical year.
Risk Premiums
Now that we have computed some average returns, it seems logical to see how they compare
with each other. Based on our previous discussion, one such comparison involves govern-
ment-issued securities. These are free of much of the variability we see in, for example, the
stock market.
The government borrows money by issuing bonds. These bonds come in different
forms. The ones we will focus on are Treasury bills. These have the shortest time to
10.3
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Investment Average Return
Large stocks 12.1%
Small stocks 16.5
Long-term corporate bonds 6.4
Long-term government bonds 6.0
U.S. Treasury bills 3.4
Inflation 3.0
Source: Morningstar, 2018, author calculations.
Average annual
returns: 1926–2017
TABLE 10.2
ros13952_ch10_310-349.indd 321 12/24/18 5:11 PM
322 P A R T 6 Risk and Return
maturity of the different government bonds. Because the government always can raise
taxes to pay its bills, this debt is virtually free of any default risk over its short life. Thus,
we will call the rate of return on such debt the risk-free return, and we will use it as a kind
of benchmark.
A particularly interesting comparison involves the virtually risk-free return on T-bills
and the very risky return on common stocks. The difference between these two returns can
be interpreted as a measure of the excess return on the average risky asset (assuming the
stock of a large U.S. corporation has about average risk compared to all risky assets).
We call this the “excess” return because it is the additional return we earn by moving
from a relatively risk-free investment to a risky one. Because it can be interpreted as a reward
for bearing risk, we will call it a risk premium.
From Table 10.2, we can calculate the risk premiums for the different investments. We
report only the nominal risk premium in Table 10.3 because there is only a slight difference
between the historical nominal and real risk premiums.
The risk premium on T-bills is shown as zero in the table because we have assumed that
they are riskless.
The First Lesson
Looking at Table 10.3, we see that the average risk premium earned by a typical large com-
mon stock is 12.1% − 3.4% = 8.7%. This is a significant reward. The fact that it exists his-
torically is an important observation, and it is the basis for our first lesson: Risky assets, on
average, earn a risk premium. Put another way: There is a reward for bearing risk.
Why is this so? Why, for example, is the risk premium for small stocks so much larger
than the risk premium for large stocks? More generally, what determines the relative sizes
of the risk premiums for the different assets? The answers to these questions are at the
heart of modern finance, and the next chapter is devoted to them. For now, part of the
answer can be found by looking at the historical variability of the returns of these differ-
ent investments. So, to get started, we now turn our attention to measuring variability in
returns.
CONCEPT QUESTIONS
10.3a What do we mean by excess return and risk premium?
10.3b What was the real (as opposed to nominal) risk premium on the common stock
portfolio?
10.3c What was the nominal risk premium on corporate bonds? The real risk premium?
10.3d What is the first lesson from capital market history?
risk premium
The excess return required
from an investment in a
risky asset over that
required from a risk-free
investment.
Investment Average Return Risk Premium
Large stocks 12.1% 8.7%
Small stocks 16.5 13.1
Long-term corporate bonds 6.4 3.0
Long-term government bonds 6.0 2.6
U.S. Treasury bills 3.4 —
Source: Morningstar, 2018, author calculations.
Average annual
returns and risk
premiums:
1926–2017
TABLE 10.3
ros13952_ch10_310-349.indd 322 12/24/18 5:11 PM
C H A P T E R 1 0 Some Lessons from Capital Market History 323
THE VARIABILITY OF RETURNS: THE
SECOND LESSON
We already have seen that the year-to-year returns on common stocks tend to be more vola-
tile than the returns on, say, long-term government bonds. We now discuss measuring this
variability so we can begin examining the subject of risk.
Frequency Distributions and Variability
To get started, we can draw a frequency distribution for the common stock returns like the
one in Figure 10.9. What we have done here is to count up the number of times the annual
return on the large stock portfolio falls within each 10 percent range. For example, in
Figure 10.9, the height of 15 in the range 20 percent to 30 percent means that 15 of the
92 annual returns were in that range. Notice also that the returns are very concentrated
between −10 and 40 percent.
What we need to do now is to actually measure the spread in returns. We know, for ex-
ample, that the return on small stocks in a typical year was 16.5 percent. We now want to
know how far the actual return deviates from this average in a typical year. In other words,
we need a measure of how volatile the return is. The variance and its square root, the
standard deviation, are the most commonly used measures of volatility. We describe how to
calculate them next.
The Historical Variance and Standard Deviation
The variance essentially measures the average squared difference between the actual returns
and the average return. The bigger this number is, the more the actual returns tend to differ
from the average return. Also, the larger the variance or standard deviation is, the more
spread out the returns will be.
10.4
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Master
variance
The average squared
difference between the
actual return and the
average return.
standard deviation
The positive square root
of the variance.
−50 −40 −30 −20 −10−80 −70 −60 10 20 30 40 50 60 70 80 900
Percent
1931 1937
2008
1930 1941
1957
1929 1947 1926 1942 1927 1928 1933
1974
19662002
1932 1948 1944 1943 1936 1935 1954
1973
1934 1956 1949 1951 1938 1958
2001
1939 1960 1952 1961 1945
1940 1970 1959 1963 1950
1946 1978 1964 1967 1955
1953 1984 1965 1976 1975
1962 1987 1968 1982 1980
1969 1992 1971 1983 1985
1977 1993 1972 1996
1998
1999
2003
1989
1981
1990 2005
1994 1979 1991
2000 2007
20092011
20172015
1986 1995
1988
2004
2006
2010
2012
2014
2016
1997
2013
Frequency
distribution of
returns on common
stocks: 1926–2017
FIGURE 10.9
Source: Morningstar, 2018, author calculations.
ros13952_ch10_310-349.indd 323 12/24/18 5:11 PM
324 P A R T 6 Risk and Return
The way we will calculate the variance and standard deviation depends on the specific
situation. In this chapter, we are looking at historical returns; so, the procedure we describe
here is the correct one for calculating the historical variance and standard deviation. If we
were examining projected future returns, then the procedure would be different. We de-
scribe this procedure in the next chapter.
To illustrate how we calculate the historical variance, suppose a particular investment
had returns of 10 percent, 12 percent, 3 percent, and −9 percent over the last four years.
The average return is (.10 + .12 + .03 − .09)/4 = .04, or 4%. Notice that the return is never
actually equal to 4 percent. Instead, the first return deviates from the average by .10 − .04 =
.06, the second return deviates from the average by .12 − .04 = .08, and so on. To compute
the variance, we square each of these deviations, add up the squares, and divide the result by
the number of returns less 1, or 3 in this case. This information is summarized in the
following table:
Year
(1)
Actual
Return
(2)
Average
Return
(3)
Deviation
(1) − (2)
(4)
Squared
Deviation
1 .10 .04 .06 .0036
2 .12 .04 .08 .0064
3 .03 .04 −.01 .0001
4 −.09 .04 −.13 .0169
Totals .16 .00 .0270
In the first column, we write down the four actual returns. In the third column, we cal-
culate the difference between the actual returns and the average by subtracting out 4 per-
cent. Finally, in the fourth column, we square the numbers in Column 3 to get the squared
deviations from the average.
The variance can now be calculated by dividing .0270, the sum of the squared devia-
tions, by the number of returns less 1. Let Var(R), or σ2 (read this as “sigma squared”),
stand for the variance of the return:
Var(R) = σ2 = .027/(4 − 1) = .009
The standard deviation is the square root of the variance. So, if SD(R), or σ, stands for
the standard deviation of the return:
SD(R() = σ = √
____
.009 ((= .09487 (, or 9.487%
The square root of the variance is used because the variance is measured in “squared”
percentages and thus is hard to interpret. The standard deviation is an ordinary percentage,
so the answer here could be written as 9.487 percent.
In the preceding table, notice that the sum of the deviations is equal to zero. This will
always be the case, and it provides a good way to check your work. In general, if we have T
historical returns, where T is some number, we can write the historical variance as:
Var(R() = 1 _____ T − 1 ([(( R 1 − ̄ R ()
2 + · · · + ( R T − ̄ R ()
2 ] [10.3]
This formula tells us to do what we did above: Take each of the T individual returns
(R1, R2, . . .) and subtract the average return, R; square the results, and add up all these
squares; and, finally, divide this total by the number of returns less 1 (= T − 1). The stand-
ard deviation is always the square root of Var(R). Standard deviations are a widely used
measure of volatility. Our nearby Work the Web box gives a real-world example.
For an easy-to-read
review of basic stats,
check out www
.robertniles.com/stats.
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C H A P T E R 1 0 Some Lessons from Capital Market History 325
Standard deviations are widely reported for mutual funds. For example, the Fidelity Magellan Fund is a large mutual fund. How volatile is it? To find out, we went to www.morningstar.com,
entered the ticker symbol FMAGX, and hit the “Ratings & Risk” link. Here is what we found:
W R K T H E W E B
QUESTIONS
1. Go to the Morningstar website at www.morningstar.com. What does the Bear Market
Percentile Rank measure?
2. Get a quote for the Fidelity Magellan fund at Morningstar. What are the five sectors
that have the highest percentage investment for this fund? What are the five stocks
with the highest percentage investment?
The standard deviation for the Fidelity Magellan Fund is 11.54 percent. When you consider the
average stock has a standard deviation of about 50 percent, this seems like a low number. The
reason for the low standard deviation has to do with the power of diversification, a topic we dis-
cuss in the next chapter. The return is the average return, so over the last three years, investors in
the Magellan Fund gained 11.52 percent per year. Also under the Volatility Measures section, you
will see the Sharpe ratio. The Sharpe ratio is calculated as the risk premium of the asset divided by
the standard deviation. As such, it is a measure of return to the level of risk taken (as measured by
standard deviation). The “beta” for the Fidelity Magellan Fund is 1.08. We will have more to say
about this number—lots more—in the next chapter.
Source: www.morningstar.com
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326 P A R T 6 Risk and Return
EXAMPLE 10.2 Calculating the Variance and Standard Deviation
Suppose the Supertech Company and the Hyperdrive Company have experienced the following
returns in the last four years:
Year Supertech Returns Hyperdrive Returns
2016 −.20 .05
2017 .50 .09
2018 .30 −.12
2019 .10 .20
What are the average returns? The variances? The standard deviations? Which investment was
more volatile?
To calculate the average returns, we add up the returns and divide by 4. The results are:
Supertech average return = R = .70/4 = .175, or 17.5%
Hyperdrive average return = R = .22/4 = .055, or 5.5%
To calculate the variance for Supertech, we can summarize the relevant calculations as follows:
Year
(1)
Actual
Return
(2)
Average
Return
(3)
Deviation
(1) − (2)
(4)
Squared
Deviation
2016 −.20 .175 −.375 .140625
2017 .50 .175 .325 .105625
2018 .30 .175 .125 .015625
2019 .10 .175 −.075 .005625
Totals .70 .000 .267500
Because there are four years of returns, we calculate the variance by dividing .2675 by (4 − 1) = 3:
Supertech Hyperdrive
Variance (σ2) .2675/3 = .0892 .0529/3 = .0176
Standard deviation (σ) √
_____
.0892 = .2986 √
_____
.0176 = .1328
For practice, verify that you get the same answer as we do for Hyperdrive. Notice that the standard
deviation for Supertech, 29.86 percent, is a little more than twice Hyperdrive’s 13.28 percent; Su-
pertech was thus the more volatile investment.
The Historical Record
Figure 10.10 summarizes much of our discussion of capital market history so far. It displays
average returns, standard deviations, and frequency distributions of annual returns on a
common scale. In Figure 10.10, notice, for example, that the standard deviation for the
small-stock portfolio (31.7 percent per year) is about 10 times larger than the T-bill portfo-
lio’s standard deviation (3.1 percent per year). We will return to these figures
momentarily.
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C H A P T E R 1 0 Some Lessons from Capital Market History 327
Normal Distribution
For many different random events in nature, a particular frequency distribution, the
normal distribution (or bell curve), is useful for describing the probability of ending up in a
given range. For example, the idea behind “grading on a curve” comes from the fact that
exam scores often resemble a bell curve.
Figure 10.11 illustrates a normal distribution and its distinctive bell shape. As you can
see, this distribution has a much cleaner appearance than the actual return distributions il-
lustrated in Figure 10.10. Even so, like the normal distribution, the actual distributions do
appear to be at least roughly mound-shaped and symmetric. When this is true, the normal
distribution is often a very good approximation.
Also, keep in mind that the distributions in Figure 10.10 are based on only 92 yearly
observations, while Figure 10.11 is, in principle, based on an infinite number. So, if we had
normal distribution
A symmetric, bell-shaped
frequency distribution that
is completely defined by
its average and standard
deviation.
Series
Arithmetic
Mean (%)
Standard
Deviation (%) Distribution (%)
Small-company stocks* 16.5 31.7
Large-company stocks 12.1 19.8
Long-term corporate bonds 6.4 8.3
Long-term government
bonds 6.0 9.9
Intermediate-term
government bonds 5.2 5.6
U.S. Treasury bills 3.4 3.1
Inflation 3.0 4.0 −90 900
*The 1933 small-company stocks total return was 142.9 percent.
Source: Morningstar, 2018, author calculations.
Historical average returns, standard deviations, and frequency distributions: 1926–2017FIGURE 10.10
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328 P A R T 6 Risk and Return
been able to observe returns for, say, 1,000 years, we might have filled in a lot of the irregu-
larities and ended up with a much smoother picture. For our purposes, it is enough to ob-
serve that the returns are at least roughly normally distributed.
The usefulness of the normal distribution stems from the fact that it is completely de-
scribed by the average and the standard deviation. If you have these two numbers, then there
is nothing else to know. For example, with a normal distribution, the probability that we end
up within one standard deviation of the average is about ⅔. The probability that we end up
within two standard deviations is about 95 percent. Finally, the probability of being more
than three standard deviations away from the average is less than 1 percent. These ranges
and the probabilities are illustrated in Figure 10.11.
To see why this is useful, recall from Figure 10.10 that the standard deviation of re-
turns on the large common stocks is 19.8 percent. The average return is 12.1 percent. So,
assuming that the frequency distribution is at least approximately normal, the probabil-
ity that the return in a given year is in the range of −7.7 percent to 31.9 percent (12.1
percent plus or minus one standard deviation, 19.8 percent) is about ⅔. This range is il-
lustrated in Figure 10.11. In other words, there is about one chance in three that the re-
turn will be outside this range. This literally tells you that, if you buy stocks in large
companies, you should expect to be outside this range in one year out of every three.
This reinforces our earlier observations about stock market volatility. However, there is
only a 5 percent chance (approximately) that we would end up outside the range of
−27.5 percent to 51.7 percent (12.1 percent plus or minus 2 × 19.8%). These points
also are illustrated in Figure 10.11.
The Second Lesson
Our observations concerning the year-to-year variability in returns are the basis for our sec-
ond lesson from capital market history. On average, bearing risk is handsomely rewarded,
but, in a given year, there is a significant chance of a dramatic change in value. Thus, our
second lesson is this: The greater the potential reward, the greater is the risk.
Thus far in this chapter, we have emphasized the year-to-year variability in returns. We
should note that even day-to-day movements can exhibit considerable volatility. For exam-
ple, on September 17, 2001, the Dow Jones Industrial Average (DJIA) plummeted 684.81
points, or 7.13 percent. By historical standards, it was one of the worst days ever for the
30 stocks that comprise the DJIA (as well as for a majority of stocks in the market). Still,
while the drop was the largest decrease in the DJIA ever in terms of points at the time, it
The normal
distribution
Illustrated returns are
based on the historical
return and standard
deviation for a portfolio
of large common
stocks.
FIGURE 10.11 Probability
Return on
large common
stocks
68%
95%
>99%
−3σ
−47.3% −27.5% −7.7% 12.1% 31.9% 51.7% 71.5%
−2σ −1σ 0 +1σ +2σ +3σ
ros13952_ch10_310-349.indd 328 12/24/18 5:11 PM
C H A P T E R 1 0 Some Lessons from Capital Market History 329
actually wasn’t quite in the top 12 largest one-day percentage decreases in history, as illus-
trated in the following table:
Top 12 One-Day Percentage Changes in the Dow
Jones Industrial Average
1 October 19, 1987 −22.61
2 October 28, 1929 −12.82
3 October 29, 1929 −11.73
4 November 6, 1929 − 9.92
5 December 18, 1899 − 8.72
6 August 12, 1932 − 8.40
7 March 14, 1907 − 8.29
8 October 26, 1987 − 8.04
9 October 15, 2008 − 7.87
10 July 21, 1933 − 7.84
11 October 18, 1937 − 7.75
12 December 1, 2008 − 7.70
Source: http://online.wsj.com/mdc/public/page/2_3047
-djia_alltime.html.
This discussion also highlights the importance of looking at returns in terms of percent-
ages rather than dollar amounts or index points. For example, the biggest one-day loss in
terms of points was on September 29, 2008, when the DJIA declined by 778 points. The
second worst was the 733-point drop of October 15, 2008. In contrast, the 5.57-point drop
in the DJIA on December 18, 1899, marked the fifth worst day in the history of the index,
but a 5.6-point loss in the DJIA in today’s market would hardly be noticed. This is precisely
why we relied on percentage returns when we examined market history in this chapter.3
2008: The Bear Growled and Investors Howled
To reinforce our point concerning stock market volatility, consider that a few short years
ago, 2008 entered the record books as one of the worst years for stock market investors in
U.S. history. How bad was it? As shown in several exhibits in the chapter (e.g., Table 10.1),
the widely followed S&P 500 index plunged 37 percent. Of the 500 stocks in the index, 485
were down for the year.
Over the period 1926–2017, only the year 1931 had a lower return than 2008
(−44 percent versus −37 percent). Making matters worse, the downdraft continued with a
further decline of 8.43 percent in January 2009. In all, from November 2007 (when the de-
cline began) through March 2009 (when it ended), the S&P 500 lost 50 percent of its value.
Figure 10.12 shows the month-by-month performance of the S&P 500 during 2008. As
indicated, returns were negative in 8 of the 12 months. Most of the damage occurred in the
fall, with investors losing almost 17 percent in October alone. Small stocks fared no better.
They also fell 37 percent for the year (with a 21 percent drop in October), their worst perfor-
mance since losing 58 percent in 1937.
As Figure 10.12 suggests, stock prices were highly volatile during the year. Oddly, the
S&P had 126 up days and 126 down days (remember the markets are closed weekends and
3By the way, as you may have noticed, what’s kind of weird is that 6 of the 12 worst days in the history of the DJIA
occurred in October, including the top 3. We have no clue as to why. Furthermore, looking back at the Mark Twain
quote near the beginning of the chapter, how do you suppose he knew? Sounds like a case for CSI: Wall Street.
ros13952_ch10_310-349.indd 329 12/24/18 5:11 PM
330 P A R T 6 Risk and Return
holidays). Of course, the down days were much worse on average. To see how extraordi-
nary volatility was in 2008, consider that there were 18 days during which the value of the
S&P changed by more than five percent. There were only 17 such moves between 1956
and 2007!
The drop in stock prices was a global phenomenon, and many of the world’s major
markets were off by much more than the S&P. China, India, and Russia, for example, all
experienced declines of more than 50 percent. Tiny Iceland saw share prices drop by more
than 90 percent for the year. Trading on the Icelandic exchange was temporarily suspended
on October 9. In what has to be a modern record for a single day, stocks fell by 76 percent
when trading resumed on October 14.
Were there any bright spots in 2008 for U.S. investors? The answer is yes because, as
stocks tanked, bonds soared, particularly U.S. Treasury bonds. In fact, long-term Treasuries
gained 40 percent, while shorter-term Treasury bonds were up 13 percent. Long-term corpo-
rate bonds did less well, but still managed to finish in positive territory, up 9 percent. These
returns were especially impressive considering that the rate of inflation, as measured by the
CPI, was essentially zero.
Of course, stock prices can be volatile in both directions. From March 2009 through
February 2011, a period of about 700 days, the S&P 500 doubled in value. This climb was
the fastest doubling since 1936 when the S&P did it in just 500 days. So, what lessons
should investors take away from this very recent, and very turbulent, bit of capital market
history? First, and most obviously, stocks have significant risk! But there is a second, equally
important lesson. Depending on the mix, a diversified portfolio of stocks and bonds might
have suffered in 2008, but the losses would have been much smaller than those experienced
by an all-stock portfolio. In other words, diversification matters, a point we will examine in
detail in our next chapter.
Using Capital Market History
Based on the discussion in this section, you should begin to have an idea of the risks and
rewards from investing. For example, in the middle of 2018, Treasury bills were paying about
2.3 percent. Suppose we had an investment that we thought had about the same risk as a
−20
−15
−10
−5
0
5
10
Jan Feb Mar Apr May Jun Jul Aug Sep Oct DecNov
S&P 500 monthly
returns: 2008
FIGURE 10.12
ros13952_ch10_310-349.indd 330 12/24/18 5:11 PM
portfolio of large-company common stocks. At a minimum, what return would this invest-
ment have to offer for us to be interested?
From Table 10.3, the risk premium on larger common stocks has been 8.7 percent his-
torically, so a reasonable estimate of our required return would be this premium plus the T-
bill rate, 8.7% + 2.3% = 11.0%. If we were thinking of starting a new business, then the risks
of doing so might resemble those of investing in small-company stocks. In this case, the risk
premium is 13.1 percent, so we might require more like 15.4 percent from such an invest-
ment, at a minimum.
We will discuss the relationship between risk and required return in more detail in the
next chapter. For now, you should notice that a projected internal rate of return, or IRR, on
a risky investment in the 10 percent to 20 percent range isn’t particularly outstanding. It
depends on how much risk there is. This, too, is an important lesson from capital market
history.
The discussion in this section shows that there is much to be learned from capital mar-
ket history. As the accompanying Finance Matters box describes, capital market history also
provides some odd coincidences.
The Super Guide to Investing
Every year, in late January or early February, about 90 mil-lion people in the United States watch television for a
prediction of how well the stock market is going to do in the
upcoming year. So you missed it this year? Maybe not. The
stock market predictor we’re talking about is the Super
Bowl!
The Super Bowl indicator has become one of the more
famous (or infamous) indicators of stock market perfor-
mance. Here’s how it works. In the 1960s, the original Na-
tional Football League (NFL) and the upstart American
Football League (AFL) were fighting for dominance. The Su-
per Bowl indicator says that if a team from the original AFL
wins the Super Bowl, the market posts a negative return for
the year, and, if a team from the original NFL wins, the mar-
ket will post a gain for the year.
So are you ready to bet the ranch on the Super Bowl
indicator? Maybe that’s not a super idea. Between 1997 and
2017, the Super Bowl indicator has only been right 10 out of
20 years. Of course, you could follow the second Super
Bowl indicator. When there are 50 points or more scored in
the game, the stock market had an average return of 18.6
percent. When 39 points or fewer are scored, the average
market return is only 3.7 percent.
The Philadelphia Eagles won the Super Bowl in 2018.
This was the Eagles’ first Super Bowl victory and the team is
an original NFL team. Was the Super Bowl predictor correct
in 2018?
For those of you who like horse racing, there is the Tri-
ple Crown winner indicator. According to this indicator, if a
horse wins the Kentucky Derby, Preakness, and Belmont
Stakes, better known as the Triple Crown, the stock market
will fall dramatically. However, when you consider that the
youngest of these races, the Kentucky Derby, began in 1875
and to date there have only been 13 Triple Crown winners,
what do you do in the 100+ years when there is no Triple
Crown winner? Of course, Justify won the Triple Crown in
2018, a negative market indicator, but the Super Bowl indica-
tor is positive. Which one should you follow?
So you want more predictors? How about the hemline
indicator, also known as the “bull markets and bare knees”
indicator? Through much of the nineteenth century, long
skirts dominated women’s fashion, and the stock market ex-
perienced many bear markets. In the 1920s, flappers re-
vealed their knees and the stock market boomed. Even the
stock market crash of October 1987 was predicted by hem-
lines. During the 1980s, miniskirts flourished, but by October
1987 a fashion shift had women wearing longer skirts.
These are only three examples of what are known as
“technical” trading rules. There are lots of others. How seri-
ously should you take them? That’s up to you, but our advice
is to keep in mind that life is full of odd coincidences. Just
because a bizarre stock market predictor seems to have
worked well in the past doesn’t mean that it’s going to work
in the future.
FINANCE MATTERS
331
ros13952_ch10_310-349.indd 331 12/24/18 5:11 PM
332 P A R T 6 Risk and Return
More on the Stock Market Risk Premium
As we have discussed, the historical stock market risk premium has been substantial. In
fact, based on standard economic models, it has been argued that the historical risk
premium is too big and is thus an overestimate of what is likely to happen in the
future.
Of course, any time we use the past to predict the future, there is the danger that the
past period we observe isn’t representative of what the future will hold. For example, in this
chapter, we studied the period 1926–2017. Perhaps investors got lucky over this period and
earned particularly high returns. Data from earlier years are available, though they are not
of the same quality. With that caveat in mind, researchers have traced returns back to 1802,
and the risk premiums seen in the pre-1926 era are perhaps a little smaller, but not dramati-
cally so.
Another possibility is that the U.S. stock market experience was unusually good. In-
vestors in at least some other major countries did not do as well because their financial
markets were nearly or completely wiped out because of revolution, war, and/or hyperinfla-
tion. A recent study addresses this issue by examining data from 1900–2010 for
17 countries.
Figure 10.13 shows the historical average stock market risk premium for all 17 countries
over the 111-year period. Looking at the numbers, the U.S. risk premium is the 7th highest
at 7.2 percent (which differs from our earlier estimate because of the differing time periods
examined). The overall average risk premium is 6.9 percent. These numbers make it clear
that U.S. investors did well, but not exceptionally so relative to investors in many other
countries.
So, is the U.S. stock market risk premium estimated from 1926–2017 too high? The evi-
dence seems to suggest that the answer is “maybe a little.” One thing we haven’t stressed so
far is that even with 111 years of data, the average risk premium is still not measured with
great precision. From a statistical standpoint, the standard error associated with the U.S.
estimated risk premium of 7.2 percent is about 2 percent.4 So, even one standard error range
covers 5.2 to 9.2 percent.
EXAMPLE 10.3 Investing in Growth Stocks
The term growth stock is frequently a euphemism for small-company stock. Are such invest-
ments suitable for “widows and orphans”? Before answering, you should consider the historical
volatility. For example, from the historical record, what is the approximate probability that you
will actually lose 15 percent or more of your money in a single year if you buy a portfolio of such
companies?
Looking back at Figure 10.10, we see that the average return on small stocks is 16.5 percent,
and the standard deviation is 31.7 percent. Assuming that the returns are approximately normal,
there is about a ⅓ probability that you will experience a return outside the range of –15.2 percent
to 48.2 percent (= 16.5% ± 31.7%).
Because the normal distribution is symmetric, the odds of being above or below this range are
equal. There is thus a ⅙ chance (half of ⅓) that you will lose more than 15.2 percent. So, you should
expect this to happen once in every six years, on average. Such investments thus can be very vola-
tile, and they are not well suited for those who cannot afford the risk.
4Recall from basic “sadistics” that the standard error of a sample mean is the sample standard deviation divided by
the square root of the sample size. In our case, the standard deviation over the 1900–2010 period (not shown) was
19.8 percent, so the standard error is .198/ √
__
111 = .019.
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C H A P T E R 1 0 Some Lessons from Capital Market History 333
CONCEPT QUESTIONS
10.4a In words, how do we calculate a variance? A standard deviation?
10.4b With a normal distribution, what is the probability of ending up more than one
standard deviation below the average?
10.4c Assuming that long-term corporate bonds have an approximately normal
distribution, what is the approximate probability of earning 14.6 percent or more in a
given year? With T-bills, approximately what is this probability?
10.4d What is the second lesson from capital market history?
Be
lgi
um
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itz
er
lan
d
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ain
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ay
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da
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lan
d UK
Ne
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rla
nd
s
U.
S.
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A
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a
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Country
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4.6%
5.1% 5.3%
5.4% 5.5% 5.6%
5.9% 6.0%
Average = 6.9%
7.2%
8.3% 8.3%
8.7%
9.0%
9.8% 9.8%
6.5% 6.6%
Stock market risk premiums for 17 countries: 1900–2010FIGURE 10.13
Source: Based on information in Dimson, Elroy, Marsh, Paul and Staunton, Michael, “The Worldwide Equity Premium: A Smaller Puzzle,” in Handbook
of the Equity Risk Premium, Mehra, Rajnish, ed., Elsevier: 2007. Updates by the authors.
ros13952_ch10_310-349.indd 333 12/24/18 5:11 PM
334 P A R T 6 Risk and Return
MORE ON AVERAGE RETURNS
Thus far in this chapter, we have looked closely at simple average returns. But there is
another way of computing an average return. The fact that average returns are calcu-
lated two different ways leads to some confusion, so our goal in this section is to ex-
plain the two approaches and also the circumstances under which each is
appropriate.
Arithmetic versus Geometric Averages
Let’s start with a simple example. Suppose you buy a particular stock for $100. Unfortu-
nately, the first year you own it, it falls to $50. The second year you own it, it rises back to
$100, leaving you where you started (no dividends were paid).
What was your average return on this investment? Common sense seems to say that
your average return must be exactly zero because you started with $100 and ended with
$100. But if we calculate the returns year-by-year, we see that you lost 50 percent the
first year (you lost half of your money). The second year, you made 100 percent (you
doubled your money). Your average return over the two years was thus (−50% +
100%)/2 = 25%!
So which is correct, 0 percent or 25 percent? The answer is that both are correct: They
just answer different questions. The 0 percent is called the geometric average return. The
25 percent is called the arithmetic average return. The geometric average return answers
the question “What was your average compound return per year over a particular period?” The
arithmetic average return answers the question “What was your return in an average year over
a particular period?”
Notice that, in previous sections, the average returns we calculated were all arithmetic
averages, so we already know how to calculate them. What we need to do now is (1) learn
how to calculate geometric averages and (2) learn the circumstances under which one aver-
age is more meaningful than the other.
Calculating Geometric Average Returns
First, to illustrate how we calculate a geometric average return, suppose a particular invest-
ment had annual returns of 10 percent, 12 percent, 3 percent, and −9 percent over the last
four years. The geometric average return over this four-year period is calculated as (1.10 ×
1.12 × 1.03 × .91)1/4 − 1 = .0366, or 3.66%. In contrast, the average arithmetic return we
have been calculating is (.10 + .12 + .03 − .09)/4 = .040, or 4.0%.
In general, if we have T years of returns, the geometric average return over these T years
is calculated using this formula:
Geometric average return = [(1 + R1) × (1 + R2) × . . . × (1 + RT)]1/T − 1 [10.4]
This formula tells us that four steps are required:
1. Take each of the T annual returns R1, R2, . . . , RT and add a one to each (after
converting them to decimals!).
2. Multiply all the numbers from Step 1 together.
3. Take the result from Step 2 and raise it to the power of 1/T.
4. Finally, subtract one from the result of Step 3. The result is the geometric average
return.
10.5
coverage online
Excel
Master
geometric average
return
The average compound
return earned per year
over a multiyear period.
arithmetic average
return
The return earned in an
average year over a
particular period.
ros13952_ch10_310-349.indd 334 12/24/18 5:11 PM
C H A P T E R 1 0 Some Lessons from Capital Market History 335
One thing you may have noticed in our examples thus far is that the geometric average
returns seem to be smaller. It turns out that this will always be true (as long as the returns
are not all identical, in which case the two “averages” would be the same). To illustrate,
Table 10.4 shows the arithmetic averages and standard deviations from Figure 10.10, along
with the geometric average returns.
As shown in Table 10.4, the geometric averages are all smaller, but the magnitude
of the difference varies quite a bit. The reason is that the difference is greater for more
volatile investments. In fact, there is a useful approximation. Assuming all the numbers
are expressed in decimals (as opposed to percentages), the geometric average return is
approximately equal to the arithmetic average return minus half the variance. For ex-
ample, looking at the large-company stocks, the arithmetic average is .121 and the
standard deviation is .198, implying that the variance is .0392. The approximate geo-
metric average is thus .121 − .0392 _____ 2 = .101, which, in this case, is close to the actual
value.
EXAMPLE 10.4 Calculating the Geometric Average Return
Calculate the geometric average return for the S&P 500 using the returns given below. To do so,
convert percentages to decimal returns, add one, and then calculate their product:
S&P 500 Returns Product
11.14% 1.1114
37.13 × 1.3713
43.31 × 1.4331
− 8.91 × .9109
−25.26 × .7474
1.4870
Notice that the number 1.4870 is what our investment is worth after five years if we started with
a $1 investment. The geometric average return is then calculated as:
Geometric average return = 1.48701/5 − 1 = .0826, or 8.26%
Thus the geometric average return is about 8.26 percent in this example. Here is a tip: If you
are using a financial calculator, you can put $1 in as the present value, $1.4870 as the future
value, and 5 as the number of periods. Then, solve for the unknown rate. You should get the
same answer we did.
Average Return
Series Geometric Arithmetic Standard Deviation
Large-company stocks 10.2% 12.1% 19.8%
Small-company stocks 12.1 16.5 31.7
Long-term corporate bonds 6.1 6.4 8.3
Long-term government bonds 5.5 6.0 9.9
Intermediate-term government bonds 5.1 5.2 5.6
U.S. Treasury bills 3.4 3.4 3.1
Inflation 2.9 3.0 4.0
Geometric versus
arithmetic average
returns: 1926–2017
TABLE 10.4
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336 P A R T 6 Risk and Return
Arithmetic Average Return
or Geometric Average Return?
When we look at historical returns, the difference between the geometric and arithmetic
average returns isn’t too hard to understand. To put it slightly differently, the geometric aver-
age tells you what you actually earned per year on average, compounded annually. The
arithmetic average tells you what you earned in a typical year. You should use whichever one
answers the question you want answered.
A somewhat trickier question concerns which average return to use when forecast-
ing future wealth levels, and there’s a lot of confusion on this point among analysts and
financial planners. First, let’s get one thing straight: If you know the true arithmetic av-
erage return, then this is what you should use in your forecast. So, for example, if you
know the arithmetic return is 10 percent, then your best guess of the value of a $1,000
investment in 10 years is the future value of $1,000 at 10 percent for 10 years, or
$2,593.74.
The problem we face, however, is that we usually only have estimates of the arithmetic
and geometric returns, and estimates have errors. In this case, the arithmetic average return
is probably too high for longer periods and the geometric average is probably too low for
shorter periods. So, you should regard long-run projected wealth levels calculated using
arithmetic averages as optimistic. Short-run projected wealth levels calculated using geomet-
ric averages are probably pessimistic.
As a practical matter, if you are using averages calculated over a long period of time
(such as the 92 years we use) to forecast up to a decade or so into the future, then you
should use the arithmetic average. If you are forecasting a few decades into the future (such
as you might do for retirement planning), then you should split the difference between the
arithmetic and geometric average returns. Finally, if for some reason you are doing very long
forecasts covering many decades, use the geometric average.
This concludes our discussion of geometric versus arithmetic averages. One last note:
In the future, when we say “average return,” we mean arithmetic average unless we explicitly
say otherwise.
CONCEPT QUESTIONS
10.5a If you want to forecast what the stock market is going to do over the next year,
should you use an arithmetic or geometric average?
10.5b If you want to forecast what the stock market is going to do over the next century,
should you use an arithmetic or geometric average?
EXAMPLE 10.5 More Geometric Averages
Take a look back at Figure 10.4. There, we showed the value of a $1 investment after 92 years. Use
the value for the large-company stock investment to check the geometric average in Table 10.4.
In Figure 10.4, the large-company investment grew to $7,346.15 over 92 years. The geometric
average return is thus:
Geometric average return = 7,346.151/92 − 1 = .102, or 10.2%
This 10.2% is the value shown in Table 10.4. For practice, check some of the other numbers in
Table 10.4 the same way.
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C H A P T E R 1 0 Some Lessons from Capital Market History 337
CAPITAL MARKET EFFICIENCY
Capital market history suggests that the market values of stocks and bonds can fluctuate widely
from year to year. Why does this occur? At least part of the answer is that prices change be-
cause new information arrives, and investors reassess asset values based on that information.
The behavior of market prices has been extensively studied. A question that has re-
ceived particular attention is whether prices adjust quickly and correctly when new informa-
tion arrives. A market is said to be efficient if this is the case. To be more precise, in an
efficient capital market, current market prices fully reflect available information. By this
we mean that, based on available information, there is no reason to believe that the current
price is too low or too high.
The concept of market efficiency is a rich one, and much has been written about it. A
full discussion of the subject goes beyond the scope of our study of business finance. How-
ever, because the concept figures so prominently in studies of market history, we briefly de-
scribe the key points here.
Price Behavior in an Efficient Market
To illustrate how prices behave in an efficient market, suppose the F-Stop Camera Corpora-
tion (FCC), through years of secret research and development, has developed a camera
whose autofocusing system will double the speed of those now available. FCC’s capital
budgeting analysis suggests that launching the new camera is a highly profitable move; in
other words, the NPV appears to be positive and substantial. The key assumption thus far is
that FCC has not released any information about the new system, so the fact of its existence
is “inside” information only.
Now, consider a share of stock in FCC. In an efficient market, its price reflects what is
known about FCC’s current operations and profitability, and it reflects market opinion
about FCC’s potential for future growth and profits. The value of the new autofocusing sys-
tem is not reflected, however, because the market is unaware of its existence.
If the market agrees with FCC’s assessment of the value of the new project, FCC’s
stock price will rise when the decision to launch is made public. Assume the announcement
is made in a press release on Wednesday morning. In an efficient market, the price of shares
in FCC will adjust quickly to this new information. Investors should not be able to buy the
stock on Wednesday afternoon and make a profit on Thursday. This would imply that it
took the stock market a full day to realize the implication of the FCC press release. If the
market is efficient, the price of shares of FCC stock on Wednesday afternoon already will re-
flect the information contained in the Wednesday morning press release.
Figure 10.14 presents three possible stock price adjustments for FCC. In the figure, Day
0 represents the announcement day. As illustrated, before the announcement, FCC’s stock
sells for $140 per share. The NPV per share of the new system is, say, $40, so the new price
will be $180 once the value of the new project is fully reflected.
The solid line in Figure 10.14 represents the path taken by the stock price in an efficient
market. In this case, the price adjusts immediately to the new information and no further
changes in the price of the stock take place. The broken line in Figure 10.14 depicts a delayed
reaction. Here, it takes the market eight days or so to fully absorb the information. Finally,
the dotted line illustrates an overreaction and subsequent adjustment to the correct price.
The broken line and the dotted line in Figure 10.14 illustrate paths that the stock price
might take in an inefficient market. If, for example, stock prices don’t adjust immediately to
new information (the broken line), then buying stock immediately following the release of
new information and then selling it several days later would be a positive NPV activity be-
cause the price is too low for several days after the announcement.
10.6
efficient capital
market
Market in which security
prices reflect available
information.
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338 P A R T 6 Risk and Return
The Efficient Markets Hypothesis
The efficient markets hypothesis (EMH) asserts that well-organized capital markets, such as the
NYSE, are efficient markets, at least as a practical matter. In other words, an advocate of the
EMH might argue that while inefficiencies may exist, they are relatively small and uncommon.
If a market is efficient, then there is a very important implication for market partici-
pants: All investments in an efficient market are zero NPV investments. The reason is not
complicated. If prices are neither too low nor too high, then the difference between the
market value of an investment and its cost is zero; hence, the NPV is zero. As a result, in an
efficient market, investors get exactly what they pay for when they buy securities, and firms
receive exactly what their stocks and bonds are worth when they sell them.
What makes a market efficient is competition among investors. Many individuals spend their
entire lives trying to find mispriced stocks. For any given stock, they study what has happened in
the past to the stock’s price and its dividends. They learn, to the extent possible, what a compa-
ny’s earnings have been, how much it owes to creditors, what taxes it pays, what businesses it is in,
what new investments are planned, how sensitive it is to changes in the economy, and so on.
Not only is there a great deal to know about any particular company, there is a powerful
incentive for knowing it, namely, the profit motive. If you know more about some company
than other investors in the marketplace, you can profit from that knowledge by investing in
the company’s stock if you have good news and by selling it if you have bad news.
The logical consequence of all this information being gathered and analyzed is that
mispriced stocks will become fewer and fewer. In other words, because of competition
among investors, the market will become increasingly efficient. A kind of equilibrium comes
into being where there is just enough mispricing around for those who are best at identifying
it to make a living at it. For most other investors, the activity of information gathering and
analysis will not pay.5 Having said this, the accompanying Finance Matters box indicates how
hard it is for anybody to “beat the market.”
efficient markets
hypothesis (EMH)
The hypothesis that actual
capital markets, such as
the New York Stock
Exchange, are efficient.
Look under the
“contents” link at
www.investorhome.com
for more info on the EMH.
Reaction of stock price to new information in efficient and inefficient marketsFIGURE 10.14
Overreaction and
correction
Delayed reaction
Efficient market reaction
220
180
140
100
−8 −6 −4 −2 0 + 2 + 4 + 6 + 8
Price ($)
Days relative
to announcement day
(Day 0)
Efficient market reaction: The price instantaneously adjusts
to and fully reflects new information; there is no tendency for
subsequent increases and decreases.
Delayed reaction: The price partially adjusts to the new
information; eight days elapse before the price completely
reflects the new information.
Overreaction and correction: The price overadjusts to the
new information; it overshoots the new price and subsequently
corrects.
5The idea behind the EMH can be illustrated by the following short story: A student was walking down the hall with her
finance professor when they both saw a $20 bill on the ground. As the student bent down to pick it up, the professor shook
her head slowly and, with a look of disappointment on her face, said patiently to the student, “Don’t bother. If it were really
there, someone else would have picked it up already.” The moral of the story reflects the logic of the efficient markets hy-
pothesis: If you think you have found a pattern in stock prices or a simple device for picking winners, you probably have not.
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Some Common Misconceptions about the EMH
No idea in finance has attracted as much attention as that of efficient markets, and not all
of the attention has been flattering. Rather than rehash the arguments here, we will be con-
tent to observe that some markets are more efficient than others. For example, financial
markets on the whole are probably much more efficient than real asset markets.
Having said this, it is the case that much of the criticism of the EMH is misguided be-
cause it is based on a misunderstanding of what the hypothesis says and what it doesn’t say.
For example, when the notion of market efficiency was first publicized and debated in the
popular financial press, it often was characterized by words to the effect that “throwing
darts at the financial page will produce a portfolio that can be expected to do as well as any
managed by professional security analysts.”
Confusion over statements of this sort has often led to a failure to understand the impli-
cations of market efficiency. For example, sometimes it is wrongly argued that market
Can the Pros Beat the Market?
2017 was a good year for investors in the Quantified STF mutual fund, which posted a gain of about 70 percent for
the year, one of the highest returns for any mutual fund. In
an industry where literally millions of dollars are at stake for
mutual fund managers, it would seem that mutual funds
should be able to consistently outperform the market. Unfor-
tunately for investors, during 2017, only 43 percent of mutual
funds outperformed their benchmarks for the year. The per-
formance of mutual funds was even worse in 2016 as only
26 percent outperformed.
Other facts point to the difficulty that mutual funds have
in beating the market. For example, over the past 50 years,
the stock market had an average return of 13.5 percent,
while the average mutual fund returned 11.8 percent. And
during the past five years, only 11 percent of mutual fund
managers had a performance each year that was in the top
half of the funds in their respective category. This underper-
formance is not limited to mutual fund managers. The
Hulbert Financial Digest, which tracks the performance of
investment letters, reported that 80 percent of investment
letters underperformed the stock market over the long term.
The year 2017 also saw the end of the “Buffett Chal-
lenge.” In 2008, famed investor Warren Buffett made a $1
million bet with Ted Seides, founder of the Protégé hedge
fund. A hedge fund is a limited partnership that pools inves-
tors’ money, similar in this respect to a mutual fund. The wa-
ger, the proceeds of which went to the charity of the winner’s
choice, was that a portfolio of five hedge funds picked by
Seides could not outperform the S&P 500. Seides conceded
defeat in September 2017, about four months early. At that
point, the S&P 500 had a cumulative return of about 85 per-
cent over the previous nine plus years, while the five hedge
funds had a cumulative return of about 22 percent.
One thing we know for sure is that past performance is
no predictor of future returns. For example, in July 1994, the
American Century Giftrust fund had been the best-performing
mutual fund for the previous 10 years, with an average an-
nual return above 20 percent. But the next 10 years weren’t
as kind to the investors in this fund. The average annual re-
turn for 1994 to 2004 was 2.87 percent, which was lower
than U.S. Treasury bills during the same period. Following
the old saying “What goes up, must come down,” other
funds have had similar stories. The Van Wagoner Emerging
Growth Fund returned 291.2 percent in 1999, only to lose
59.7 percent and 64.6 percent the next two years. Similarly,
the Oppenheimer Enterprise Fund gained 105.75 percent in
1999 but lost 40.6 percent in 2000, followed by two more
years of double-digit losses.
Sometimes, we see proposed evidence showing that mu-
tual fund managers collectively can beat the market. Consider
2005, when the S&P 500 gained about 3 percent. Diversified
U.S. stock funds averaged 7 percent for the year, so it appears,
at first glance, that mutual fund managers outperformed the
market. However, in 2008, only 42 percent of all managers
outperformed the market, with an average return about 1 per-
cent lower than the market return. Over the years, the track
record of the pros is relatively clear: More often than not, they
underperform. In fact, based on historical averages, about 70
percent of all managers will underperform in a typical year.
The inability of the pros to consistently beat the market
doesn’t prove that markets are efficient. The evidence, how-
ever, does lend some credence to the semistrong form version
of market efficiency. Plus, it adds to a growing body of evi-
dence that tends to support a basic premise: While it may be
possible to outperform the market for relatively short periods of
time, it is very difficult to do so consistently over the long haul.
FINANCE MATTERS
339
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340 P A R T 6 Risk and Return
efficiency means that it doesn’t matter how you invest your money because the efficiency of
the market will protect you from making a mistake. However, a random dart-thrower might
wind up with all of the darts sticking into one or two high-risk stocks that deal in genetic
engineering. Would you really want all of your money in two such stocks?
What efficiency does imply is that the price a firm will obtain when it sells a share of its
stock is a “fair” price in the sense that it reflects the value of that stock given the information avail-
able about the firm. Shareholders do not have to worry that they are paying too much for a stock
with a low dividend or some other sort of characteristic because the market already has incorpo-
rated that characteristic into the price. We sometimes say the information has been “priced in.”
The concept of efficient markets can be explained further by replying to a frequent objec-
tion. It is sometimes argued that the market cannot be efficient because stock prices fluctuate
from day to day. If the prices are right, the argument goes, then why do they change so much
and so often? From our earlier discussion, we can see that these price movements are in no way
inconsistent with efficiency. Investors are bombarded with information every day. The fact that
prices fluctuate is, at least in part, a reflection of that information flow. In fact, the absence of
price movements in a world that changes as rapidly as ours would suggest inefficiency.
The Forms of Market Efficiency
It is common to distinguish between three forms of market efficiency. Depending on the
degree of efficiency, we say that markets are either weak form efficient, semistrong form effi-
cient, or strong form efficient. The difference between these forms relates to what information
is reflected in prices.
We start with the extreme case. If the market is strong form efficient, then all informa-
tion of every kind is reflected in stock prices. In such a market, there is no such thing as in-
side information. Therefore, in our FCC example, we apparently were assuming that the
market was not strong form efficient.
Casual observation, particularly in recent years, suggests that inside information does
exist and it can be valuable to possess. Whether it is lawful or ethical to use that information
is another issue. In any event, we conclude that private information about a particular stock
may exist that is not currently reflected in the price of the stock. For example, prior knowl-
edge of a takeover attempt could be very valuable.
The second form of efficiency, semistrong efficiency, is the most controversial. If a
market is semistrong form efficient, then all public information is reflected in the stock
price. The reason this form is controversial is that it implies that security analysts who try to
identify mispriced stocks using, for example, financial statement information are wasting
their time because that information is already reflected in the current price.
The third form of efficiency, weak form efficiency, suggests that, at a minimum, the
current price of a stock reflects its own past prices. In other words, studying past prices in
an attempt to identify mispriced securities is futile if the market is weak form efficient.
While this form of efficiency might seem rather mild, it implies that searching for patterns
in historical prices that are useful in identifying mispriced stocks will not work (this prac-
tice, known as “technical” analysis, is quite common).
What does capital market history say about market efficiency? Here again, there is
great controversy. At the risk of going out on a limb, the evidence does seem to tell us three
things. First: Prices do appear to respond very rapidly to new information, and the response
is at least not grossly different from what we would expect in an efficient market. Second:
The future of market prices, particularly in the short run, is very difficult to predict based on
publicly available information. Third: If mispriced stocks do exist, then there is no obvious
means of identifying them. Put another way: Simpleminded schemes based on public infor-
mation will probably not be successful.
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C H A P T E R 1 0 Some Lessons from Capital Market History 341
CONCEPT QUESTIONS
10.6a What is an efficient market?
10.6b What are the forms of market efficiency?
SUMMARY AND CONCLUSIONS
This chapter has explored the subject of capital market history. Such history is useful be-
cause it tells us what to expect in the way of returns from risky assets. We summed up our
study of market history with two key lessons:
1. Risky assets, on average, earn a risk premium. There is a reward for bearing risk.
2. The greater the potential reward from a risky investment, the greater is the risk.
These lessons have significant implications for the financial manager. We will be con-
sidering these implications in the chapters ahead.
We also discussed the concept of market efficiency. In an efficient market, prices adjust
quickly and correctly to new information. Consequently, asset prices in efficient markets are
rarely too high or too low. How efficient capital markets (such as the NYSE) are is a matter of
debate, but, at a minimum, they are probably much more efficient than most real asset markets.
POP QUIZ!
Can you answer the following questions? If your class is using Connect, log on to
SmartBook to see if you know the answers to these and other questions, check out
the study tools, and find out what topics require additional practice!
Section 10.1 Say you buy a share of stock for $50. Its price rises to $55, and it pays a
$2 annual dividend. You do not sell the stock. What is your dividend yield for the year?
Section 10.3 What investments have the lowest historical risk premium?
Section 10.4 If Stock ABC has a mean return of 10 percent with a standard devia-
tion of 5 percent, what is the approximate probability of earning a negative return?
Section 10.5 If you use a geometric average to project short-run wealth levels, how
would you expect your results to skew?
Section 10.6 Why do stock prices fluctuate from day to day?
CHAPTER REVIEW AND SELF-TEST PROBLEMS
10.1 Recent Return History Use Table 10.1 to calculate the average return over the years
1997–2001 for large-company stocks, long-term government bonds, and Treasury
bills. (See Problem 9.)
10.2 More Recent Return History Calculate the standard deviations using information
from Problem 10.1. Which of the investments was the most volatile over this period?
(See Problem 7.)
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342 P A R T 6 Risk and Return
■ Answers to Chapter Review and Self-Test Problems
10.1 We calculate the averages as follows:
Actual Returns and Averages
Year
Large-Company
Stocks
Long-Term
Government Bonds
Treasury
Bills
1997 .3336 .1770 .0519
1998 .2858 .1922 .0486
1999 .2104 −.1276 .0480
2000 −.0910 .2216 .0598
2001 −.1189 .0530 .0333
Average: .1240 .1032 .0483
10.2 We first need to calculate the deviations from the average returns. Using the averages
from Problem 10.1, we get:
Deviations from Average Returns
Year
Large-Company
Stocks
Long-Term
Government Bonds
Treasury
Bills
1997 .2096 .0738 .0036
1998 .1618 .0890 .0003
1999 .0864 −.2308 −.0003
2000 −.2150 .1184 .0115
2001 −.2429 −.0502 −.0150
Total: .0000 .0000 .0000
We square these deviations and calculate the variances and standard deviations:
Squared Deviations from Average Returns
Year
Large-Company
Stocks
Long-Term
Government Bonds
Treasury
Bills
1997 .043941 .005441 .000013
1998 .026186 .007914 .000000
1999 .007468 .053287 .000000
2000 .046216 .014009 .000132
2001 .058991 .002524 .000226
Variance: .0457 .0208 .0001
Standard deviation: .2138 .1442 .0096
To calculate the variances, we added up the squared deviations and divided by 4, the
number of returns less 1. Notice that the stocks had substantially greater volatility
with a larger average return. Once again, such investments are risky, particularly over
short periods of time.
CRITICAL THINKING AND CONCEPTS REVIEW
LO 3 10.1 Investment Selection Given that Madrigal Pharmaceuticals was up by
516 percent for 2017, why didn’t all investors hold Madrigal?
LO 3 10.2 Investment Selection Given that Sears Holdings was down by 61 percent
for 2017, why did some investors hold the stock? Why didn’t they sell out
before the price declined so sharply?
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C H A P T E R 1 0 Some Lessons from Capital Market History 343
LO 3 10.3 Risk and Return We have seen that over long periods of time, stock
investments have tended to substantially outperform bond investments.
However, it is not at all uncommon to observe investors with long horizons
holding entirely bonds. Are such investors irrational?
LO 4 10.4 Market Efficiency Implications Explain why a characteristic of an
efficient market is that investments in that market have zero NPVs.
LO 4 10.5 Efficient Markets Hypothesis A stock market analyst is able to identify
mispriced stocks by comparing the average price for the last 10 days to the
average price for the last 60 days. If this is true, what do you know about
the market?
LO 4 10.6 Semistrong Efficiency If a market is semistrong form efficient, is it also
weak form efficient? Explain.
LO 4 10.7 Efficient Markets Hypothesis What are the implications of the efficient
markets hypothesis for investors who buy and sell stocks in an attempt to
“beat the market”?
LO 4 10.8 Stocks versus Gambling Critically evaluate the following statement:
Playing the stock market is like gambling. Such speculative investing has no
social value, other than the pleasure people get from this form of gambling.
LO 4 10.9 Efficient Markets Hypothesis There are several celebrated investors and
stock pickers frequently mentioned in the financial press who have
recorded huge returns on their investments over the past two decades. Is
the success of these particular investors an invalidation of the EMH?
Explain.
LO 4 10.10 Efficient Markets Hypothesis For each of the following scenarios, discuss
whether profit opportunities exist from trading in the stock of the firm
under the conditions that (1) the market is not weak form efficient, (2) the
market is weak form but not semistrong form efficient, (3) the market is
semistrong form but not strong form efficient, and (4) the market is strong
form efficient.
a. The stock price has risen steadily each day for the past 30 days.
b. The financial statements for a company were released three days ago,
and you believe you’ve uncovered some anomalies in the company’s
inventory and cost control reporting techniques that are causing the
firm’s true liquidity strength to be understated.
c. You observe that the senior management of a company has been
buying a lot of the company’s stock on the open market over the
past week.
QUESTIONS AND PROBLEMS
Select problems are available in McGraw-Hill Connect. Please see the pack-
aging options section of the Preface for more information.
BASIC (Questions 1–18)
1. Calculating Returns Suppose a stock had an initial price of $87 per share,
paid a dividend of $2.15 per share during the year, and had an ending share
price of $98. Compute the percentage total return. What was the dividend
yield? The capital gains yield?
LO 1
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344 P A R T 6 Risk and Return
2. Calculating Returns Rework Problem 1 assuming the ending share price
is $78.
3. Calculating Dollar Returns You purchased 250 shares of a particular stock
at the beginning of the year at a price of $104.32. The stock paid a dividend
of $2.34 per share, and the stock price at the end of the year was $113.65.
What was your dollar return on this investment?
4. Calculating Returns Suppose you bought a bond with an annual coupon
rate of 5.5 percent one year ago for $1,017. The bond sells for $1,041 today.
a. Assuming a $1,000 face value, what was your total dollar return on this
investment over the past year?
b. What was your total nominal rate of return on this investment over the
past year?
c. If the inflation rate last year was 3 percent, what was your total real rate
of return on this investment?
5. Nominal versus Real Returns What was the arithmetic average annual
return on large-company stocks from 1926 through 2017:
a. In nominal terms?
b. In real terms?
6. Bond Returns What is the historical real return on long-term government
bonds? On long-term corporate bonds?
7. Calculating Returns and Variability Using the following returns, calculate
the arithmetic average returns, the variances, and the standard deviations for
X and Y.
Returns
Year X Y
1 14% 41%
2 −13 − 9
3 11 23
4 18 −13
5 8 42
8. Risk Premiums Refer to Table 10.1 in the text and look at the period from
1973 through 1978.
a. Calculate the arithmetic average returns for large-company stocks and
T-bills over this time period.
b. Calculate the standard deviation of the returns for large-company stocks
and T-bills over this time period.
c. Calculate the observed risk premium in each year for the large-company
stocks versus the T-bills. What was the arithmetic average risk premium
over this period? What was the standard deviation of the risk premium
over this period?
d. Is it possible for the risk premium to be negative before an investment
is undertaken? Can the risk premium be negative after the fact?
Explain.
LO 1
LO 1
LO 1
LO 2
LO 2
LO 1
LO 2
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C H A P T E R 1 0 Some Lessons from Capital Market History 345
9. Calculating Returns and Variability You’ve observed the following returns
on Yamauchi Corporation’s stock over the past five years: −10 percent,
24 percent, 21 percent, 11 percent, and 8 percent.
a. What was the arithmetic average return on the stock over this five-year
period?
b. What was the variance of the returns over this period? The standard
deviation?
10. Calculating Real Returns and Risk Premiums For Problem 9, suppose the
average inflation rate over this period was 3.1 percent and the average T-bill
rate over the period was 4.1 percent.
a. What was the average real return on the stock?
b. What was the average nominal risk premium on the stock?
11. Calculating Real Rates Given the information in Problem 10, what was the
average real risk-free rate over this time period? What was the average real
risk premium?
12. Effects of Inflation Look at Table 10.1 and Figure 10.7 in the text. When
were T-bill rates at their highest over the period from 1926 through 2017?
Why do you think they were so high during this period? What relationship
underlies your answer?
13. Calculating Returns You purchased a zero-coupon bond one year ago
for $267.35. The market interest rate is now 5.3 percent. If the bond had
25 years to maturity when you originally purchased it, what was your total
return for the past year? Assume semiannual compounding.
14. Calculating Returns You bought a share of 4.5 percent preferred stock for
$105.35 last year. The market price for your stock is now $103.18. What is
your total return for last year?
15. Calculating Returns You bought a stock three months ago for $51.27 per
share. The stock paid no dividends. The current share price is $55.36. What
is the APR of your investment? The EAR?
16. Calculating Real Returns Refer to Table 10.1. What was the average real
return for Treasury bills from 1926 through 1932?
17. Return Distributions Refer back to Figure 10.10. What range of returns
would you expect to see 68 percent of the time for long-term corporate
bonds? What about 95 percent of the time?
18. Return Distributions Refer back to Figure 10.10. What range of returns
would you expect to see 68 percent of the time for large-company stocks?
What about 95 percent of the time?
INTERMEDIATE (Questions 19–26)
19. Calculating Returns and Variability You find a certain stock that had
returns of 15 percent, −17 percent, 23 percent, and 11 percent for four of
the last five years. If the average return of the stock over this period was
10 percent, what was the stock’s return for the missing year? What is the
standard deviation of the stock’s returns?
20. Arithmetic and Geometric Returns A stock has had returns of −26 percent,
12 percent, 34 percent, −8 percent, 27 percent, and 23 percent over the last
six years. What are the arithmetic and geometric average returns for the stock?
LO 1
LO 1
LO 1
LO 3
LO 2
LO 1
LO 1
LO 1
LO 1
LO 3
LO 3
LO 1
LO 1
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346 P A R T 6 Risk and Return
21. Arithmetic and Geometric Returns A stock has had the following year-end
prices and dividends:
Year Price Dividend
1 $64.10 —
2 74.05 $1.10
3 67.61 1.25
4 76.25 1.45
5 82.70 1.60
6 93.15 1.75
What are the arithmetic and geometric average returns for the stock?
22. Calculating Returns Refer to Table 10.1 in the text and look at the period
from 1973 through 1980.
a. Calculate the average return for Treasury bills and the average annual
inflation rate (consumer price index) for this period.
b. Calculate the standard deviation of Treasury bill returns and inflation
over this time period.
c. Calculate the real return for each year. What is the average real return
for Treasury bills?
d. Many people consider Treasury bills to be risk-free. What does this tell
you about the potential risks of Treasury bills?
23. Calculating Investment Returns You bought one of Rocky Mountain
Manufacturing Co.’s 5.7 percent coupon bonds one year ago for $1,032.15.
These bonds make annual payments and mature nine years from now.
Suppose you decide to sell your bonds today, when the required return on the
bonds is 5.1 percent. If the inflation rate was 3.5 percent over the past year,
what would be your total real return on the investment?
24. Using Return Distributions Suppose the returns on long-term government
bonds are normally distributed. Based on the historical record, what is the
approximate probability that your return on these bonds will be less than
−3.9 percent in a given year? What range of returns would you expect to see
95 percent of the time? What range would you expect to see 99 percent of
the time?
25. Using Return Distributions Assuming that the returns from holding small-
company stocks are normally distributed, what is the approximate probability
that your money will double in value in a single year? What about triple in
value?
26. Distributions In the previous problem, what is the probability that the
return is less than −100 percent (think)? What are the implications for the
distribution of returns?
CHALLENGE (Questions 27–28)
27. Using Probability Distributions Suppose the returns on large-company
stocks are normally distributed. Based on the historical record, use the
NORMDIST function in Excel® to determine the probability that in any
given year you will lose money by investing in large-company common
stocks.
LO 1
LO 3
LO 2
LO 1
LO 1
LO 3
LO 1
LO 3
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C H A P T E R 1 0 Some Lessons from Capital Market History 347
28. Using Probability Distributions Suppose the returns on long-term
corporate bonds and T-bills are normally distributed. Based on the historical
record, use the NORMDIST function in Excel® to answer the following
questions:
a. What is the probability that in any given year, the return on long-term
corporate bonds will be greater than 10 percent? Less than 0 percent?
b. What is the probability that in any given year, the return on T-bills will
be greater than 10 percent? Less than 0 percent?
c. In 1979, the return on long-term corporate bonds was –4.18 percent.
How likely is it that such a low return will recur at some point in the
future? T-bills had a return of 10.56 percent in this same year. How likely
is it that such a high return on T-bills will recur at some point in the
future?
LO 3
WHAT’S ON
THE WEB?
Historical Interest Rates Go to the Federal Reserve Bank of St. Louis website at www
.stlouisfed.org and find the “FRED®” link and the “Interest Rates” link. You will find a
list of links for different historical interest rates. Follow the “10-Year Treasury Constant
Maturity Rate” link and you will find the monthly 10-year Treasury note interest rates.
Calculate the average annual 10-year Treasury interest rate for 2017 and 2018. Compare
this number to the long-term government bond returns and the U.S. Treasury bill returns
found in Table 10.1. How does the 10-year Treasury interest rate compare to these
numbers? Do you expect this relationship to always hold? Why or why not?
EXCEL MASTER IT! PROBLEM
As we have seen, over the 1926–2017 period, small-company stocks had the highest re-
turn and the highest risk, while U.S. Treasury bills had the lowest return and the lowest
risk. While we certainly hope you have a 92-year holding period, it is likely your invest-
ment will be for fewer years. One way risk and return are examined over shorter invest-
ment periods is by using rolling returns and standard deviations. Suppose you have a
series of annual returns, and you want to calculate a three-year rolling average return.
You would calculate the first rolling average at Year 3 using the returns for the first three
years. The next rolling average would be calculated using the returns from Years 2, 3, and
4, and so on.
a. Using the annual returns for large-company stocks and Treasury bills, calculate both
the 5- and 10-year rolling average returns and standard deviations.
b. Over how many 5-year periods did Treasury bills outperform large-company stocks?
How many 10-year periods?
c. Over how many 5-year periods did Treasury bills have a larger standard deviation than
large-company stocks? Over how many 10-year periods?
d. Graph the rolling 5-year and 10-year average returns for large-company stocks and
Treasury bills.
e. What conclusions do you draw from the preceding results?
coverage online
Excel
Master
ros13952_ch10_310-349.indd 347 12/24/18 5:11 PM
348 P A R T 6 Risk and Return
Story, they informed you that the company stock
was expected to be publicly sold in three to five
years. If you needed to sell the stock before it be-
came publicly traded, the company would buy it
back at the then-current appraised value.
2. Arias S&P 500 Index Fund. This mutual fund tracks
the S&P 500. Stocks in the fund are weighted ex-
actly the same as they are in the S&P 500. This
means that the fund’s return is approximately the
return of the S&P 500, minus expenses. With an
index fund, the manager is not required to research
stocks and make investment decisions, so fund ex-
penses are usually low. The Arias S&P 500 Index
Fund charges expenses of .20 percent of assets
per year.
3. Arias Small-Cap Fund. This fund primarily invests in
small capitalization stocks. As such, the returns of
the fund are more volatile. The fund also can invest
10 percent of its assets in companies based outside
the United States. This fund charges 1.70 percent of
assets in expenses per year.
4. Arias Large-Company Stock Fund. This fund invests
primarily in large capitalization stocks of companies
based in the United States. The fund is managed
by Melissa Arias and has outperformed the market
in six of the last eight years. The fund charges 1.50
percent in expenses.
5. Arias Bond Fund. This fund invests in long-term
corporate bonds issued by U.S.-domiciled compa-
nies. The fund is restricted to investments in bonds
with an investment grade credit rating. This fund
charges 1.40 percent in expenses.
6. Arias Money Market Fund. This fund invests in
short-term, high-credit-quality debt instruments,
which include Treasury bills. As such, the return on
money market funds is only slightly higher than the
return on Treasury bills. Because of the credit qual-
ity and short-term nature of the investments, there
is only a very slight risk of negative return. The fund
charges .60 percent in expenses.
You recently graduated from college, and your job search led you to S&S Air. Because you felt the com-
pany’s business was headed skyward, you accepted the
job offer. As you are finishing your employment paper-
work, Chris Guthrie, who works in the finance depart-
ment, stops by to inform you about the company’s new
401(k) plan.
A 401(k) is a type of retirement plan offered by many
companies. A 401(k) is tax deferred, which means that
any deposits you make into the plan are deducted from
your current income, so no current taxes are paid on the
money. Assume your salary will be $40,000 per year. If
you contribute $3,000 to the 401(k) plan, you will pay
taxes only on $37,000 in income. No taxes will be due
on any capital gains or plan income while you are in-
vested in the plan, but you will pay taxes when you with-
draw the money at retirement. You can contribute up to
15 percent of your salary to the plan. As is common, S&S
Air also has a 5 percent match program. This means that
the company will match your contribution dollar-
for-dollar up to 5 percent of your salary, but you must
contribute to get the match.
The 401(k) plan has several options for investments,
most of which are mutual funds. As you know, a mutual
fund is a portfolio of assets. When you purchase shares
in a mutual fund, you are actually purchasing partial
ownership of the fund’s assets, similar to purchasing
shares of stock in a company. The return of the fund is
the weighted average of the return of the assets owned
by the fund, minus any expenses. The largest expense
is typically the management fee paid to the fund man-
ager, who makes all of the investment decisions for the
fund. S&S Air uses Arias Financial Services as its 401(k)
plan administrator.
Chris Guthrie then explains that the retirement in-
vestment options offered for employees are as follows:
1. Company stock. One option is stock in S&S Air. The
company is currently privately held. The price you
would pay for the stock is based on an annual ap-
praisal, less a 20 percent discount. When you in-
terviewed with the owners, Mark Sexton and Todd
CHAPTER CASE
A Job at S&S Air
ros13952_ch10_310-349.indd 348 12/24/18 5:12 PM
C H A P T E R 1 0 Some Lessons from Capital Market History 349
1. What advantages/disadvantages do the mutual
funds offer compared to company stock for your
retirement investing?
2. Notice that, for every dollar you invest, S&S Air
also invests a dollar. What return on your invest-
ment does this represent? What does your answer
suggest about matching programs?
3. Assume you decide you should invest at least part
of your money in large capitalization stocks of
companies based in the United States. What are
the advantages and disadvantages of choosing
the Arias Large-Company Stock Fund compared
to the Arias S&P 500 Index Fund?
4. The returns of the Arias Small-Cap Fund are
the most volatile of all the mutual funds offered
in the 401(k) plan. Why would you ever want to
invest in this fund? When you examine the ex-
penses of the mutual funds, you will notice that
this fund also has the highest expenses.
Will this affect your decision to invest in this
fund?
5. A measure of risk-adjusted performance that of-
ten is used in practice is the Sharpe ratio. The
Sharpe ratio is calculated as the risk premium of
an asset divided by its standard deviation.
The standard deviations and returns for the
funds over the past 10 years are listed here. As-
suming a risk-free rate of 3.1 percent, calculate the
Sharpe ratio for each of these. In broad terms,
what do you suppose the Sharpe ratio is intended
to measure?
Q U E S T I O N S
10-Year Annual Return Standard Deviation
Arias S&P 500 Index Fund 11.80% 19.35%
Arias Small-Cap Fund 15.12 27.95
Arias Large-Company Stock Fund 11.15 21.16
Arias Bond Fund 7.92 11.45
ros13952_ch10_310-349.indd 349 12/24/18 5:12 PM
350
Please visit us at essentialsofcorporatefinance.blogspot.com for the latest developments in the world of corporate finance.
In 2018, Hormel, Microsoft, and Okta all made major announce-ments. In particular, Hormel, the famed Spam manufacturer, an-
nounced that its earnings rose from $.39 per share in the first
quarter of 2017 to $.44 per share in first quarter of 2018. Microsoft
announced earnings of $.96 per share for the quarter, a 12 percent
increase over the previous year. And Okta, which provides business
identity solutions, announced that it lost $26 million in the most
recent quarter.
You probably expect that these three cases represent good
news for Hormel and Microsoft and bad news for Okta, and usually
you would be right. But here, Hormel’s stock price dropped about
1 percent, Microsoft’s stock price dropped about 2 percent, and
Okta’s stock price jumped more than 3 percent. So when is good
news really good news? The answer is fundamental to understanding risk and return, and—
the good news is—this chapter explores it in detail.
This chapter continues the discussion we began in the previous chapter. We’ve
seen pretty clearly that some investments have greater risks than others. We now be-
gin to drill down a bit to investigate one of the most fundamental problems in finance:
Just what is risk? What we will learn is that risk is not always what it seems, and the
reward for bearing risk is more subtle than we have indicated so far. Understanding
how risks are rewarded is important for everyone in business for the simple reason
that business is risky, and only businesses that manage risk wisely will survive over
the long haul.
LEARNING OBJECTIVES
After studying this chapter, you should
be able to:
LO 1 Calculate expected returns.
LO 2 Explain the impact of
diversification.
LO 3 Define the systematic risk principle.
LO 4 Discuss the security market line
and the risk-return trade-off.
Risk and Return 11
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C H A P T E R 1 1 Risk and Return 351
In our last chapter, we learned some important lessons from capital market history. Most important, there is a reward, on average, for bearing risk. We called this reward a risk
premium. The second lesson is that this risk premium is larger for riskier investments. This
chapter explores the economic and managerial implications of this basic idea.
Thus far, we have concentrated mainly on the return behavior of a few large portfolios.
We need to expand our consideration to include individual assets. Specifically, we have two
tasks to accomplish. First, we have to define risk and then discuss how to measure it. We
then must quantify the relationship between an asset’s risk and its required return.
When we examine the risks associated with individual assets, we find there are two
types of risk: systematic and unsystematic. This distinction is crucial because, as we will see,
systematic risk affects almost all assets in the economy, at least to some degree, while unsys-
tematic risk affects at most a small number of assets. We then develop the principle of diver-
sification, which shows that highly diversified portfolios will tend to have almost no
unsystematic risk.
The principle of diversification has an important implication: To a diversified investor,
only systematic risk matters. It follows that in deciding whether or not to buy a particular
individual asset, a diversified investor will only be concerned with that asset’s systematic
risk. This is a key observation, and it allows us to say a great deal about the risks and returns
on individual assets. In particular, it is the basis for a famous relationship between risk and
return called the security market line, or SML. To develop the SML, we introduce the equally
famous “beta” coefficient, one of the centerpieces of modern finance. Beta and the SML
are key concepts because they supply us with at least part of the answer to the question of
how to go about determining the required return on an investment.
EXPECTED RETURNS AND VARIANCES
In our previous chapter, we discussed how to calculate average returns and variances using
historical data. We now begin to discuss how to analyze returns and variances when the in-
formation we have concerns future possible returns and their probabilities.
Expected Return
We start with a straightforward case. Consider a single period of time, say, a year. We have
two stocks, L and U, which have the following characteristics: Stock L is expected to have a
return of 25 percent in the coming year. Stock U is expected to have a return of 20 percent
for the same period.
In a situation like this, if all investors agreed on the expected returns, why would any-
one want to hold Stock U? After all, why invest in one stock when the expectation is that
another will do better? Clearly, the answer must depend on the risk of the two investments.
The return on Stock L, although it is expected to be 25 percent, could actually turn out to be
higher or lower.
Suppose the economy booms. In this case, we think Stock L will have a 70 percent re-
turn. If the economy enters a recession, we think the return will be −20 percent. In this
case, we say that there are two states of the economy, which means that these are the only two
possible situations. This setup is oversimplified, of course, but it allows us to illustrate some
key ideas without a lot of computation.
Suppose we think a boom and a recession are equally likely to happen, for a 50–50
chance of each. Table 11.1 illustrates the basic information we have described and some
additional information about Stock U. Notice that Stock U earns 30 percent if there is a
recession and 10 percent if there is a boom.
11.1
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352 P A R T 6 Risk and Return
Obviously, if you buy one of these stocks, say Stock U, what you earn in any particular
year depends on what the economy does during that year. However, suppose the probabili-
ties stay the same through time. If you hold U for a number of years, you’ll earn 30 percent
about half the time and 10 percent the other half. In this case, we say that your
expected return on Stock U, E(RU), is 20 percent:
E(RU) = .50 × 30% + .50 × 10% = 20%
In other words, you should expect to earn 20 percent from this stock, on average.
For Stock L, the probabilities are the same, but the possible returns are different. Here
we lose 20 percent half the time, and we gain 70 percent the other half. The expected return
on L, E(RL), is thus 25 percent:
E(RL) = .50 × −20% + .50 × 70% = 25%
Table 11.2 illustrates these calculations.
In the previous chapter, we defined the risk premium as the difference between the re-
turn on a risky investment and that on a risk-free investment, and we calculated the histori-
cal risk premiums on some different investments. Using our projected returns, we can
calculate the projected, or expected, risk premium as the difference between the expected re-
turn on a risky investment and the certain return on a risk-free investment.
Suppose risk-free investments are currently offering 8 percent. We will say that the risk-
free rate, which we label as Rf , is 8 percent. Given this, what is the projected risk premium
on Stock U? On Stock L? Because the expected return on Stock U, E(RU), is 20 percent, the
projected risk premium is:
Risk premium = Expected return − Risk-free rate [11.1]
= E(RU) − Rf
= 20% − 8%
= 12%
Similarly, the risk premium on Stock L is 25% − 8% = 17%.
expected return
Return on a risky asset
expected in the future.
State of
Economy
Probability of
State of
Economy
Security Returns if
State Occurs
Stock L Stock U
Recession .5 −20% 30%
Boom &.5 70 10
1.0
TABLE 11.1
States of the
economy and stock
returns
(1)
State of
Economy
(2)
Probability
of State of
Economy
Stock L Stock U
(3)
Rate of
Return if
State
Occurs
(4)
Product
(2) × (3)
(5)
Rate of
Return if
State
Occurs
(6)
Product
(2) × (5)
Recession .5 −.20 −.10 .30 .15
Boom & .5 .70 && .35 .10 .05
1.0 E(RL) = .25 E(RU ) = .20
TABLE 11.2
Calculation of
expected return
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C H A P T E R 1 1 Risk and Return 353
In general, the expected return on a security or other asset is equal to the sum of the
possible returns multiplied by their probabilities. So, if we had 100 possible returns, we
would multiply each one by its probability and then add the results. The result would be the
expected return. The risk premium would then be the difference between this expected re-
turn and the risk-free rate.
EXAMPLE 11.1 Unequal Probabilities
Look again at Tables 11.1 and 11.2. Suppose you thought a boom would occur only 20 percent of the
time instead of 50 percent. What are the expected returns on Stocks U and L in this case? If the
risk-free rate is 10 percent, what are the risk premiums?
The first thing to notice is that a recession must occur 80 percent of the time (1 − .20 = .80)
because there are only two possibilities. With this in mind, we see that Stock U has a 30 percent
return in 80 percent of the years and a 10 percent return in 20 percent of the years. To calculate the
expected return, we again multiply the possibilities by the probabilities and add up the results:
E(RU) = .80 × 30% + .20 × 10% = 26%
Table 11.3 summarizes the calculations for both stocks. Notice that the expected return on L is
−2 percent.
The risk premium for Stock U is 26% − 10% = 16% in this case. The risk premium for Stock L is
negative: −2% − 10% = −12%. This is a little odd, but, for reasons we discuss later, it is not
impossible.
Calculating the Variance
To calculate the variances of the returns on our two stocks, we first determine the squared
deviations from the expected returns. We then multiply each possible squared deviation by
its probability. We add these, and the result is the variance. The standard deviation, as al-
ways, is the square root of the variance.
To illustrate, Stock U from earlier has an expected return of E(RU) = 20%. In a given
year, it will actually return either 30 percent or 10 percent. The possible deviations are thus
30% − 20% = 10% and 10% − 20% = −10%. In this case, the variance is:
Variance = σ2U = .50 × (.10)
2 + .50 × (−.10)2 = .01
The standard deviation is the square root of this:
Standard deviation = σU = = .10, or 10%
Table 11.4 summarizes these calculations for both stocks. Notice that Stock L has a
much larger variance.
√.01
Stock L Stock U
(1)
State of
Economy
(2)
Probability
of State of
Economy
(3)
Rate of
Return if
State Occurs
(4)
Product
(2) × (3)
(5)
Rate of
Return if
State Occurs
(6)
Product
(2) × (5)
Recession .8 −.20 −.16 .30 .24
Boom &.2 .70 .14 .10 .02
1.0 E(RL) = −.02 E(RU) = .26
Calculation of
expected return
TABLE 11.3
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354 P A R T 6 Risk and Return
(1)
State of
Economy
(2)
Probability of
State of
Economy
(3)
Return Deviation
from Expected
Return
(4)
Squared Return
Deviation from
Expected Return
(5)
Product
(2) × (4)
Stock L
Recession .5 −.20 − .25 = −.45 −.452 = .2025 .10125
Boom &.5 .70 − .25 = .45 &&&&&& .452 = .2025 .10125
1.0 σ L
2 = .2025
Stock U
Recession .5 .30 − .20 = .10 &&&&&& .102 = .01 .00500
Boom & .5 .10 − .20 = −.10 −.102 = .01 .00500
1.0 σ U 2 = .0100
Stock L Stock U
Expected return, E(R) 25% &20%
Variance, σ2 .2025 .0100
Standard deviation, σ 45% 10%
Calculation of
variance
TABLE 11.4
When we put the expected return and variability information for our two stocks
together, we have:
EXAMPLE 11.2 More Unequal Probabilities
Going back to Example 11.1, what are the variances on the two stocks once we have unequal prob-
abilities? The standard deviations?
We can summarize the needed calculations as follows:
(1)
State of
Economy
(2)
Probability
of State of
Economy
(3)
Return Deviation
from Expected
Return
(4)
Squared Return
Deviation from
Expected Return
(5)
Product
(2) × (4)
Stock L
Recession .80 −.20 − (−.02) = −.18 .0324 .02592
Boom .20 &&&&&&&&.70 − (−.02) = .72 .5184 .10368
σ
L
2 = .12960
Stock U
Recession .80 .30 − .26 = .04 .0016 .00128
Boom .20 &&&.10 − .26 = −.16 .0256 .00512
σ
U
2 = .00640
Stock L has a higher expected return, but U has less risk. You could get a 70 percent return
on your investment in L, but you could also lose 20 percent. Notice that an investment in U
will always pay at least 10 percent.
Which of these two stocks should you buy? We can’t really say; it depends on your per-
sonal preferences. We can be reasonably sure, however, that some investors would prefer L
to U and some would prefer U to L.
You’ve probably noticed that the way we calculated expected returns and variances here
is somewhat different from the way we did it in the last chapter. The reason is that, in Chap-
ter 10, we were examining actual historical returns, so we estimated the average return and
the variance based on some actual events. Here, we have projected future returns and their
associated probabilities, so this is the information with which we must work.
ros13952_ch11_350-388.indd 354 12/24/18 5:24 PM
C H A P T E R 1 1 Risk and Return 355
PORTFOLIOS
Thus far in this chapter, we have concentrated on individual assets considered separately.
However, most investors actually hold a portfolio of assets. All we mean by this is that inves-
tors tend to own more than just a single stock, bond, or other asset. Given that this is so,
portfolio return and portfolio risk are of obvious relevance. Accordingly, we now discuss
portfolio expected returns and variances.
Portfolio Weights
There are many equivalent ways of describing a portfolio. The most convenient approach is
to list the percentages of the total portfolio’s value that are invested in each portfolio asset.
We call these percentages the portfolio weights.
For example, if we have $50 in one asset and $150 in another, then our total portfolio
is worth $200. The percentage of our portfolio in the first asset is $50/$200 = .25. The
percentage of our portfolio in the second asset is $150/$200, or .75. Our portfolio weights
are .25 and .75. Notice that the weights have to add up to 1.00 because all of our money is
invested somewhere.1
Portfolio Expected Returns
Let’s go back to Stocks L and U. You put half your money in each. The portfolio weights are
obviously .50 and .50. What is the pattern of returns on this portfolio? The expected
return?
To answer these questions, suppose the economy actually enters a recession. In this
case, half your money (the half in L) loses 20 percent. The other half (the half in U) gains
30 percent. Your portfolio return, RP, in a recession will be:
RP = .50 × −20% + .50 × 30% = 5%
Table 11.5 summarizes the remaining calculations. Notice that when a boom occurs, your
portfolio will return 40 percent:
RP = .50 × 70% + .50 × 10% = 40%
As indicated in Table 11.5, the expected return on your portfolio, E(RP), is 22.5 percent.
We can save ourselves some work by calculating the expected return more directly.
Given these portfolio weights, we could have reasoned that we expect half of our money to
11.2
portfolio
Group of assets such as
stocks and bonds held by
an investor.
portfolio weight
Percentage of a portfolio’s
total value in a particular
asset.
CONCEPT QUESTIONS
11.1a How do we calculate the expected return on a security?
11.1b In words, how do we calculate the variance of the expected return?
1Some of it could be in cash, of course, but we would then consider the cash to be one of the portfolio assets.
Based on these calculations, the standard deviation for L is: σ L = √
_____
.1296 = .36, or 36% .
The standard deviation for U is much smaller: σ U = √
_____
.0064 = .08, or 8% .
ros13952_ch11_350-388.indd 355 12/24/18 5:24 PM
356 P A R T 6 Risk and Return
earn 25 percent (the half in L) and half of our money to earn 20 percent (the half in U).
Our portfolio expected return is thus:
E(RP) = .50 × E(RL) + .50 × E(RU)
= .50 × 25% + .50 × 20%
= .225, or 22.5%
This is the same portfolio expected return we had before.
This method of calculating the expected return on a portfolio works no matter how
many assets there are in the portfolio. Suppose we had n assets in our portfolio, where n is
any number. If we let xi stand for the percentage of our money in Asset i, then the expected
return is:
E(RP) = x1 × E(R1) + x2 × E(R2) + · · · + xn × E(Rn) [11.2]
This says that the expected return on a portfolio is a straightforward combination of the
expected returns on the assets in that portfolio. This seems somewhat obvious, but, as we
will examine next, the obvious approach is not always the right one.
(1)
State of
Economy
(2)
Probability of
State of Economy
(3)
Portfolio Return if State Occurs
(4)
Product
(2) × (3)
Recession .50 .50 × −20% + .50 × 30% = 5% 2.5%
Boom .50 .50 × 70% + .50 × 10% = 40% 20
1.00 E(RP) = 22.5%
Expected return on
an equally weighted
portfolio of Stock L
and Stock U
TABLE 11.5
EXAMPLE 11.3 Portfolio Expected Return
Suppose we have the following projections on three stocks:
State of
Economy
Probability
of State
Returns
Stock A Stock B Stock C
Boom .40 10% 15% 20%
Bust .60 8 4 0
We want to calculate portfolio expected returns in two cases. First: What would be the expected
return on a portfolio with equal amounts invested in each of the three stocks? Second: What would
be the expected return if half of the portfolio were in A, with the remainder equally divided between
B and C?
From our earlier discussions, the expected returns on the individual stocks are (check these
for practice):
E(RA) = 8.8%
E(RB) = 8.4%
E(RC) = 8.0%
If a portfolio has equal investments in each asset, the portfolio weights are all the same. Such a
portfolio is said to be equally weighted. Because there are three stocks in this case, the weights are
all equal to ⅓. The portfolio expected return is thus:
E(RP) = ⅓ × 8.8% + ⅓ × 8.4% + ⅓ × 8.0% = 8.4%
In the second case, verify that the portfolio expected return is 8.5 percent.
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C H A P T E R 1 1 Risk and Return 357
Portfolio Variance
From our discussion above, the expected return on a portfolio that contains equal invest-
ments in Stocks U and L is 22.5 percent. What is the standard deviation of return on this
portfolio? Simple intuition might suggest that half of the money has a standard deviation of
45 percent and the other half has a standard deviation of 10 percent, so the portfolio’s
standard deviation might be calculated as:
σP = .50 × 45% + .50 × 10% = 27.5%
Unfortunately, this approach is completely incorrect!
Let’s see what the standard deviation really is. Table 11.6 summarizes the relevant cal-
culations. As we see, the portfolio’s variance is about .031, and its standard deviation is less
than we thought—it’s only 17.5 percent. What is illustrated here is that the variance on a
portfolio is not generally a simple combination of the variances of the assets in the
portfolio.
We can illustrate this point a little more dramatically by considering a slightly different
set of portfolio weights. Suppose we put 2 ⁄11 (about 18 percent) in L and the other 9 ⁄11 (about
82 percent) in U. If a recession occurs, this portfolio will have a return of:
Rp =
2/11 × −20% +
9/11 × 30% = 20.91%
If a boom occurs, this portfolio will have a return of:
Rp =
2/11 × 70% +
9/11 × 10% = 20.91%
Notice that the return is the same no matter what happens. No further calculations are
needed: This portfolio has a zero variance. Apparently, combining assets into portfolios can
substantially alter the risks faced by the investor. This is a crucial observation, and we will
begin to explore its implications in the next section.
(1)
State of
Economy
(2)
Probability of
State of
Economy
(3)
Portfolio
Return if State
Occurs
(4)
Squared Deviation from
Expected Return
(5)
Product
(2) × (4)
Recession .50 5% (.05 − .225)2 = .030625 .0153125
Boom .50 40 (.40 − .225)2 = .030625 .0153125
1.00 σ P 2 = .030625
σ P & =& √
_______
.030625 & = &.&175, or 17.5%
Variance on an
equally weighted
portfolio of Stock L
and Stock U
TABLE 11.6
EXAMPLE 11.4 Portfolio Variance and Standard Deviation
In Example 11.3, what are the standard deviations on the two portfolios? To answer, we first have to
calculate the portfolio returns in the two states. We will work with the second portfolio, which has
50 percent in Stock A and 25 percent in each of Stocks B and C. The relevant calculations can be
summarized as follows:
State of
Economy
Probability
of State
Returns
Stock A Stock B Stock C Portfolio
Boom .40 10% 15% 20% 13.75%
Bust .60 8 4 0 5.00
(continued)
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358 P A R T 6 Risk and Return
ANNOUNCEMENTS, SURPRISES,
AND EXPECTED RETURNS
Now that we know how to construct portfolios and evaluate their returns, we begin to
describe more carefully the risks and returns associated with individual securities. Thus
far, we have measured volatility by looking at the difference between the actual return on
an asset or portfolio, R, and the expected return, E(R). We now look at why such devia-
tions exist.
Expected and Unexpected Returns
To begin, for concreteness, we consider the return on the stock of a company called Flyers.
What will determine this stock’s return in, say, the coming year?
The return on any stock traded in a financial market is composed of two parts. First,
the normal, or expected, return from the stock is the part of the return that shareholders in
the market predict or expect. This return depends on the information shareholders have that
bears on the stock, and it is based on the market’s understanding today of the important
factors that will influence the stock in the coming year.
The second part of the return on the stock is the uncertain, or risky, part. This is the
portion that comes from unexpected information revealed within the year. A list of all pos-
sible sources of such information would be endless, but here are a few examples:
• News about research on Flyers.
• Government figures released on gross domestic product (GDP).
• The results from the latest arms control talks.
• The news that Flyers’s sales figures are higher than expected.
• A sudden, unexpected drop in interest rates.
11.3
The portfolio return when the economy booms is calculated as:
.50 × 10% + .25 × 15% + .25 × 20% = 13.75%
The return when the economy goes bust is calculated the same way. The expected return on the
portfolio is .085. The variance is:
σ 2 = .40 × (.1375 − .085)2 + .60 × (.05 − .085)2
= .0018375
The standard deviation is about 4.3 percent. For our equally weighted portfolio, verify that the
standard deviation is about 5.4 percent.
CONCEPT QUESTIONS
11.2a What is a portfolio weight?
11.2b How do we calculate the expected return on a portfolio?
11.2c Is there a simple relationship between the standard deviation on a portfolio and the
standard deviations of the assets in the portfolio?
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C H A P T E R 1 1 Risk and Return 359
Based on this discussion, one way to express the return on Flyers’s stock in the coming
year would be:
Total return = Expected return + Unexpected return
R = E(R) + U
[11.3]
where R stands for the actual total return in the year, E(R) stands for the expected part of
the return, and U stands for the unexpected part of the return. What this says is that the
actual return, R, differs from the expected return, E(R), because of surprises that occur dur-
ing the year. In any given year, the unexpected return will be positive or negative, but,
through time, the average value of U will be zero. This means that, on average, the actual
return equals the expected return.
Announcements and News
We need to be careful when we talk about the effect of news items on the return. For exam-
ple, suppose Flyers’s business is such that the company prospers when GDP grows at a rela-
tively high rate and suffers when GDP is relatively stagnant. In this case, in deciding what
return to expect this year from owning stock in Flyers, shareholders either implicitly or ex-
plicitly must think about what GDP is likely to be for the year.
When the government actually announces GDP figures for the year, what will happen
to the value of Flyers’s stock? Obviously, the answer depends on what figure is released.
More to the point, however, the impact depends on how much of that figure is new
information.
At the beginning of the year, market participants will have some idea or forecast of
what the yearly GDP will be. To the extent that shareholders have predicted GDP, that pre-
diction already will be factored into the expected part of the return on the stock, E(R). On
the other hand, if the announced GDP is a surprise, then the effect will be part of U, the
unanticipated portion of the return.
Suppose shareholders in the market had forecast that the GDP increase this year would
be .5 percent. If the actual announcement this year is exactly .5 percent, the same as the
forecast, then the shareholders don’t really learn anything, and the announcement isn’t
news. There will be no impact on the stock price as a result. This is like receiving confirma-
tion of something that you suspected all along; it doesn’t reveal anything new.
A common way of saying that an announcement isn’t news is to say that the market has
already “discounted” the announcement. The use of the word discount here is different from
the use of the term in computing present values, but the spirit is the same. When we dis-
count a dollar in the future, we say it is worth less to us because of the time value of money.
When we say that we discount an announcement, or a news item, we mean that it has less of
an impact on the market because the market already knew much of it.
For example, going back to Flyers, suppose the government announces that the actual
GDP increase during the year has been 1.5 percent. Now shareholders have learned some-
thing, namely, that the increase is one percentage point higher than they had forecast. This
difference between the actual result and the forecast, one percentage point in this example,
is sometimes called the innovation or the surprise.
An announcement, then, can be broken into two parts, the anticipated, or expected,
part and the surprise, or innovation:
Announcement = Expected part + Surprise [11.4]
The expected part of any announcement is the part of the information that the market uses
to form the expectation, E(R), of the return on the stock. The surprise is the news that influ-
ences the unanticipated return on the stock, U.
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360 P A R T 6 Risk and Return
To take another example, if shareholders knew in January that the president of the firm
was going to resign, the official announcement in February would be fully expected and
would be discounted by the market. Because the announcement was expected before Febru-
ary, its influence on the stock would have taken place before February. The announcement
itself will contain no surprise, and the stock’s price shouldn’t change at all when it is actu-
ally made.
The fact that only the unexpected, or surprise, part of an announcement matters
explains why two companies can make similar announcements but experience different
stock price reactions. For example, to open the chapter, we compared Hormel, Micro-
soft, and Okta. In Hormel’s case, even though the company’s earnings had grown
about 13 percent to $.44 per share, analysts’ estimates for the stock pegged EPS at
$.45, so the company came in below expectations. In Microsoft’s case, even though the
company had exceeded analysts’ estimates, the company was trading at high valua-
tions, with high PE and EV/EBITDA multiples, so the earnings “beat” was not enough
to impress investors, who were expecting even better numbers. And while Okta re-
ported a loss for the quarter, the loss was only $.09 per share, much better than the
expected $.16 per share.
Our discussion of market efficiency in the previous chapter bears on this discussion.
We are assuming that relevant information known today is already reflected in the expected
return. This is identical to saying that the current price reflects relevant publicly available
information. We are thus implicitly assuming that markets are at least reasonably efficient in
the semistrong form sense.
Henceforth, when we speak of news, we will mean the surprise part of an announce-
ment and not the portion that the market has expected and therefore already
discounted.
CONCEPT QUESTIONS
11.3a What are the two basic parts of a return?
11.3b Under what conditions will an announcement have no effect on common stock
prices?
RISK: SYSTEMATIC AND UNSYSTEMATIC
The unanticipated part of the return, that portion resulting from surprises, is the true risk of
any investment. After all, if we always receive exactly what we expect, then the investment is
perfectly predictable and, by definition, risk-free. In other words, the risk of owning an asset
comes from surprises—unanticipated events.
There are important differences, though, among various sources of risk. Look back
at our previous list of news stories. Some of these stories are directed specifically at
Flyers, and some are more general. Which of the news items are of specific importance
to Flyers?
Announcements about interest rates or GDP are clearly important for nearly all compa-
nies, whereas the news about Flyers’s president, its research, or its sales is of specific inter-
est to Flyers. We distinguish between these two types of events because, as we shall see, they
have very different implications.
11.4
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C H A P T E R 1 1 Risk and Return 361
Systematic and Unsystematic Risk
The first type of surprise, the one that affects a large number of assets, we will label
systematic risk. Because systematic risks have marketwide effects, they are sometimes
called market risks.
The second type of surprise we will call unsystematic risk. An unsystematic risk is one
that affects a single asset or a small group of assets. Because these risks are unique to indi-
vidual companies or assets, they are sometimes called unique or asset-specific risks. We will
use these terms interchangeably.
As we have seen, uncertainties about general economic conditions, such as GDP, inter-
est rates, or inflation, are examples of systematic risks. These conditions affect nearly all
companies to some degree. An unanticipated increase, or surprise, in inflation, for exam-
ple, affects wages and the costs of the supplies that companies buy; it affects the value of
the assets that companies own; and it affects the prices at which companies sell their prod-
ucts. Forces such as these, to which all companies are susceptible, are the essence of sys-
tematic risk.
In contrast, the announcement of an oil strike by a company primarily will affect that
company and, perhaps, a few others (such as primary competitors and suppliers). It is un-
likely to have much of an effect on the world oil market, however, or on the affairs of com-
panies not in the oil business, so this is an unsystematic event.
Systematic and Unsystematic Components of Return
The distinction between a systematic risk and an unsystematic risk is never really as exact as
we make it out to be. Even the most narrow and peculiar bit of news about a company rip-
ples through the economy. This is true because every enterprise, no matter how tiny, is a
part of the economy. It’s like the tale of a kingdom that was lost because one horse lost a
shoe. This is mostly hairsplitting, however. Some risks are clearly much more general than
others. We’ll see some evidence on this point in a moment.
The distinction between the types of risk allows us to break down the surprise portion,
U, of the return on Flyers’s stock into two parts. From before, we had the actual return bro-
ken down into its expected and surprise components:
R = E(R) + U
We now recognize that the total surprise for Flyers, U, has a systematic and an unsystematic
component, so:
R = E(R) + Systematic portion + Unsystematic portion [11.5]
Because it is traditional, we will use the Greek letter epsilon, #, to stand for the unsys-
tematic portion. And because systematic risks are often called market risks, we will use the
letter m to stand for the systematic part of the surprise. With these symbols, we can rewrite
the total return:
R = E(R) + U
= E(R) + m + ε
The important thing about the way we have broken down the total surprise, U, is that the
unsystematic portion, #, is more or less unique to Flyers. For this reason, it is unrelated to
the unsystematic portion of the return on most other assets. To see why this is important,
we need to return to the subject of portfolio risk.
systematic risk
A risk that influences a
large number of assets.
Also market risk.
unsystematic risk
A risk that affects at most
a small number of assets.
Also unique or asset-
specific risk.
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362 P A R T 6 Risk and Return
CONCEPT QUESTIONS
11.4a What are the two basic types of risk?
11.4b What is the distinction between the two types of risk?
DIVERSIFICATION AND PORTFOLIO RISK
We saw earlier that portfolio risks, in principle, can be quite different from the risks of the
assets that make up the portfolio. We now look more closely at the riskiness of an individual
asset versus the risk of a portfolio of many different assets. We will examine once again
some market history to get an idea of what happens with actual investments in U.S. capital
markets.
The Effect of Diversification: Another Lesson
from Market History
In the previous chapter, we saw that the standard deviation of the annual return on a
portfolio of 500 large common stocks has historically been about 20 percent per year (see
Figure 10.10, for example). Does this mean that the standard deviation of the annual return
on a typical stock in that group of 500 is about 20 percent? As you might suspect by now,
the answer is no. This is an extremely important observation.
To examine the relationship between portfolio size and portfolio risk, Table 11.7 illus-
trates typical average annual standard deviations for portfolios that contain different num-
bers of randomly selected NYSE securities.
11.5
For more on risk and
diversification, visit www
.investopedia.com
/university.
Sources: These figures are from Table 1 in Statman, Meir, “How Many Stocks Make a Diversified Portfolio?” Journal
of Financial and Quantitative Analysis, vol. 22, September 1987, 353–64. They were derived from Elton, E. J.
and Gruber, M. J., “Risk Reduction and Portfolio Size: An Analytical Solution,” Journal of Business, vol. 50,
October 1977, 415–37.
(1)
Number of Stocks
in Portfolio
(2)
Average Standard
Deviation of Annual
Portfolio Returns
(3)
Ratio of Portfolio
Standard Deviation to
Standard Deviation
of a Single Stock
1 49.24% 1.00
2 37.36 .76
4 29.69 .60
6 26.64 .54
8 24.98 .51
10 23.93 .49
20 21.68 .44
30 20.87 .42
40 20.46 .42
50 20.20 .41
100 19.69 .40
200 19.42 .39
300 19.34 .39
400 19.29 .39
500 19.27 .39
1,000 19.21 .39
Standard deviations
of annual portfolio
returns
TABLE 11.7
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C H A P T E R 1 1 Risk and Return 363
In Column 2 of Table 11.7, we see that the standard deviation for a “portfolio” of one
security is about 49 percent. What this means is that, if you randomly selected a single NYSE
stock and put all your money into it, your standard deviation of return would typically be
a substantial 49 percent per year. If you were to randomly select two stocks and invest half
your money in each, your standard deviation would be about 37 percent on average, and so on.
The important thing to notice in Table 11.7 is that the standard deviation declines as the
number of securities is increased. By the time we have 100 randomly chosen stocks, the port-
folio’s standard deviation has declined by about 60 percent, from 49 percent to about 20 per-
cent. With 500 securities, the standard deviation is 19.27 percent, similar to the 19.8 percent
we saw in our previous chapter for the large common stock portfolio. The small difference
exists because the portfolio securities and time periods examined are not identical.
The Principle of Diversification
Figure 11.1 illustrates the point we’ve been discussing. What we have plotted is the standard
deviation of return versus the number of stocks in the portfolio. Notice in Figure 11.1 that
the benefit in terms of risk reduction from adding securities drops off as we add more and
more. By the time we have 10 securities, most of the effect is already realized, and by the
time we get to 30 or so, there is very little remaining benefit.
Figure 11.1 illustrates two key points. First: Some of the riskiness associated with indi-
vidual assets can be eliminated by forming portfolios. The process of spreading an invest-
ment across assets (and thereby forming a portfolio) is called diversification. The
principle of diversification tells us that spreading an investment across many assets will
eliminate some of the risk. The green shaded area in Figure 11.1, labeled “diversifiable risk,”
is the part that can be eliminated by diversification.
principle of
diversification
Spreading an investment
across a number of assets
will eliminate some, but
not all, of the risk.
Diversifiable risk
49.2
23.9
19.2
Nondiversifiable
risk
101 20 30 40 1,000
Number of stocks
in portfolio
Average annual
standard deviation (%)
FIGURE 11.1
Portfolio
diversification
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364 P A R T 6 Risk and Return
The second point is equally important: There is a minimum level of risk that cannot be
eliminated by diversifying. This minimum level is labeled “nondiversifiable risk” in
Figure 11.1. Taken together, these two points are another important lesson from capital mar-
ket history: Diversification reduces risk, but only up to a point. Put another way: Some risk
is diversifiable and some is not.
Diversification and Unsystematic Risk
From our discussion of portfolio risk, we know that some of the risk associated with indi-
vidual assets can be diversified away and some cannot. We are left with an obvious question:
Why is this so? It turns out that the answer hinges on the distinction we made earlier be-
tween systematic and unsystematic risk.
By definition, an unsystematic risk is one that is particular to a single asset or, at most,
a small group. For example, if the asset under consideration is stock in a single company,
the discovery of positive NPV projects such as successful new products and innovative cost
savings will tend to increase the value of the stock. Unanticipated lawsuits, industrial acci-
dents, strikes, and similar events will tend to decrease future cash flows and thereby reduce
share values.
Here is the important observation: If we only held a single stock, then the value of our
investment would fluctuate because of company-specific events. If we hold a large portfolio,
on the other hand, some of the stocks in the portfolio will go up in value because of positive
company-specific events and some will go down in value because of negative events. The net
effect on the overall value of the portfolio will be relatively small, however, as these effects
will tend to cancel each other out.
Now we see why some of the variability associated with individual assets is eliminated by
diversification. When we combine assets into portfolios, the unique, or unsystematic, events—
both positive and negative—tend to “wash out” once we have more than a few assets.
This is an important point that bears restating:
Unsystematic risk is essentially eliminated by diversification, so a relatively large
portfolio has almost no unsystematic risk.
In fact, the terms diversifiable risk and unsystematic risk are often used interchangeably.
Diversification and Systematic Risk
We’ve seen that unsystematic risk can be eliminated by diversifying. What about systematic
risk? Can it also be eliminated by diversification? The answer is no because, by definition, a
systematic risk affects almost all assets to some degree. As a result, no matter how many
assets we put into a portfolio, the systematic risk doesn’t go away. Thus, for obvious reasons,
the terms systematic risk and nondiversifiable risk are used interchangeably.
Because we have introduced so many different terms, it is useful to summarize our dis-
cussion before moving on. What we have seen is that the total risk of an investment, as
measured by the standard deviation of its return, can be written as:
Total risk = Systematic risk + Unsystematic risk [11.6]
Systematic risk is also called nondiversifiable risk or market risk. Unsystematic risk is also
called diversifiable risk, unique risk, or asset-specific risk. For a well-diversified portfolio, the
unsystematic risk is negligible. For such a portfolio, essentially all of the risk is systematic.
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C H A P T E R 1 1 Risk and Return 365
CONCEPT QUESTIONS
11.5a What happens to the standard deviation of return for a portfolio if we increase the
number of securities in the portfolio?
11.5b What is the principle of diversification?
11.5c Why is some risk diversifiable?
11.5d Why can’t systematic risk be diversified away?
SYSTEMATIC RISK AND BETA
The question that we now begin to address is this: What determines the size of the risk pre-
mium on a risky asset? Put another way: Why do some assets have a larger risk premium
than other assets? The answer to these questions, as we discuss next, is also based on the
distinction between systematic and unsystematic risk.
The Systematic Risk Principle
Thus far, we’ve seen that the total risk associated with an asset can be decomposed into two
components: systematic and unsystematic risk. We also have seen that unsystematic risk can
be essentially eliminated by diversification. The systematic risk present in an asset, on the
other hand, cannot be eliminated by diversification.
Based on our study of capital market history, we know that there is a reward, on aver-
age, for bearing risk. However, we now need to be more precise about what we mean by risk.
The systematic risk principle states that the reward for bearing risk depends only on the
systematic risk of an investment. The underlying rationale for this principle is straightfor-
ward: Because unsystematic risk can be eliminated at virtually no cost (by diversifying),
there is no reward for bearing it. Put another way: The market does not reward risks that are
borne unnecessarily.
The systematic risk principle has a remarkable and very important implication:
The expected return on an asset depends only on that asset’s systematic risk.
There is an obvious corollary to this principle: No matter how much total risk an asset has,
only the systematic portion is relevant in determining the expected return (and the risk
premium) on that asset.
Measuring Systematic Risk
Because systematic risk is the crucial determinant of an asset’s expected return, we need
some way of measuring the level of systematic risk for different investments. The specific
measure we will use is called the beta coefficient, for which we will use the Greek symbol β.
A beta coefficient, or beta for short, tells us how much systematic risk a particular asset has
relative to an average asset. By definition, an average asset has a beta of 1.0 relative to itself.
An asset with a beta of .50, therefore, has half as much systematic risk as an average asset;
an asset with a beta of 2.0 has twice as much.
11.6
For more on beta, see
money.cnn.com.
systematic risk
principle
The expected return on a
risky asset depends only
on that asset’s systematic
risk.
beta coefficient
Amount of systematic risk
present in a particular
risky asset relative to that
in an average risky asset.
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366 P A R T 6 Risk and Return
The reported beta for Sears is 1.44, which means that Sears has about one and one-half times
the systematic risk of a typical stock. You would expect that the company is very risky and, looking
at the other numbers, we agree. Sears’s ROA is negative 8.07 percent, which indicates the company
lost money over the past year, but the ROE is not reported. Why? If you look at the book value per
share, it is negative because of the company’s cumulative losses. In this case, the larger the loss, the
larger the ROE! That’s not good. Given this, Sears appears to be a good candidate for a high beta.
QUESTIONS
1. Has Sears’s ROE “improved” since this was written? Check out the current numbers on
the website to see.
2. What growth rate are analysts projecting for Sears? How does this growth rate com-
pare to the industry?
W R K T H E W E B
Suppose you want to find the beta for a company like Sears. One way is to go to the web. We went to finance.yahoo.com and entered the ticker symbol for Sears (SHLD). Here is part of
what we found:
Source: finance.yahoo.com, 2018.
Table 11.8 contains the estimated beta coefficients for the stocks of some well-known
companies. The range of betas in Table 11.8 is typical for stocks of large U.S. corporations.
Betas outside this range occur, but they are less common. See our nearby Work the Web box
to learn how to find betas online.
The important thing to remember is that the expected return, and thus the risk pre-
mium, on an asset depends only on its systematic risk. Because assets with larger betas have
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Beta, Beta, Who’s Got the Beta?
Based on what we’ve studied so far, you can see that beta is a pretty important topic. You might wonder, then, are
all published betas created equal? Read on for a partial an-
swer to this question.
We did some checking on betas and found some inter-
esting results. The Value Line Investment Survey is one of
the best-known sources for information on publicly traded
companies. However, with the explosion of online investing,
there has been a corresponding increase in the amount of
investment information available online. We decided to com-
pare the betas presented by Value Line to those reported by
Yahoo! Finance (finance.yahoo.com) and CNN Money
(money.cnn.com). What we found leads to an important note
of caution.
Consider Microsoft, with its beta reported on the Inter-
net as 1.28, which is larger than Value Line’s beta of 1.00.
Microsoft wasn’t the only stock that showed a divergence in
betas from different sources. In fact, for most of the technol-
ogy companies we looked at, Value Line reported betas that
were significantly lower than their online cousins. For exam-
ple, the online beta for Cisco Systems was 1.22, but Value
Line reported 1.05. The online beta for eBay was 1.49 versus
a Value Line beta of 1.00. Value Line’s betas are not always
lower. For example, the online beta for Adobe (maker of the
ubiquitous Acrobat software) was .80, compared to Value
Line’s 1.10.
We also found some unusual, and even hard-to-believe,
estimates for beta. Caesars Entertainment had a very low
online beta of .01, while Value Line reported Caesars’s beta
as 1.60. The online estimate for Southern Company was .03,
compared to Value Line’s .54. Perhaps the most outrageous
reported betas were the online betas for SPO Global and
Sunnylife Global, with betas of 155.23 and –263.53 (notice
the negative sign!), respectively. Value Line did not report a
beta for these companies. How do you suppose we should
interpret a beta of –263.53?
There are a few lessons to be learned from all of this.
First, not all betas are created equal. Some are computed
using weekly returns and some using daily returns. Some
are computed using 60 months of stock returns; some con-
sider more or less. Some betas are computed by comparing
the stock to the S&P 500 index, while others use alternative
indices. Finally, some reporting firms (including Value Line)
make adjustments to raw betas to reflect information other
than the fluctuation in stock prices.
The second lesson is perhaps more subtle. We are in-
terested in knowing what the betas of the stocks will be in
the future, but betas have to be estimated using historical
data. Anytime we use the past to predict the future, there is
the danger of a poor estimate. As we will see later in the
chapter (and in the next one), it is very unlikely that SPO
Global has a beta anything like 155.23 or that Sunnylife
Global has a beta of –263.53. Instead, the estimates are al-
most certainly poor ones. The moral of the story is that, as
with any financial tool, beta is not a black box that should be
taken without question.
FINANCE MATTERS
Beta coefficients for
selected companies
TABLE 11.8Company Beta Coefficient (βi)
Macy’s .54
Facebook .81
Ford .85
Pfizer .93
Costco 1.05
Home Depot 1.06
Apple 1.15
Prudential 1.46
Amazon 1.70
Source: finance.yahoo.com, 2018.
greater systematic risks, they will have greater expected returns. Thus, from Table 11.8, an
investor who buys stock in Ford, with a beta of .85, should expect to earn less, on average,
than an investor who buys stock in Apple, with a beta of 1.15. To learn more about “real-
world” betas, see the nearby Finance Matters box.
367
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368 P A R T 6 Risk and Return
EXAMPLE 11.6 Portfolio Betas
Suppose we had the following investments:
Security Amount Invested Expected Return Beta
Stock A $1,000 8% .80
Stock B 2,000 12 .95
Stock C 3,000 15 1.10
Stock D 4,000 18 1.40
What is the expected return on this portfolio? What is the beta of this portfolio? Does this portfolio
have more or less systematic risk than an average asset?
To answer, we first have to calculate the portfolio weights. Notice that the total amount in-
vested is $10,000. Of this, $1,000/$10,000 = .10, or 10% is invested in Stock A. Similarly, 20 percent
is invested in Stock B, 30 percent is invested in Stock C, and 40 percent is invested in Stock D. The
expected return, E(RP), is thus:
E(RP) = .10 × E(RA) + .20 × E(RB) + .30 × E(RC) + .40 × E(RD)
= .10 × 8% + .20 × 12% + .30 × 15% + .40 × 18%
= 14.9%
EXAMPLE 11.5 Total Risk versus Beta
Consider the following information on two securities. Which has greater total risk? Which has
greater systematic risk? Greater unsystematic risk? Which asset will have a higher risk premium?
Standard Deviation Beta
Security A 40% .50
Security B 20 1.50
From our discussion in this section, Security A has greater total risk, but it has substantially less
systematic risk. Because total risk is the sum of systematic and unsystematic risk, Security A must
have greater unsystematic risk. Finally, from the systematic risk principle, Security B will have a
higher risk premium and a greater expected return, despite the fact that it has less total risk.
Portfolio Betas
Earlier, we saw that the total riskiness of a portfolio has no simple relationship to the risks
of the assets in the portfolio. A portfolio beta, however, can be calculated like a portfolio
expected return. For example, looking again at Table 11.8, suppose you put half of your
money in Ford and half in Prudential. What would the beta of this combination be? Be-
cause Ford has a beta of .85 and Prudential has a beta of 1.46, the portfolio’s beta, βP,
would be:
βP = .50 × βFord + .50 × βPrudential
= .50 × .85 + .50 × 1.46
= 1.16
In general, if we had a large number of assets in a portfolio, we would multiply each asset’s
beta by its portfolio weight and then add the results to get the portfolio’s beta.
Betas are easy to find on
the web. Try finance
.yahoo.com and money
.cnn.com.
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C H A P T E R 1 1 Risk and Return 369
CONCEPT QUESTIONS
11.6a What is the systematic risk principle?
11.6b What does a beta coefficient measure?
11.6c How do you calculate a portfolio beta?
11.6d True or false: The expected return on a risky asset depends on that asset’s total risk.
Explain.
THE SECURITY MARKET LINE
We’re now in a position to see how risk is rewarded in the marketplace. To begin, suppose
that Asset A has an expected return of E(RA) = 20% and a beta of βA = 1.6. Furthermore,
the risk-free rate is Rf = 8%. Notice that a risk-free asset, by definition, has no systematic risk
(or unsystematic risk, for that matter), so a risk-free asset has a beta of 0.
Beta and the Risk Premium
Consider a portfolio made up of Asset A and a risk-free asset. We can calculate some differ-
ent possible portfolio expected returns and betas by varying the percentages invested in
these two assets. For example, if 25 percent of the portfolio is invested in Asset A, then the
expected return is:
E(RP) = .25 × E(RA) + (1 − .25) × Rf
= .25 × 20% + .75 × 8%
= 11.0%
Similarly, the beta on the portfolio, βP , would be:
βP = .25 × βA + (1 − .25) × 0
= .25 × 1.6
= .40
Notice that, because the weights have to add up to 1, the percentage invested in the risk-free
asset is equal to 1 minus the percentage invested in Asset A.
One thing that you might wonder about is whether it is possible for the percentage in-
vested in Asset A to exceed 100 percent. The answer is yes. The way this can happen is for
the investor to borrow at the risk-free rate. Suppose an investor has $100 and borrows an
additional $50 at 8 percent, the risk-free rate. The total investment in Asset A would be
$150, or 150 percent of the investor’s wealth. The expected return in this case would be:
E(RP) = 1.50 × E(RA) + (1 − 1.50) × Rf
= 1.50 × 20% − .50 × 8%
= 26.0%
11.7
Similarly, the portfolio beta, βP, is:
βP = .10 × βA + .20 × βB + .30 × βC + .40 × βD
= .10 × .80 + .20 × .95 + .30 × 1.10 + .40 × 1.40
= 1.16
This portfolio thus has an expected return of 14.9 percent and a beta of 1.16. Because the beta is
larger than 1.0, this portfolio has greater systematic risk than an average asset.
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370 P A R T 6 Risk and Return
The beta on the portfolio would be:
βP = 1.50 × βA + (1 − 1.50) × 0
= 1.50 × 1.6
= 2.4
We can calculate some other possibilities as follows:
Percentage of
Portfolio in Asset A
Portfolio Expected
Return
Portfolio
Beta
0% 8% .0
25 11 .4
50 14 .8
75 17 1.2
100 20 1.6
125 23 2.0
150 26 2.4
In Figure 11.2A, these portfolio expected returns are plotted against the portfolio betas.
Notice that all the combinations fall on a straight line.
The Reward-to-Risk Ratio What is the slope of the straight line in Figure 11.2A? As
always, the slope of a straight line is equal to “the rise over the run.” In this case, as we move
out of the risk-free asset into Asset A, the beta increases from 0 to 1.6 (a “run” of 1.6). At
the same time, the expected return goes from 8 percent to 20 percent, a “rise” of 12 percent.
The slope of the line is thus 12%/1.6 = 7.50%.
Notice that the slope of our line is the risk premium on Asset A, E(RA) − Rf , divided
by Asset A’s beta, βA:
Slope =
E(RA) − Rf _______ βA
= 20% − 8% _________ 1.6
= 7.50%
What this tells us is that Asset A offers a reward-to-risk ratio of 7.50 percent.2 In other words,
Asset A has a risk premium of 7.50 percent per “unit” of systematic risk.
Portfolio expected
returns and betas for
Asset A
FIGURE 11.2A
E(RA) = 20%
Rf = 8%
1.6 = βA
Portfolio expected
return (E(RP))
Portfolio
beta (βP)
Asset A
= 7.50%= βA
E(RA) − Rf
2This ratio is sometimes called the Treynor index, after one of its originators.
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C H A P T E R 1 1 Risk and Return 371
The Basic Argument Now suppose we consider a second asset, Asset B. This asset
has a beta of 1.2 and an expected return of 16 percent. Which investment is better, Asset A
or Asset B? You might think that, once again, we really cannot say. Some investors might
prefer A; some investors might prefer B. Actually, however, we can say: A is better because,
as we shall demonstrate, B offers inadequate compensation for its level of systematic risk, at
least relative to A.
To begin, we calculate different combinations of expected returns and betas for portfo-
lios of Asset B and a risk-free asset as we did for Asset A. For example, if we put 25 percent
in Asset B and the remaining 75 percent in the risk-free asset, the portfolio’s expected return
would be:
E(RP) = .25 × E(RB) + (1 − .25) × Rf
= .25 × 16% + .75 × 8%
= 10.0%
Similarly, the beta on the portfolio, βP, would be:
βP = .25 × βB + (1 − .25) × 0
= .25 × 1.2
= .30
Some other possibilities are as follows:
Percentage of
Portfolio in Asset B
Portfolio Expected
Return
Portfolio
Beta
0% 8% .0
25 10 .3
50 12 .6
75 14 .9
100 16 1.2
125 18 1.5
150 20 1.8
When we plot these combinations of portfolio expected returns and portfolio betas in
Figure 11.2B, we get a straight line as we did for Asset A.
Portfolio expected
returns and betas for
Asset B
Portfolio expected
return (E(RP))
Portfolio
beta (βP)
Rf = 8%
E(RB) = 16%
Asset B
1.2 = βB
= 6.67%= βB
E(RB) − Rf
FIGURE 11.2B
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372 P A R T 6 Risk and Return
The key thing to notice is that when we compare the results for Assets A and B, as in
Figure 11.2C, the line describing the combinations of expected returns and betas for Asset
A is higher than the one for Asset B. What this tells us is that for any given level of system-
atic risk (as measured by β), some combination of Asset A and the risk-free asset always
offers a larger return. This is why we were able to state that Asset A is a better investment
than Asset B.
Another way of seeing that A offers a superior return for its level of risk is to note that
the slope of our line for Asset B is:
Slope =
E(RB) − Rf ________ βB
= 16% − 8% _________ 1.2 = 6.67%
Thus, Asset B has a reward-to-risk ratio of 6.67 percent, which is less than the 7.5 percent
offered by Asset A.
The Fundamental Result The situation we have described for Assets A and B can-
not persist in a well-organized, active market because investors would be attracted to Asset
A and away from Asset B. As a result, Asset A’s price would rise and Asset B’s price would
fall. Because prices and returns move in opposite directions, the result would be that A’s
expected return would decline and B’s would rise.
This buying and selling would continue until the two assets plotted on exactly the same
line, which means they would offer the same reward for bearing risk. In other words, in an
active, competitive market, we must have that:
E(RA) − Rf ________ βA
=
E(RB) − Rf ________ βB
This is the fundamental relationship between risk and return.
Our basic argument can be extended to more than two assets. In fact, no matter how
many assets we had, we would always reach the same conclusion:
The reward-to-risk ratio must be the same for all the assets in the market.
Portfolio expected
returns and betas for
both assets
FIGURE 11.2C
E(RA) = 20%
Rf = 8%
1.6 = βA
Portfolio e xpected
return (E(RP))
Portfolio
beta (βP)
E(RB) = 16%
= 7.50%
= 6.67%
Asset A
Asset B
1.2 = βB
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C H A P T E R 1 1 Risk and Return 373
This result is really not so surprising. What it says, for example, is that, if one asset has twice
as much systematic risk as another asset, its risk premium will be twice as large.
Because all of the assets in the market must have the same reward-to-risk ratio, they all
must plot on the same line. This argument is illustrated in Figure 11.3. As shown, Assets A
and B plot directly on the line and thus have the same reward-to-risk ratio. If an asset plotted
above the line, such as C in Figure 11.3, its price would rise, and its expected return would
fall until it plotted exactly on the line. Similarly, if an asset plotted below the line, such as D
in Figure 11.3, its expected return would rise until it, too, plotted directly on the line.
The arguments we have presented apply to active, competitive, well-functioning mar-
kets. The financial markets, such as the NYSE, best meet these criteria. Other markets, such
as real asset markets, may or may not. For this reason, these concepts are most useful in
examining financial markets. We thus focus on such markets here. However, as we discuss in
a later section, the information about risk and return gleaned from financial markets is cru-
cial in evaluating the investments that a corporation makes in real assets.
EXAMPLE 11.7 Buy Low, Sell High
An asset is said to be overvalued if its price is too high given its expected return and risk. Suppose
you observe the following situation:
Security Expected Return Beta
Fama Co. 14% 1.3
French Co. 10 .8
The risk-free rate is currently 6 percent. Is one of the two securities above overvalued relative to
the other?
To answer, we compute the reward-to-risk ratio for both. For Fama, this ratio is (14% − 6%)/1.3 =
6.15%. For French, this ratio is 5 percent. What we conclude is that French offers an insufficient ex-
pected return for its level of risk, at least relative to Fama. Because its expected return is too low, its
price is too high. In other words, French is overvalued relative to Fama, and we would expect to see
its price fall relative to Fama’s. Notice that we also could say Fama is undervalued relative to French.
Expected returns and
systematic risk
FIGURE 11.3
=
E(Ri) − Rf
βi
Rf
βA
Asset expected
return (E(Ri))
Asset
beta (βi)
E(RA)
E(RB)
E(RD)
E(RC)
βB βC βD
The fundamental relationship between beta and expected return is that all assets
must have the same reward-to-risk ratio, [E(Ri) − Rf ]/βi . This means that they would
all plot on the same straight line. Assets A and B are examples of this behavior.
Asset C’s expected return is too high; Asset D’s is too low.
A
B
C
D
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374 P A R T 6 Risk and Return
The Security Market Line
The line that results when we plot expected returns and beta coefficients is obviously of
some importance, so it’s time we gave it a name. This line, which we use to describe the re-
lationship between systematic risk and expected return in financial markets, is usually called
the security market line, or SML*. After NPV, the SML is arguably the most important con-
cept in modern finance.
Market Portfolios It will be very useful to know the equation of the SML. There are
many different ways we could write it, but one way is particularly common. Suppose we
consider a portfolio made up of all of the assets in the market. Such a portfolio is called a
market portfolio, and we will express the expected return on this market portfolio as E(RM).
Because all the assets in the market must plot on the SML, so must a market portfolio
made up of those assets. To determine where it plots on the SML, we need to know the beta
of the market portfolio, βM. Because this portfolio is representative of all of the assets in the
market, it must have average systematic risk. In other words, it has a beta of 1.0. We, there-
fore, could write the slope of the SML as:
SML slope =
E( R M “) − R f ________ β M
=
E( R M “) − R f ________ 1 = E( R M “) − R f
The term E(RM) − Rf is often called the market risk premium because it is the risk
premium on a market portfolio.
The Capital Asset Pricing Model To finish up, if we let E(Ri) and βi stand for the
expected return and beta, respectively, on any asset in the market, then we know that asset
must plot on the SML. As a result, we know that its reward-to-risk ratio is the same as the
overall market’s:
E( R i *) − * R f _______ β i
= E( R M *) − R f
If we rearrange this, then we can write the equation for the SML as:
E(Ri) = Rf + [E(RM) − Rf] × βi [11.7]
This result is identical to the famous capital asset pricing model (CAPM).
What the CAPM shows is that the expected return for a particular asset depends on
three things:
1. The pure time value of money. As measured by the risk-free rate, Rf , this is the reward
for merely waiting for your money, without taking any risk.
2. The reward for bearing systematic risk. As measured by the market risk premium,
[E(RM) − Rf], this component is the reward the market offers for bearing an average
amount of systematic risk in addition to waiting.
3. The amount of systematic risk. As measured by βi, this is the amount of systematic risk
present in a particular asset, relative to an average asset.
By the way, the CAPM works for portfolios of assets just as it does for individual assets.
In an earlier section, we saw how to calculate a portfolio’s β. To find the expected return on
a portfolio, we use this β in the CAPM equation.
Figure 11.4 summarizes our discussion of the SML and the CAPM. As before, we plot
expected return against beta. Now we recognize that, based on the CAPM, the slope of the
SML is equal to the market risk premium, [E(RM) − Rf].
security market line
(SML)
Positively sloped straight
line displaying the
relationship between
expected return and beta.
market risk premium
Slope of the security
market line; the difference
between the expected
return on a market
portfolio and the risk-free
rate.
_
capital asset pricing
model (CAPM)
Equation of the security
market line showing the
relationship between
expected return and beta.
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C H A P T E R 1 1 Risk and Return 375
Going back to Figure 11.3, C plots above the SML and D plots below the SML. In port-
folio management terms, the distance between a portfolio’s actual return and the SML is
often called alpha. When an asset plots on the SML, it earns exactly the return it should
earn based on its level of risk, or beta. A positive alpha means that the asset (or portfolio)
has earned a return in excess of what it should earn based on its beta. Of course, an asset
can have a negative alpha, which is less than desirable.
This concludes our presentation of concepts related to the risk-return trade-off. For fu-
ture reference, Table 11.9 summarizes the various concepts in the order in which we dis-
cussed them.
alpha
The excess return an asset
earns based on the level
of risk taken.
The security market
line, or SML
FIGURE 11.4
= E(RM) − Rf
E(RM)
Rf
βM = 1.0
The slope of the security market line is equal to the market risk
premium, i.e., the reward for bearing an average amount of
systematic risk. The equation describing the SML can be written:
E(Ri) = Rf + [E(RM) − Rf] × βi
This is the capital asset pricing model, or CAPM.
Asset
expected
return (E(Ri))
Asset
beta (βi)
EXAMPLE 11.8 Risk and Return
Suppose the risk-free rate is 4 percent, the market risk premium is 7 percent, and a particular stock
has a beta of 1.3. Based on the CAPM, what is the expected return on this stock? What would the
expected return be if the beta were to double?
With a beta of 1.3, the risk premium for the stock would be 1.3 × 7%, or 9.1 percent. The risk-
free rate is 4 percent, so the expected return is 13.1 percent. If the beta doubled to 2.6, the risk
premium would double to 18.2 percent, so the expected return would be 22.2 percent.
CONCEPT QUESTIONS
11.7a What is the fundamental relationship between risk and return in well-functioning
markets?
11.7b What is the security market line? Why must all assets plot directly on it in a well-
functioning market?
11.7c What is the capital asset pricing model, or CAPM? What does it tell us about the
required return on a risky investment?
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376 P A R T 6 Risk and Return
I. Total return
The total return on an investment has two components: the expected return and the unexpected
return. The unexpected return comes about because of unanticipated events. The risk from
investing stems from the possibility of an unanticipated event.
II. Total risk
The total risk of an investment is measured by the variance or, more commonly, the standard
deviation of its return.
III. Systematic and unsystematic risks
Systematic risks (also called market risks) are unanticipated events that affect almost all assets
to some degree because the effects are economywide. Unsystematic risks are unanticipated
events that affect single assets or small groups of assets. Unsystematic risks are also called
unique or asset-specific risks.
IV. The effect of diversification
Some, but not all, of the risk associated with a risky investment can be eliminated by diversification.
The reason is that unsystematic risks, which are unique to individual assets, tend to wash out in a
large portfolio, but systematic risks, which affect all of the assets in a portfolio to some extent, do not.
V. The systematic risk principle and beta
Because unsystematic risk can be freely eliminated by diversification, the systematic risk principle
states that the reward for bearing risk depends only on the level of systematic risk. The level of
systematic risk in a particular asset, relative to the average, is given by the beta of that asset.
VI. The reward-to-risk ratio and the security market line
The reward-to-risk ratio for Asset i is the ratio of its risk premium, E(Ri − Rf), to its beta, βi:
E(Ri) − Rf _______
βi
In a well-functioning market, this ratio is the same for every asset. As a result, when asset
expected returns are plotted against asset betas, all assets plot on the same straight line,
called the security market line (SML).
VII. The capital asset pricing model
From the SML, the expected return on Asset i can be written:
E(Ri) = Rf + [E(RM) − Rf] × βi
This is the capital asset pricing model (CAPM). The expected return on a risky asset thus has
three components. The first is the pure time value of money, Rf!!!!; the second is the market risk
premium, [E(RM) − Rf]; and the third is the beta for that asset, βi.
Summary of risk and
return concepts
TABLE 11.9
THE SML AND THE COST OF CAPITAL:
A PREVIEW
Our goal in studying risk and return is twofold. First, risk is an extremely important consid-
eration in almost all business decisions, so we want to discuss what risk is and how it is re-
warded in the market. Our second purpose is to learn what determines the appropriate
discount rate for future cash flows. We briefly discuss this second subject now; we discuss it
in more detail in Chapter 12.
The Basic Idea
The security market line tells us the reward for bearing risk in financial markets. At an abso-
lute minimum, any new investment our firm undertakes must offer an expected return that
is no worse than what the financial markets offer for the same risk. The reason for this is
that our shareholders always can invest for themselves in the financial markets.
The only way we benefit our shareholders is by finding investments with expected re-
turns that are superior to what the financial markets offer for the same risk. Such an
11.8
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C H A P T E R 1 1 Risk and Return 377
investment will have a positive NPV. So, if we ask: “What is the appropriate discount rate?”
the answer is that we should use the expected return offered in financial markets on invest-
ments with the same systematic risk.
In other words, to determine whether or not an investment has a positive NPV, we es-
sentially compare the expected return on that new investment to what the financial market
offers on an investment with the same beta. This is why the SML is so important; it tells us
the “going rate” for bearing risk in the economy.
The Cost of Capital
The appropriate discount rate on a new project is the minimum expected rate of return an
investment must offer to be attractive. This minimum required return often is called the
cost of capital associated with the investment. It is called this because the required return is
what the firm must earn on its capital investment in a project just to break even. It
thus can be interpreted as the opportunity cost associated with the firm’s capital
investment.
Notice that when we say an investment is attractive if its expected return exceeds what
is offered in financial markets for investments of the same risk, we are effectively using the
internal rate of return, or IRR, criterion that we developed and discussed in Chapter 8. The
only difference is that now we have a much better idea of what determines the required re-
turn on an investment. This understanding will be critical when we discuss cost of capital
and capital structure in Part Seven of our book.
CONCEPT QUESTIONS
11.8a If an investment has a positive NPV, would it plot above or below the SML? Why?
11.8b What is meant by the term cost of capital?
cost of capital
The minimum required
return on a new
investment.
This chapter has covered the essentials of risk. Along the way, we have introduced a
number of definitions and concepts. The most important of these is the security
market line, or SML. The SML is important because it tells us the reward offered in finan-
cial markets for bearing risk. Once we know this, we have a benchmark against which we
compare the returns expected from real asset investments to determine if they are
desirable.
Because we have covered quite a bit of ground, it’s useful to summarize the basic eco-
nomic logic underlying the SML as follows:
1. Based on capital market history, there is a reward for bearing risk. This reward is the
risk premium on an asset.
2. The total risk associated with an asset has two parts: systematic risk and
unsystematic risk. Unsystematic risk can be freely eliminated by diversification (this
is the principle of diversification), so only systematic risk is rewarded. As a result,
the risk premium on an asset is determined by its systematic risk. This is the
systematic risk principle.
SUMMARY AND CONCLUSIONS
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378 P A R T 6 Risk and Return
3. An asset’s systematic risk, relative to the average, can be measured by its beta
coefficient, βi. The risk premium on an asset is then given by its beta coefficient
multiplied by the market risk premium, [E(RM) − Rf] × βi.
4. The expected return on an asset, E(Ri), is equal to the risk-free rate, Rf , plus the risk
premium:
E( R i ) = R f + [E( R M ) − R f ] × β i
This is the equation of the SML, and it is often called the capital asset pricing model,
or CAPM.
This chapter completes our discussion of risk and return and concludes Part Six of our
book. Now that we have a better understanding of what determines a firm’s cost of capital
for an investment, the next several chapters examine more closely how firms raise the long-
term capital needed for investment.
POP QUIZ!
Can you answer the following questions? If your class is using Connect, log on to
SmartBook to see if you know the answers to these and other questions, check out
the study tools, and find out what topics require additional practice!
Section 11.1 What does variance measure?
Section 11.3 What is the equation for total return?
Section 11.4 What all will unsystematic risk affect?
Section 11.5 What type of risk is not reduced by diversification?
Section 11.6 By definition, what is the beta of the average asset equal to?
Section 11.7 What does the security market line show?
CHAPTER REVIEW AND SELF-TEST PROBLEMS
11.1 Expected Return and Standard Deviation This problem will give you some
practice calculating measures of prospective portfolio performance. There are two
assets and three states of the economy:
(1)
State of
Economy
(2)
Probability
of State
of Economy
(3)
Stock A
Rate of Return
if State Occurs
(4)
Stock B
Rate of Return
if State Occurs
Recession .10 −.20 .30
Normal .60 .10 .20
Boom .30 .70 .50
What are the expected returns and standard deviations for these two stocks? (See
Problem 7.)
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C H A P T E R 1 1 Risk and Return 379
11.2 Portfolio Risk and Return In the previous problem, suppose you have
$20,000 total. If you put $6,000 in Stock A and the remainder in Stock B, what
will be the expected return and standard deviation on your portfolio? (See
Problem 10.)
11.3 Risk and Return Suppose you observe the following situation:
Security Beta Expected Return
Cooley, Inc. 1.6 19%
Moyer Co. 1.2 16
If the risk-free rate is 8 percent, are these securities correctly priced? What would the
risk-free rate have to be if they are correctly priced? (See Problems 19 and 20.)
11.4 CAPM Suppose the risk-free rate is 8 percent. The expected return on the market is
14 percent. If a particular stock has a beta of .60, what is its expected return based
on the CAPM? If another stock has an expected return of 20 percent, what must its
beta be? (See Problem 13.)
■ Answers to Chapter Review and Self-Test Problems
11.1 The expected returns are the possible returns multiplied by the associated
probabilities:
E(RA) = .10 × −.20 + .60 × .10 + .30 × .70 = .25, or 25%
E(RB) = .10 × .30 + .60 × .20 + .30 × .50 = .30, or 30%
The variances are given by the sums of the squared deviations from the expected
returns multiplied by their probabilities:
σ2A = .10 × (−.20 − .25)
2 + .60 × (.10 − .25)2 + .30 × (.70 − .25)2
= .10 × (−.45)2 + .60 × (−.15)2 + .30 × (.45)2
= .10 × .2025 + .60 × .0225 + .30 × .2025
= .0945
σ2B = .10 × (.30 − .30)
2 + .60 × (.20 − .30)2 + .30 × (.50 − .30)2
= .10 × (.00)2 + .60 × (−.10)2 + .30 × (.20)2
= .10 × .00 + .60 × .01 + .30 × .04
= .0180
The standard deviations are thus:
σ A
=
√
_____
.0945 = .3074, or 30.74%
σ B
=
√
_____
.0180 = .1342, or 13.42%
11.2 The portfolio weights are $6,000/$20,000 = .30 and $14,000/$20,000 = .70. The
expected return is thus:
E(RP) = .30 × E(RA) + .70 × E(RB)
= .30 × 25% + .70 × 30%
= 28.50%
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380 P A R T 6 Risk and Return
Alternatively, we could calculate the portfolio’s return in each of the states:
(1)
State of
Economy
(2)
Probability of
State of Economy
(3)
Portfolio Return
if State Occurs
Recession .10 .30 × −.20 + .70 × .30 = .15
Normal .60 .30 × .10 + .70 × .20 = .17
Boom .30 .30 × .70 + .70 × .50 = .56
The portfolio’s expected return is:
E(RP) = .10 × .15 + .60 × .17 + .30 × .56 = .2850, or 28.50%
This is the same as we had before.
The portfolio’s variance is:
σ2P = .10 × (.15 − .285)
2 + .60 × (.17 − .285)2 + .30 × (.56 − .285)2
= .03245
So the standard deviation is √
______
.03245 = .1801, or 18.01%
11.3 If we compute the reward-to-risk ratios, we get ( 19% − 8% ) / 1.6 = 6.88% for Cooley
versus 6.67% for Moyer. Relative to that of Cooley, Moyer’s expected return is too
low, so its price is too high.
If they are correctly priced, then they must offer the same reward-to-risk ratio.
The risk-free rate would have to be such that:
(19% − Rf )/1.6 = (16% − Rf )/1.2
With a little algebra, we find that the risk-free rate must be 7 percent:
(19% − Rf ) = (16% − Rf ) (1.6/1.2)
19% − 16% × 4/3 = Rf − Rf × 4/3
Rf = 7%
11.4 Because the expected return on the market is 14 percent, the market risk premium is
14% − 8% = 6% (the risk-free rate is 8 percent). The first stock has a beta of .60, so
its expected return is 8% + .60 × 6% = 11.6%.
For the second stock, notice that the risk premium is 20% − 8% = 12%.
Because this is twice as large as the market risk premium, the beta must be exactly
equal to 2. We can verify this using the CAPM:
E(Ri) = Rf + [E(RM) − Rf] × βi
20% = 8% + (14% − 8%) × βi
βi = 12%/6% = 2.0
CRITICAL THINKING AND CONCEPTS REVIEW
LO 2 11.1 Diversifiable and Nondiversifiable Risks In broad terms, why is some risk
diversifiable? Why are some risks nondiversifiable? Does it follow that an
investor can control the level of unsystematic risk in a portfolio, but not the
level of systematic risk?
LO 3 11.2 Information and Market Returns Suppose the government announces
that, based on a just-completed survey, the growth rate in the economy is
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C H A P T E R 1 1 Risk and Return 381
likely to be 2 percent in the coming year, as compared to 5 percent for the
year just completed. Will security prices increase, decrease, or stay the
same following this announcement? Does it make any difference whether or
not the 2 percent figure was anticipated by the market? Explain.
LO 3 11.3 Systematic versus Unsystematic Risk Classify the following events as
mostly systematic or mostly unsystematic. Is the distinction clear in every case?
a. Short-term interest rates increase unexpectedly.
b. The interest rate a company pays on its short-term debt borrowing is
increased by its bank.
c. Oil prices unexpectedly decline.
d. An oil tanker ruptures, creating a large oil spill.
e. A manufacturer loses a multimillion-dollar product liability suit.
f. A Supreme Court decision substantially broadens producer liability for
injuries suffered by product users.
LO 3 11.4 Systematic versus Unsystematic Risk Indicate whether the following
events might cause stocks in general to change price, and whether they
might cause Big Widget Corp.’s stock to change price.
a. The government announces that inflation unexpectedly jumped by 2
percent last month.
b. Big Widget’s quarterly earnings report, just issued, generally fell in line
with analysts’ expectations.
c. The government reports that economic growth last year was 3 percent,
which generally agreed with most economists’ forecasts.
d. The directors of Big Widget die in a plane crash.
e. Congress approves changes to the tax code that will increase the top
marginal corporate tax rate. The legislation had been debated for the
previous six months.
LO 1 11.5 Expected Portfolio Returns If a portfolio has a positive investment in
every asset, can the expected return on the portfolio be greater than that on
every asset in the portfolio? Can it be less than that on every asset in the
portfolio? If you answer yes to one or both of these questions, give an
example to support your answer.
LO 2 11.6 Diversification True or false: The most important characteristic in
determining the expected return of a well-diversified portfolio is the
variances of the individual assets in the portfolio. Explain.
LO 3 11.7 Portfolio Risk If a portfolio has a positive investment in every asset, can
the standard deviation on the portfolio be less than that on every asset in
the portfolio? What about the portfolio beta?
LO 4 11.8 Beta and CAPM Is it possible that a risky asset could have a beta of zero?
Explain. Based on the CAPM, what is the expected return on such an
asset? Is it possible that a risky asset could have a negative beta? What does
the CAPM predict about the expected return on such an asset? Can you
give an explanation for your answer?
LO 2 11.9 Corporate Downsizing In recent years, it has been common for
companies to experience significant stock price changes in reaction to
announcements of massive layoffs. Critics charge that such events
encourage companies to fire longtime employees and that Wall Street is
cheering them on. Do you agree or disagree?
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382 P A R T 6 Risk and Return
LO 1 11.10 Earnings and Stock Returns As indicated by a number of examples in this
chapter, earnings announcements by companies are closely followed by,
and frequently result in, share price revisions. Two issues should come to
mind. First: Earnings announcements concern past periods. If the market
values stocks based on expectations of the future, why are numbers
summarizing past performance relevant? Second: These announcements
concern accounting earnings. Going back to Chapter 2, such earnings may
have little to do with cash flow, so again, why are they relevant?
QUESTIONS AND PROBLEMS
Select problems are available in McGraw-Hill Connect. Please see the pack-
aging options section of the Preface for more information.
BASIC (Questions 1–24)
1. Determining Portfolio Weights What are the portfolio weights for a
portfolio that has 185 shares of Stock A that sell for $64 per share and 115
shares of Stock B that sell for $49 per share?
2. Portfolio Expected Return You own a portfolio that has $3,140 invested
in Stock A and $4,300 invested in Stock B. If the expected returns on these
stocks are 9 percent and 14 percent, respectively, what is the expected return
on the portfolio?
3. Portfolio Expected Return You own a portfolio that is 25 percent invested
in Stock X, 35 percent in Stock Y, and 40 percent in Stock Z. The expected
returns on these three stocks are 10 percent, 13 percent, and 15 percent,
respectively. What is the expected return on the portfolio?
4. Portfolio Expected Return You have $10,000 to invest in a stock portfolio.
Your choices are Stock X with an expected return of 12.5 percent and Stock
Y with an expected return of 9.5 percent. If your goal is to create a portfolio
with an expected return of 11.2 percent, how much money will you invest in
Stock X? In Stock Y?
5. Calculating Expected Return Based on the following information, calculate
the expected return.
State of
Economy
Probability of
State of Economy
Rate of Return if
State Occurs
Recession .30 −.13
Boom .70 .21
6. Calculating Expected Return Based on the following information, calculate
the expected return.
State of
Economy
Probability of
State of Economy
Rate of Return if
State Occurs
Recession .15 −.12
Normal .60 .10
Boom .25 .27
LO 1
LO 1
LO 1
LO 1
LO 1
LO 1
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C H A P T E R 1 1 Risk and Return 383
7. Calculating Returns and Standard Deviations Based on the following
information, calculate the expected returns and standard deviations for the
two stocks.
State of
Economy
Probability of
State of Economy
Rate of Return if State Occurs
Stock A Stock B
Recession .10 .02 −.30
Normal .50 .10 .18
Boom .40 .15 .31
8. Calculating Expected Returns A portfolio is invested 20 percent in Stock
G, 35 percent in Stock J, and 45 percent in Stock K. The expected returns
on these stocks are 9.6 percent, 10.9 percent, and 14.3 percent, respectively.
What is the portfolio’s expected return? How do you interpret your answer?
9. Returns and Standard Deviations Consider the following information:
State of
Economy
Probability of
State of Economy
Rate of Return if State Occurs
*Stock A Stock B Stock C
Boom .60 .18 .04 .31
Bust .40 .03 .16 −.11
a. What is the expected return on an equally weighted portfolio of these
three stocks?
b. What is the variance of a portfolio invested 20 percent each in A and B
and 60 percent in C?
10. Returns and Standard Deviations Consider the following information:
State of
Economy
Probability of
State of Economy
Rate of Return if State Occurs
Stock A Stock B Stock C
Boom .15 .33 .45 .33
Good .55 .11 .10 .17
Poor .20 .02 .02 −.05
Bust .10 −.12 −.25 −.09
a. Your portfolio is invested 25 percent each in A and C and 50 percent in
B. What is the expected return of the portfolio?
b. What is the variance of this portfolio? The standard deviation?
11. Calculating Portfolio Betas You own a stock portfolio invested 15 percent
in Stock Q, 25 percent in Stock R, 40 percent in Stock S, and 20 percent
in Stock T. The betas for these four stocks are .78, .87, 1.13, and 1.45,
respectively. What is the portfolio beta?
12. Calculating Portfolio Betas You own a portfolio equally invested in a risk-
free asset and two stocks. If one of the stocks has a beta of 1.29 and the total
portfolio is equally as risky as the market, what must the beta be for the other
stock in your portfolio?
13. Using CAPM A stock has a beta of 1.14, the expected return on the market
is 10.9 percent, and the risk-free rate is 3.6 percent. What must the expected
return on this stock be?
LO 1
LO 1
LO 1
LO 2
LO 1
LO 2
LO 3
LO 3
LO 4
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384 P A R T 6 Risk and Return
14. Using CAPM A stock has an expected return of 11.4 percent, the risk-free
rate is 3.7 percent, and the market risk premium is 6.8 percent. What must
the beta of this stock be?
15. Using CAPM A stock has an expected return of 10.9 percent, its beta is .90,
and the risk-free rate is 2.8 percent. What must the expected return on the
market be?
16. Using CAPM A stock has an expected return of 10.2 percent and a beta of
.91, and the expected return on the market is 10.8 percent. What must the
risk-free rate be?
17. Using CAPM A stock has a beta of 1.15 and an expected return of 11.4
percent. A risk-free asset currently earns 3.5 percent.
a. What is the expected return on a portfolio that is equally invested in the
two assets?
b. If a portfolio of the two assets has a beta of .7, what are the portfolio weights?
c. If a portfolio of the two assets has an expected return of 9 percent, what
is its beta?
d. If a portfolio of the two assets has a beta of 2.30, what are the portfolio
weights? How do you interpret the weights for the two assets in this
case? Explain.
18. Using the SML Asset W has an expected return of 11.6 percent and a beta
of 1.23. If the risk-free rate is 3.15 percent, complete the following table for
portfolios of Asset W and a risk-free asset. Illustrate the relationship between
portfolio expected return and portfolio beta by plotting the expected returns
against the betas. What is the slope of the line that results?
Percentage of Portfolio
in Asset W
Portfolio
Expected Return
Portfolio
Beta
0%
25
50
75
100
125
150
19. Reward-to-Risk Ratios Stock Y has a beta of 1.20 and an expected return of
11.4 percent. Stock Z has a beta of .80 and an expected return of 8 percent.
If the risk-free rate is 2.5 percent and the market risk premium is 7 percent,
are these stocks correctly priced?
20. Reward-to-Risk Ratios In the previous problem, what would the risk-free
rate have to be for the two stocks to be correctly priced relative to each other?
21. Portfolio Returns Using information from Table 10.2 on capital market
history, determine the return on a portfolio that was equally invested in large-
company stocks and long-term corporate bonds. What was the return on a
portfolio that was equally invested in small stocks and Treasury bills?
22. Portfolio Expected Return You have $250,000 to invest in a stock portfolio.
Your choices are Stock H, with an expected return of 13.4 percent, and
Stock L, with an expected return of 10.2 percent. If your goal is to create a
portfolio with an expected return of 11.3 percent, how much money will you
invest in Stock H? In Stock L?
LO 4
LO 4
LO 4
LO 4
LO 4
LO 4
LO 4
LO 1
LO 1
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C H A P T E R 1 1 Risk and Return 385
23. Calculating Portfolio Weights Stock J has a beta of 1.23 and an expected return
of 13.25 percent, while Stock K has a beta of .84 and an expected return of 10.60
percent. You want a portfolio with the same risk as the market. How much will
you invest in each stock? What is the expected return of your portfolio?
24. Calculating Portfolio Weights and Expected Return You have a portfolio
with the following:
Stock
Number
of Shares Price
Expected
Return
W 525 $43 10%
X 780 29 15
Y 435 94 11
Z 680 51 14
What is the expected return of your portfolio?
INTERMEDIATE (Questions 25–27)
25. Portfolio Returns and Deviations Consider the following information on a
portfolio of three stocks:
State of
Economy
Probability of
State of
Economy
Stock A Rate
of Return
Stock B Rate
of Return
Stock C Rate
of Return
Boom .15 .04 .33 .55
Normal .60 .09 .13 .19
Bust .25 .15 −.14 −.28
a. If your portfolio is invested 40 percent each in A and B and 20 percent in C,
what is the portfolio’s expected return? The variance? The standard deviation?
b. If the expected T-bill rate is 3.75 percent, what is the expected risk
premium on the portfolio?
26. CAPM Using the CAPM, show that the ratio of the risk premiums on two
assets is equal to the ratio of their betas.
27. Analyzing a Portfolio You want to create a portfolio equally as risky as the
market, and you have $500,000 to invest. Given this information, fill in the
rest of the following table:
Asset Investment Beta
Stock A $85,000 .80
Stock B 165,000 1.15
Stock C 1.40
Risk-free asset
CHALLENGE (Questions 28–30)
28. Analyzing a Portfolio You have $100,000 to invest in either Stock D, Stock
F, or a risk-free asset. You must invest all of your money. Your goal is to
create a portfolio that has an expected return of 11.4 percent. If D has an
expected return of 13.6 percent, F has an expected return of 9.7 percent, the
risk-free rate is 3.8 percent, and you invest $50,000 in Stock D, how much
will you invest in Stock F?
LO 1
LO 1
LO 1
LO 2
LO 4
LO 2
LO 1
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386 P A R T 6 Risk and Return
29. SML Suppose you observe the following situation:
State of
Economy
Probability
of State
Return if State Occurs
Stock A Stock B
Bust .15 −.08 −.10
Normal .60 .11 .09
Boom .25 .30 .27
a. Calculate the expected return on each stock.
b. Assuming the capital asset pricing model holds and Stock A’s beta is greater
than Stock B’s beta by .30, what is the expected market risk premium?
30. Systematic versus Unsystematic Risk Consider the following information
on Stocks I and II:
State of
Economy
Probability of State
of Economy
Rate of Return if State Occurs
Stock I Stock II
Recession .25 .04 −.22
Normal .60 .22 .15
Irrational exuberance .15 .16 .45
The market risk premium is 7 percent, and the risk-free rate is 4 percent.
Which stock has more systematic risk? Which one has more unsystematic
risk? Which stock is “riskier”? Explain.
LO 4
LO 3
EXCEL MASTER IT! PROBLEM
WHAT’S ON
THE WEB?
11.1 Expected Return You want to find the expected return for Honeywell using the CAPM.
First, you need the market risk premium. Use the average large-company stock return in
Table 10.3 to estimate the market risk premium. Next, go to money.cnn.com and find the
current interest rate for three-month Treasury bills. Finally, go to finance.yahoo.com, enter
the ticker symbol HON, and find the beta for Honeywell. What is the expected return for
Honeywell using CAPM? What assumptions have you made to arrive at this number?
11.2 Portfolio Beta You have decided to invest in an equally weighted portfolio consisting
of American Express, Procter & Gamble, Home Depot, and DuPont and need to find the
beta of your portfolio. Go to finance.yahoo.com and find the ticker symbols for each of
these companies. Next, find the beta for each company. What is the beta for your portfolio?
11.3 Beta Which stocks have the highest and lowest betas? Go to finance.yahoo.com
and locate the Stock Screener. Enter 0 as the maximum value. How many stocks have a
beta less than zero? Which stock has the lowest beta? Go back to the screener and enter
3 as the minimum value. How many stocks have a beta greater than 3? What about
greater than 4? Which stock has the highest beta?
The CAPM is one of the most thoroughly researched models in financial economics. When
beta is estimated in practice, a variation of CAPM called the market model is often used. To
derive the market model, we start with the CAPM:
E(Ri) = Rf + β[E(RM) − Rf]
coverage online
Excel
Master
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C H A P T E R 1 1 Risk and Return 387
Because CAPM is an equation, we can subtract the risk-free rate from both sides, which
gives us:
E(Ri) − Rf = β[E(RM) − Rf]
This equation is deterministic, that is, exact. In a regression, we realize that there is some
indeterminate error. We need to formally recognize this in the equation by adding epsilon,
which represents this error:
E(Ri) − Rf = β[E(RM) − Rf] + ε
Finally, think of the above equation in a regression. Because there is no intercept in the
equation, the intercept is zero. However, when we estimate the regression equation, we can
add an intercept term, which we will call alpha:
E(Ri) − Rf = αi + β[E(RM) − Rf] + ε
This equation is often called the “market” model, though it is not the only equation with
that name, which is a source of confusion. The intercept term is known as Jensen’s alpha,
and it represents the “excess” return. If CAPM holds exactly, this intercept should be zero.
If you think of alpha in terms of the SML, if the alpha is positive, the stock plots above the
SML, and if the alpha is negative, the stock plots below the SML.
a. You want to estimate the market model for an individual stock and a mutual fund.
First, go to finance.yahoo.com and download the adjusted prices for the last 61
months for an individual stock, a mutual fund, and the S&P 500. Next, go to the
Federal Reserve Bank of St. Louis website at www.stlouisfed.org. You should find the
“FRED®” database there. Look for the “1-Month Treasury Constant Maturity
Rate” and download these data. This series will be the proxy for the risk-free rate.
When using this rate, you should be aware that this interest rate is the annualized
interest rate. Because we are using monthly stock returns, you will need to adjust the
1-month T-bill rate. For the stock and mutual fund you select, estimate the beta and
alpha using the market model. When you estimate the regression model, find the box
that says “Residuals” and check this box when you do each regression. Because you
are saving the residuals, you may want to save the regression output in a new
worksheet.
1. Are the alpha and beta for each regression statistically different from zero?
2. How do you interpret the alpha and beta for the stock and the mutual fund?
3. Which of the two regression estimates has the higher R-squared? Is this what you
would have expected? Why?
b. In part (a), you asked Excel to return the residuals of the regression, which is the
epsilon in the regression equation. If you remember back to basic statistics, the
residuals are the distance from each observation to the regression line. In this context,
the residuals are the part of the monthly return that is not explained by the market
model estimate. The residuals can be used to calculate the appraisal ratio, which is the
alpha divided by the standard deviation of the residuals.
1. What do you think the appraisal ratio is intended to measure?
2. Calculate the appraisal ratios for the stock and the mutual fund. Which has a
better appraisal ratio?
3. Often, the appraisal ratio is used to evaluate the performance of mutual fund
managers. Why do you think the appraisal ratio is used more often for mutual
funds, which are portfolios, than for individual stocks?
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388 P A R T 6 Risk and Return
such as automotive night vision, commercial products
that require minute temperature difference measure-
ments, recreational marine usage, and firefighting.
Covili and Wyatt currently uses a commercial data
vendor for information about its positions. Because of
this, Paul is unsure exactly how the numbers provided
are calculated. The data provider considers its methods
proprietary, and it will not disclose how stock betas and
other information are calculated. Paul is uncomfortable
with not knowing exactly how these numbers are being
computed and also believes that it could be less expen-
sive to calculate the necessary statistics in-house. To
explore this question, Paul has asked Joey to do the fol-
lowing assignments:
Joey Moss, a recent finance graduate, has just begun his job with the investment firm of Covili and Wyatt.
Paul Covili, one of the firm’s founders, has been talking
to Joey about the firm’s investment portfolio.
As with any investment, Paul is concerned about the
risk of the investment as well as the potential return.
More specifically, because the company holds a diversi-
fied portfolio, Paul is concerned about the systematic risk
of current and potential investments. One position the
company currently holds is stock in FLIR Systems, Inc.
(FLIR). FLIR Systems designs, manufactures, and markets
thermal imaging and infrared camera systems. Although
better known for its military applications, the company
has divisions that design products for other applications
CHAPTER CASE
The Beta for FLIR Systems
1. Go to finance.yahoo.com and download the end-
ing monthly stock prices for FLIR Systems (FLIR)
for the last 60 months. Be sure to use the adjusted
closing price to account for any stock splits and
dividend payments. Next, download the ending
value of the S&P 500 index over the same period.
For the historical risk-free rate, go to the Federal
Reserve Bank of St. Louis website (www.stlouis-
fed.org) and find the three-month Treasury bill
constant maturity rate. Download this file. What
are the monthly returns, average monthly returns,
and standard deviations for FLIR Systems stock,
the three-month Treasury bill, and the S&P 500 for
this period?
2. Beta is often estimated by linear regression. A
model often used is called the market model,
which is:
Rt − Rft = αi + βi [RMt − Rft] + εt
In this regression, Rt is the return on the stock
and Rft is the risk-free rate for the same period.
RMt is the return on a stock market index such as
the S&P 500 index. αi is the regression intercept,
and βi is the slope (and the stock’s estimated
beta). εt represents the residuals for the regres-
sion. What do you think is the motivation for this
particular regression? The intercept, αi, is often
called Jensen’s alpha. What does it measure? If
an asset has a positive Jensen’s alpha, where
would it plot with respect to the SML? What is the
financial interpretation of the residuals in the
regression?
3. Use the market model to estimate the beta for
FLIR Systems using the last 60 months of returns
(the regression procedure in Excel is one easy
way to do this). Plot the monthly returns on FLIR
Systems against the index and also show the
fitted line.
4. Compare your beta for FLIR Systems to the beta
you find on finance.yahoo.com. How similar are
they? Why might they be different?
Q U E S T I O N S
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389
With more than 115,000 employees on five continents, Germany- based BASF is a major international company. BASF
operates in a variety of industries, including agriculture, oil and gas,
chemicals, and plastics. In an attempt to increase value, BASF
launched Vision 2020, a comprehensive plan that included all func-
tions within the company and challenged and encouraged all
employees to act in an entrepreneurial manner. The major financial
component of the strategy was that the company expected to earn
its weighted average cost of capital, or WACC, plus a premium. So,
what exactly is the WACC?
The WACC is the minimum return a company needs to earn to
satisfy all of its investors, including stockholders, bondholders, and
preferred stockholders. In 2017, for example, BASF pegged its cost
of capital at 10 percent, the same WACC that it used during 2016,
but down slightly from the 11 percent used from 2011 to 2015. In this chapter, we learn how to
compute a firm’s cost of capital and find out what it means to the firm and its investors. We
also will learn when to use the firm’s cost of capital and, perhaps more important, when not
to use it.
From our chapters on capital budgeting, we know that the discount rate, or required
return, on an investment is a critical input. Thus far, however, we haven’t discussed how
to come up with that particular number, so it’s time now to do so. This chapter brings
together many of our earlier discussions dealing with stocks and bonds, capital budgeting,
and risk and return. Our goal is to illustrate how firms go about determining the required
return on a proposed investment. Understanding required returns is important to everyone
because all proposed projects, whether they relate to marketing, management, account-
ing, or any other area, must offer returns in excess of their required returns to be
acceptable.
Cost of Capital12
LEARNING OBJECTIVES
After studying this chapter, you should be
able to:
LO 1 Determine a firm’s cost of equity
capital.
LO 2 Determine a firm’s cost of debt.
LO 3 Determine a firm’s overall cost of
capital.
LO 4 Identify some of the pitfalls
associated with a firm’s overall
cost of capital and what to do
about them.
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PART SEVEN Long-Term Financing
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390 P A R T 7 Long-Term Financing
Suppose you have just become the president of a large company and the first decision you face is whether to go ahead with a plan to renovate the company’s warehouse
distribution system. The plan will cost the company $50 million, and it is expected to save
$12 million per year after taxes over the next six years.
This is a familiar problem in capital budgeting. To address it, you would determine the
relevant cash flows, discount them, and, if the net present value is positive, take on the
project; if the NPV is negative, you would scrap it. So far, so good; but what should you use
as the discount rate?
From our discussion of risk and return, you know that the correct discount rate
depends on the riskiness of the warehouse distribution system. In particular, the new project
will have a positive NPV only if its return exceeds what the financial markets offer on invest-
ments of similar risk. We called this minimum required return the cost of capital associated
with the project.1
Thus, to make the right decision as president, you must examine what the capital mar-
kets have to offer and use this information to arrive at an estimate of the project’s cost of
capital. Our primary purpose in this chapter is to describe how to go about doing this.
There are a variety of approaches to this task, and a number of conceptual and practical
issues arise.
One of the most important concepts we develop is that of the weighted average cost of
capital (WACC). This is the cost of capital for the firm as a whole, and it can be interpreted
as the required return on the overall firm. In discussing the WACC, we will recognize the
fact that a firm will normally raise capital in a variety of forms and that these different
forms of capital may have different costs associated with them.
We also recognize in this chapter that taxes are an important consideration in deter-
mining the required return on an investment because we are always interested in valuing the
aftertax cash flows from a project. Therefore, we will discuss how to incorporate taxes
explicitly into our estimates of the cost of capital.
THE COST OF CAPITAL: SOME PRELIMINARIES
In Chapter 11, we developed the security market line, or SML, and used it to explore the
relationship between the expected return on a security and its systematic risk. We concen-
trated on how the risky returns from buying securities looked from the viewpoint of, for ex-
ample, a shareholder in the firm. This helped us understand more about the alternatives
available to an investor in the capital markets.
In this chapter, we turn things around a bit and look more closely at the other side of
the problem, which is how these returns and securities look from the viewpoint of the com-
panies that issue the securities. The important fact to note is that the return an investor in a
security receives is the cost of that security to the company that issued it.
Required Return versus Cost of Capital
When we say that the required return on an investment is, say, 10 percent, we usually mean
that the investment will have a positive NPV only if its return exceeds 10 percent. Another
12.1
1The terms cost of money and hurdle rate also are used.
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C H A P T E R 1 2 Cost of Capital 391
way of interpreting the required return is to observe that the firm must earn 10 percent on
the investment to compensate its investors for the use of the capital needed to finance the
project. This is why we also could say that 10 percent is the cost of capital associated with
the investment.
To illustrate the point further, imagine we are evaluating a risk-free project. In this
case, how to determine the required return is obvious: We look at the capital markets
and observe the current rate offered by risk-free investments, and we use this rate to
discount the project’s cash flows. Thus, the cost of capital for a risk-free investment is the
risk-free rate.
If this project is risky, then, assuming that all the other information is unchanged, the
required return is obviously higher. In other words, the cost of capital for this project, if it is
risky, is greater than the risk-free rate, and the appropriate discount rate would exceed the
risk-free rate.
We will henceforth use the terms required return, appropriate discount rate, and cost of
capital more or less interchangeably because, as the discussion in this section suggests, they
all mean essentially the same thing. The key fact to grasp is that the cost of capital associ-
ated with an investment depends on the risk of that investment. In other words, it’s the use
of the money, not the source, that matters. This is one of the most important lessons in
corporate finance, so it bears repeating:
The cost of capital depends primarily on the use of the funds, not the source.
It is a common error to forget this crucial point and fall into the trap of thinking that the
cost of capital for an investment depends primarily on how and where the capital is
raised.
Financial Policy and Cost of Capital
We know that the particular mixture of debt and equity a firm chooses to employ—its capital
structure—is a managerial variable. In this chapter, we will take the firm’s financial policy as
given. In particular, we will assume that the firm has a fixed debt-equity ratio that it main-
tains. This ratio reflects the firm’s target capital structure. How a firm might choose that
ratio is the subject of a later chapter.
From our discussion above, we know that a firm’s overall cost of capital will reflect the
required return on the firm’s assets as a whole. Given that a firm uses both debt and equity
capital, this overall cost of capital will be a mixture of the returns needed to compensate its
creditors and its stockholders. In other words, a firm’s cost of capital will reflect both its
cost of debt capital and its cost of equity capital. We discuss these costs separately in the
sections that follow.
CONCEPT QUESTIONS
12.1a What is the primary determinant of the cost of capital for an investment?
12.1b What is the relationship between the required return on an investment and the cost
of capital associated with that investment?
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392 P A R T 7 Long-Term Financing
THE COST OF EQUITY
We begin with the most difficult question on the subject of cost of capital: What is the
firm’s overall cost of equity? The reason this is a difficult question is that there is no way of
directly observing the return that the firm’s equity investors require on their investment.
Instead, we must somehow estimate it. This section discusses two approaches to determin-
ing the cost of equity: the dividend growth model approach and the security market line, or
SML, approach.
The Dividend Growth Model Approach
The easiest way to estimate the cost of equity capital is to use the dividend growth model we
developed in Chapter 7. Recall that, under the assumption that the firm’s dividend will grow
at a constant rate, g, the price per share of the stock, P0, can be written as:
P0 =
D0 × (1 + g() __________ RE − g
=
D1 ______ RE − g
where D0 is the dividend just paid and D1 is the next period’s projected dividend. Notice that
we have used the symbol RE (the E stands for equity) for the required return on the stock.
As we discussed in Chapter 7, we can rearrange this to solve for RE as follows:
RE = D1/P0 + g [12.1]
Because RE is the return that the shareholders require on the stock, it can be interpreted as
the firm’s cost of equity capital.
Implementing the Approach To estimate RE using the dividend growth model ap-
proach, we obviously need three pieces of information: P0, D0, and g. Of these, for a publicly
traded, dividend-paying company, the first two can be observed directly, so they are easily ob-
tained.2 Only the third component, the expected growth rate in dividends, must be estimated.
To illustrate how we estimate RE , suppose Greater States Public Service, a large public
utility, paid a dividend of $4 per share last year. The stock currently sells for $60 per share.
You estimate that the dividend will grow steadily at 6 percent per year into the indefinite
future. What is the cost of equity capital for Greater States?
Using the dividend growth model, we calculate that the expected dividend for the com-
ing year, D1, is:
D1 = D0 × (1 + g)
= $4 × 1.06
= $4.24
Given this, the cost of equity, RE , is:
RE = D1/P0 + g
= $4.24/$60 + .06
= .1307, or 13.07%
The cost of equity is thus 13.07 percent.
Estimating g To use the dividend growth model, we must come up with an estimate for
g, the growth rate. There are essentially two ways of doing this: (1) use historical growth
12.2
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cost of equity
The return that equity
investors require on their
investment in the firm.
2Notice that if we have D0 and g, we can calculate D1 by multiplying D0 by (1 + g).
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C H A P T E R 1 2 Cost of Capital 393
rates or (2) use analysts’ forecasts of future growth rates. Analysts’ forecasts are available
from a variety of sources. Naturally, different sources will have different estimates, so one
approach might be to obtain multiple estimates and then average them.
Alternatively, we might observe dividends for the previous, say, five years; calculate the
year-to-year growth rates; and average them. Suppose we observe the following for some
company:
Year Dividend
2015 $1.10
2016 1.20
2017 1.35
2018 1.40
2019 1.55
We can calculate the percentage change in the dividend for each year as follows:
Year Dividend Dollar Change Percentage Change
2015 $1.10 — —
2016 1.20 $.10 9.09%
2017 1.35 .15 12.50
2018 1.40 .05 3.70
2019 1.55 .15 10.71
Notice that we calculated the change in the dividend on a year-to-year basis and then ex-
pressed the change as a percentage. Thus, in 2016, for example, the dividend rose from $1.10
to $1.20, for an increase of $.10. This represents a $.10/$1.10 = .0909, or 9.09% increase.
If we average the four growth rates, the result is (9.09 + 12.50 + 3.70 + 10.71)/
4 = .09, or 9%, so we could use this as an estimate for the expected growth rate, g. Notice
that this 9 percent growth rate we have calculated is a simple, or arithmetic, average. Going
back to Chapter 10, we also could calculate a geometric growth rate. Here, the dividend
grows from $1.10 to $1.55 over a four-year period. What’s the compound, or geometric,
growth rate? See if you don’t agree that it’s 8.95 percent; you can view this as a time value of
money problem where $1.10 is the present value and $1.55 is the future value.
As usual, the geometric average (8.95 percent) is lower than the arithmetic average
(9.00 percent), but the difference here is not likely to be of any practical significance. In
general, if the dividend has grown at a relatively steady rate, as we assume when we use this
approach, then it can’t make much difference which way we calculate the average dividend
growth rate.
Advantages and Disadvantages of the Approach The primary advantage of
the dividend growth model approach is its simplicity. It is both easy to understand and easy
to use. However, there are a number of associated practical problems and disadvantages.
First and foremost, the dividend growth model is obviously only applicable to compa-
nies that pay dividends. This means that the approach is useless in many cases. Further-
more, even for companies that do pay dividends, the key underlying assumption is that the
dividend grows at a constant rate. As our example above illustrates, this will never be exactly
the case. More generally, the model is really only applicable to cases in which reasonably
steady growth is likely to occur.
Aggregate growth
estimates can be found at
www.zacks.com
/earnings.
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394 P A R T 7 Long-Term Financing
A second problem is that the estimated cost of equity is very sensitive to the estimated
growth rate. For a given stock price, an upward revision of g by just one percentage point,
for example, increases the estimated cost of equity by at least a full percentage point.
Because D1 will probably be revised upward as well, the increase will actually be somewhat
larger than that.
Finally, this approach really does not explicitly consider risk. Unlike the SML approach
(which we consider next), this one has no direct adjustment for the riskiness of the invest-
ment. For example, there is no allowance for the degree of certainty or uncertainty sur-
rounding the estimated growth rate in dividends. As a result, it is difficult to say whether or
not the estimated return is commensurate with the level of risk.3
The SML Approach
In Chapter 11, we discussed the security market line, or SML. Our primary conclusion was
that the required or expected return on a risky investment depends on three things:
1. The risk-free rate, Rf
2. The market risk premium, E(RM) − Rf
3. The systematic risk of the asset relative to that in an average risky asset, which we
called its beta coefficient, β
Using the SML, we can write the expected return on the company’s equity, E(RE), as:
E(RE) = Rf + βE × [E(RM) − Rf]
where βE is the estimated beta for the equity. To make the SML approach consistent with the
dividend growth model, we will drop the Es denoting expectations and henceforth write the
required return from the SML, RE , as:
RE = Rf + βE × (RM − Rf) [12.2]
Implementing the Approach To use the SML approach, we need a risk-free rate,
Rf; an estimate of the market risk premium, RM − Rf ; and an estimate of the relevant beta,
βE. In Chapter 10, we saw that one estimate of the market risk premium is about 7 percent.
U.S. Treasury bills are paying about 1.90 percent as this is being written, so we will use
this as our risk-free rate. Beta coefficients for publicly traded companies are widely
available.4
To illustrate, in Chapter 11, we saw that Apple had an estimated beta of 1.15
(Table 11.8). We could thus estimate Apple’s cost of equity as:
RApple = Rf + βApple × (RM − Rf)
= 1.90% + 1.15 × 7%
= 9.95%
Thus, using the SML approach, Apple’s cost of equity is about 10 percent.
Both betas and T-bill
rates can be found at
www.bloomberg.com.
3There is an implicit adjustment for risk because the current stock price is used. All other things being equal, the
higher the risk, the lower is the stock price. Further, the lower the stock price, the greater is the cost of equity, again
assuming that all the other information is the same.
4Beta coefficients can be estimated directly by using historical data. For a discussion of how to do this, see
Chapters 10, 11, and 12 in S. A. Ross, R. W. Westerfield, J. F. Jaffe, and B. D. Jordan, Corporate Finance, 12th ed.
(Chicago, IL: McGraw-Hill Education, 2019).
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C H A P T E R 1 2 Cost of Capital 395
Advantages and Disadvantages of the Approach The SML approach has
two primary advantages. First: It explicitly adjusts for risk. Second: It is applicable to com-
panies other than those with steady dividend growth. Thus, it may be useful in a wider
variety of circumstances.
There are drawbacks, of course. The SML approach requires that two things be estimated:
the market risk premium and the beta coefficient. To the extent that our estimates are poor,
the resulting cost of equity will be inaccurate. For example, our estimate of the market risk
premium, 7 percent, is based on about 100 years of returns on a particular portfolio of stocks.
Using different time periods or different stocks could result in very different estimates.
Finally, as with the dividend growth model, we essentially rely on the past to predict the
future when we use the SML approach. Economic conditions can change very quickly, so,
as always, the past may not be a good guide to the future. In the best of all worlds, both
approaches (dividend growth model and SML) are applicable and result in similar answers.
If this happens, we might have some confidence in our estimates. We also might wish to
compare the results to those for other, similar companies as a reality check.
EXAMPLE 12.1 The Cost of Equity
Suppose stock in Alpha Air Freight has a beta of 1.2. The market risk premium is 8 percent, and the
risk-free rate is 6 percent. Alpha’s last dividend was $2 per share, and the dividend is expected to
grow at 8 percent indefinitely. The stock currently sells for $30. What is Alpha’s cost of equity
capital?
We can start off by using the SML. Doing this, we find that the expected return on the common
stock of Alpha Air Freight is:
RE = Rf + βE × (RM − Rf)
= 6% + 1.2 × 8%
= 15.6%
This suggests that 15.6 percent is Alpha’s cost of equity. We next use the dividend growth model. The
projected dividend is D0 × (1 + g) = $2 × 1.08 = $2.16, so the expected return using this approach is:
RE! = D1/P0 + g
= $2.16/$30 + .08
= 15.2%
Our two estimates are reasonably close, so we might average them to find that Alpha’s cost of eq-
uity is approximately 15.4 percent.
THE COSTS OF DEBT AND PREFERRED STOCK
In addition to ordinary equity, firms use debt and, to a lesser extent, preferred stock to
finance their investments. As we discuss next, determining the costs of capital associated
with these sources of financing is much easier than determining the cost of equity.
12.3
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CONCEPT QUESTIONS
12.2a What do we mean when we say that a corporation’s cost of equity capital is 16
percent?
12.2b What are two approaches to estimating the cost of equity capital?
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396 P A R T 7 Long-Term Financing
The Cost of Debt
The cost of debt is the return that the firm’s creditors demand on new borrowing. In princi-
ple, we could determine the beta for the firm’s debt and then use the SML to estimate the
required return on debt just as we estimate the required return on equity. This isn’t really
necessary, however.
Unlike a firm’s cost of equity, its cost of debt normally can be observed either directly
or indirectly because the cost of debt is the interest rate the firm must pay on new borrow-
ing, and we can observe interest rates in the financial markets. For example, if the firm al-
ready has bonds outstanding, then the yield to maturity on those bonds is the market-required
rate on the firm’s debt.
Alternatively, if we knew that the firm’s bonds were rated, say, AA, then we could find
out what the interest rate was on newly issued AA-rated bonds. Either way, there is no need
to actually estimate a beta for the debt because we can directly observe the rate we want to
know.
There is one thing to be careful about, though. The coupon rate on the firm’s outstand-
ing debt is irrelevant here. That tells us roughly what the firm’s cost of debt was back when
the bonds were issued, not what the cost of debt is today.5 This is why we have to look at the
yield on the debt in today’s marketplace. For consistency with our other notation, we will
use the symbol RD for the cost of debt.
cost of debt
The return that lenders
require on the firm’s debt.
EXAMPLE 12.2 The Cost of Debt
Suppose the General Tool Company issued a 30-year, 7 percent bond eight years ago. The
bond is currently selling for 96 percent of its face value, or $960. What is General Tool’s cost
of debt?
Going back to Chapter 6, we need to calculate the yield to maturity on this bond. Because
the bond is selling at a discount, the yield is apparently greater than 7 percent, but not much
greater because the discount is fairly small. You can verify that the yield to maturity is about
7.37 percent, assuming semiannual coupons. General Tool’s cost of debt, RD, is thus
7.37 percent.
The Cost of Preferred Stock
Determining the cost of preferred stock is quite straightforward. As we discussed in Chapters
6 and 7, preferred stock has a fixed dividend paid every period forever, so a share of pre-
ferred stock is essentially a perpetuity. The cost of preferred stock, RP , is thus:
RP = D/P0 [12.3]
where D is the fixed dividend and P0 is the current price per share of the preferred stock.
Notice that the cost of preferred stock is equal to the dividend yield on the preferred stock.
Alternatively, preferred stocks are rated in much the same way as bonds, so the cost of pre-
ferred stock can be estimated by observing the required returns on other, similarly rated
shares of preferred stock.
5The firm’s cost of debt based on its historic borrowing is sometimes called the embedded debt cost.
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C H A P T E R 1 2 Cost of Capital 397
THE WEIGHTED AVERAGE COST OF CAPITAL
Now that we have the costs associated with the main sources of capital the firm employs, we
need to worry about the specific mix. As we mentioned above, we will take this mix, which
is the firm’s capital structure, as given for now. Also, we will focus mostly on debt and ordi-
nary equity in this discussion.
The Capital Structure Weights
We will use the symbol E (for equity) to stand for the market value of the firm’s equity. We
calculate this by taking the number of shares outstanding and multiplying it by the price per
share. Similarly, we will use the symbol D (for debt) to stand for the market value of the
firm’s debt. For long-term debt, we calculate this by multiplying the market price of a single
bond by the number of bonds outstanding.
If there are multiple bond issues (as there normally would be), we repeat this calcula-
tion for each and then add the results. If there is debt that is not publicly traded (because it
is held by a life insurance company, for example), we must observe the yield on similar,
publicly traded debt and then estimate the market value of the privately held debt using this
yield as the discount rate. For short-term debt, the book (accounting) values and market
values should be somewhat similar, so we might use the book values as estimates of the
market values.
Finally, we will use the symbol V (for value) to stand for the combined market value of
the debt and equity:
V = E + D [12.4]
If we divide both sides by V, we can calculate the percentages of the total capital repre-
sented by the debt and equity:
100% = E/V + D/V [12.5]
12.4
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EXAMPLE 12.3 Alabama Power’s Cost of Preferred Stock
In 2018, Alabama Power had an issue of preferred stock that traded on the NYSE. The stock paid
$1.25 annually per share and sold for $25.85 per share. What was Alabama Power’s cost of pre-
ferred stock?
Using Equation 12.3, the cost of preferred stock was:
RP = D/P0
= $1.25/$25.85
= .0484, or 4.84%
So, Alabama Power’s cost of preferred stock appears to have been just under 5 percent.
CONCEPT QUESTIONS
12.3a How can the cost of debt be calculated?
12.3b How can the cost of preferred stock be calculated?
12.3c Why is the coupon rate a bad estimate of a firm’s cost of debt?
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398 P A R T 7 Long-Term Financing
These percentages can be interpreted like portfolio weights, and they often are called
the capital structure weights.
For example, if the total market value of a company’s stock was calculated as $200
million and the total market value of the company’s debt was calculated as $50 million,
then the combined value would be $250 million. Of this total, E/V = $200/$250 = .80,
so 80 percent of the firm’s financing would be equity and the remaining 20 percent would
be debt.
We emphasize here that the correct way to proceed is to use the market values of the
debt and equity. Under certain circumstances, such as when considering a privately
owned company, it may not be possible to get reliable estimates of these quantities. In
this case, we might go ahead and use the accounting values for debt and equity. While
this would probably be better than nothing, we would have to take the answer with a
grain of salt.
Taxes and the Weighted Average Cost of Capital
There is one final issue we need to discuss. Recall that we are always concerned with after-
tax cash flows. If we are determining the discount rate appropriate to those cash flows, then
the discount rate also needs to be expressed on an aftertax basis.
As we discussed previously in various places in this book (and as we will discuss later),
the interest paid by a corporation is deductible for tax purposes. Payments to stockholders,
such as dividends, are not. What this means, effectively, is that the government pays some of
the interest. Thus, in determining an aftertax discount rate, we need to distinguish between
the pretax and the aftertax cost of debt.
To illustrate, suppose a firm borrows $1 million at 9 percent interest. The corporate tax
rate is 21 percent. What is the aftertax interest rate on this loan? The total interest bill will be
$90,000 per year. This amount is tax deductible, however, so the $90,000 interest reduces our
tax bill by .21 × $90,000 = $18,900. The aftertax interest bill is thus $90,000 − 18,900 =
$71,100. The aftertax interest rate is thus $71,100/$1 million = .0711, or 7.11%.
Notice that, in general, the aftertax interest rate is equal to the pretax rate multiplied by
1 minus the tax rate. Thus, if we use the symbol TC to stand for the corporate tax rate, then
the aftertax rate that we use for the cost of debt can be written as RD × (1 − TC). For exam-
ple, using the numbers above, we find that the aftertax interest rate is 9% × (1 − .21) =
7.11%.
Collecting the various topics we have discussed in this chapter, we now have the capital
structure weights along with the cost of equity and the aftertax cost of debt. To calculate the
firm’s overall cost of capital, we multiply the capital structure weights by the associated
costs and add the pieces. The result is the weighted average cost of capital, or WACC.
WACC = (E/V) × RE + (D/V) × RD × (1 − TC) [12.6]
This WACC has a very straightforward interpretation. It is the overall return the firm must
earn on its existing assets to maintain the value of its stock. This is an important point, so it
bears repeating:
The WACC is the overall return the firm must earn on its existing assets to maintain
the value of its stock.
The WACC is also the required return on any investments by the firm that have essen-
tially the same risks as existing operations. So, if we were evaluating the cash f lows
weighted average
cost of capital
(WACC)
The WACC is the overall
return the firm must earn
on its existing assets to
maintain the value of its
stock.
ros13952_ch12_389-423.indd 398 12/24/18 5:26 PM
from a proposed expansion of our existing operations, this is the discount rate we
would use.
If a firm uses preferred stock in its capital structure, then our expression for the WACC
needs a simple extension. If we define P/V as the percentage of the firm’s financing that
comes from preferred stock, then the WACC is:
WACC = (E/V) × RE + (P/V) × RP + (D/V) × RD × (1 − TC) [12.7]
where RP is the cost of preferred stock.
The WACC is increasingly being used by corporations to evaluate financial perfor-
mance. The accompanying Finance Matters box provides some details on how this is being
done.
EVA: An Old Idea Moves into the Modern Age
You might not think of Briggs and Stratton, Coca-Cola, and Microsoft as having much in common. However, all
three have linked their fortunes to a way of managing and
measuring corporate performance that depends critically on
the cost of capital. It goes by many names, but consulting
firm Stern Stewart & Co., a well-known advocate, calls its
particular flavor “economic value added,” or EVA. Stock-
holder value added (SVA) is a common variant. Whatever the
name, EVA and its cousins have become an important tool
for corporate management since the mid-1990s.
Briefly stated, EVA is a method of measuring financial
performance. To compute EVA, you must calculate your
overall cost of capital. Then, you identify how much capital is
tied up in your business. Next, you multiply the amount of
capital by the cost of capital. The result is the amount, in dol-
lars, you should be providing to your investors. Subtract out
your actual operating cash flow, and the difference is a
measure of EVA. A positive value means that you earned
more than your cost of capital, thereby creating value, and
vice versa (this is a quick overview; for more detail, visit
www.eva.com).
Each year, Stern Stewart & Co. prepares the Stern Stew-
art 1000, a ranking of the 1,000 largest U.S. companies
based on their respective EVAs. Over the history of the Stern
Stewart 1000, several companies have shown consistently
strong performances. For example, Microsoft, Intel, and Exx-
onMobil often appear near the top of the list. The list also
has perennial poor performers, and some of the names may
surprise you, for example, General Motors, Time Warner, and
Goodyear Tire & Rubber. Evidently, a well-known brand
name does not always result in shareholder wealth.
One thing the Stern Stewart 1000 has done is to show
the changing face of the economy. For instance, Intel, Cisco
Systems, and eBay all have ranked rather well on the list.
Consider that Intel is the oldest of these companies, having
been publicly traded since 1971, while eBay has been pub-
licly traded only since 1998. This highlights the dramatic im-
pact of technology companies on the economy. Of course,
not all technology-related companies have performed as
well.
According to Bennett Stewart, one of the cofounders
of Stern Stewart, EVA shows an important distinction be-
tween accounting income and economic profit. Account-
ing rules dictate that the interest expense a company
incurs must be deducted from its reported profit, but those
same rules forbid deducting a charge for the shareholders’
funds used by a firm. In economic terms, equity capital is in
fact a very costly financing source because shareholders
bear the risk of being paid last, after all other stakeholders
and investors are paid. But according to accountants,
shareholder equity is essentially free. This oversight has
dire practical consequences. For instance, it means that
the profit figure accountants certify to be correct can con-
flict with the net present value decision rule. This conflict
occurs when accounting rules lead to a focus on the ac-
countant’s bottom line rather than the more important
question of whether a project’s projected return exceeds
its required return.
While EVA and its variants are sound in principle, they
still have shortcomings. For one thing, they are typically
computed using asset book values instead of market values.
For another, they sometimes are based on accounting meas-
ures of income when cash flow would be a better choice.
Nonetheless, potential problems aside, the concept of EVA
focuses management attention on creating wealth for inves-
tors. That, in itself, makes EVA a worthwhile tool.
FINANCE MATTERS
399
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400 P A R T 7 Long-Term Financing
Solving the Warehouse Problem and Similar Capital
Budgeting Problems
Now we can use the WACC to solve the warehouse problem we posed at the beginning of
the chapter. However, before we rush to discount the cash flows at the WACC to estimate
NPV, we need to first make sure we are doing the right thing.
Going back to first principles, we need to find an alternative in the financial markets
that is comparable to the warehouse renovation. To be comparable, an alternative must be
of the same risk as the warehouse project. Projects that have the same risk are said to be in
the same risk class.
The WACC for a firm reflects the risk and the target capital structure of the firm’s ex-
isting assets as a whole. As a result, strictly speaking, the firm’s WACC is the appropriate
discount rate only if the proposed investment is a replica of the firm’s existing operating
activities.
In broader terms, whether or not we can use the firm’s WACC to value the ware-
house project depends on whether the warehouse project is in the same risk class as the
firm. We will assume that this project is an integral part of the overall business of the
firm. In such cases, it is natural to think that the cost savings will be as risky as the gen-
eral cash flows of the firm, and the project thus will be in the same risk class as the over-
all firm. More generally, projects like the warehouse renovation that are intimately related
to the firm’s existing operations often are viewed as being in the same risk class as the
overall firm.
We now can see what the president should do. Suppose the firm has a target debt-
equity ratio of 1/3. From Chapter 3, we know that a debt-equity ratio of D/E = 1/3 implies
that E/V is .75 and D/V is .25. Further suppose the cost of debt is 10 percent and the cost
of equity is 20 percent. Assuming a 21 percent tax rate, the WACC will then be:
WACC = (E/V) × RE + (D/V) × RD × (1 − TC)
= .75 × 20% + .25 × 10% × (1 − .21)
= 16.98%
EXAMPLE 12.4 Calculating the WACC
The B. B. Lean Co. has 1.4 million shares of stock outstanding. The stock currently sells for $20 per
share. The firm’s debt is publicly traded and was recently quoted at 93 percent of face value. It has
a total face value of $5 million, and it is currently priced to yield 11 percent. The risk-free rate is
8 percent, and the market risk premium is 7 percent. You’ve estimated that Lean has a beta of .74.
If the corporate tax rate is 21 percent, what is the WACC of Lean Co.?
We first can determine the cost of equity and the cost of debt. From the SML, the cost of equity
is 8% + .74 × 7% = 13.18%. The total value of the equity is 1.4 million × $20 = $28 million. The pre-
tax cost of debt is the current yield to maturity on the outstanding debt, 11 percent. The debt sells
for 93 percent of its face value, so its current market value is .93 × $5 million = $4.65 million. The
total market value of the equity and debt together is $28 + 4.65 = $32.65 million.
From here, we can calculate the WACC easily enough. The percentage of equity used by Lean
to finance its operations is $28/$32.65 = .8576, or 85.76%. Because the weights have to add up to
1.0, the percentage of debt is 1.0 − .8576 = .1424, or 14.24%. The WACC is thus:
WACC = (E/V) × RE + (D/V) × RD × (1 − TC!!)
= .8576 × 13.18% + .1424 × 11% × (1 − .21)
= 12.54%
B. B. Lean thus has an overall weighted average cost of capital of 12.54 percent.
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C H A P T E R 1 2 Cost of Capital 401
Recall that the warehouse project had a cost of $50 million and expected aftertax cash flows
(the cost savings) of $12 million per year for six years. The NPV is thus:
NPV = − $50 + 12 _________ (1 + WACC() 1 + ( · ( · ( · ( +
12 _________ (1 + WACC() 6
Because the cash flows are in the form of an ordinary annuity, we can calculate this NPV
using 16.98 percent (the WACC) as the discount rate as follows:
NPV = − $50 + 12 ×
1 − [1 /(1 + .1698)6]
_______________ .1698
= −$50 + 12 × 3.5915
= −$6.90 million
Should the firm take on the warehouse renovation? The project has a negative NPV
using the firm’s WACC. This means that the financial markets offer superior projects in the
same risk class (namely, the firm itself). The answer is clear: The project should be rejected.
For future reference, our discussion of the WACC is summarized in Table 12.1. Our upcom-
ing Finance Matters box discusses a different use of the WACC.
Calculating the WACC for Eastman Chemical
In this section, we illustrate how to calculate the WACC for Eastman Chemical, a well-
known chemical, plastics, and fiber producer. Our goal is to take you through, on a step-by-
step basis, the process of finding and using the information needed using online sources. As
you will see, there is a fair amount of detail involved, but the necessary information is, for
the most part, readily available.
You can find the WACC
for many companies at
www.thatswacc.com.
I. The cost of equity, RE
A. Dividend growth model approach (from Chapter 7):
R E = D 1 / P 0 + g
where D1 is the expected dividend in one period, g is the dividend growth rate, and P0 is
the current stock price.
B. SML approach (from Chapter 11):
R E = R f + β E × ( R M − R f 7)
where Rf is the risk-free rate, RM is the expected return on the overall market, and βE is
the systematic risk of the equity.
II. The cost of debt, RD
A. For a firm with publicly held debt, the cost of debt can be measured as the yield to
maturity on the outstanding debt. The coupon rate is irrelevant. Yield to maturity is
covered in Chapter 6.
B. If the firm has no publicly traded debt, then the cost of debt can be measured as the yield
to maturity on similarly rated bonds (bond ratings are discussed in Chapter 6).
III. The weighted average cost of capital, WACC
A. The firm’s WACC is the overall required return on the firm as a whole. It is the appropriate
discount rate to use for cash flows similar in risk to the overall firm.
B. The WACC is calculated as:
WACC = (E / V!) × R E + (D / V7) × R D × (1 − T C 7)
where TC is the corporate tax rate, E is the market value of the firm’s equity, D is the
market value of the firm’s debt, and V = E + D. Note that E/V is the percentage of the
firm’s financing (in market value terms) that is equity and D/V is the percentage that is
debt.
Summary of capital
cost calculations
TABLE 12.1
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The Cost of Capital, Texas Style
We have seen how the WACC is used in the corporate world. It also is used by state governments to value
property for tax purposes. Property valuation can be
tricky. The value of a home depends on what it could be
sold for, which is not too hard to estimate, but how do you
value an oil or gas field? For the Texas Comptroller of
Public Accounts, the answer is to estimate the present
As you can see, the 2017 WACC numbers for the com-
panies are similar. Range has the lowest WACC at 12.05 per-
cent and Energen has the highest at 17.91 percent, but most
other companies are in the 14 to 16 percent range. The aver-
age WACC for a company in this industry is 14.64 percent,
with a standard deviation of 1.66 percent. When Texas uses
this calculation, a 2 percent adjustment factor is added, plus
any property-specific risk adjustment.
value of the future cash flows of the property. As you
know by now, the cost of capital depends on the use of
funds, not the source of funds. So, Texas calculates the
WACC for companies in the oil industry and adjusts the
industry average WACC for company-specific factors. The
table below shows the state’s calculations for integrated
oil companies.
Notice that the Texas Comptroller of Public Accounts
calculated these numbers on a pretax, rather than aftertax,
basis. In other words, the state did not account for the tax
deductibility of interest payments in this calculation. The rea-
son is that the state adjusts the cost of capital for taxes on a
company-by-company basis.
FINANCE MATTERS
402
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C H A P T E R 1 2 Cost of Capital 403
Eastman’s Cost of Equity Our first stop is the stock price for Eastman, avail-
able at finance.yahoo.com (ticker: “EMN”). As of mid-2018, here’s what the screen
looked like:
Source: finance.yahoo.com
We next looked under the “Statistics” link. Here is what we found:
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404 P A R T 7 Long-Term Financing
According to this screen, Eastman has 142.76 million shares of stock outstanding. The
book value per share is $38.88, but the stock sells for $98.53. Total equity is therefore about
$5.551 billion on a book value basis, but it is closer to $14.066 billion on a market value basis.
To estimate Eastman’s cost of equity, we will assume a market risk premium of 7 per-
cent, similar to what we saw in Chapter 10. Eastman’s beta on Yahoo! is .98, which is
about the same as the beta of the average stock. To confirm this, we look at the beta re-
ported in Value Line. The beta there was 1.20, while the beta reported at www.reuters.com
was 1.37. Because we have three different betas for the stock, we decided to go with the
Value Line beta of 1.20, which is about the average. According to the bond section of
finance.yahoo.com, T-bills were paying about 1.98 percent. Using the CAPM to estimate the
cost of equity, we find:
RE = .0198 + 1.20(.07) = .1038, or 10.38%
Eastman only has paid dividends for a few years, so calculating the future growth rate for the
dividend discount model is problematic. However, under the “Analysis” link at finance
.yahoo.com, we found the following:
Analysts estimate the growth in earnings per share for the company will be 10.47 percent
for the next five years. The link between earnings growth and dividends is discussed in a
later chapter, but this would be a very high long-run growth rate for dividends. The divi-
dend growth rate estimate reported by Value Line was a more plausible 6.5 percent, so
we will use that instead. The estimated cost of equity using the dividend discount model
is thus:
R E = ( ( $2(.(24 _ $98(.(53 ) + .065 = (.0877, or 8.77%
Notice that the estimates for the cost of equity are similar in this case. In broader terms,
remember that each method of estimating the cost of equity relies on different assumptions,
so different estimates should not surprise us. If the estimates are different, there are two
simple solutions. First, we could ignore one of the estimates. We would look at each esti-
mate to see if one of them seemed too high or too low to be reasonable. Second, we could
average the two estimates. Averaging the two estimates for Eastman’s cost of equity gives us
a cost of equity of 9.58 percent. Because this seems like a reasonable number, we will use it
in calculating the cost of capital.
Eastman’s Cost of Debt Eastman has 11 long-term bond issues that account for
essentially all of its long-term debt. To calculate the cost of debt, we will have to combine
these 11 issues. What we will do is compute a weighted average. We went to finra-markets
.morningstar.com/BondCenter/ to find quotes on the bonds. We should note here that
finding the yield to maturity for all of a company’s outstanding bond issues on a single
day is unusual. If you remember our previous discussion on bonds, the bond market is not
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C H A P T E R 1 2 Cost of Capital 405
as liquid as the stock market, and, on many days, individual bond issues may not trade. To
find the book value of the bonds, we went to www.sec.gov and found the 10-Q report
dated March 31, 2018, and filed with the SEC on May 7, 2018. The basic information is
as follows:
Coupon
Rate Maturity
Book Value
(face value, in
$ millions)
Price
(% of par)
Yield to
Maturity
5.50% 2019 $250 103.354% 2.974%
2.70 2020 798 7799.373 3.124
4.50 2021 192 102.220 3.487
3.60 2022 753 7799.691 3.681
1.25 2023 920 77 88.846 3.715
7.25 2024 197 117.005 3.850
7.625 2024 43 116.540 4.447
3.80 2025 689 77 98.998 3.971
7.60 2027 195 124.517 4.200
4.80 2042 493 77 99.498 4.835
4.65 2044 871 7798.030 4.782
$5,401
To calculate the weighted average cost of debt, we take the percentage of the total debt
represented by each issue and multiply by the yield on the issue. We then add to get the
overall weighted average debt cost. We use both book values and market values here for
comparison. The results of the calculations are as follows:
Coupon
Rate
Book Value
(in millions)
Percentage
of Total
Market Value
(in millions)
Percentage
of Total
Yield to
Maturity Book Values
Market
Values
5.50% $250 .05 777$258.39 .05 2.97% .14% .14%
2.70 798 .15 793.00 .15 3.12 .46 .46
4.50 192 .04 192.26 .04 3.49 .12 .13
3.60 753 .14 750.67 .14 3.68 .51 .51
1.25 920 .17 817.38 .15 3.72 .63 .57
7.25 197 .04 230.50 .04 3.85 .14 .17
7.625 43 .01 77 50.11 .01 4.45 .04 .04
3.80 689 .13 682.10 .13 3.97 .51 .50
7.60 195 .04 242.81 .05 4.20 .15 .19
4.80 493 .09 490.53 .09 4.84 .44 .44
4.65 871 .16 853.84 .16 4.78 .77 .76
$5,401 1.00 $5,365.58 1.00 3.92% 7773.92%
As these calculations show, Eastman’s cost of debt is 3.92 percent on a book value ba-
sis and 3.92 percent on a market value basis. Thus, for Eastman, whether market values or
book values are used makes no difference. The reason is that the market values and book
values are similar. This often will be the case and explains why companies frequently use
book values for debt in WACC calculations. Also, Eastman has no preferred stock, so we
don’t need to consider the cost of preferred.
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406 P A R T 7 Long-Term Financing
So how does our estimate of the WACC for Eastman compare to others? One place to find esti-mates for WACC is www.valuepro.net. We went there and found the following information for
Eastman.
W R K T H E W E B
As you can see, ValuePro estimates the WACC for Eastman as 7.88 percent, which is almost
identical to our estimate of 7.79 percent. The methods used by this site are not identical to ours,
but they are similar in the most important regards. However, notice that several important esti-
mates differ. For example, ValuePro uses a market risk premium of 3 percent, while our estimate
was 7 percent. Using our estimate of the market risk premium in the ValuePro website results in a
WACC estimate of 11.93 percent, which is higher than our estimate. Visit the site to learn more if
you are so inclined.
Source: valuepro.net
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C H A P T E R 1 2 Cost of Capital 407
Eastman’s WACC We now have the various pieces necessary to estimate Eastman’s
WACC. First, we need to calculate the capital structure weights. On a book value basis,
Eastman’s equity and debt are worth $5.551 billion and $5.401 billion, respectively. The to-
tal value is $10.952 billion, so the equity and debt percentages are $5.551 billion/$10.952
billion = .51 and $5.401 billion/$10.952 billion = .49, respectively. Assuming a tax rate of
21 percent, Eastman’s WACC is:
WACC = .51 × 9.58% + .49 × 3.92% × (1 − .21)
= 6.38%
Thus, using book value capital structure weights, we get about 6.38 percent for Eastman’s
WACC.
If we use market value weights, however, the WACC will be higher. To see why, notice
that on a market value basis, Eastman’s equity and debt are worth $14.066 billion and
$5.366 billion, respectively. The capital structure weights are therefore $14.066
billion/$19.432 billion = .72 for equity and $5.366 billion/$19.432 billion = .28 for debt, so
the equity percentage is much higher. With these weights, Eastman’s WACC is:
WACC = .72 × 9.58% + .28 × 3.92% × (1 − .21)
= 7.79%
Thus, using market value weights, we get 7.79 percent for Eastman’s WACC, which is notice-
ably higher than the 6.38 percent WACC we got using book value weights.
As this example illustrates, using book values can lead to trouble, particularly if equity
book values are used. Going back to Chapter 3, recall that we discussed the market-to-book
ratio (the ratio of market value per share to book value per share). This ratio is often sub-
stantially bigger than 1. For Eastman, for example, verify that it’s about 2.53, so book values
significantly overstate the percentage of Eastman’s financing that comes from debt. In addi-
tion, if we were computing a WACC for a company that did not have publicly traded stock,
we would try to come up with a suitable market-to-book ratio by looking at publicly traded
companies, and we would then use this ratio to adjust the book value of the company under
consideration. As we have seen, failure to do so can lead to significant underestimation of
the WACC. See our nearby Work the Web box for more on the WACC.
CONCEPT QUESTIONS
12.4a How is the WACC calculated?
12.4b Why do we multiply the cost of debt by (1 − TC) when we compute the WACC?
12.4c Under what conditions is it correct to use the WACC to determine NPV?
DIVISIONAL AND PROJECT
COSTS OF CAPITAL
As we have seen, using the WACC as the discount rate for future cash flows is only appro-
priate when the proposed investment is similar to the firm’s existing activities. This is not as
restrictive as it sounds. If we were in the pizza business, for example, and we were thinking
of opening a new location, then the WACC would be the discount rate to use. The same
would be true of a retailer thinking of a new store, a manufacturer thinking of expanding
production, or a consumer products company thinking of expanding its markets.
12.5
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408 P A R T 7 Long-Term Financing
Nonetheless, despite the usefulness of the WACC as a benchmark, there will clearly be
situations where the cash flows under consideration have risks distinctly different from
those of the overall firm. We consider how to cope with this problem next.
The SML and the WACC
When we are evaluating investments with risks that are substantially different from those of
the overall firm, the use of the WACC will potentially lead to poor decisions. Figure 12.1
illustrates why.
In Figure 12.1, we have plotted an SML corresponding to a risk-free rate of 7 percent
and a market risk premium of 8 percent. To keep things simple, we consider an all-equity
company with a beta of 1. As we have indicated, the WACC and the cost of equity are
exactly equal to 15 percent for this company because there is no debt.
Suppose our firm uses its WACC to evaluate all investments. This means that any in-
vestment with a return of greater than 15 percent will be accepted and any investment with
a return of less than 15 percent will be rejected. We know from our study of risk and return,
however, that a desirable investment is one that plots above the SML. As Figure 12.1 illus-
trates, using the WACC for all types of projects can result in the firm’s incorrectly accepting
relatively risky projects and incorrectly rejecting relatively safe ones.
For example, consider Point A. This project has a beta of βA = .60 compared to the
firm’s beta of 1.0. It has an expected return of 14 percent. Is this a desirable investment? The
answer is yes because its required return is only:
Required return = Rf + βA × (RM − Rf)
= 7% + .60 × 8%
= 11.8%
Expected
return
16%
15%
14%
Rf = 7%
Incorrect
rejection
A
B
Incorrect
acceptance
WACC = 15%
= 8%
SML
βA = .60 βfirm = 1.0 βB = 1.2
Beta
If a firm uses its WACC to make accept-reject decisions for all types of projects, it will
have a tendency toward incorrectly accepting risky projects and incorrectly rejecting
less risky projects.
FIGURE 12.1
The security market
line, SML, and the
weighted average
cost of capital, WACC
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C H A P T E R 1 2 Cost of Capital 409
However, if we use the WACC as a cutoff, then this project will be rejected because its
return is less than 15 percent. This example illustrates that a firm that uses its WACC as a
cutoff will tend to reject profitable projects with risks less than those of the overall firm.
At the other extreme, consider Point B. This project has a beta of βB = 1.2. It offers a
16 percent return, which exceeds the firm’s cost of capital. This is not a good investment,
however, because, given its level of systematic risk, its return is inadequate. Nonetheless, if
we use the WACC to evaluate it, it will appear to be attractive. So the second error that will
arise if we use the WACC as a cutoff is that we will tend to make unprofitable investments
with risks greater than those of the overall firm. As a consequence, through time, a firm that
uses its WACC to evaluate all projects will have a tendency to both accept unprofitable
investments and become increasingly risky.
Divisional Cost of Capital
The same type of problem with the WACC can arise in a corporation with more than one
line of business. Suppose a corporation has two divisions, a regulated electric company and
an electronics manufacturing operation. The first of these (the electric operation) has rela-
tively low risk; the second has relatively high risk.
In this case, the firm’s overall cost of capital is really a mixture of two different costs of
capital, one for each division. If the two divisions were competing for resources, and the
firm used a single WACC as a cutoff, which division would tend to be awarded greater funds
for investment?
The answer is that the riskier division would tend to have greater returns (ignoring the
greater risk), so it would tend to be the “winner.” The less glamorous operation might have
great profit potential that would end up being ignored. Large corporations in the United
States are aware of this problem, and many work to develop separate divisional costs of
capital.
The Pure Play Approach
We’ve seen that using the firm’s WACC inappropriately can lead to problems. How can we
come up with the appropriate discount rates in such circumstances? Because we cannot
observe the returns on these investments, there generally is no direct way of coming up with
a beta, for example. Instead, what we must do is examine other investments outside the firm
that are in the same risk class as the one we are considering and use the market-required
returns on these investments as the discount rate. In other words, we will try to determine
what the cost of capital is for such investments by trying to locate some similar investments
in the marketplace.
For example, going back to our electric division, suppose we want to come up with a
discount rate to use for that division. What we can do is identify several other electric com-
panies that have publicly traded securities. We might find that a typical electric company
has a beta of .80, AA-rated debt, and a capital structure that is about 80 percent debt and 20
percent equity. Using this information, we could develop a WACC for a typical electric com-
pany and use this as our discount rate.
Alternatively, if we were thinking of entering a new line of business, we would try to
develop the appropriate cost of capital by looking at the market-required returns on compa-
nies already in that business. In the language of Wall Street, a company that focuses only on
a single line of business is called a pure play. For example, if you wanted to bet on the price
of crude oil by purchasing common stocks, you would try to identify companies that dealt
exclusively with this product because they would be the most affected by changes in the
price of crude oil. Such companies would be called pure plays on the price of crude oil.
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410 P A R T 7 Long-Term Financing
What we try to do here is to find companies that focus as exclusively as possible on
the type of project in which we are interested. Our approach, therefore, is called the
pure play approach to estimating the required return on an investment. To illustrate,
suppose McDonald’s decides to enter the hotel business with a line of hotels called Mc-
Rooms. The risks involved are quite different from those in the fast-food business. As a
result, McDonald’s would need to look at companies already in the hotel business to
compute a cost of capital for the new division. An obvious “pure play” candidate would
be La Quinta, which is predominately in this line of business. Marriott may not be as
good a choice as it operates high-end motels and resorts, residential properties, and
timeshares.
In Chapter 3, we discussed the subject of identifying similar companies for comparison
purposes. The same problems we described there come up here. The most obvious one is
that we may not be able to find any suitable companies. In this case, how to objectively de-
termine a discount rate becomes a very difficult question. Even so, the important thing is to
be aware of the issue so that we at least reduce the possibility of the kinds of mistakes that
can arise when the WACC is used as a cutoff on all investments.
The Subjective Approach
Because of the difficulties that exist in objectively establishing discount rates for individual
projects, firms often adopt an approach that involves making subjective adjustments to the
overall WACC. To illustrate, suppose a firm has an overall WACC of 14 percent. It places all
proposed projects into four categories as follows:
Category Examples Adjustment Factor Discount Rate
High risk New products + 6% 20%
Moderate risk Cost savings, expansion of
existing lines
+ 0 14
Low risk Replacement of existing
equipment
−4 10
Mandatory Pollution control equipment n/a n/a
n/a = Not applicable.
The effect of this crude partitioning is to assume that all projects either fall into one of
three risk classes or else are mandatory. In this last case, the cost of capital is irrelevant be-
cause the project must be taken. Of course, the firm’s WACC may change through time as
economic conditions change. As this happens, the discount rates for the different types of
projects also will change.
Within each risk class, some projects will presumably have more risk than others, and
the danger of incorrect decisions still will exist. Figure 12.2 illustrates this point. Comparing
Figures 12.1 and 12.2, we see that similar problems exist, but the magnitude of the potential
error is less with the subjective approach. For example, the project labeled “A” would be
accepted if the WACC were used, but it is rejected once it is classified as a high-risk invest-
ment. What this illustrates is that some risk adjustment, even if it is subjective, is probably
better than no risk adjustment.
It would be better, in principle, to objectively determine the required return for each
project separately. However, as a practical matter, it may not be possible to go much beyond
subjective adjustments because either the necessary information is unavailable or else the
cost and effort required are not worthwhile.
pure play approach
Use of a weighted
average cost of capital
that is unique to a
particular project, based
on companies in similar
lines of business.
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C H A P T E R 1 2 Cost of Capital 411
COMPANY VALUATION WITH THE WACC
When valuing a company, our approach is the same as the one we used for individual
capital projects like the warehouse renovation, but there is one issue we have to deal
with. When we look at an entire company, we often will see an interest deduction
because the company has borrowed money. But as we have consistently emphasized,
interest paid is a financing cost, not an operating cost. However, because interest paid is
a tax-deductible expense, a company’s tax bill is lower than it would have been had the
company not used debt financing. We will have much more to say about this in a later
chapter.
For now, to calculate cash flow from assets, we need to first calculate what the firm’s
tax bill would have been if it had not used debt financing. To do that, we take earnings
before interest and taxes (EBIT) and multiply it by the firm’s tax rate (TC) to get the firm’s
“would-have-been” tax bill, which we will call the “adjusted” taxes and label Taxes*:
Taxes* = EBIT × TC [12.8]
12.6
CONCEPT QUESTIONS
12.5a What are the likely consequences if a firm uses its WACC to evaluate all proposed
investments?
12.5b What is the pure play approach to determining the appropriate discount rate? When
might it be used?
The security market
line, SML, and the
subjective approach
FIGURE 12.2Expected
return
Beta
20%
WACC = 14%
10%
Rf = 7%
Low risk
(−4%)
Moderate risk
(+ 0%)
= 8%
A
With the subjective approach, the firm places projects into one of several risk classes.
The discount rate used to value the project is then determined by adding (for high risk) or
subtracting (for low risk) an adjustment factor to or from the firm’s WACC. This results in
fewer incorrect decisions than if the firm used the WACC to make the decisions.
High risk
(+ 6%)
SML
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412 P A R T 7 Long-Term Financing
Next, we will calculate cash flow from assets the usual way, except we will use the
adjusted taxes. We will call this the “adjusted” cash flow from assets, CFA*, which we calcu-
late as:
CFA* = EBIT + Depreciation − Taxes* − Change in NWC − Capital spending [12.9]
= EBIT + Depreciation − EBIT × TC − Change in NWC − Capital spending
Our adjusted cash flow, CFA*, is often called “free cash flow,” but as we mentioned much
earlier in our book, that phrase means different things to different people, so we will stick
with CFA* to avoid confusion.
Notice that we could simplify our CFA* calculation a bit by writing it as:
CFA* = EBIT × (1 − TC ) + Depreciation − Change in NWC − Capital spending [12.10]
The term EBIT × (1 − TC) is what net income would have been if the firm had used no
debt, and the sum of the first two terms is our bottom-up definition of operating cash flow
from Chapter 9.
At this point, if the firm is growing steadily, we can value it using our growing perpetu-
ity formula (as we did earlier in this chapter to value shares of stock when dividends grow
steadily). For example, suppose you project CFA* for the coming year as CFA*1 = $120
million. You think this amount will grow indefinitely at g = 5 percent per year. You’ve esti-
mated the firm’s WACC to be 9 percent, so the value of the firm today (V0) is:
Firm value today = V0 =
CFA1 _________ WACC − g =
$120 ________ .09 − .05 = $3 billion
In sum, valuing a firm is no different from valuing a project, except for the fact that we have
to adjust the taxes to remove the effect of any debt financing.
We also can consider the impact of nonconstant growth (as we did in an earlier chap-
ter on stock valuation using the dividend growth model). In this case, we assume that con-
stant growth begins at Time t in the future. In that case, we can write the value of the firm
today as:
V0 =
CFA1 _________ 1 + WACC +
CFA2 ___________ (1 + WACC)2 +
CFA3 ___________ (1 + WACC)3 + % +
CFAt + Vt _________ 1 + WACC [12.11]
Here, Vt is value of the firm at Time t, which we again calculate using the growing per-
petuity formula:
Vt =
CFAt!+ 1 _________ WACC − g [12.12]
As always, notice that the tricky part is that to get the value at Time t, we have to use the
cash flow that occurs at the end of that period at Time t + 1. Also, the value of the firm in
the future, Vt, often is referred to as the “terminal value.”
*
* * * *
*
EXAMPLE 12.5 Valuing Feline Fancy
A guest on the popular show Great White Tank is attempting to raise money for her new company,
Feline Fancy, which makes cat toys. The potential investor wants to value the company, which is
privately held. Because of this, he uses the pure play approach to determine that the appropriate
WACC for the company is 8 percent. The relevant tax rate is 21 percent.
Feline Fancy currently has $40 million in debt and 3.5 million shares outstanding. Sales this
coming year are expected to be $30 million, and that amount is expected to grow at 15 percent per
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C H A P T E R 1 2 Cost of Capital 413
year for the following four years. After that, sales are expected to grow at 2 percent indefinitely.
EBIT this coming year will be $10 million. EBIT, depreciation, capital spending, and the change in net
working capital will grow at the same rate as sales. What value would you assign to Feline Fancy as
a whole? What price per share would you assign?
To value the company, we begin by estimating the adjusted cash flow from assets (CFA*) for
the next five years. The Year 1 values are the projections in millions for next year:
Year 1 Year 2 Year 3 Year 4 Year 5
EBIT $10.00 $11.50 $13.23 $15.21 $17.49
Depreciation 1.50 1.73 1.98 2.28 2.62
Taxes* 2.10 2.42 2.78 3.19 3.67
Change in NWC .80 .92 1.06 1.22 1.40
Capital spending 2.40 2.76 3.17 3.65 4.20
CFA* $6.20 $7.13 $8.20 $9.43 $10.84
Because the CFA* will grow at 2 percent after Year 5, the terminal value of the company in Year
5 will be:
V 5 =
$10#.#84 ( 1 + .02 ) ___________ .08 − .02 = $184#.#35 million
We now can find the value of the company today by discounting the first five CFA* values and the
terminal value back to the present using the WACC. Doing so, we find:
V 0 =
$6#.#20 _____ 1#.#08 +
$7#.#13 _____ 1# .08 2 +
$8#.#20 _____ 1# .08 3 +
$9#.#43 _____ 1# .08 4 +
$10#.#84 + 184#.#35 ____________ 1# .08 5 = $158#.#14 million
To find the value of equity, we subtract the $40 million in debt, resulting in a total equity value of
$118.14 million. To find the share price, we divide this by the number of shares (3.5 million), which
gives us a share price of:
Price per share = $118.14/3.5 = $33.75
Another common way to calculate the terminal value is to use a target ratio, similar to the way
we used the PE and price-sales ratios in Chapter 7. For example, suppose the potential investor
believes the appropriate price-sales ratio when the company’s growth rate slows is 3 times. Sales
in Year 5 are projected at $30 million × 1.154 = $52.47 million (notice that we compounded the $30
million forward four years because $30 million is sales by the end of Year 1, not sales from last year).
So, the new estimated terminal value is:
V5 = 3 × $52.47 million = $157.41 million
So, with this new terminal value, the value of the company today will be:
V 0 =
$6#.#20 _____ 1.08 +
$7#.#13 _____ 1.08 2 +
$8#.#20 _____ 1.08 3 +
$9#.#43 _____ 1.08 4 +
$10#.#84 + 157.41 ___________ 1.08 5 = $139#.#80 million
See for yourself if you don’t agree that using this terminal value will result in an estimated per share
value of $28.52.
CONCEPT QUESTIONS
12.6a Why do we adjust a firm’s taxes when we do a firm valuation?
12.6b Why do you think we might prefer to use a ratio when calculating the terminal value
when we value a firm?
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414 P A R T 7 Long-Term Financing
SUMMARY AND CONCLUSIONS
This chapter has discussed cost of capital. The most important concept is the weighted av-
erage cost of capital, or WACC, which we interpreted as the required rate of return on the
overall firm. It is also the discount rate appropriate for cash flows that are similar in risk to
the overall firm. We described how the WACC can be calculated, and we illustrated how it
can be used in certain types of analysis.
We also pointed out situations in which it is inappropriate to use the WACC as the
discount rate. To handle such cases, we described some alternative approaches to develop-
ing discount rates, such as the pure play approach.
POP QUIZ!
Can you answer the following questions? If your class is using Connect, log on to
SmartBook to see if you know the answers to these and other questions, check out
the study tools, and find out what topics require additional practice!
Section 12.1 What are the components used to construct the WACC?
Section 12.2 What is the required return on a stock, according to the constant divi-
dend growth model, if the growth rate is zero?
Section 12.3 What is the equation for finding the cost of preferred stock?
Section 12.4 A company has a borrowing rate of 15 percent and a tax rate of 21
percent. What is its aftertax cost of debt?
Section 12.5 True or False: Projects should always be discounted at the firm’s over-
all cost of capital.
CHAPTER REVIEW AND SELF-TEST PROBLEMS
12.1 Calculating the Cost of Equity Suppose stock in Boone Corporation has a beta of
.90. The market risk premium is 7 percent, and the risk-free rate is 8 percent.
Boone’s last dividend was $1.80 per share, and the dividend is expected to grow at
7 percent indefinitely. The stock currently sells for $25. What is Boone’s cost of
equity capital? (See Problem 1.)
12.2 Calculating the WACC In addition to the information in the previous problem,
suppose Boone has a target debt-equity ratio of 50 percent. Its cost of debt is 8 percent,
before taxes. If the tax rate is 21 percent, what is the WACC? (See Problem 9.)
■ Answers to Chapter Review and Self-Test Problems
12.1 We start off with the SML approach. Based on the information given, the expected
return on Boone’s common stock is:
RE = Rf + βE × (RM − Rf)
= 8% + .9 × 7%
= 14.3%
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C H A P T E R 1 2 Cost of Capital 415
We now use the dividend growth model. The projected dividend is D0 × (1 + g) =
$1.80 × 1.07 = $1.926, so the expected return using this approach is:
RE = D1/P0 + g
= $1.926/$25 + .07
= .14704, or 14.704%
Because these two estimates, 14.3 percent and 14.7 percent, are fairly close, we will
average them. Boone’s cost of equity is approximately 14.5 percent.
12.2 Because the target debt-equity ratio is .50, Boone uses $.50 in debt for every $1.00 in
equity. In other words, Boone’s target capital structure is ⅓ debt and ⅔ equity. The
WACC is thus:
WACC = (E/V) × RE + (D/V) × RD × (1 − TC)
= 2⁄3 × 14.5% +
1⁄3 × 8% × (1 − .21)
= 11.775%
CRITICAL THINKING AND CONCEPTS REVIEW
LO 3 12.1 WACC On the most basic level, if a firm’s WACC is 12 percent, what does
this mean?
LO 3 12.2 Book Values versus Market Values In calculating the WACC, if you had
to use book values for either debt or equity, which would you choose? Why?
LO 4 12.3 Project Risk If you can borrow all the money you need for a project at 6
percent, doesn’t it follow that 6 percent is your cost of capital for the project?
LO 4 12.4 WACC and Taxes Why do we use an aftertax figure for cost of debt but
not for cost of equity?
LO 1 12.5 DGM Cost of Equity Estimation What are the advantages of using the
dividend growth model (DGM) for determining the cost of equity capital?
What are the disadvantages? What specific piece of information do you
need to find the cost of equity using this model? What are some of the ways
in which you could get an estimate of this number?
LO 1 12.6 SML Cost of Equity Estimation What are the advantages of using the SML
approach to finding the cost of equity capital? What are the disadvantages?
What are the specific pieces of information needed to use this method? Are
all of these variables observable, or do they need to be estimated? What are
some of the ways in which you could get these estimates?
LO 2 12.7 Cost of Debt Estimation How do you determine the appropriate cost of
debt for a company? Does it make a difference if the company’s debt is
privately placed as opposed to being publicly traded? How would you
estimate the cost of debt for a firm whose only debt issues are privately
held by institutional investors?
LO 4 12.8 Cost of Capital Suppose Tom O’Bedlam, president of Bedlam Products, Inc.,
has hired you to determine the firm’s cost of debt and cost of equity capital.
a. The stock currently sells for $50 per share, and the dividend per share
will probably be about $5. Tom argues, “It will cost us $5 per share to
use the stockholders’ money this year, so the cost of equity is equal to
10 percent (= $5/$50).” What’s wrong with this conclusion?
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416 P A R T 7 Long-Term Financing
b. Based on the most recent financial statements, Bedlam Products’ total
liabilities are $8 million. Total interest expense for the coming year will
be about $1 million. Tom therefore reasons, “We owe $8 million, and
we will pay $1 million interest. Therefore, our cost of debt is obviously
$1 million/$8 million = .125, or 12.5%.” What’s wrong with this
conclusion?
c. Based on his own analysis, Tom is recommending that the company
increase its use of equity financing, because “Debt costs 12.5 percent,
but equity only costs 10 percent; thus equity is cheaper.” Ignoring all
the other issues, what do you think about the conclusion that the cost
of equity is less than the cost of debt?
LO 4 12.9 Company Risk versus Project Risk Both Dow Chemical Company, a large
natural gas user, and Superior Oil, a major natural gas producer, are
thinking of investing in natural gas wells near Houston. Both are all-equity–
financed companies. Dow and Superior are looking at identical projects.
They’ve analyzed their respective investments, which would involve a
negative cash flow now and positive expected cash flows in the future.
These cash flows would be the same for both firms. No debt would be used
to finance the projects. Each company estimates that its project would have
a net present value of $1 million at an 18 percent discount rate and a −$1.1
million NPV at a 22 percent discount rate. Dow has a beta of 1.25, whereas
Superior has a beta of .75. The expected risk premium on the market is 8
percent, and risk-free bonds are yielding 12 percent. Should either company
proceed? Should both? Explain.
LO 4 12.10 Divisional Cost of Capital Under what circumstances would it be
appropriate for a firm to use different costs of capital for its different
operating divisions? If the overall firm WACC was used as the hurdle
rate for all divisions, would the riskier divisions or the more
conservative divisions tend to get most of the investment projects? Why?
If you were to try to estimate the appropriate cost of capital for different
divisions, what problems might you encounter? What are two techniques
you could use to develop a rough estimate for each division’s cost of
capital?
QUESTIONS AND PROBLEMS
Select problems are available in McGraw-Hill Connect. Please see the pack-
aging options section of the Preface for more information.
BASIC (Questions 1–19)
1. Calculating Cost of Equity The Pierce Co. just issued a dividend of $2.35
per share on its common stock. The company is expected to maintain a
constant 5 percent growth rate in its dividends indefinitely. If the stock sells
for $44 a share, what is the company’s cost of equity?
2. Calculating Cost of Equity Hoolahan Corporation’s common stock has a
beta of .87. If the risk-free rate is 3.6 percent and the expected return on the
market is 11 percent, what is the company’s cost of equity capital?
LO 1
LO 1
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C H A P T E R 1 2 Cost of Capital 417
3. Estimating the DCF Growth Rate Suppose Potter Ltd. just issued a
dividend of $1.82 per share on its common stock. The company paid
dividends of $1.36, $1.46, $1.53, and $1.68 per share in the last four years,
respectively. If the stock currently sells for $55, what is your best estimate of
the company’s cost of equity capital using arithmetic and geometric growth
rates?
4. Calculating Cost of Preferred Stock Sixth Fourth Bank has an issue of
preferred stock with a $3.80 stated dividend that just sold for $89 per share.
What is the bank’s cost of preferred stock?
5. Calculating Cost of Debt ICU Window, Inc., is trying to determine its cost
of debt. The firm has a debt issue outstanding with seven years to maturity
that is quoted at 103 percent of face value. The issue makes semiannual
payments and has an embedded cost of 5.1 percent annually. What is the
company’s pretax cost of debt? If the tax rate is 21 percent, what is the
aftertax cost of debt?
6. Calculating Cost of Debt Jiminy’s Cricket Farm issued a 30-year, 6.3
percent semiannual bond eight years ago. The bond currently sells for 110
percent of its face value. The company’s tax rate is 22 percent.
a. What is the pretax cost of debt?
b. What is the aftertax cost of debt?
c. Which is more relevant, the pretax or the aftertax cost of debt? Why?
7. Calculating Cost of Debt For the firm in Problem 6, suppose the book
value of the debt issue is $135 million. In addition, the company has a
second debt issue, a zero coupon bond with 12 years left to maturity; the
book value of this issue is $65 million, and it sells for 64.3 percent of par.
What is the total book value of debt? The total market value? What is the
aftertax cost of debt now?
8. Calculating WACC Baron Corporation has a target capital structure of 75
percent common stock, 5 percent preferred stock, and 20 percent debt. Its
cost of equity is 11.3 percent, the cost of preferred stock is 4.9 percent, and
the pretax cost of debt is 5.8 percent. The relevant tax rate is 23 percent.
a. What is the company’s WACC?
b. The company president has approached you about the company’s capital
structure. He wants to know why the company doesn’t use more
preferred stock financing because it costs less than debt. What would
you tell the president?
9. Taxes and WACC Caddie Manufacturing has a target debt-equity ratio
of .45. Its cost of equity is 10.3 percent, and its pretax cost of debt is 6.4
percent. If the tax rate is 21 percent, what is the company’s WACC?
10. Finding the Target Capital Structure Fama’s Llamas has a WACC of 8.95
percent. The company’s cost of equity is 10.4 percent, and its pretax cost of
debt is 5.3 percent. The tax rate is 21 percent. What is the company’s target
debt-equity ratio?
11. Book Value versus Market Value Masterson, Inc., has 4.1 million shares
of common stock outstanding. The current share price is $84, and the book
value per share is $11. The company also has two bond issues outstanding.
The first bond issue has a face value of $70 million, has a coupon rate of
LO 1
LO 1
LO 2
LO 2
LO 2
LO 3
LO 3
LO 3
LO 4
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418 P A R T 7 Long-Term Financing
5.1 percent, and sells for 98 percent of par. The second issue has a face value
of $50 million, has a coupon rate of 5.60 percent, and sells for 108 percent
of par. The first issue matures in 20 years, the second in 12 years.
a. What are the company’s capital structure weights on a book value basis?
b. What are the company’s capital structure weights on a market value basis?
c. Which are more relevant, the book or market value weights? Why?
12. Calculating the WACC In Problem 11, suppose the most recent dividend
was $3.95 and the dividend growth rate is 5 percent. Assume that the overall
cost of debt is the weighted average of that implied by the two outstanding
debt issues. Both bonds make semiannual payments. The tax rate is 21
percent. What is the company’s WACC?
13. WACC Clifford, Inc., has a target debt-equity ratio of .65. Its WACC is 8.1
percent, and the tax rate is 23 percent.
a. If the company’s cost of equity is 11 percent, what is its pretax cost of
debt?
b. If the aftertax cost of debt is 3.8 percent, what is the cost of equity?
14. Finding the WACC Given the following information for Lightning Power
Co., find the WACC. Assume the company’s tax rate is 21 percent.
Debt: 16,000 6.2 percent coupon bonds outstanding, $1,000
par value, 25 years to maturity, selling for 108 percent
of par; the bonds make semiannual payments.
Common stock: 535,000 shares outstanding, selling for $81 per share;
beta is 1.20.
Preferred stock: 20,000 shares of 4.2 percent preferred stock
outstanding, currently selling for $92 per share. The
par value is $100.
Market: 7 percent market risk premium and 3.1 percent risk-
free rate.
15. Finding the WACC Hankins Corporation has 5.4 million shares of common
stock outstanding; 290,000 shares of 5.2 percent preferred stock outstanding,
par value of $100; and 125,000 5.7 percent semiannual bonds outstanding,
par value $1,000 each. The common stock currently sells for $72 per share
and has a beta of 1.13, the preferred stock currently sells for $103 per share,
and the bonds have 20 years to maturity and sell for 103 percent of par. The
market risk premium is 6.8 percent, T-bills are yielding 4.3 percent, and the
firm’s tax rate is 23 percent.
a. What is the firm’s market value capital structure?
b. If the firm is evaluating a new investment project that has the same risk
as the firm’s typical project, what rate should the firm use to discount
the project’s cash flows?
16. SML and WACC An all-equity firm is considering the following projects:
Project Beta IRR
W .80 9.3%
X .90 11.4
Y 1.10 12.1
Z 1.35 15.1
LO 3
LO 3
LO 3
LO 3
LO 4
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C H A P T E R 1 2 Cost of Capital 419
The T-bill rate is 4 percent, and the expected return on the market is 12 percent.
a. Which projects have a higher expected return than the firm’s 12 percent
cost of capital?
b. Which projects should be accepted?
c. Which projects will be incorrectly accepted or rejected if the firm’s
overall cost of capital were used as a hurdle rate?
17. Calculating the WACC You are given the following information concerning
Parrothead Enterprises:
Debt: 13,000 6.4 percent coupon bonds outstanding, with 15
years to maturity and a quoted price of 107. These
bonds pay interest semiannually.
Common stock: 345,000 shares of common stock selling for $76.50
per share. The stock has a beta of .90 and will pay a
dividend of $3.80 next year. The dividend is expected
to grow by 5 percent per year indefinitely.
Preferred stock: 10,000 shares of 4.4 percent preferred stock selling at
$86 per share.
Market: 11 percent expected return, risk-free rate of 3.6
percent, and a 22 percent tax rate.
Calculate the company’s WACC.
18. Calculating Capital Structure Weights Ace Industrial Machines issued
195,000 zero coupon bonds four years ago. The bonds originally had 30
years to maturity with a yield to maturity of 5.2 percent. Interest rates
have recently decreased, and the bonds now have a yield to maturity of
4.9 percent. If the company has a $73 million market value of equity, what
weight should it use for debt when calculating the cost of capital?
19. Calculating the WACC Gnomes R Us is considering a new project. The
company has a debt-equity ratio of .62. The company’s cost of equity is 11.8
percent, and the aftertax cost of debt is 4.9 percent. The firm feels that the
project is riskier than the company as a whole and that it should use an
adjustment factor of + 3 percent. What is the WACC it should use for the
project?
INTERMEDIATE (Questions 20–26)
20. Calculating Cost of Equity Stock in CDB Industries has a beta of 1.10.
The market risk premium is 7.2 percent, and T-bills are currently yielding 4.1
percent. The most recent dividend was $2.56 per share, and dividends are
expected to grow at an annual rate of 5 percent indefinitely. If the stock sells
for $45 per share, what is your best estimate of the company’s cost of equity?
21. WACC and NPV Hankins, Inc., is considering a project that will result in
initial aftertax cash savings of $4.3 million at the end of the first year, and
these savings will grow at a rate of 1.9 percent per year indefinitely. The firm
has a target debt-equity ratio of .40, a cost of equity of 10.8 percent, and an
aftertax cost of debt of 3.2 percent. The cost-saving proposal is somewhat
riskier than the usual project the firm undertakes; management uses the
subjective approach and applies an adjustment factor of + 2 percent to the
cost of capital for such risky projects. Under what circumstances should the
company take on the project?
LO 3
LO 3
LO 3
LO 2
LO 4
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420 P A R T 7 Long-Term Financing
22. Calculating the Cost of Debt Ying Import has several bond issues
outstanding, each making semiannual interest payments. The bonds are listed
in the table below. If the corporate tax rate is 24 percent, what is the aftertax
cost of the company’s debt?
Bond Coupon Rate Price Quote Maturity Face Value
1 6.5% 109.0 5 years $30,000,000
2 5.3 97.4 8 years 50,000,000
3 6.9 110.5 15½ years 65,000,000
4 7.3 109.8 25 years 85,000,000
23. Calculating the Cost of Equity Gabriel Industries stock has a beta of 1.12.
The company just paid a dividend of $1.15, and the dividends are expected
to grow at 4 percent. The expected return on the market is 11.4 percent, and
Treasury bills are yielding 3.8 percent. The most recent stock price is $85.
a. Calculate the cost of equity using the dividend growth model method.
b. Calculate the cost of equity using the SML method.
c. Why do you think your estimates in (a) and (b) are so different?
24. Adjusted Cash Flow from Assets Dewey Corp. is expected to have an EBIT
of $2.45 million next year. Depreciation, the increase in net working capital,
and capital spending are expected to be $180,000, $85,000, and $185,000,
respectively. All are expected to grow at 18 percent per year for four
years. The company currently has $13 million in debt and 800,000 shares
outstanding. After Year 5, the adjusted cash flow from assets is expected to
grow at 2.5 percent indefinitely. The company’s WACC is 9.1 percent and the
tax rate is 21 percent. What is the price per share of the company’s stock?
25. Adjusted Cash Flow from Assets In the previous problem, instead of
a perpetual growth rate in adjusted cash flow from assets, you decide to
calculate the terminal value of the company with the price-sales ratio. You
believe that Year 5 sales will be $27.4 million and the appropriate price-sales
ratio is 1.9. What is your new estimate of the current share price?
26. Adjusted Cash Flow from Assets You have looked at the current financial
statements for Reigle Homes, Co. The company has an EBIT of $3.25
million this year. Depreciation, the increase in net working capital, and
capital spending were $245,000, $115,000, and $495,000, respectively. You
expect that over the next five years, EBIT will grow at 15 percent per year,
depreciation and capital spending will grow at 20 percent per year, and NWC
will grow at 10 percent per year. The company has $19.5 million in debt and
400,000 shares outstanding. After Year 5, the adjusted cash flow from assets
is expected to grow at 3.2 percent indefinitely. The company’s WACC is 9.25
percent, and the tax rate is 21 percent. What is the price per share of the
company’s stock?
CHALLENGE (Questions 27–28)
27. WACC and NPV Photochronograph Corporation (PC) manufactures time
series photographic equipment. It is currently at its target debt-equity ratio
of .35. It’s considering building a new $37 million manufacturing facility.
LO 2
LO 1
LO 3
LO 3
LO 3
LO 3
ros13952_ch12_389-423.indd 420 12/24/18 5:26 PM
C H A P T E R 1 2 Cost of Capital 421
This new plant is expected to generate aftertax cash flows of $5.1 million in
perpetuity. There are three financing options:
a. A new issue of common stock: The required return on the company’s new
equity is 15 percent.
b. A new issue of 20-year bonds: If the company issues these new bonds at
an annual coupon rate of 7 percent, they will sell at par.
c. Increased use of accounts payable financing: Because this financing is part
of the company’s ongoing daily business, the company assigns it a cost
that is the same as the overall firm WACC. Management has a target
ratio of accounts payable to long-term debt of .15. (Assume there is no
difference between the pretax and aftertax accounts payable cost.)
What is the NPV of the new plant? Assume that the company has a 21 percent
tax rate.
28. Project Evaluation This is a comprehensive project evaluation problem
bringing together much of what you have learned in this and previous
chapters. Suppose you have been hired as a financial consultant to Defense
Electronics, Inc. (DEI), a large, publicly traded firm that is the market
share leader in radar detection systems (RDSs). The company is looking at
setting up a manufacturing plant overseas to produce a new line of RDSs.
This will be a five-year project. The company bought some land three years
ago for $4.5 million in anticipation of using it as a toxic dump site for
waste chemicals, but it built a piping system to safely discard the chemicals
instead. If the land were sold today, the net proceeds would be $5.5 million
after taxes. In five years, the land will be worth $5.8 million after taxes.
The company wants to build its new manufacturing plant on this land; the
plant will cost $21.2 million to build. The following market data on DEI’s
securities are current:
Debt: 60,000 6.2 percent coupon bonds outstanding, 25
years to maturity, selling for 98 percent of par; the
bonds have a $1,000 par value each and make
semiannual payments.
Common stock: 1,350,000 shares outstanding, selling for $97 per
share; the beta is 1.15.
Preferred stock: 90,000 shares of 5.7 percent preferred stock
outstanding, par value of $100, selling for $95 per
share.
Market: 7 percent expected market risk premium; 3.8 percent
risk-free rate.
DEI’s tax rate is 25 percent. The project requires $825,000 in initial net work-
ing capital investment to get operational.
a. Calculate the project’s Time 0 cash flow, taking into account all side
effects.
b. The new RDS project is somewhat riskier than a typical project for DEI,
primarily because the plant is being located overseas. Management has
told you to use an adjustment factor of + 2 percent to account for this
increased riskiness. Calculate the appropriate discount rate to use when
evaluating DEI’s project.
LO 3
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422 P A R T 7 Long-Term Financing
c. The manufacturing plant has an eight-year tax life, and DEI uses
straight-line depreciation. At the end of the project (i.e., the end of
Year 5), the plant can be scrapped for $2.4 million. What is the aftertax
salvage value of this manufacturing plant?
d. The company will incur $3.6 million in annual fixed costs. The plan is to
manufacture 13,500 RDSs per year and sell them at $10,800 per
machine; the variable production costs are $9,900 per RDS. What is the
annual operating cash flow, OCF, from this project?
e. Finally, DEI’s president wants you to throw all your calculations, all your
assumptions, and everything else into a report for the chief financial
officer; all he wants to know is what the RDS project’s internal rate of
return, IRR, and net present value, NPV, are. What will you report?
12.1 Cost of Equity Go to finance.yahoo.com and look up the information for Activision
Blizzard (ATVI), a video game company in the S&P 500. You want to estimate the cost
of equity for the company. First, find the current Treasury bill rate. Next, find the beta
for ATVI. Using the historical market risk premium, what is the estimated cost of equity
for ATVI using the CAPM? Now find the analysts’ growth rate estimates for the next five
years for the company. Using this growth rate in the dividend growth model, what is the
estimated cost of equity? Now find the dividends paid by the company over the past five
years and calculate the arithmetic and geometric growth rates in dividends. Using these
growth rates, what is the estimated cost of equity? Looking at these four estimates, what
cost of equity would you use for the company?
12.2 Cost of Debt Go to finra-markets.morningstar.com/BondCenter/ and look up the
outstanding bonds for Nike. Record the most recent price and YTM of each bond issue.
Now go to www.sec.gov and find the most recent 10-Q or 10-K report filed by the
company and find the book value of each bond issue. Assuming Nike’s tax rate is 21
percent, what is the cost of debt using book value weights? What is the cost of debt using
market value weights? Which of these numbers is more relevant?
WHAT’S ON
THE WEB?
You want to calculate the WACC for auto parts retailer AutoZone (AZO). Complete the
following steps to construct a spreadsheet that can be updated.
a. Using an input for the ticker symbol, create hyperlinks to the web pages that you will
need to find all of the information necessary to calculate the cost of equity. Use a
market risk premium of 7 percent when using CAPM.
b. Create hyperlinks to go to the FINRA bond quote website and the SEC EDGAR
database and find the information for the company’s bonds. Create a table that
calculates the cost of debt for the company. Assume the tax rate is 21 percent.
c. Finally, calculate the market value weights for debt and equity. What is the WACC for
AutoZone?
EXCEL MASTER IT! PROBLEM
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Master
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C H A P T E R 1 2 Cost of Capital 423
purchase price. After the order is taken, the car is made
to order, typically within 45 days. LMI’s growth to date has
come from its profits. When the company had sufficient
capital, it would expand production. Relatively little formal
analysis has been used in its capital budgeting process.
Rachel has just read about capital budgeting techniques
and has come to you for help. For starters, the company
has never attempted to determine its cost of capital, and
Rachel would like you to perform the analysis. Because
the company is privately owned, it is difficult to determine
the cost of equity for the company. Rachel wants you to
use the pure play approach to estimate the cost of capital
for LMI, and she has chosen Tesla Motors as a representa-
tive company. The following questions will lead you
through the steps to calculate this estimate.
You have recently been hired by Layton Motors, Inc. (LMI), in its relatively new treasury management de-
partment. LMI was founded eight years ago by Rachel
Layton. Rachel found a method to manufacture a
cheaper battery that will hold a larger charge, giving a
car powered by the battery a range of 700 miles before
requiring a recharge. The cars manufactured by LMI are
midsized and carry a price that allows the company to
compete with other mainstream auto manufacturers.
The company is privately owned by Rachel and her fam-
ily, and it had sales of $197 million last year.
LMI primarily sells to customers who buy the cars
online, although it does have a limited number of com-
pany-owned dealerships. The customer selects any cus-
tomization and makes a deposit of 20 percent of the
CHAPTER CASE
Cost of Capital for Layton Motors
1. Most publicly traded corporations are required to
submit quarterly (10-Q) and annual (10-K) reports
to the SEC detailing the financial operations of the
company over the past quarter or year, respec-
tively. These corporate filings are available on the
SEC website at www.sec.gov. Go to the SEC web-
site and search for SEC filings made by Tesla Mo-
tors (TSLA). Find the most recent 10-Q or 10-K, and
download the form. Look on the balance sheet to
find the book value of debt and the book value of
equity.
2. To estimate the cost of equity for TSLA, go to fi-
nance.yahoo.com and enter the ticker symbol
TSLA. Follow the links to answer the following
questions: What is the most recent stock price
listed for TSLA? What is the market value of eq-
uity, or market capitalization? How many shares
of stock does TSLA have outstanding? What
is the most recent annual dividend? Can you use
the dividend discount model in this case? What is
the beta for TSLA? Now go back to
finance.yahoo.com and find the current U.S.
Treasury bond rates. What is the yield on
three-month Treasury bills? Using the historical
market risk premium, what is the cost of equity
for TSLA using CAPM?
3. You now need to calculate the cost of debt for
TSLA. Go to finra-markets.morningstar.com/Bond-
Center/, enter TSLA as the company, and find the
yield to maturity for each of TSLA’s bonds. What is
the weighted average cost of debt for TSLA using
the book value weights and using the market
value weights? Does it make a difference in this
case if you use book value weights or market
value weights?
4. You now have all the necessary information to cal-
culate the weighted average cost of capital for
TSLA. Calculate this using book value weights
and market value weights, assuming TSLA has a
21 percent marginal tax rate. Which number is
more relevant?
5. You used TSLA as a pure play company to esti-
mate the cost of capital for LMI. Are there any po-
tential problems with this approach in this
situation?
Q U E S T I O N S
ros13952_ch12_389-423.indd 423 12/24/18 5:26 PM
424
Please visit us at essentialsofcorporatefinance.blogspot.com for the latest developments in the world of corporate finance.
In addition to lowering the corporate tax rate from 35 percent to 21 percent, the Tax Cuts and Jobs Act of 2017, which was passed in
December of that year, limited the tax deductibility of interest expense.
The deduction of interest expense is now limited to 30 percent of “ad-
justable tax income,” roughly equivalent to earnings before interest
and taxes. Earlier in 2017, with the new law being discussed, corpora-
tions responded. For example, BHP announced plans to repurchase
$2.5 billion of its bonds, Walmart repurchased $8.5 billion of its debt,
and Sprint repurchased $1 billion of its debt. In fact, through the middle
of October 2017, U.S. corporations announced plans to repurchase
$178.5 billion in debt, more than double the $80 billion of repurchases
for the same period in 2016, and way more than the $18 billion in 2014.
A firm’s choice of how much debt it should have relative to equity is known as a capital
structure decision. Such a choice has many implications for a firm and is far from being a set-
tled issue in either theory or practice. In this chapter, we discuss the basic ideas underlying
capital structures and how firms choose them.
A firm’s capital structure is really a reflection of its borrowing policy. Should we borrow a
lot of money or a little? At first glance, it probably seems that debt is something to be avoided.
After all, the more debt a firm has, the greater is the risk of bankruptcy. What we learn is that
debt is really a double-edged sword, and, properly used, debt can be enormously beneficial
to the firm.
A good understanding of the effects of debt financing is important because the role of
debt is so misunderstood, and many firms (and individuals) are far too conservative in their
use of debt. Having said this, we also can say that firms sometimes err in the opposite direc-
tion, becoming much too heavily indebted, with bankruptcy as the unfortunate consequence.
Striking the right balance is what the capital structure issue is all about.
Leverage and
Capital Structure 13
LEARNING OBJECTIVES
After studying this chapter, you should
be able to:
LO 1 Discuss the effect of financial
leverage.
LO 2 Analyze the impact of taxes and
bankruptcy on capital structure
choice.
LO 3 Identify the essentials of the
bankruptcy process.
ros13952_ch13_424-456.indd 424 12/24/18 5:30 PM
C H A P T E R 1 3 Leverage and Capital Structure 425
Thus far, we have taken the firm’s capital structure as given. Debt-equity ratios don’t drop on firms from the sky, of course, so now it’s time to wonder where they do come from.
Going back to Chapter 1, we call decisions about a firm’s debt-equity ratio capital structure
decisions.1
For the most part, a firm can choose any capital structure that it wants. If management
so desired, a firm could issue bonds and use the proceeds to buy back some stock, thereby
increasing the debt-equity ratio. Alternatively, it could issue stock and use the money to pay
off some debt, thereby reducing the debt-equity ratio. Activities such as these that alter the
firm’s existing capital structure are called capital restructurings. In general, such restructur-
ings take place whenever the firm substitutes one capital structure for another while leaving
the firm’s assets unchanged.
Because the assets of a firm are not directly affected by a capital restructuring, we can
examine the firm’s capital structure decision separately from its other activities. This means
that a firm can consider capital restructuring decisions in isolation from its investment de-
cisions. In this chapter, then, we will ignore investment decisions and focus on the long-term
financing, or capital structure, question.
What we will see in this chapter is that capital structure decisions can have important
implications for the value of the firm and its cost of capital. We also will find that important
elements of the capital structure decision are easy to identify, but precise measures of these
elements are generally not obtainable. As a result, we are only able to give an incomplete
answer to the question of what the best capital structure might be for a particular firm at a
particular time.
THE CAPITAL STRUCTURE QUESTION
How should a firm go about choosing its debt-equity ratio? Here, as always, we assume that
the guiding principle is to choose the course of action that maximizes the value of a share of
stock. However, when it comes to capital structure decisions, this is essentially the same
thing as maximizing the value of the whole firm, and, for convenience, we will tend to frame
our discussion in terms of firm value.
In Chapter 12, we discussed the concept of the firm’s weighted average cost of capital,
or WACC. You may recall that the WACC tells us that the firm’s overall cost of capital is a
weighted average of the costs of the various components of the firm’s capital structure.
When we described the WACC, we took the firm’s capital structure as given. Thus, one im-
portant issue that we will want to explore in this chapter is what happens to the cost of
capital when we vary the amount of debt financing, or the debt-equity ratio.
A primary reason for studying the WACC is that the value of the firm is maximized
when the WACC is minimized. To see this, recall that the WACC is the discount rate appro-
priate for the firm’s overall cash flows. Because values and discount rates move in opposite
directions, minimizing the WACC will maximize the value of the firm’s cash flows.
Thus, we will want to choose the firm’s capital structure so that the WACC is mini-
mized. For this reason, we will say that one capital structure is better than another if it re-
sults in a lower weighted average cost of capital. Further, we say that a particular debt-equity
ratio represents the optimal capital structure if it results in the lowest possible WACC. This
optimal capital structure is sometimes called the firm’s target capital structure as well.
13.1
1It is conventional to refer to decisions regarding debt and equity as capital structure decisions. However, the term
financial structure would be more accurate, and we use the terms interchangeably.
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426 P A R T 7 Long-Term Financing
CONCEPT QUESTIONS
13.1a What is the relationship between the WACC and the value of the firm?
13.1b What is an optimal capital structure?
THE EFFECT OF FINANCIAL LEVERAGE
In this section, we examine the impact of financial leverage on the payoffs to stockholders.
As you may recall, financial leverage refers to the extent to which a firm relies on debt. The
more debt financing a firm uses in its capital structure, the more financial leverage it
employs.
As we describe, financial leverage can dramatically alter the payoffs to shareholders in
the firm. Remarkably, however, financial leverage may not affect the overall cost of capital.
If this is true, then a firm’s capital structure is irrelevant because changes in capital struc-
ture won’t affect the value of the firm. We return to this issue a little later.
The Impact of Financial Leverage
We start by illustrating how financial leverage works. For now, we ignore the impact of
taxes. Also, for ease of presentation, we describe the impact of leverage in terms of its ef-
fects on earnings per share, EPS, and return on equity, ROE. These are, of course, account-
ing numbers and, as such, are not our primary concern. Using cash flows instead of these
accounting numbers would lead to precisely the same conclusions, but a little more work
would be needed. We discuss the impact of leverage on market values in a subsequent
section.
Financial Leverage, EPS, and ROE: An Example The Trans Am Corporation
currently has no debt in its capital structure. The CFO, Ms. Morris, is considering a restruc-
turing that would involve issuing debt and using the proceeds to buy back some of the out-
standing equity. Table 13.1 presents both the current and proposed capital structures. As
shown, the firm’s assets have a market value of $8 million, and there are 400,000 shares
outstanding. Because Trans Am is an all-equity firm, the price per share is $20.
The proposed debt issue would raise $4 million; the interest rate would be 10 percent.
The stock sells for $20 per share, so the $4 million in new debt would be used to purchase
$4 million/$20 = 200,000 shares, leaving 200,000 outstanding. After the restructuring,
Trans Am would have a capital structure that was 50 percent debt, so the debt-equity ratio
would be 1. Notice that, for now, we assume that the stock price will remain at $20.
13.2
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Master
Current and
proposed capital
structures for the
Trans Am
Corporation
TABLE 13.1 Current Proposed
Assets $8,000,000 $8,000,000
Debt $ 0 $4,000,000
Equity $8,000,000 $4,000,000
Debt-equity ratio 0 1
Share price $20 $20
Shares outstanding 400,000 200,000
Interest rate 10% 10%
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C H A P T E R 1 3 Leverage and Capital Structure 427
To investigate the impact of the proposed restructuring, Ms. Morris has prepared
Table 13.2, which compares the firm’s current capital structure to the proposed capital
structure under three scenarios. The scenarios reflect different assumptions about the firm’s
EBIT. Under the expected scenario, EBIT is $1 million. In the recession scenario, EBIT
falls to $500,000. In the expansion scenario, it rises to $1.5 million.
To illustrate some of the calculations in Table 13.2, consider the expansion case. EBIT
is $1.5 million. With no debt (the current capital structure) and no taxes, net income is also
$1.5 million. In this case, there are 400,000 shares worth $8 million total. EPS is therefore
$1.5 million/400,000 = $3.75 per share. Also, because accounting return on equity, ROE,
is net income divided by total equity, ROE is $1.5 million/$8 million = .1875, or
18.75 percent.2
With $4 million in debt (the proposed capital structure), things are somewhat different.
Because the interest rate is 10 percent, the interest bill is $400,000. With EBIT of
$1.5 million, interest of $400,000, and no taxes, net income is $1.1 million. Now there are
only 200,000 shares worth $4 million total. EPS is therefore $1.1 million/200,000 =
$5.50 per share versus the $3.75 per share that we calculated above. Furthermore, ROE is
$1.1 million/$4 million = .275, or 27.5 percent. This is well above the 18.75 percent we
calculated for the current capital structure.
EPS versus EBIT The impact of leverage is evident in Table 13.2 when the effect of the
restructuring on EPS and ROE is examined. In particular, the variability in both EPS and
ROE is much larger under the proposed capital structure. This illustrates how financial
leverage acts to magnify gains and losses to shareholders.
In Figure 13.1, we take a closer look at the effect of the proposed restructuring. This
figure plots earnings per share, EPS, against earnings before interest and taxes, EBIT, for
the current and proposed capital structures. The first line, labeled “No debt,” represents the
case of no leverage. This line begins at the origin, indicating that EPS would be zero if EBIT
were zero. From there, every $400,000 increase in EBIT increases EPS by $1 (because there
are 400,000 shares outstanding).
Capital structure
scenarios for the
Trans Am
Corporation
TABLE 13.2Current Capital Structure: No Debt
Recession Expected Expansion
EBIT $500,000 $1,000,000 $1,500,000
Interest 0 0 0
Net income $500,000 $1,000,000 $1,500,000
ROE 6.25% 12.50% 18.75%
EPS $1.25 $2.50 $3.75
Proposed Capital Structure: Debt = $4 million
Recession Expected Expansion
EBIT $500,000 $1,000,000 $1,500,000
Interest 400,000 88 400,000 400,000
Net income $100,000 $888 600,000 $1,100,000
ROE 2.50% 15.00% 27.50%
EPS $.50 $3.00 $5.50
2ROE is discussed in some detail in Chapter 3.
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428 P A R T 7 Long-Term Financing
The second line represents the proposed capital structure. Here, EPS is negative if
EBIT is zero. This follows because $400,000 of interest must be paid regardless of the firm’s
profits. Because there are 200,000 shares in this case, EPS is −$2 per share as shown. Sim-
ilarly, if EBIT were $400,000, EPS would be exactly zero.
The important thing to notice in Figure 13.1 is that the slope of the line in this second
case is steeper. In fact, for every $400,000 increase in EBIT, EPS rises by $2, so the line is
twice as steep. This tells us that EPS is twice as sensitive to changes in EBIT because of the
financial leverage employed.
Another observation to make in Figure 13.1 is that the lines intersect. At that point,
EPS is exactly the same for both capital structures. To find this point, note that EPS is
equal to EBIT/400,000 in the no-debt case. In the with-debt case, EPS is (EBIT −
$400,000)/200,000. If we set these equal to each other, EBIT is:
EBIT/400,000 = (EBIT − $400,000)/200,000
EBIT = 2 × (EBIT − $400,000)
EBIT = $800,000
When EBIT is $800,000, EPS is $2 per share under either capital structure. This is la-
beled as the break-even point in Figure 13.1; we also could call it the indifference point. If
EBIT is above this level, leverage is beneficial; if it is below this point, it is not.
There is another, more intuitive, way of seeing why the break-even point is $800,000.
Notice that if the firm has no debt and its EBIT is $800,000, its net income is also $800,000.
In this case, the ROE is $800,000/$8,000,000 = .10, or 10 percent. This is precisely the
same as the interest rate on the debt, so the firm earns a return that is just sufficient to pay
the interest.
Financial leverage:
EPS and EBIT for the
Trans Am
Corporation
FIGURE 13.1
Earnings before
interest and
taxes ($)
Advantage
to debt
Disadvantage
to debt
Break-even point
1,200,000400,000 800,000
With debt4
3
2
1
0
−1
−2
No debt
Earnings per
share ($)
ros13952_ch13_424-456.indd 428 12/24/18 5:30 PM
C H A P T E R 1 3 Leverage and Capital Structure 429
Corporate Borrowing and Homemade Leverage
Based on Tables 13.1 and 13.2 and Figure 13.1, Ms. Morris draws the following
conclusions:
1. The effect of financial leverage depends on the company’s EBIT. When EBIT is
relatively high, leverage is beneficial.
2. Under the expected scenario, leverage increases the returns to shareholders, as
measured by both ROE and EPS.
3. Shareholders are exposed to more risk under the proposed capital structure because
the EPS and ROE are much more sensitive to changes in EBIT in this case.
4. Because of the impact that financial leverage has on both the expected return to
stockholders and the riskiness of the stock, capital structure is an important
consideration.
The first three of these conclusions are clearly correct. Does the last conclusion neces-
sarily follow? Surprisingly, the answer is no. As we discuss next, the reason is that share-
holders can adjust the amount of financial leverage by borrowing and lending on their own.
This use of personal borrowing to alter the degree of financial leverage is called
homemade leverage.
We now will illustrate that it actually makes no difference whether or not Trans Am
adopts the proposed capital structure because any stockholder who prefers the proposed
capital structure can create it using homemade leverage. To begin, the first part of Table
13.3 shows what will happen to an investor who buys $2,000 worth of Trans Am stock if the
proposed capital structure is adopted. This investor purchases 100 shares of stock. From
Table 13.2, EPS will be either $.50, $3, or $5.50, so the total earnings for 100 shares will
either be $50, $300, or $550 under the proposed capital structure.
Now, suppose Trans Am does not adopt the proposed capital structure. In this case,
EPS will be $1.25, $2.50, or $3.75. The second part of Table 13.3 demonstrates how a
stockholder who prefers the payoffs under the proposed structure can create them using
homemade leverage
The use of personal
borrowing to change the
overall amount of financial
leverage to which an
individual is exposed.
EXAMPLE 13.1 Break-Even EBIT
The MPD Corporation has decided in favor of a capital restructuring. Currently, MPD uses no debt
financing. Following the restructuring, however, debt will be $1 million. The interest rate on the debt
will be 9 percent. MPD currently has 200,000 shares outstanding, and the price per share is $20. If
the restructuring is expected to increase EPS, what is the minimum level for EBIT that MPD’s man-
agement must be expecting? Ignore taxes in answering.
To answer, we calculate the break-even EBIT. At any EBIT above this, the increased financial
leverage will increase EPS, so this will tell us the minimum level for EBIT. Under the old capital struc-
ture, EPS is EBIT/200,000. Under the new capital structure, the interest expense will be $1 million ×
.09 = $90,000. Furthermore, with the $1 million proceeds, MPD will repurchase $1 million/20 =
50,000 shares of stock, leaving 150,000 outstanding. EPS is thus (EBIT – $90,000)/150,000.
Now that we know how to calculate EPS under both scenarios, we set the two expressions for
EPS equal to each other and solve for the break-even EBIT:
EBIT/200,000 = (EBIT − $90,000)/150,000
EBIT = (4/3) × (EBIT − $90,000)
EBIT = $360,000
Verify that, in either case, EPS is $1.80 when EBIT is $360,000. Management at MPD is apparently
of the opinion that EPS will exceed $1.80.
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430 P A R T 7 Long-Term Financing
personal borrowing. To do this, the stockholder borrows $2,000 at 10 percent on his or her
own. Our investor uses this amount, along with the original $2,000, to buy 200 shares of
stock. As shown, the net payoffs are exactly the same as those for the proposed capital
structure.
How did we know to borrow $2,000 to create the right payoffs? We are trying to repli-
cate Trans Am’s proposed capital structure at the personal level. The proposed capital struc-
ture results in a debt-equity ratio of 1. To replicate this capital structure at the personal level,
the stockholder must borrow enough to create this same debt-equity ratio. Because the
stockholder has $2,000 in equity invested, borrowing another $2,000 will create a personal
debt-equity ratio of 1.
This example demonstrates that investors always can increase financial leverage them-
selves to create a different pattern of payoffs. It thus makes no difference whether or not
Trans Am chooses the proposed capital structure.
Proposed capital
structure versus
original capital
structure with
homemade leverage
TABLE 13.3
EXAMPLE 13.2 Unlevering the Stock
In our Trans Am example, suppose management adopted the proposed capital structure. Further,
suppose that an investor who owned 100 shares preferred the original capital structure. Show how
this investor could “unlever” the stock to recreate the original payoffs.
To create leverage, investors borrow on their own. To undo leverage, investors must loan out
money. For Trans Am, the corporation borrowed an amount equal to half its value. The investor can
unlever the stock by loaning out money in the same proportion. In this case, the investor sells 50
shares for $1,000 total and then loans out the $1,000 at 10 percent. The payoffs are calculated in
the following table.
Recession Expected Expansion
EPS (proposed structure) $88888 .50 $ 3.00 $888 5.50
Earnings for 50 shares 25.00 150.00 275.00
Plus: Interest on $1,000 @ 10% 100.00 100.00 100.00
Total payoff $125.00 $250.00 $375.00
These are precisely the payoffs the investor would have experienced under the original capital
structure.
Proposed Capital Structure
Recession Expected Expansion
EPS $ .50 $ 3.00 $ 5.50
Earnings for 100 shares 50.00 300.00 550.00
Net cost = 100 shares at $20 = $2,000
Original Capital Structure and Homemade Leverage
Recession Expected Expansion
EPS $ 1.25 $ 2.50 $ 3.75
Earnings for 200 shares 250.00 500.00 750.00
Less: Interest on $2,000 at 10% 200.00 200.00 200.00
Net earnings $ 50.00 $300.00 $550.00
Net cost = 200 shares at $20 − Amount borrowed = $4,000 − 2,000 = $2,000
ros13952_ch13_424-456.indd 430 12/24/18 5:30 PM
C H A P T E R 1 3 Leverage and Capital Structure 431
CONCEPT QUESTIONS
13.2a What is the impact of financial leverage on stockholders?
13.2b What is homemade leverage?
13.2c Why is Trans Am’s capital structure irrelevant?
CAPITAL STRUCTURE AND THE COST
OF EQUITY CAPITAL
We have seen that there is nothing special about corporate borrowing because investors can
borrow or lend on their own. As a result, whichever capital structure Trans Am chooses, the
stock price will be the same. Trans Am’s capital structure is thus irrelevant, at least in the
simple world we have examined.
Our Trans Am example is based on a famous argument advanced by two Nobel laure-
ates, Franco Modigliani and Merton Miller, whom we will henceforth call M&M. What we
illustrated for the Trans Am Corporation is a special case of M&M Proposition I. M&M
Proposition I states that it is completely irrelevant how a firm chooses to arrange its
finances.
M&M Proposition I: The Pie Model
One way to illustrate M&M Proposition I is to imagine two firms that are identical on the
left-hand side of the balance sheet. Their assets and operations are exactly the same. The
right-hand sides are different because the two firms finance their operations differently. In
this case, we can view the capital structure question in terms of a “pie” model. Why we
choose this name is apparent in Figure 13.2. Figure 13.2 gives two possible ways of cutting
up this pie between the equity slice, E, and the debt slice, D: 40%–60% and 60%–40%. How-
ever, the size of the pie in Figure 13.2 is the same for both firms because the value of the
assets is the same. This is precisely what M&M Proposition I states: The size of the pie
doesn’t depend on how it is sliced.
The Cost of Equity and Financial Leverage: M&M
Proposition II
Although changing the capital structure of the firm may not change the firm’s total value,
it does cause important changes in the firm’s debt and equity. We now examine what
13.3
coverage online
Excel
Master
M&M Proposition I
The value of a firm is
independent of its capital
structure.
Two pie models of
capital structure
Value of firm
Stocks
40% Bonds
60%
Stocks
60%
Bonds
40%
Value of firm FIGURE 13.2
ros13952_ch13_424-456.indd 431 12/24/18 5:30 PM
432 P A R T 7 Long-Term Financing
happens to a firm financed with debt and equity when the debt-equity ratio is changed. To
simplify our analysis, we will continue to ignore taxes.
Based on our discussion in Chapter 12, if we ignore taxes, the weighted average cost of
capital, WACC, is:
WACC = (E / V)) × R E + (D / V)) × R D
where V = E + D. We also saw that one way of interpreting the WACC is as the required
return on the firm’s overall assets. To remind us of this, we use the symbol RA to stand for
the WACC and write:
R A = (E / V)) × R E + (D / V)) × R D
If we rearrange this to solve for the cost of equity capital, we see that:
RE = RA + (RA − RD) × (D/E ) [13.1]
This is the famous M&M Proposition II, which tells us that the cost of equity depends on
three things: the required rate of return on the firm’s assets, RA; the firm’s cost of debt, RD;
and the firm’s debt-equity ratio, D/E.
Figure 13.3 summarizes our discussion thus far by plotting the cost of equity capital,
RE , against the debt-equity ratio. As shown, M&M Proposition II indicates that the cost of
equity, RE , is given by a straight line with a slope of (RA − RD). The y-intercept corresponds
to a firm with a debt-equity ratio of zero, so RA = RE in that case. Figure 13.3 shows that, as
the firm raises its debt-equity ratio, the increase in leverage raises the risk of the equity and
therefore the required return, or cost of equity (RE).
Notice in Figure 13.3 that the WACC doesn’t depend on the debt-equity ratio; it’s the
same no matter what the debt-equity ratio is. This is another way of stating M&M Proposi-
tion I: The firm’s overall cost of capital is unaffected by its capital structure. As illustrated,
the fact that the cost of debt is lower than the cost of equity is exactly offset by the increase
in the cost of equity from borrowing. In other words, the change in the capital structure
weights (E/V and D/V) is exactly offset by the change in the cost of equity (RE), so the
WACC stays the same.
M&M Proposition II
A firm’s cost of equity
capital is a positive linear
function of its capital
structure.
The cost of equity
and the WACC: M&M
Propositions I and II
with no taxes
FIGURE 13.3 Cost of capital
(%) RE
WACC = RA
RD
Debt-equity ratio
(D/E)
RE = RA + (RA − RD) × (D/E ) by M&M Proposition II
where V = D + E
RA = WACC = (E/V ) × RE + (D/V ) × RD
ros13952_ch13_424-456.indd 432 12/24/18 5:30 PM
C H A P T E R 1 3 Leverage and Capital Structure 433
Business and Financial Risk
M&M Proposition II shows that the firm’s cost of equity can be broken down into two com-
ponents. The first component, RA, is the required return on the firm’s overall assets, and it
depends on the nature of the firm’s operating activities. The risk inherent in a firm’s opera-
tions is called the business risk of the firm’s equity. Referring back to Chapter 11, we see
that this business risk depends on the systematic risk of the firm’s assets. The greater a
firm’s business risk, the greater RA will be, and, all other things being the same, the greater
will be the firm’s cost of equity.
The second component in the cost of equity, (RA − RD) × (D/E), is determined by the
firm’s financial structure. For an all-equity firm, this component is zero. As the firm begins
to rely on debt financing, the required return on equity rises. This occurs because the debt
financing increases the risks borne by the stockholders. This extra risk that arises from the
use of debt financing is called the financial risk of the firm’s equity.
The total systematic risk of the firm’s equity thus has two parts: business risk and fi-
nancial risk. The first part (the business risk) depends on the firm’s assets and operations
and is not affected by capital structure. Given the firm’s business risk (and its cost of
debt), the second part (the financial risk) is completely determined by financial policy. As
we have illustrated, the firm’s cost of equity rises when it increases its use of financial
leverage because the financial risk of the equity increases while the business risk remains
the same.
business risk
The equity risk that comes
from the nature of the
firm’s operating activities.
financial risk
The equity risk that comes
from the financial policy
(i.e., capital structure) of
the firm.
EXAMPLE 13.3 The Cost of Equity Capital
The Ricardo Corporation has a weighted average cost of capital (ignoring taxes) of 12 percent. It
can borrow at 8 percent. Assuming that Ricardo has a target capital structure of 80 percent equity
and 20 percent debt, what is its cost of equity? What is the cost of equity if the target capital struc-
ture is 50 percent equity? Calculate the WACC, using your answers to verify that it is the same in
both cases.
According to M&M Proposition II, the cost of equity, RE!!, is:
RE = RA + (RA − RD) × (D/E)
In the first case, the debt-equity ratio is .2/.8 = .25, so the cost of the equity is:
RE = 12% + (12% − 8%) × .25
= 13%
In the second case, verify that the debt-equity ratio is 1.0, so the cost of equity is 16 percent.
We can now calculate the WACC assuming that the percentage of equity financing is 80 per-
cent, the cost of equity is 13 percent, and the tax rate is zero:
WACC = (E/V ) × RE + (D/V ) × RD
= .80 × 13% + .20 × 8%
= 12%
In the second case, the percentage of equity financing is 50 percent and the cost of equity is
16 percent. The WACC is:
WACC = (E/V ) × RE + (D/V ) × RD
= .50 × 16% + .50 × 8%
= 12%
As we calculated, the WACC is 12 percent in both cases.
ros13952_ch13_424-456.indd 433 12/24/18 5:30 PM
434 P A R T 7 Long-Term Financing
CONCEPT QUESTIONS
13.3a What does M&M Proposition I state?
13.3b What are the three determinants of a firm’s cost of equity?
13.3c The total systematic risk of a firm’s equity has two parts. What are they?
CORPORATE TAXES AND CAPITAL STRUCTURE
Debt has two distinguishing features that we have not taken into proper account. First, as we
have mentioned in a number of places, interest paid on debt is tax deductible. This is good
for the firm, and it may be an added benefit to debt financing. Second, failure to meet debt
obligations can result in bankruptcy. This is not good for the firm, and it may be an added
cost of debt financing. Because we haven’t explicitly considered either of these two features
of debt, we may get a different answer about capital structure once we do. Accordingly, we
consider taxes in this section and bankruptcy in the next one.
Our discussion here will assume that all interest paid is tax deductible. In reality, how-
ever, the Tax Cuts and Jobs Act of 2017 placed limits on the amount of interest that can be
deducted. Specifically, for 2018 through 2021, the net interest deduction is limited to at
most 30 percent of EBITDA. After 2021, it drops to 30 percent of EBIT. The term “net in-
terest” means interest paid less interest earned (if any). Also, the limits aren’t exactly based
on EBITDA and EBIT because of some adjustments, but the differences will be minor in
most cases. Importantly, any interest that can’t be deducted in a particular year can be car-
ried forward and deducted later. Thus, the tax deductibility isn’t lost; it is deferred.
We can start by considering what happens when we consider the effect of corporate
taxes. To do this, we will examine two firms, Firm U (unlevered) and Firm L (levered).
These two firms are identical on the left-hand side of the balance sheet, so their assets and
operations are the same.
We assume that EBIT is expected to be $1,000 every year forever for both firms. The
difference between the two firms is that Firm L has issued $1,000 worth of perpetual bonds
on which it pays 8 percent interest each year. The interest bill is thus .08 × $1,000 = $80
every year forever. Also, we assume that the corporate tax rate is 21 percent.
For our two firms, U and L, we can now calculate the following:
Firm U Firm L
EBIT $1,000 $1,000.00
Interest 88888880 80.00
Taxable income $1,000 $ 920.00
Taxes (21%) 8888210 193.20
Net income $ 88790 $ 726.80
The Interest Tax Shield
To simplify things, we will assume that depreciation is zero. We also will assume that capital
spending is zero and that there are no additions to NWC. In this case, cash flow from assets
is equal to EBIT − Taxes. For Firms U and L, we thus have:
Cash Flow from Assets Firm U Firm L
88888EBIT $1,000 $1,000.00
−Taxes 88888888888888888888888888888210 193.20
888888Total $ 88790 $ 806.80
13.4
ros13952_ch13_424-456.indd 434 12/24/18 5:30 PM
C H A P T E R 1 3 Leverage and Capital Structure 435
We immediately see that capital structure is now having some effect because the cash
flows from U and L are not the same even though the two firms have identical assets.
To see what’s going on, we can compute the cash flow to stockholders and bondholders.
Cash Flow Firm U Firm L
To stockholders $ 790 $ 726.80
To bondholders 0 888 80.00
Total $ 790 $ 806.80
What we are seeing is that the total cash flow to L is $16.80 more. This occurs because L’s tax
bill (which is a cash outflow) is $16.80 less. The fact that interest is deductible for tax purposes
has generated a tax saving equal to the interest payment ($80) multiplied by the corporate
tax rate (21 percent): $80 × .21 = $16.80. We call this tax saving the interest tax shield.
Taxes and M&M Proposition I
Because the debt is perpetual, the same $16.80 shield will be generated every year forever.
The aftertax cash flow to L will thus be the same $790 that U earns plus the $16.80 tax
shield. Because L’s cash flow is always $16.80 greater, Firm L is worth more than Firm U by
the value of this $16.80 perpetuity.
Because the tax shield is generated by paying interest, it has the same risk as the debt,
and 8 percent (the cost of debt) is, therefore, the appropriate discount rate. The value of the
tax shield is thus:
PV = $16).)80 ______
.08
=
.21 × $1,000 × .08
_____________
.08
= .)21 × $1,000 = $210
As our example illustrates, the present value of the interest tax shield can be written as:
Present value of the interest tax shield = (TC × D × RD)/RD
= TC × D
[13.2]
We have now come up with another famous result, M&M Proposition I with corporate
taxes. We have seen that the value of Firm L, VL, exceeds the value of Firm U, VU, by the
present value of the interest tax shield, TC × D. M&M Proposition I with taxes therefore
states that:
VL = VU + TC × D [13.3]
The effect of borrowing in this case is illustrated in Figure 13.4. We have plotted the value
of the levered firm, VL, against the amount of debt, D. M&M Proposition I with corporate
taxes implies that the relationship is given by a straight line with a slope of TC .
In Figure 13.4, we also have drawn a horizontal line representing VU. As is shown, the
distance between the two lines is TC × D, the present value of the tax shield.
As Figure 13.4 indicates, the value of the firm goes up by $.21 for every $1 in debt. In
other words, the NPV per dollar of debt is $.21. It is difficult to imagine why any corporation
would not borrow to the absolute maximum under these circumstances.
Conclusion
The result of our analysis in this section is that, once we include taxes, capital structure defi-
nitely matters. However, we immediately reach the illogical conclusion that the optimal
capital structure is 100 percent debt. Of course, we have not yet considered the impact of
bankruptcy, so our story may change. For future reference, Table 13.4 contains a summary
of the various M&M calculations and conclusions.
interest tax shield
The tax saving attained by
a firm from the tax
deductibility of interest
expense.
ros13952_ch13_424-456.indd 435 12/24/18 5:30 PM
436 P A R T 7 Long-Term Financing
M&M Proposition I
with taxes
FIGURE 13.4
Total debt
(D )
Value of
the firm
(VL)
VU
VU
VU = Value of firm
with no debt
VL = VU + TC × D
= Value of firm
with debt
TC × D = Present
value of
tax shield
on debt
= TC
The value of the firm increases as total debt increases because of the interest
tax shield. This is the basis of M&M Proposition I with taxes.
I. The no-tax case
A. Proposition I: The value of the leveraged firm (VL) is equal to the value of the unleveraged
firm (VU):
VL = VU
B. Implications of Proposition I:
1. A firm’s capital structure is irrelevant.
2. A firm’s weighted average cost of capital, WACC, is the same no matter what mixture
of debt and equity is used to finance the firm.
C. Proposition II: The cost of equity, RE!!, is:
RE = RA + (RA − RD) × D/E
where RA is the WACC, RD is the cost of debt, and D/E is the debt-equity ratio.
D. Implications of Proposition II:
1. The cost of equity rises as the firm increases its use of debt financing.
2. The risk of the equity depends on two things: the riskiness of the firm’s operations
(business risk) and the degree of financial leverage (financial risk). Business risk
determines RA; financial risk is determined by D/E.
II. The tax case
A. Proposition I with taxes: The value of the leveraged firm (VL) is equal to the value of the
unleveraged firm (VU) plus the present value of the interest tax shield:
VL = VU + TC × D
where TC is the corporate tax rate and D is the amount of debt.
B. Implications of Proposition I with taxes:
1. Debt financing is highly advantageous, and, in the extreme, a firm’s optimal capital
structure is 100 percent debt.
2. A firm’s weighted average cost of capital, WACC, decreases as the firm relies more
heavily on debt financing.
Modigliani and Miller
summary
TABLE 13.4
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C H A P T E R 1 3 Leverage and Capital Structure 437
CONCEPT QUESTIONS
13.4a What is the relationship between the value of an unlevered firm and the value of a
levered firm once we consider the effect of corporate taxes?
13.4b If we only consider the effect of taxes, what is the optimum capital structure?
BANKRUPTCY COSTS
One limit to the amount of debt a firm might use comes in the form of bankruptcy costs. As
the debt-equity ratio rises, so too does the probability that the firm will be unable to pay its
bondholders what was promised to them. When this happens, ownership of the firm’s assets
ultimately is transferred from the stockholders to the bondholders.
In principle, a firm becomes bankrupt when the value of its assets equals the value of
its debt. When this occurs, the value of equity is zero, and the stockholders turn over control
of the firm to the bondholders. At this point, the bondholders hold assets whose value is
exactly equal to what is owed on the debt. In a perfect world, there are no costs associated
with this transfer of ownership, and the bondholders don’t lose anything.
This idealized view of bankruptcy is not, of course, what happens in the real world.
Ironically, it is expensive to go bankrupt. As we discuss, the costs associated with bank-
ruptcy eventually may offset the tax-related gains from leverage.
Direct Bankruptcy Costs
When the value of a firm’s assets equals the value of its debt, then the firm is economically
bankrupt in the sense that the equity has no value. However, the formal turning over of the
assets to the bondholders is a legal process, not an economic one. There are legal and ad-
ministrative costs to bankruptcy, and it has been remarked that bankruptcies are to lawyers
what blood is to sharks.
Because of the expenses associated with bankruptcy, bondholders won’t get all that
they are owed. Some fraction of the firm’s assets will “disappear” in the legal process of
going bankrupt. These are the legal and administrative expenses associated with the bank-
ruptcy proceeding. We call these costs direct bankruptcy costs.
Indirect Bankruptcy Costs
Because it is expensive to go bankrupt, a firm will spend resources to avoid doing so. When
a firm is having significant problems in meeting its debt obligations, we say that it is experi-
encing financial distress. Some financially distressed firms ultimately file for bankruptcy,
but most do not because they are able to recover or otherwise survive.
The costs of avoiding a bankruptcy filing incurred by a financially distressed firm are
called indirect bankruptcy costs. We use the term financial distress costs to refer generi-
cally to the direct and indirect costs associated with going bankrupt and/or avoiding a bank-
ruptcy filing.
The problems that come up in financial distress are particularly severe, and the finan-
cial distress costs are thus larger, when the stockholders and the bondholders are different
groups. Until the firm is legally bankrupt, the stockholders control it. They, of course, will
take actions in their own economic interests. Because the stockholders can be wiped out in
a legal bankruptcy, they have a very strong incentive to avoid a bankruptcy filing.
The bondholders, on the other hand, are primarily concerned with protecting the value
of the firm’s assets and will try to take control away from the stockholders. They have a
13.5
direct bankruptcy
costs
The costs that are directly
associated with
bankruptcy, such as legal
and administrative
expenses.
indirect bankruptcy
costs
The costs of avoiding a
bankruptcy filing incurred
by a financially distressed
firm.
financial distress
costs
The direct and indirect
costs associated with
going bankrupt or
experiencing financial
distress.
ros13952_ch13_424-456.indd 437 12/24/18 5:30 PM
438 P A R T 7 Long-Term Financing
strong incentive to seek bankruptcy to protect their interests and keep stockholders from
further dissipating the assets of the firm. The net effect of all this fighting is that a long,
drawn-out, and potentially quite expensive legal battle gets started.
Meanwhile, as the wheels of justice turn in their ponderous way, the assets of the firm
lose value because management is busy trying to avoid bankruptcy instead of running the
business. Normal operations are disrupted, and sales are lost. Valuable employees leave,
potentially fruitful programs are dropped to preserve cash, and otherwise profitable invest-
ments are not taken.
These are all indirect bankruptcy costs, or costs of financial distress. Whether or not
the firm ultimately goes bankrupt, the net effect is a loss of value because the firm chose to
use debt in its capital structure. It is this possibility of loss that limits the amount of debt
that a firm will choose to use.
CONCEPT QUESTIONS
13.5a What are direct bankruptcy costs?
13.5b What are indirect bankruptcy costs?
OPTIMAL CAPITAL STRUCTURE
Our previous two sections have established the basis for an optimal capital structure. A firm
will borrow because the interest tax shield is valuable. At relatively low debt levels, the prob-
ability of bankruptcy and financial distress is low, and the benefit from debt outweighs the
cost. At very high debt levels, the possibility of financial distress is a chronic, ongoing prob-
lem for the firm, so the benefit from debt financing may be more than offset by the financial
distress costs. Based on our discussion, it would appear that an optimal capital structure
exists somewhere in between these extremes.
The Static Theory of Capital Structure
The theory of capital structure that we have outlined is called the static theory of capital
structure. It says that firms borrow up to the point where the tax benefit from an extra dollar
in debt is exactly equal to the cost that comes from the increased probability of financial
distress. We call this the static theory because it assumes that the firm is fixed in terms of its
assets and operations, and it only considers possible changes in the debt-equity ratio.
The static theory is illustrated in Figure 13.5, which plots the value of the firm, VL,
against the amount of debt, D. In Figure 13.5, we have drawn lines corresponding to three
different stories. The first is M&M Proposition I with no taxes. This is the horizontal line
extending from VU, and it indicates that the value of the firm is unaffected by its capital
structure. The second case, M&M Proposition I with corporate taxes, is given by the up-
ward-sloping straight line. These two cases are exactly the same as the ones we previously
illustrated in Figure 13.4.
The third case in Figure 13.5 illustrates our current discussion: The value of the firm
rises to a maximum and then declines beyond that point. This is the picture that we get from
our static theory. The maximum value of the firm, VL*, is reached at a debt level of D*, so
this is the optimal amount of borrowing. Put another way, the firm’s optimal capital struc-
ture is composed of D*/VL* in debt and (1 − D*/VL*) in equity.
The final thing to notice in Figure 13.5 is that the difference between the value of
the firm in our static theory and the M&M value of the firm with taxes is the loss in
13.6
static theory of
capital structure
Theory that a firm borrows
up to the point where the
tax benefit from an extra
dollar in debt is exactly
equal to the cost that
comes from the increased
probability of financial
distress.
ros13952_ch13_424-456.indd 438 12/24/18 5:30 PM
C H A P T E R 1 3 Leverage and Capital Structure 439
value from the possibility of financial distress. Also, the difference between the static
theory value of the firm and the M&M value with no taxes is the gain from leverage, net of
distress costs.
Optimal Capital Structure and the Cost of Capital
As we discussed earlier, the capital structure that maximizes the value of the firm is also the
one that minimizes the cost of capital. With the help of Figure 13.6, we can illustrate this
point and tie together our discussion of capital structure and cost of capital. As we have
seen, there are essentially three cases. We will use the simplest of the three cases as a start-
ing point and then build up to the static theory of capital structure. Along the way, we will
pay particular attention to the connection between capital structure, firm value, and cost of
capital.
Figure 13.6 illustrates the original M&M, no-tax, no-bankruptcy argument in Case I.
This is the most basic case. In the top part, we have plotted the value of the firm, VL, against
total debt, D. When there are no taxes, bankruptcy costs, or other real-world imperfections,
we know that the total value of the firm is not affected by its debt policy, so VL is constant.
The bottom part of Figure 13.6 tells the same story in terms of the cost of capital. Here, the
weighted average cost of capital, WACC, is plotted against the debt-equity ratio, D/E. As
with total firm value, the overall cost of capital is not affected by debt policy in this basic
case, so the WACC is constant.
Next, we consider what happens to the original M&M arguments once taxes are intro-
duced. As Case II illustrates, the firm’s value now critically depends on its debt policy. The
more the firm borrows, the more it is worth. From our earlier discussion, we know that this
The static theory of
capital structure: The
optimal capital
structure and the
value of the firm
Value of
the firm
(VL)
Total debt
(D )
Present value of tax
shield on debt Financial distress
costs
Actual firm value
D *
Optimal amount
of debt
Maximum
firm value VL*
VU = Value of firm
with no debt
VL = VU + TC × D
= Value of firm
with debt
VU
According to the static theory, the gain from the tax shield on debt is offset by financial
distress costs. An optimal capital structure exists that balances the additional gain from
leverage against the added financial distress costs.
FIGURE 13.5
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440 P A R T 7 Long-Term Financing
The capital structure
question
FIGURE 13.6
Value
of the
firm
(VL)
Weighted
average
cost of
capital
(%)
Case II
M&M (with taxes)
Case II
M&M (with taxes)
Case III
Static theory
Case III
Static theory
Case I
M&M (no taxes)
Case I
M&M (no taxes)
Total
debt (D )
Debt-equity ratio
(D/E )
Financial distress
costs
Net gain from leverage
VL*
WACC*
D*
D*/E*
VU
Case II
With corporate taxes and no bankruptcy costs, the value of the firm increases and the
weighted average cost of capital decreases as the amount of debt goes up.
Case III
With corporate taxes and bankruptcy costs, the value of the firm, VL, reaches a maximum
at D*, the optimal amount of borrowing. At the same time, the weighted average cost of
capital, WACC, is minimized at D*/ E*.
Case I
With no taxes or bankruptcy costs, the value of the firm and its weighted average cost of
capital are not affected by capital structures.
ros13952_ch13_424-456.indd 440 12/24/18 5:30 PM
C H A P T E R 1 3 Leverage and Capital Structure 441
happens because interest payments are tax deductible, and the gain in firm value is equal to
the present value of the interest tax shield.
In the bottom part of Figure 13.6, notice how the WACC declines as the firm uses more
and more debt financing. As the firm increases its financial leverage, the cost of equity does
increase, but this increase is more than offset by the tax break associated with debt financ-
ing. As a result, the firm’s overall cost of capital declines.
To finish our story, we include the impact of bankruptcy, or financial distress, costs
to get Case III. As is shown in the top part of Figure 13.6, the value of the firm will not be
as large as we previously indicated. The reason is that the firm’s value is reduced by the
present value of the potential future bankruptcy costs. These costs grow as the firm bor-
rows more and more, and they eventually overwhelm the tax advantage of debt financing.
The optimal capital structure occurs at D*, the point at which the tax saving from an ad-
ditional dollar in debt financing is exactly balanced by the increased bankruptcy costs
associated with the additional borrowing. This is the essence of the static theory of capital
structure.
The bottom part of Figure 13.6 presents the optimal capital structure in terms of the
cost of capital. Corresponding to D*, the optimal debt level, is the optimal debt-to-equity
ratio, D*/E*. At this level of debt financing, the lowest possible weighted average cost of
capital, WACC*, occurs.
Capital Structure: Some Managerial Recommendations
The static model that we have described is not capable of identifying a precise optimal capi-
tal structure, but it does point out two of the more relevant factors: taxes and financial dis-
tress. We can draw some limited conclusions concerning these.
Taxes First of all, the tax benefit from leverage is obviously only important to firms that
are in a tax-paying position. Firms with substantial accumulated losses will get little value
from the interest tax shield. Furthermore, firms that have substantial tax shields from other
sources, such as depreciation, will get less benefit from leverage.
Also, not all firms have the same tax rate. The higher the tax rate, the greater the incen-
tive to borrow.
Financial Distress Firms with a greater risk of experiencing financial distress will
borrow less than firms with a lower risk of financial distress. For example, all other things
being equal, the greater the volatility in EBIT, the less a firm should borrow.
In addition, financial distress is more costly for some firms than for others. The costs
of financial distress depend primarily on the firm’s assets. In particular, financial distress
costs will be determined by how easily ownership of those assets can be transferred.
For example, a firm with mostly tangible assets that can be sold without great loss in
value will have an incentive to borrow more. For firms that rely heavily on intangibles, such
as employee talent or growth opportunities, debt will be less attractive since these assets ef-
fectively cannot be sold.
CONCEPT QUESTIONS
13.6a Can you describe the trade-off that defines the static theory of capital structure?
13.6b What are the important factors in making capital structure decisions?
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442 P A R T 7 Long-Term Financing
OBSERVED CAPITAL STRUCTURES
No two firms have identical capital structures. Nonetheless, there are some regular elements
that we see when we start looking at actual capital structures. We discuss a few of
these next.
The most striking thing we observe about capital structures, particularly in the United
States, is that most corporations seem to have relatively low debt-equity ratios. In fact, most
corporations use much less debt financing than equity financing. To illustrate, Table 13.5
presents median debt ratios and debt-equity ratios for various U.S. industries classified by
SIC code (we discussed such codes in Chapter 3).
In Table 13.5, what is most striking is the wide variation across industries, ranging
from essentially no debt for drug and computer companies to relatively heavy debt us-
age in the airline and cable television industries. Notice that these last two industries
are the only ones for which more debt is used than equity, and most of the other indus-
tries rely far more heavily on equity than debt. This is true even though many of the
companies in these industries pay substantial taxes. Table 13.5 makes it clear that cor-
porations, in general, have not issued debt up to the point that tax shelters have been
completely used up, and we conclude that there must be limits to the amount of debt
corporations can use. Take a look at our nearby Work the Web box for more on actual
capital structures.
Different industries have different operating characteristics in terms of, for example,
EBIT volatility and asset types, and there does appear to be some connection between these
characteristics and capital structure. Our story involving tax savings and financial distress
costs undoubtedly supplies part of the reason, but, to date, there is no fully satisfactory the-
ory that explains these regularities in capital structures.
13.7
Capital structures for
U.S. industries
TABLE 13.5
Industry
Ratio of
Debt to
Total
Capital (%)*
Ratio of
Debt to
Equity (%)
Number of
Companies
SIC
Code
Representative
Companies
Electric utilities 48.54 94.31 33 491 American Electric
Power, Southern Co.
Computer equipment 9.09 10.02 48 357 Apple, Cisco
Paper 27.75 38.40 24 26 Avery Dennison,
Weyerhaeuser
Petroleum refining 32.27 47.65 18 29 Chevron, Sunoco
Airlines 63.92 177.19 10 4512 Delta, Southwest
Pay television 63.56 193.88 5 484 Dish Network, TiVo
Motor vehicles 17.77 21.60 25 371 Ford, Winnebago
Fabric apparel 15.86 18.84 14 23 Guess, Jones Apparel
Department stores 27.40 37.73 8 531 JCPenney, Macy’s
Eating places 23.40 30.54 42 5812 McDonald’s, Papa
John’s
Drugs 7.80 8.46 194 283 Merck, Pfizer
Steel works 19.96 24.95 9 331 Nucor, U.S. Steel
*Debt is the book value of preferred stock and long-term debt, including amounts due in one year. Equity is
the market value of outstanding shares. Total capital is the sum of debt and equity. Median values
are shown.
Source: Cost of Capital, 2010 Yearbook (Chicago: Morningstar, 2010).
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C H A P T E R 1 3 Leverage and Capital Structure 443
QUESTIONS
1. The ratios shown for these companies are based on July 2018 figures. Go to www
.reuters.com and find the current long-term debt-to-equity and total debt-to-equity ra-
tios for both American Electric Power (AEP) and Johnson & Johnson (JNJ). How have
these ratios changed over this time?
2. Go to www.reuters.com and find the long-term debt-to-equity and total debt-to-equity
ratios for Bank of America (BAC), Tesla (TSLA), and Chevron (CVX). Why do you think
these three companies use such differing amounts of debt?
W R K T H E W E B
When it comes to capital structure, all companies (and industries) are not created equal. To illus-trate, we looked up some capital structure information on American Electric Power (AEP) and
Johnson & Johnson (JNJ) using the “Financials” area of www.reuters.com. American Electric Power’s
capital structure looks like this (note that leverage ratios are expressed as percentages on this site):
For every dollar of equity, American Electric Power has long-term debt of $.9421 and total
debt of $1.2005. Compare this result to Johnson & Johnson:
For every dollar of equity, Johnson & Johnson has only $.3805 of long-term debt and total debt
of $.4807. When we examine the industry and sector averages, the differences are again apparent.
The electric utility industry on average has $1.3202 of long-term debt and $1.5669 of total debt for
every dollar of equity. By comparison, the healthcare industry on average has only $.1003 of long-
term debt and $.1407 of total debt for every dollar of equity. Thus, we see that choice of capital
structure is a management decision, but it also clearly is influenced by industry characteristics.
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444 P A R T 7 Long-Term Financing
CONCEPT QUESTIONS
13.7a Do U.S. corporations rely heavily on debt financing?
13.7b What regularities do we observe in capital structures?
A QUICK LOOK AT THE BANKRUPTCY PROCESS
As we have discussed, one of the consequences of using debt is the possibility of financial
distress, which can be defined in several ways:
1. Business failure. This term is usually used to refer to a situation in which a business
has terminated with a loss to creditors, but even an all-equity firm can fail.
2. Legal bankruptcy. Firms or creditors bring petitions to a federal court for bankruptcy.
Bankruptcy is a legal proceeding for liquidating or reorganizing a business.
3. Technical insolvency. Technical insolvency occurs when a firm is unable to meet its
financial obligations.
4. Accounting insolvency. Firms with negative net worth are insolvent on the books. This
happens when the total book liabilities exceed the book value of the total assets.
We now very briefly discuss some of the terms and more relevant issues associated with
bankruptcy and financial distress.
Liquidation and Reorganization
Firms that cannot or choose not to make contractually required payments to creditors have
two basic options: liquidation or reorganization. Liquidation means termination of the firm
as a going concern, and it involves selling off the assets of the firm. The proceeds, net of
selling costs, are distributed to creditors in order of established priority. Reorganization is
the option of keeping the firm a going concern; it often involves issuing new securities to
replace old securities. Liquidation or reorganization is the result of a bankruptcy proceed-
ing. Which occurs depends on whether the firm is worth more “dead or alive.”
Bankruptcy Liquidation Chapter 7 of the Federal Bankruptcy Reform Act of 1978
deals with “straight” liquidation. The following sequence of events is typical:
1. A petition is filed in a federal court. A corporation may file a voluntary petition, or
involuntary petitions may be filed against the corporation by several of its creditors.
2. A trustee-in-bankruptcy is elected by the creditors to take over the assets of the debtor
corporation. The trustee will attempt to liquidate the assets.
3. When the assets are liquidated, after payment of the bankruptcy administration costs,
the proceeds are distributed among the creditors.
4. If any proceeds remain, after expenses and payments to creditors, they are distributed
to the shareholders.
The distribution of the proceeds of the liquidation occurs according to the following
priority list:
1. Administrative expenses associated with the bankruptcy.
2. Other expenses arising after the filing of an involuntary bankruptcy petition but before
the appointment of a trustee.
13.8
bankruptcy
A legal proceeding for
liquidating or reorganizing
a business. Also, the
transfer of some or all of a
firm’s assets to its
creditors.
The SEC has a good
overview of the
bankruptcy process in its
“Investor Reports/
Publications” link of
www.sec.gov.
liquidation
Termination of the firm as
a going concern.
reorganization
Financial restructuring of a
failing firm to attempt to
continue operations as a
going concern.
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C H A P T E R 1 3 Leverage and Capital Structure 445
3. Wages, salaries, and commissions.
4. Contributions to employee benefit plans.
5. Consumer claims.
6. Government tax claims.
7. Payment to unsecured creditors.
8. Payment to preferred stockholders.
9. Payment to common stockholders.
This priority list for liquidation is a reflection of the absolute priority rule (APR). The higher
a claim is on this list, the more likely it is to be paid. In many of these categories, there are
various limitations and qualifications that we omit for the sake of brevity.
Two qualifications to this list are in order. The first concerns secured creditors. Such
creditors are entitled to the proceeds from the sale of the security and are outside this order-
ing. However, if the secured property is liquidated and provides cash insufficient to cover
the amount owed, the secured creditors join with unsecured creditors in dividing the re-
maining liquidated value. In contrast, if the secured property is liquidated for proceeds
greater than the secured claim, the net proceeds are used to pay unsecured creditors and
others. The second qualification to the APR is that, in reality, what happens, and who gets
what in the event of bankruptcy, is subject to much negotiation, and, as a result, the APR is
frequently not followed.
Bankruptcy Reorganization Corporate reorganization takes place under Chap ter 11
of the Federal Bankruptcy Reform Act of 1978. The general objective of a proceeding under
Chapter 11 is to plan to restructure the corporation with some provision for repayment of
creditors. A typical sequence of events follows:
1. A voluntary petition can be filed by the corporation, or an involuntary petition can be
filed by creditors.
2. A federal judge either approves or denies the petition. If the petition is approved, a
time for filing proofs of claims is set.
3. In most cases, the corporation (the “debtor in possession”) continues to run the
business.
4. The corporation (and, in certain cases, the creditors) submits a reorganization plan.
5. Creditors and shareholders are divided into classes. A class of creditors accepts the
plan if a majority of the class agrees to the plan.
6. After its acceptance by creditors, the plan is confirmed by the court.
7. Payments in cash, property, and securities are made to creditors and shareholders.
The plan may provide for the issuance of new securities.
8. For some fixed length of time, the firm operates according to the provisions of the
reorganization plan.
The corporation may wish to allow the old stockholders to retain some participation in
the firm. Needless to say, this may involve some protest by the holders of unsecured
debt.
To give you some idea of the costs associated with a bankruptcy, consider the case
of Lehman Brothers, which filed for bankruptcy in September 2008. The company
wanted to reorganize through the bankruptcy process, but complications arose almost
from the bankruptcy filing date. Because of the complexity of many of Lehman’s assets,
unwinding and selling them was difficult and time-consuming. Eventually, Lehman
absolute priority
rule (APR)
The rule establishing
priority of claims in
liquidation.
The American Bankruptcy
Institute provides
extensive information
on bankruptcy. See www
.abi.org.
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446 P A R T 7 Long-Term Financing
exited bankruptcy about three and a half years later in March 2012. Some of the firms
that were involved in the Lehman bankruptcy were Alvarez & Marsal, which billed about
$512 million in fees; Weil, Gotshal, & Manges, which billed $383 million; and Milbank,
Tweed, Hadley, & McCloy, which billed $133 million. In all, Lehman’s bankruptcy costs
were $2.2 billion in fees. The next-largest bankruptcy fees appear to have been paid to
those involved in energy giant Enron’s bankruptcy. The fees in that case reached a mere
$1 billion.
So-called prepackaged bankruptcies are a relatively new phenomenon. What happens is
that the corporation secures the necessary approval of a bankruptcy plan from a majority of
its creditors first, and then it files for bankruptcy. As a result, the company enters bank-
ruptcy and reemerges almost immediately.
In some cases, the bankruptcy procedure is needed to invoke the “cram-down” power of
the bankruptcy court. Under certain circumstances, a class of creditors can be forced to
accept a bankruptcy plan even if they vote not to approve it, hence the remarkably apt de-
scription “cram down.”
In 2005, Congress passed the most significant overhaul of U.S. bankruptcy laws in the
last 25 years, the Bankruptcy Abuse Prevention and Consumer Protection Act of 2005
(BAPCPA). Most of the changes were aimed at individual debtors, but corporations
also were affected. Before BAPCPA, a bankrupt company had the exclusive right to submit
reorganization plans to the bankruptcy court. It has been argued that this exclusivity is one
reason some companies have remained in bankruptcy for so long. Under the new law, after
18 months, creditors can submit their own plan for the court’s consideration. This change is
likely to speed up bankruptcies and also lead to more “prepacks” (to learn about prepacks,
see our nearby Finance Matters box).
One controversial change made by BAPCPA has to do with so-called key employee re-
tention plans, or KERPs. Strange as it may sound, bankrupt companies routinely give bonus
payments to executives, even though the executives may be the same ones who led the com-
pany into bankruptcy in the first place. Such bonuses are intended to keep valuable employ-
ees from moving to more successful firms, but critics have argued they often are abused.
The new law permits KERPs only if the employee in question actually has a job offer from
another company.
Recently, Section 363 of the bankruptcy code has been in the news. In a traditional
Chapter 11 filing, the bankruptcy plan is described to creditors and shareholders in a pro-
spectus-like disclosure. The plan then must be approved by a vote involving the interested
parties. A Section 363 bankruptcy is more like an auction. An initial bidder, known as a
stalking horse, bids on all or part of the bankrupt company’s assets. Other bidders are then
invited into the process to determine the highest bid for the company’s assets. The main
advantage of a Section 363 bankruptcy is speed. Because a traditional bankruptcy requires
the approval of interested parties, it is not uncommon for the process to take several years,
while a Section 363 bankruptcy is generally much quicker. For example, in the middle of
2009, both General Motors and Chrysler sped through the bankruptcy process in less than
45 days with the help of Section 363 sales.
Financial Management and the Bankruptcy Process
It may seem a little odd, but the right to go bankrupt is very valuable. There are several
reasons this is true. First of all, from an operational standpoint, when a firm files for bank-
ruptcy, there is an immediate “stay” on creditors, usually meaning that payments to
Get the latest on
bankruptcy at www
.bankruptcydata.com.
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Bankruptcy, “Prepack” Style
On March 21, 2018, Southeastern Grocers, owner of Winn-Dixie and Bi-Lo grocery stores, filed for Chapter 11 reorga-
nization under the U.S. bankruptcy code. A firm in this situation
reasonably could be expected to spend a year or more in bank-
ruptcy. Not so with Southeastern Grocers. The company exited
bankruptcy in May 2018, about two months later. In this case,
the company’s debt was reduced to $600 million, and creditors
were given an equity stake in the company. Even though South-
eastern Grocers had a brief stay in bankruptcy, the all-time
record belongs to Blue Bird, maker of the iconic yellow school
buses. Blue Bird’s stay in bankruptcy was one day!
Firms typically file for bankruptcy to seek protection
from their creditors, essentially admitting that they cannot
meet their financial obligations as they are then structured.
Once in bankruptcy, the firm attempts to reorganize its op-
erations and finances so that it can survive. A key to this
process is that most of the creditors ultimately must give
their approval to the restructuring plan. The time a firm
spends in Chapter 11 depends on many things, but it usually
depends most on the time it takes to get creditors to agree
to a plan of reorganization.
Blue Bird was able to expedite its bankruptcy by filing a
presolicited, or prepackaged, bankruptcy, often called a pre-
pack. The idea is simple. Before filing for bankruptcy, the
firm approaches its creditors with a plan for reorganization.
The two sides negotiate a settlement and agree on the de-
tails of how the firm’s finances will be restructured. Then, the
firm puts together the necessary paperwork for the bank-
ruptcy court before filing for bankruptcy. A filing is a prepack
if the firm essentially walks into court and, at the same time,
files a reorganization plan complete with the documentation
of its creditors’ approval, which is exactly what Blue Bird did.
The key to the prepackaged reorganization process is
that both sides have something to gain and something to
lose. If bankruptcy is imminent, it may make sense for the
creditors to expedite the process even though they are
likely to take a financial loss in the restructuring. Blue Bird’s
bankruptcy was relatively painless for most of its creditors.
Several different classes of creditors were involved. Bank
loans were converted into senior secured notes, and senior
bondholders exchanged their bonds for new bonds with the
same face value and terms. Of course, the old stockholders
received nothing, and, in fact, had their shares canceled.
For a firm, operating in bankruptcy can be a difficult
process. The bankruptcy court typically has a great deal of
oversight over the firm’s day-to-day operations, and putting
together a reorganization plan to emerge from bankruptcy
can be a tremendous drain on management time, time that
would be better spent making the firm profitable again. Also,
news that a firm is in bankruptcy can make skittish custom-
ers turn to competitors, endangering the future health of the
firm. A prepack can’t completely eliminate these problems,
but by speeding up the bankruptcy process, it can reduce
the headaches involved.
FINANCE MATTERS
447
creditors will cease, and creditors will have to await the outcome of the bankruptcy process
to find out if and how much they will be paid. This stay gives the firm time to evaluate its
options, and it prevents what is usually termed a “race to the courthouse steps” by creditors
and others.
Beyond this, some bankruptcy filings are actually strategic actions intended to improve
a firm’s competitive position, and firms have filed for bankruptcy even though they were not
insolvent at the time. Probably the most famous example is Continental Airlines. In 1983,
following deregulation of the airline industry, Continental found itself competing with newly
established airlines that had much lower labor costs. In response, Continental filed for reor-
ganization under Chapter 11 even though it was not insolvent.
Continental argued that, based on pro forma data, it would become insolvent in the
future, and a reorganization was therefore necessary. By filing for bankruptcy, Continental
was able to terminate its existing labor agreements, lay off large numbers of workers, and
slash wages for the remaining employees. In other words, at least in the eyes of critics,
Continental essentially used the bankruptcy process as a vehicle for reducing labor costs.
Congress has subsequently modified bankruptcy laws to make it more difficult, though not
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448 P A R T 7 Long-Term Financing
impossible, for companies to abrogate a labor contract through the bankruptcy process. For
example, Delta Air Lines filed for bankruptcy in 2005, in part to renegotiate the contracts
with its union employees.
Other famous examples of strategic bankruptcies exist. For example, Manville (then
known as Johns-Manville) and Dow Corning filed for bankruptcies because of expected fu-
ture losses resulting from litigations associated with asbestos and silicone breast implants,
respectively. Similarly, in the then-largest-ever bankruptcy, Texaco filed in 1987 after Penn-
zoil was awarded a $10.3 billion judgment against the company. Texaco later settled for $3.5
billion and emerged from bankruptcy.
The 2008 recession shows how an economic downturn can result in bankruptcy for le-
vered firms. Table 13.6 contains the ten largest bankruptcy filings in the United States from
2008 through mid-2018. As you can see, seven of the ten occurred immediately after the re-
cession. At the top of the list, the Lehman Brothers collapse was the largest in U.S. history,
but the 2003 bankruptcy filing of Italian dairy company Parmalat may have topped them all
in terms of relative importance. This company, by itself, represented 1.5 percent of the Ital-
ian gross national product!
Agreements to Avoid Bankruptcy
When a firm defaults on an obligation, it can avoid a bankruptcy filing. Because the legal
process of bankruptcy can be lengthy and expensive, it is often in everyone’s best interest to
devise a “workout” that avoids a bankruptcy filing. Much of the time, creditors can work
with the management of a company that has defaulted on a loan contract. Voluntary ar-
rangements to restructure, or “reschedule,” the company’s debt can be and often are made.
This may involve extension, which postpones the date of payment, or composition, which al-
lows a reduced payment.
CONCEPT QUESTIONS
13.8a What is the APR (in connection with bankruptcy proceedings)?
13.8b What is the difference between liquidation and reorganization?
Company Date of Filing Liabilities ($ millions)
Lehman Brothers Holdings, Inc. September 15, 2008 $613,000
General Motors Corp. June 1, 2009 172,810
CIT Group, Inc. November 1, 2009 64,901
Chrysler, LLC April 30, 2009 55,200
Energy Future Holdings Corp. April 29, 2014 49,701
MF Global Holdings Ltd. October 31, 2011 39,684
AMR Corp. November 29, 2011 29,552
General Growth Properties, Inc. April 22, 2009 27,294
Thornburg Mortgage, Inc. May 1, 2009 24,700
Charter Ccommunications, Inc. March 27, 2009 24,186
Ten largest U.S.
bankruptcy filings
TABLE 13.6
Source: Edward I. Altman, NYU Salomon Center, Stern School of Business.
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C H A P T E R 1 3 Leverage and Capital Structure 449
SUMMARY AND CONCLUSIONS
The ideal mixture of debt and equity for a firm—its optimal capital structure—is the one that
maximizes the value of the firm and minimizes the overall cost of capital. If we ignore taxes,
financial distress costs, and any other imperfections, we find that there is no ideal mixture.
Under these circumstances, the firm’s capital structure is irrelevant.
If we consider the effect of corporate taxes, we find that capital structure matters a
great deal. This conclusion is based on the fact that interest is tax deductible and thus gen-
erates a valuable tax shield. Unfortunately, we also find that the optimal capital structure is
100 percent debt, which is not something we observe in healthy firms.
We next introduced costs associated with bankruptcy, or, more generally, financial dis-
tress. These costs reduce the attractiveness of debt financing. We concluded that an optimal
capital structure exists when the net tax saving from an additional dollar in interest just
equals the increase in expected financial distress costs. This is the essence of the static the-
ory of capital structure.
When we examine actual capital structures, we find two regularities. First, firms in
the United States typically do not use great amounts of debt, but they pay substantial
taxes. This suggests that there is a limit to the use of debt financing to generate tax shields.
Second, there is wide variation in the use of debt across industries, suggesting that the
nature of a firm’s assets and operations is an important determinant of its capital
structure.
POP QUIZ!
Can you answer the following questions? If your class is using Connect, log on to
SmartBook to see if you know the answers to these and other questions, check out
the study tools, and find out what topics require additional practice!
Section 13.3 What assumptions are necessary for M&M Proposition I to hold?
Section 13.5 What are indirect costs of bankruptcy?
Section 13.6 The static theory of capital structure is based on the theory that firms
use leverage up to the point where the marginal value of what two things are
equal?
Section 13.7 What would generally receive the lowest priority when the assets of a
Chapter 7 bankruptcy firm are distributed?
CHAPTER REVIEW AND SELF-TEST PROBLEMS
13.1 EBIT and EPS Suppose the GNR Corporation has decided in favor of a capital
restructuring that involves increasing its existing $5 million in debt to $25 million. The
interest rate on the debt is 12 percent and is not expected to change. The firm currently
has 1 million shares outstanding, and the price per share is $40. If the restructuring is
expected to increase the ROE, what is the minimum level for EBIT that GNR’s
management must be expecting? Ignore taxes in your answer. (See Problem 4.)
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450 P A R T 7 Long-Term Financing
13.2 M&M Proposition II (no taxes) The Pro Bono Corporation has a WACC of 20
percent. Its cost of debt is 12 percent. If Pro Bono’s debt-equity ratio is 2, what is its
cost of equity capital? Ignore taxes in your answer. (See Problem 10.)
13.3 M&M Proposition I (with corporate taxes) Suppose TransGlobal Co. currently has
no debt and its equity is worth $20,000. If the corporate tax rate is 21 percent, what
will the value of the firm be if TransGlobal borrows $6,000 and uses the proceeds to
buy up stock? (See Problem 14.)
■ Answers to Chapter Review and Self-Test Problems
13.1 To answer, we can calculate the break-even EBIT. At any EBIT above this, the
increased financial leverage will increase EPS. Under the old capital structure, the
interest bill is $5 million × .12 = $600,000. There are 1 million shares of stock, so,
ignoring taxes, EPS is (EBIT − $600,000)/1 million.
Under the new capital structure, the interest expense will be $25 million × .12 =
$3 million. Furthermore, the debt rises by $20 million. This amount is sufficient to
repurchase $20 million/40 = 500,000 shares of stock, leaving 500,000 outstanding.
EPS is thus (EBIT − $3 million)/500,000.
Now that we know how to calculate EPS under both scenarios, we set the two ex-
pressions for EPS equal to each other and solve for the break-even EBIT:
(EBIT − $600,000)/1 million = (EBIT − $3 million)/500,000
EBIT − $600,000 = 2 × (EBIT − $3 million)
EBIT = $5,400,000
Verify that, in either case, EPS is $4.80 when EBIT is $5.4 million.
13.2 According to M&M Proposition II (no taxes), the cost of equity is:
RE = RA + (RA − RD) × (D/E)
= 20% + (20% − 12%) × 2
= 36%
13.3 After the debt issue, TransGlobal will be worth the original $20,000 plus the present
value of the tax shield. According to M&M Proposition I with taxes, the present
value of the tax shield is TC × D, or .21 × $6,000 = $1,260, so the firm is worth
$20,000 + 1,260 = $21,260.
CRITICAL THINKING AND CONCEPTS REVIEW
LO 1 13.1 Business Risk versus Financial Risk Explain what is meant by business
and financial risk. Suppose Firm A has greater business risk than Firm B.
Is it true that Firm A also has a higher cost of equity capital? Explain.
LO 1 13.2 M&M Propositions How would you answer in the following debate?
Q: Isn’t it true that the riskiness of a firm’s equity will rise if the firm
increases its use of debt financing?
A: Yes, that’s the essence of M&M Proposition II.
Q: And isn’t it true that, as a firm increases its use of borrowing, the
likelihood of default increases, which increases the risk of the firm’s debt?
A: Yes.
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C H A P T E R 1 3 Leverage and Capital Structure 451
Q: In other words, increased borrowing increases the risk of the equity and
the debt?
A: That’s right.
Q: Well, given that the firm uses only debt and equity financing, and given
that the risk of both is increased by increased borrowing, does it not
follow that increasing debt increases the overall risk of the firm and
therefore decreases the value of the firm?
A: ??
LO 1 13.3 Optimal Capital Structure Is there an easily identifiable debt-equity ratio
that will maximize the value of a firm? Why or why not?
LO 1 13.4 Observed Capital Structures Refer to the observed capital structures
given in Table 13.5 of the text. What do you notice about the types of
industries with respect to their average debt-equity ratios? Are certain types
of industries more likely to be highly leveraged than others? What are some
possible reasons for this observed segmentation? Do the operating results
and tax history of the firms play a role? How about their future earnings
prospects? Explain.
LO 1 13.5 Financial Leverage Why is the use of debt financing referred to as using
financial “leverage”?
LO 1 13.6 Homemade Leverage What is homemade leverage?
LO 3 13.7 Bankruptcy and Corporate Ethics As mentioned in the text, some firms
have filed for bankruptcy because of actual or likely litigation-related losses.
Is this a proper use of the bankruptcy process?
LO 3 13.8 Bankruptcy and Corporate Ethics Firms sometimes use the threat of a
bankruptcy filing to force creditors to renegotiate terms. Critics argue that
in such cases, the firm is using bankruptcy laws “as a sword rather than a
shield.” Is this an ethical tactic?
LO 3 13.9 Bankruptcy and Corporate Ethics As mentioned in the text, Continental
Airlines filed for bankruptcy, at least in part as a means of reducing labor
costs. Whether this move was ethical, or proper, was hotly debated. Give
both sides of the argument.
LO 1 13.10 Capital Structure Goal What is the basic goal of financial management
with regard to capital structure?
BASIC (Questions 1–13)
1. EBIT and Leverage Minion, Inc., has no debt outstanding and a total
market value of $211,875. Earnings before interest and taxes, EBIT, are
projected to be $14,300 if economic conditions are normal. If there is strong
expansion in the economy, then EBIT will be 20 percent higher. If there is a
recession, then EBIT will be 35 percent lower. The company is considering
a $33,900 debt issue with an interest rate of 6 percent. The proceeds will
LO 1
QUESTIONS AND PROBLEMS
Select problems are available in McGraw-Hill Connect. Please see the pack-
aging options section of the Preface for more information.
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452 P A R T 7 Long-Term Financing
be used to repurchase shares of stock. There are currently 7,500 shares
outstanding. Ignore taxes for this problem.
a. Calculate earnings per share, EPS, under each of the three economic
scenarios before any debt is issued. Also, calculate the percentage
changes in EPS when the economy expands or enters a recession.
b. Repeat part (a) assuming that the company goes through with
recapitalization. What do you observe? Assume the stock price remains
constant.
2. EBIT, Taxes, and Leverage Repeat parts (a) and (b) in Problem 1 assuming
the company has a tax rate of 21 percent.
3. ROE and Leverage Suppose the company in Problem 1 has a market-to-
book ratio of 1.0 and the stock price remains constant.
a. Calculate return on equity, ROE, under each of the three economic
scenarios before any debt is issued. Also, calculate the percentage changes
in ROE for economic expansion and recession, assuming no taxes.
b. Repeat part (a) assuming the firm goes through with the proposed
recapitalization.
c. Repeat parts (a) and (b) of this problem assuming the firm has a tax
rate of 21 percent.
4. Break-Even EBIT Trapper Corporation is comparing two different capital
structures, an all-equity plan (Plan I) and a levered plan (Plan II). Under
Plan I, the company would have 320,000 shares of stock outstanding. Under
Plan II, there would be 240,000 shares of stock outstanding and $2,272,000
in debt outstanding. The interest rate on the debt is 10 percent, and there are
no taxes.
a. If EBIT is $700,000, which plan will result in the higher EPS?
b. If EBIT is $950,000, which plan will result in the higher EPS?
c. What is the break-even EBIT?
5. M&M and Stock Value In Problem 4, use M&M Proposition I to find the
price per share of equity under each of the two proposed plans. What is the
value of the firm?
6. Break-Even EBIT and Leverage Honeycutt Co. is comparing two different
capital structures. Plan I would result in 12,700 shares of stock and $109,250
in debt. Plan II would result in 9,800 shares of stock and $247,000 in debt.
The interest rate on the debt is 10 percent.
a. Ignoring taxes, compare both of these plans to an all-equity plan
assuming that EBIT will be $79,000. The all-equity plan would result in
15,000 shares of stock outstanding. Which of the three plans has the
highest EPS? The lowest?
b. In part (a), what are the break-even levels of EBIT for each plan as
compared to that for an all-equity plan? Is one higher than the other? Why?
c. Ignoring taxes, when will EPS be identical for Plans I and II?
d. Repeat parts (a), (b), and (c) assuming that the corporate tax rate is
21 percent. Are the break-even levels of EBIT different from before?
Why or why not?
LO 2
LO 1
LO 2
LO 1
LO 1
LO 1
LO 2
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C H A P T E R 1 3 Leverage and Capital Structure 453
7. Leverage and Stock Value Ignoring taxes in Problem 6, what is the price
per share of equity under Plan I? Plan II? What principle is illustrated by
your answers?
8. Homemade Leverage FCOJ, Inc., a prominent consumer products firm,
is debating whether or not to convert its all-equity capital structure to
one that is 30 percent debt. Currently, there are 7,400 shares outstanding
and the price per share is $55. EBIT is expected to remain at $20,900 per
year forever. The interest rate on new debt is 8 percent, and there are no
taxes.
a. Melanie, a shareholder of the firm, owns 100 shares of stock. What is
her cash flow under the current capital structure, assuming the firm has
a dividend payout rate of 100 percent?
b. What will Melanie’s cash flow be under the proposed capital structure
of the firm? Assume that she keeps all 100 of her shares.
c. Suppose FCOJ does convert, but Melanie prefers the current all-equity
capital structure. Show how she could unlever her shares of stock to
recreate the original capital structure.
d. Using your answer to part (c), explain why FCOJ’s choice of capital
structure is irrelevant.
9. Homemade Leverage Pagemaster Enterprises is considering a change from
its current capital structure. The company currently has an all-equity capital
structure and is considering a capital structure with 25 percent debt. There
are currently 8,100 shares outstanding at a price per share of $50. EBIT is
expected to remain constant at $44,000. The interest rate on new debt is 7
percent and there are no taxes.
a. Rebecca owns $17,000 worth of stock in the company. If the firm has a
100 percent payout, what is her cash flow?
b. What would her cash flow be under the new capital structure assuming
that she keeps all of her shares?
c. Suppose the company does convert to the new capital structure. Show
how Rebecca can maintain her current cash flow.
d. Under your answer to part (c), explain why the company’s choice of
capital structure is irrelevant.
10. Calculating WACC Brown Industries has a debt-equity ratio of 1.5. Its
WACC is 9.6 percent, and its cost of debt is 5.7 percent. There is no
corporate tax.
a. What is the company’s cost of equity capital?
b. What would the cost of equity be if the debt-equity ratio were 2.0? What
if it were .5? What if it were zero?
11. Calculating WACC Irving Corp. has no debt but can borrow at 6.4 percent.
The firm’s WACC is currently 10.9 percent, and there is no corporate tax.
a. What is the company’s cost of equity?
b. If the firm converts to 30 percent debt, what will its cost of equity be?
c. If the firm converts to 60 percent debt, what will its cost of equity be?
d. What is the company’s WACC in part (b)? In part (c)?
LO 1
LO 1
LO 1
LO 1
LO 1
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454 P A R T 7 Long-Term Financing
12. M&M and Taxes Tatum can borrow at 6.7 percent. The company currently
has no debt, and the cost of equity is 12.9 percent. The current value of the
firm is $595,000. What will the value be if the company borrows $310,000
and uses the proceeds to repurchase shares? The corporate tax rate is
21 percent.
13. Interest Tax Shield Hayward Co. has a 22 percent tax rate. Its total interest
payment for the year just ended was $14.3 million. What is the interest tax
shield? How do you interpret this amount?
INTERMEDIATE (Questions 14–16)
14. M&M Bird Enterprises has no debt. Its current total value is $47 million.
Ignoring taxes, what will the company’s value be if it sells $18.4 million in
debt? Suppose now that the company’s tax rate is 23 percent. What will its
overall value be if it sells $18.4 million in debt? Assume debt proceeds are
used to repurchase equity.
15. M&M In the previous question, what is the debt-equity ratio in both cases?
16. M&M Horford Co. has no debt. Its cost of capital is 8.9 percent. Suppose
the company converts to a debt-equity ratio of 1.0. The interest rate on the
debt is 5.7 percent. Ignoring taxes, what is the company’s new cost of equity?
What is its new WACC?
CHALLENGE (Questions 17–20)
17. Firm Value Calvert Corporation expects an EBIT of $22,300 every year
forever. The company currently has no debt, and its cost of equity is 15
percent.
a. What is the current value of the company?
b. Suppose the company can borrow at 10 percent. If the corporate tax rate
is 21 percent, what will the value of the firm be if the company takes on
debt equal to 50 percent of its unlevered value? What if it takes on debt
equal to 100 percent of its unlevered value?
c. What will the value of the firm be if the company takes on debt equal to
50 percent of its levered value? What if the company takes on debt equal
to 100 percent of its levered value?
18. Firm Value What is the cost of capital for a firm that is 100 percent debt
financed? What is the value of the firm?
19. Cost of Equity and Leverage Assuming a world of corporate taxes only,
show that the cost of equity, RE, is as follows: RE = RU + (RU − RD) × (D/E)
× (1 − TC).
20. Business and Financial Risk Assume a firm’s debt is risk-free, so that the
cost of debt equals the risk-free rate, Rf. Define βA as the firm’s asset beta—
that is, the systematic risk of the firm’s assets. Define βE to be the beta of
the firm’s equity. Use the capital asset pricing model (CAPM) along with
M&M Proposition II to show that βE = βA × (1 + D/E), where D/E is the
debt-equity ratio. Assume the tax rate is zero.
LO 2
LO 2
LO 1
LO 1
LO 1
LO 2
LO 2
LO 2
LO 2
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C H A P T E R 1 3 Leverage and Capital Structure 455
WHAT’S ON
THE WEB?
13.1 Capital Structure Go to www.reuters.com and enter the ticker symbol AMGN for
Amgen, a biotechnology company. Find the long-term debt-equity and total debt-equity
ratios. How does Amgen compare to the industry, sector, and S&P 500 in these areas?
Now answer the same question for Edison International (EIX), the parent company of
Southern California Edison, a utility company. How do the capital structures of Amgen
and Edison International compare? Can you think of possible explanations for the
difference between these two companies?
13.2 Capital Structure Go to finance.yahoo.com and find the stock screener. Use the
stock screener to answer the following questions. How many companies have debt-equity
ratios greater than 2? Greater than 5? Greater than 10? What company has the highest
debt-equity ratio? What is the ratio? Now find how many companies have a negative
debt-equity ratio. What is the lowest debt-equity ratio? What does it mean if a company
has a negative debt-equity ratio?
EXCEL MASTER IT! PROBLEM
The TL Corporation currently has no debt outstanding. Josh Culberson, the CFO, is consid-
ering restructuring the company by issuing debt and using the proceeds to repurchase out-
standing equity. The company’s assets are worth $40 million, the stock price is $25 per
share, and there are 1,600,000 shares outstanding. In the expected state of the economy,
EBIT is expected to be $3 million. If there is a recession, EBIT would fall to $1.8 million; in
an expansion, EBIT would increase to $4.3 million. If the company issues debt, it will issue
a combination of short-term debt and long-term debt. The ratio of short-term debt to long-
term debt will be .20. The short-term debt will have an interest rate of 3 percent and the
long-term debt will have an interest rate of 8 percent.
a. On the applicable worksheet, fill in the values in each table. For the debt-equity ratio,
create a spinner that changes the debt-equity ratio. The resulting debt-equity ratio
should range from 0 to 10 at increments of .1.
b. Graph the EBIT and EPS for the TL Corporation on the same graph using a scatter
plot.
c. What is the break-even EBIT between the current capital structure and the new capital
structure?
d. To illustrate the new capital structure, you would like to create a pie chart. One type
of pie chart that is available is the pie-in-pie chart. Using the pie-in-pie chart, graph the
equity and total debt in the main pie chart and the short-term debt and long-term debt
in the secondary pie chart. Note, if you right-click on a data series in the chart and
select Format Data Series, the Series Options will permit you to display the series by a
customized choice. In the customization, you can select which data series you want
displayed in the primary pie chart and the secondary pie chart.
coverage online
Excel
Master
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456 P A R T 7 Long-Term Financing
Stephenson’s annual pretax earnings by $11 million in
perpetuity. Kim Weyand, the company’s new CFO, has
been put in charge of the project. Kim has determined
that the company’s current cost of capital is 12.5 percent.
She feels that the company would be more valuable if it
included debt in its capital structure, so she is evaluating
whether the company should issue debt to entirely fi-
nance the project. Based on some conversations with
investment banks, she thinks that the company can issue
bonds at par value with a coupon rate of 8 percent. From
her analysis, she also believes that a capital structure in
the range of 70 percent equity/30 percent debt would be
optimal. If the company goes beyond 30 percent debt, its
bonds would carry a lower rating and a much higher cou-
pon because the possibility of financial distress and the
associated costs would rise sharply. Stephenson has a
21 percent corporate tax rate (state and federal).
Stephenson Real Estate Company was founded 25 years ago by the current CEO, Robert Stephenson.
The company purchases real estate, including land and
buildings, and rents the property to tenants. The com-
pany has shown a profit every year for the past 18 years,
and the shareholders are satisfied with the company’s
management. Prior to founding Stephenson Real Estate,
Robert was the founder and CEO of a failed alpaca farm-
ing operation. The resulting bankruptcy made him ex-
tremely averse to debt financing. As a result, the
company is entirely equity financed, with 8.5 million
shares of common stock outstanding. The stock cur-
rently trades at $44.50 per share.
Stephenson is evaluating a plan to purchase a huge
tract of land in the southeastern United States for
$50 million. The land will subsequently be leased to ten-
ant farmers. This purchase is expected to increase
CHAPTER CASE
Stephenson Real Estate Recapitalization
1. If Stephenson wishes to maximize its total market
value, would you recommend that it issue debt or
equity to finance the land purchase? Explain.
2. Construct Stephenson’s market value balance
sheet before it announces the purchase.
3. Suppose Stephenson decides to issue equity to
finance the purchase.
a. What is the net present value of the project?
b. Construct Stephenson’s market value
balance sheet after it announces that the
firm will finance the purchase using equity.
What would be the new price per share of
the firm’s stock? How many shares will
Stephenson need to issue to finance the
purchase?
c. Construct Stephenson’s market value
balance sheet after the equity issue but
before the purchase has been made.
How many shares of common stock
does Stephenson have outstanding?
What is the price per share of the firm’s
stock?
d. Construct Stephenson’s market value
balance sheet after the purchase has been
made.
4. Suppose Stephenson decides to issue debt to fi-
nance the purchase.
a. What will the market value of the
Stephenson Company be if the purchase is
financed with debt?
b. Construct Stephenson’s market value
balance sheet after both the debt issue and
the land purchase. What is the price per
share of the firm’s stock?
5. Which method of financing maximizes the per-
share stock price of Stephenson’s equity?
Q U E S T I O N S
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457
On May 1, 2018, Apple announced a broad plan to reward stockholders for the recent success of the firm’s business.
Under the plan, Apple would (1) boost its annual dividend by 16 per-
cent, from 63 cents per share to 73 cents per share, and (2) repur-
chase about $100 billion of its common stock. Investors cheered,
bidding up the stock price by about 2.3 percent on the announce-
ment. Why were investors pleased? To find out, this chapter ex-
plores these actions and their implications for shareholders.
This chapter is about dividend policy. In Chapter 7, we saw that
the value of a share of stock depends on all the future dividends
that will be paid to shareholders. In that analysis, we took the future
stream of dividends as given. What we now examine is how corpo-
rations decide on the size and timing of dividend payments. What
we would like to find out is how to establish an optimal dividend policy, meaning a dividend
policy that maximizes the stock price. What we discover, among other things, is that it is not
at all clear how to do this, or even if there is such a thing as an optimal dividend policy!
Dividends and
Dividend Policy14
LEARNING OBJECTIVES
After studying this chapter, you should
be able to:
LO 1 Discuss dividend types and how
dividends are paid.
LO 2 Explain the issues surrounding
dividend policy decisions.
LO 3 Differentiate between cash and
stock dividends.
LO 4 Explain why share repurchases are
an alternative to dividends.
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Dividend policy is an important subject in corporate finance, and dividends are a major cash outlay for many corporations. At first glance, it may seem obvious that a firm
would always want to give as much as possible back to its shareholders by paying dividends.
It might seem equally obvious, however, that a firm always can invest the money for its
shareholders instead of paying it out. The heart of the dividend policy question is just this:
Should the firm pay out money to its shareholders, or should the firm take that money and
invest it for its shareholders?
It may seem surprising, but much research and economic logic suggest that dividend
policy doesn’t matter. In fact, it turns out that the dividend policy issue is much like the
capital structure question. The important elements are not difficult to identify, but the inter-
actions between those elements are complex, and no easy answer exists.
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458 P A R T 7 Long-Term Financing
Dividend policy is controversial. Many implausible reasons are given for why dividend
policy might be important, and many of the claims made about dividend policy are eco-
nomically illogical. Even so, in the real world of corporate finance, determining the most
appropriate dividend policy is considered an important issue. It could be that financial
managers who worry about dividend policy are wasting time, but it also could be true that
we are missing something important in our discussions.
In part, all discussions of dividends are plagued by the “two-handed lawyer” problem.
President Truman, while discussing the legal implications of a possible presidential deci-
sion, asked his staff to set up a meeting with a lawyer. Supposedly, Mr. Truman said, “But I
don’t want one of those two-handed lawyers.” When asked what a two-handed lawyer was,
he replied, “You know, a lawyer who says, ‘On the one hand I recommend you do so and so
because of the following reasons, but on the other hand I recommend that you don’t do it
because of these other reasons.’”
Unfortunately, any sensible treatment of dividend policy will appear to have been writ-
ten by a two-handed lawyer (or, in fairness, several two-handed financial economists). On
the one hand, there are many good reasons for corporations to pay high dividends, but, on
the other hand, there are also many good reasons to pay low dividends.
We cover three broad topics that relate to dividends and dividend policy in this chapter.
First, we describe the various kinds of dividends and how dividends are paid. Second, we
consider an idealized case in which dividend policy doesn’t matter. We then discuss the limi-
tations of this case and present some real-world arguments for both high- and low-dividend
payouts. Finally, we conclude the chapter by looking at some strategies that corporations
might employ to implement a dividend policy, and we discuss share repurchases as an alter-
native to dividends.
CASH DIVIDENDS AND DIVIDEND PAYMENT
The term dividend usually refers to cash paid out of earnings. If a payment is made from
sources other than current or accumulated retained earnings, the term distribution, rather
than dividend, is used. However, it is acceptable to refer to a distribution from earnings as a
dividend and a distribution from capital as a liquidating dividend. More generally, any direct
payment by the corporation to the shareholders may be considered a dividend or a part of
dividend policy.
Dividends come in several different forms. The basic types of cash dividends are:
1. Regular cash dividends
2. Extra dividends
3. Special dividends
4. Liquidating dividends
Later in the chapter, we discuss dividends paid in stock instead of cash, and we also con-
sider an alternative to cash dividends, a stock repurchase.
Cash Dividends
The most common type of dividend is a cash dividend. Commonly, public companies pay
regular cash dividends four times a year. As the name suggests, these are cash payments made
directly to shareholders, and they are made in the regular course of business. In other words,
management sees nothing unusual about the dividend and no reason why it won’t be
continued.
14.1
dividend
Payment made out of a
firm’s earnings to its
owners, in the form of
either cash or stock.
distribution
Payment made by a firm
to its owners from sources
other than current or
accumulated retained
earnings.
regular cash
dividend
Cash payment made by a
firm to its owners in the
normal course of business,
usually quarterly.
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C H A P T E R 1 4 Dividends and Dividend Policy 459
Sometimes firms will pay a regular cash dividend and an extra cash dividend. By calling
part of the payment “extra,” management is indicating that that part may or may not be re-
peated in the future. A special dividend is similar, but the name usually indicates that this
dividend is viewed as a truly unusual or one-time event and it won’t be repeated. Finally, the
payment of a liquidating dividend usually means that some or all of the business has been
liquidated, that is, sold off.
However it is labeled, a cash dividend payment reduces corporate cash and retained earn-
ings, except in the case of a liquidating dividend (where paid-in capital may be reduced).
Of course, there are other types of dividends. Companies listed on the Japanese Nikkei
stock market have given shareholders alternative dividends in the form of food items, pre-
paid phone cards, and so forth. For example, McDonald’s Holdings Company (Japan) gave
its shareholders coupon books for free hamburgers.
Standard Method of Cash Dividend Payment
The decision to pay a dividend rests in the hands of the board of directors of the corpora-
tion. When a dividend has been declared, it becomes a liability of the firm and cannot be
rescinded easily. Sometime after it has been declared, a dividend is distributed to all share-
holders as of some specific date.
Commonly, the amount of the cash dividend is expressed in terms of dollars per share
(dividends per share). As we have seen in other chapters, it is also expressed as a percentage
of the market price (the dividend yield) or as a percentage of net income or earnings per
share (the dividend payout).
Dividend Payment: A Chronology
The mechanics of a cash dividend payment can be illustrated by the example in Figure 14.1
and the following description:
1. Declaration date. On January 15, the board of directors passes a resolution to pay a
dividend of $1 per share on February 16 to all holders of record as of January 30.
2. Ex-dividend date. To make sure that dividend checks go to the right people, brokerage
firms and stock exchanges establish an ex-dividend date. This date is two business days
before the date of record (discussed next). If you buy the stock before this date, then
you are entitled to the dividend. If you buy on this date or after, then the previous
owner will get the dividend.
declaration date
Date on which the board
of directors passes a
resolution to pay a
dividend.
ex-dividend date
Date two business days
before the date of record,
establishing those
individuals entitled to a
dividend.
Thursday,
January
15
Declaration
date
Wednesday,
January
28
Ex-dividend
date
Friday,
January
30
Record
date
Monday,
February
16
Payment
date
1. Declaration date: The board of directors declares a payment of dividends.
2. Ex-dividend date: A share of stock goes ex dividend on the date the seller
is entitled to keep the dividend; under NYSE rules, shares are traded ex
dividend on and after the second business day before the record date.
3. Record date: The declared dividends are distributable to those who are
shareholders of record as of this specific date.
4. Payment date: The dividend checks are mailed to shareholders of record.
Example of the
procedure for
dividend payment
FIGURE 14.1
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460 P A R T 7 Long-Term Financing
In Figure 14.1, Wednesday, January 28, is the ex-dividend date. Before this date, the
stock is said to trade “with dividend,” or “cum dividend.” Afterwards, the stock trades “ex
dividend.”
The ex-dividend date convention removes any ambiguity about who is entitled to the
dividend. Because the dividend is valuable, the stock price will be affected when the stock
goes “ex.” We examine this effect below.
3. Date of record. Based on its records, the corporation prepares a list on January 30 of
all individuals believed to be stockholders. These are the holders of record, and January
30 is the date of record (or record date). The word believed is important here. If you
bought the stock just before this date, the corporation’s records might not reflect that
fact because of mailing or other delays. Without some modification, some of the
dividend checks would get mailed to the wrong people. This is the reason for the ex-
dividend day convention.
4. Date of payment. The dividend checks are mailed on February 16.
More on the Ex-Dividend Date
The ex-dividend date is important and is a common source of confusion. We examine what
happens to the stock when it goes ex, meaning that the ex-dividend date arrives. To illus-
trate, suppose we have a stock that sells for $10 per share. The board of directors declares a
dividend of $1 per share, and the record date is Tuesday, June 12. Based on our discussion
above, we know that the ex date will be two business (not calendar) days earlier, on Friday,
June 8.
If you buy the stock on Thursday, June 7, right as the market closes, you’ll get the $1
dividend because the stock is trading cum dividend. If you wait and buy the stock right as
the market opens on Friday, you won’t get the $1 dividend. What will happen to the value of
the stock overnight?
If you think about it, the stock is obviously worth about $1 less on Friday morning, so
its price will drop by this amount between close of business on Thursday and the Friday
opening. In general, we expect that the value of a share of stock will go down by about the
dividend amount when the stock goes ex dividend. The key word here is about. Because divi-
dends are taxed, the actual price drop might be closer to some measure of the aftertax value
of the dividend. Determining this value is complicated because of the different tax rates and
tax rules that apply for different buyers. The series of events described here is illustrated in
Figure 14.2.
date of record
Date by which holders
must be on record to
receive a dividend.
date of payment
Date that the dividend
checks are mailed.
Price = $10
Price = $9
$1 is the ex-dividend price drop
−t −2 −1 0 + 1 + 2 t
Ex date
The stock price will fall by the amount of the dividend on the ex
date (Time 0). If the dividend is $1 per share, the price will be
equal to $10 − 1 = $9 on the ex date.
Before ex date (Time −1)
On ex date (Time 0)
Dividend = $0
Dividend = $1
Price = $10
Price = $ 9
FIGURE 14.2
Price behavior
around the
ex-dividend date for
a $1 cash dividend
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C H A P T E R 1 4 Dividends and Dividend Policy 461
As an example of the price drop on the ex-dividend date, we examine the large
dividend paid by Warrior Met Coal, operator of coal mines in Alabama, in November
2017. The dividend was $11.21 per share at a time when the stock price was around
$30, so the dividend was about 40 percent of the total stock price, a truly special
dividend.
The stock went ex dividend on November 24, 2017. The stock price chart here
shows the change in Warrior stock four days prior to the ex-dividend date and on the
ex-dividend date.
The stock closed at $29.90 on November 22 (November 23 was a holiday) and
opened at $18.65 on November 24—a drop of $11.25. With a 20 percent tax rate on divi-
dends, we would have expected a drop of about $9, so the actual price dropped more than
we would have expected. We discuss dividends and taxes in more detail in a subsequent
section.
EXAMPLE 14.1 “Ex” Marks the Day
The board of directors of Divided Airlines has declared a dividend of $2.50 per share payable on
Tuesday, May 30, to shareholders of record as of Tuesday, May 9. Cal Icon buys 100 shares of Di-
vided on Tuesday, May 2, for $150 per share. What is the ex date? Describe the events that will oc-
cur with regard to the cash dividend and the stock price.
The ex date is two business days before the date of record, Tuesday, May 9, so the stock will
go ex on Friday, May 5. Cal buys the stock on Tuesday, May 2, so Cal purchases the stock cum divi-
dend. In other words, Cal will get $2.50 × 100 = $250 in dividends. The check will be mailed on
Tuesday, May 30. When the stock does go ex on Friday, its value will drop overnight by about $2.50
per share.
CONCEPT QUESTIONS
14.1a What are the different types of cash dividends?
14.1b What are the mechanics of the cash dividend payment?
14.1c How should the price of a stock change when the stock goes ex dividend?
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462 P A R T 7 Long-Term Financing
DOES DIVIDEND POLICY MATTER?
To decide whether or not dividend policy matters, we first have to define what we mean by
dividend policy. All other things being the same, of course dividends matter. Dividends are
paid in cash, and cash is something that everybody likes. The question we will be discussing
here is whether the firm should pay out cash now or invest the cash and pay it out later.
Dividend policy, therefore, is the time pattern of dividend payout. In particular, should the
firm pay out a large percentage of its earnings now or a small (or even zero) percentage?
This is the dividend policy question.
An Illustration of the Irrelevance of Dividend Policy
A powerful argument can be made that dividend policy does not matter. We illustrate this by
considering the simple case of Wharton Corporation. Wharton is an all-equity firm that has
existed for 10 years. The current financial managers plan to dissolve the firm in 2 years. The
total cash flows the firm will generate, including the proceeds from liquidation, are $10,000
in each of the next 2 years.
Current Policy: Dividends Set Equal to Cash Flow At the present time, divi-
dends at each date are set equal to the cash flow of $10,000. There are 100 shares outstand-
ing, so the dividend per share will be $100. In Chapter 7, we showed that the value of the
stock is equal to the present value of the future dividends. Assuming a 10 percent required
return, the value of a share of stock today, P0, is:
P0 =
D1 ______ (1 + R)1 +
D2 ______ (1 + R)2
= $100 _____ 1.10 +
$100 _____ 1.102
= $173.55
The firm as a whole is thus worth: 100 × $173.55 = $17,355.
Several members of the board of Wharton have expressed dissatisfaction with the cur-
rent dividend policy and have asked you to analyze an alternative policy.
Alternative Policy: Initial Dividend Greater Than Cash Flow Another pol-
icy is for the firm to pay a dividend of $110 per share on the first date (Date 1), which is,
of course, a total dividend of $11,000. Because the cash flow is only $10,000, an extra
$1,000 must somehow be raised. One way to do this is to issue $1,000 worth of bonds
or stock at Date 1. Assume that stock is issued. The new stockholders will desire enough
cash flow at Date 2 so that they earn the required 10 percent return on their Date 1
investment.
What is the value of the firm with this new dividend policy? The new stockholders in-
vest $1,000. They require a 10 percent return, so they will demand $1,000 × 1.10 = $1,100
of the Date 2 cash flow, leaving only $8,900 to the old stockholders. The dividends to the
old stockholders will be:
Date 1 Date 2
Aggregate dividends to old stockholders $11,000 $8,900
Dividends per share 110 89
14.2
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C H A P T E R 1 4 Dividends and Dividend Policy 463
The present value of the dividends per share is therefore:
P 0 =
$110 ____ 1.10 +
$89 ____ 1.10 2 = $173.55
This is the same value we had before.
The value of the stock is unaffected by this switch in dividend policy even though we
had to sell some new stock to finance the dividend. In fact, no matter what pattern of divi-
dend payout the firm chooses, the value of the stock will always be the same in this example.
In other words, for the Wharton Corporation, dividend policy makes no difference. The
reason is simple: Any increase in a dividend at some point in time is exactly offset by a de-
crease somewhere else, so the net effect, once we account for time value, is zero.
A Test
Our discussion to this point can be summarized by considering the following true-false test
questions:
1. True or false: Dividends are irrelevant.
2. True or false: Dividend policy is irrelevant.
The first statement is surely false, and the reason follows from common sense. Clearly,
investors prefer higher dividends to lower dividends at any single date if the dividend level is
held constant at every other date. To be more precise regarding the first question, if the divi-
dend per share at a given date is raised, while the dividend per share at every other date is
held constant, the stock price will rise. The reason is that the present value of the future divi-
dends must go up if this occurs. This action can be accomplished by management decisions
that improve productivity, increase tax savings, strengthen product marketing, or otherwise
improve cash flow.
The second statement is true, at least in the simple case we have been examining.
Dividend policy by itself cannot raise the dividend at one date while keeping it the same
at all other dates. Rather, dividend policy merely establishes the trade-off between divi-
dends at one date and dividends at another date. Once we allow for time value, the present
value of the dividend stream is unchanged. Thus, in this simple world, dividend policy
does not matter because managers choosing either to raise or to lower the current divi-
dend do not affect the current value of their firm. However, we have ignored several real-
world factors that might lead us to change our minds; we pursue some of these in
subsequent sections.
Some Real-World Factors Favoring a Low Payout
The example we used to illustrate the irrelevance of dividend policy ignored taxes and
flotation costs. We will now see that these factors might lead us to prefer a low-dividend
payout.
Taxes U.S. tax laws are complex, and they affect dividend policy in a number of
ways. The key tax feature has to do with the taxation of dividend income and capital
gains. For individual shareholders, effective tax rates on dividend income are higher
than the tax rates on capital gains. Historically, dividends received have been taxed
as ordinary income. Capital gains have been taxed at somewhat lower rates, and the tax
on a capital gain is deferred until the stock is sold. This second aspect of capital gains
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464 P A R T 7 Long-Term Financing
taxation makes the effective tax rate much lower because the present value of the tax
is less.1
A firm that adopts a low-dividend payout will reinvest the money instead of paying it
out. This reinvestment increases the value of the firm and of the equity. All other things be-
ing equal, the net effect is that the expected capital gains portion of the return will be higher
in the future. So the fact that capital gains are taxed favorably may lead us to prefer this
approach.
Recent tax law changes have led to a renewed interest in the effect of taxes on corpo-
rate dividend policies. As we previously noted, historically, dividends have been taxed as
ordinary income (at ordinary income tax rates). In 2003, this changed dramatically. The
maximum tax rate on dividends was lowered from the 35–39 percent range to 15 percent,
giving corporations a much larger tax incentive to pay dividends. In 2018, the tax rate on
dividends was 0 percent, 15 percent, or 20 percent, depending on the individual’s
income.
Flotation Costs In our example illustrating that dividend policy doesn’t matter, we
saw that the firm could sell some new stock if necessary to pay a dividend. As we discuss in
our next chapter, selling new stock can be very expensive. If we include the costs of selling
stock (“flotation” costs) in our argument, then we will find that the value of the stock de-
creases if we sell new stock.
More generally, imagine two firms identical in every way except that one pays out a
greater percentage of its cash flow in the form of dividends. Because the other firm plows
back more, its equity grows faster. If these two firms are to remain identical, then the one
with the higher payout will have to periodically sell some stock to catch up. Because this is
expensive, a firm might be inclined to have a low payout.
Dividend Restrictions In some cases, a corporation may face restrictions on its abil-
ity to pay dividends. For example, as we discussed in Chapter 6, a common feature of a
bond indenture is a covenant prohibiting dividend payments above some level. Also, a cor-
poration may be prohibited by state law from paying dividends if the dividend amount ex-
ceeds the firm’s retained earnings.
Some Real-World Factors Favoring a High Payout
In this section, we consider reasons a firm might pay its shareholders higher dividends
even if it means the firm must issue more shares of stock to finance the dividend
payments.
Desire for Current Income It has been argued that many individuals desire current
income. The classic example is the group of retired people and others living on a fixed in-
come, the proverbial “widows and orphans.” It is argued that this group is willing to pay a
premium to get a higher dividend yield.
1In fact, capital gains taxes can sometimes be avoided altogether. Although we do not recommend this particular
tax-avoidance strategy, the capital gains tax may be avoided by dying. Your heirs are not considered to have a capi-
tal gain, so the tax liability dies when you do. In this instance, you can take it with you.
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C H A P T E R 1 4 Dividends and Dividend Policy 465
It is easy to see, however, that this argument is irrelevant in our simple case. An indi-
vidual preferring high current cash flow but holding low-dividend securities easily could sell
off shares to provide the necessary funds. Similarly, an individual desiring a low current
cash flow but holding high-dividend securities could reinvest the dividends. Thus, in a world
of no transaction costs, a policy of high current dividends would be of no value to the
stockholder.
The current-income argument may have relevance in the real world. Here, the sale of
low-dividend stocks would involve brokerage fees and other transaction costs. Such a sale
also might trigger capital gains taxes. These direct cash expenses could be avoided by an
investment in high-dividend securities. In addition, the expenditure of the stockholder’s
own time when selling securities and the natural (though not necessarily rational) fear of
consuming out of principal might further lead many investors to buy high-dividend
securities.
Tax and Legal Benefits from High Dividends Earlier we saw that dividends
were taxed unfavorably for individual investors. This fact is a powerful argument for a low
payout. However, there are a number of other investors who do not receive unfavorable
tax treatment from holding high-dividend yield, rather than low-dividend yield,
securities.
Corporate investors A significant tax break on dividends occurs when a corporation
owns stock in another corporation. A corporate stockholder receiving either common or
preferred dividends is granted a 50 percent (or more) dividend exclusion. The 50 percent
exclusion does not apply to capital gains, so this group is taxed unfavorably on capital
gains.
As a result of the dividend exclusion, high-dividend, low-capital-gains stocks may be
more appropriate for corporations to hold. In fact, this is why corporations hold a substan-
tial percentage of the outstanding preferred stock in the economy. This tax advantage of
dividends also leads some corporations to hold high-yielding stocks instead of long-term
bonds because there is no similar tax exclusion of interest payments to corporate
bondholders.
Tax-exempt investors We have pointed out both the tax advantages and the tax disad-
vantages of a low-dividend payout. Of course, this discussion is irrelevant to those in zero
tax brackets. This group includes some of the largest investors in the economy, such as pen-
sion funds, endowment funds, and trust funds.
There are some legal reasons for large institutions to favor high-dividend yields. First,
institutions such as pension funds and trust funds are often set up to manage money for the
benefit of others. The managers of such institutions have a fiduciary responsibility to invest
the money prudently. It has been considered imprudent in courts of law to buy stock in
companies with no established dividend record.
Second, institutions such as university endowment funds and trust funds are frequently
prohibited from spending any of the principal. Such institutions therefore might prefer high-
dividend-yield stocks so they have some ability to spend. Like widows and orphans, this
group thus prefers current income. Unlike widows and orphans, this group is very large in
terms of the amount of stock owned.
Overall, individual investors (for whatever reason) may have a desire for current income
and thus may be willing to pay the dividend tax. In addition, some very large investors such
as corporations and tax-free institutions may have a very strong preference for high-dividend
payouts.
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466 P A R T 7 Long-Term Financing
Clientele Effects: A Resolution of Real-World Factors?
In our earlier discussion, we saw that some groups (wealthy individuals, for example) have
an incentive to pursue low-payout (or zero-payout) stocks. Other groups (corporations, for
example) have an incentive to pursue high-payout stocks. Companies with high payouts
thus will attract one group, and low-payout companies will attract another.
These different groups are called clienteles, and what we have described is a
clientele effect. The clientele effect argument states that different groups of investors desire
different levels of dividends. When a firm chooses a particular dividend policy, the only ef-
fect is to attract a particular clientele. If a firm changes its dividend policy, then it attracts a
different clientele.
What we are left with is a simple supply and demand argument. Suppose 40 percent of
all investors prefer high dividends, but only 20 percent of the firms pay high dividends.
Here, the high-dividend firms will be in short supply; thus, their stock prices will rise. Con-
sequently, low-dividend firms will find it advantageous to switch policies until 40 percent of
all firms have high payouts. At this point, the dividend market is in equilibrium. Further
changes in dividend policy are pointless because all of the clienteles are satisfied. The divi-
dend policy for any individual firm is now irrelevant.
To see if you understand the clientele effect, consider the following statement: In spite
of the theoretical argument that dividend policy is irrelevant or that firms should not pay
dividends, many investors like high dividends; because of this fact, a firm can boost its share
price by having a higher dividend payout ratio. True or false?
The answer is “false” if clienteles exist. As long as enough high-dividend firms satisfy
the dividend-loving investors, a firm won’t be able to boost its share price by paying high
dividends. An unsatisfied clientele must exist for this to happen, and there is no evidence
that this is the case.
CONCEPT QUESTIONS
14.2a Are dividends irrelevant?
14.2b What are some of the reasons for a low payout?
14.2c What are the implications of dividend clienteles for payout policies?
STOCK REPURCHASES: AN ALTERNATIVE
TO CASH DIVIDENDS
Thus far in our chapter, we have considered cash dividends. However, cash dividends are
not the only way corporations distribute cash. Instead, a company can repurchase its own
stock. Repurchases (or buybacks) have become an increasingly popular tool, and the amount
spent on repurchases has become huge. For example, in 2017, $519 billion of stock was re-
purchased by S&P 500 companies, a tremendous increase from the recent low of $138 bil-
lion in 2009.
Another way to see how important repurchases have become is to compare them to
cash dividends. Consider Figure 14.3, which shows aggregate real (inflation-adjusted)
dividends and stock repurchases by publicly held U.S. industrial firms for the period
1971–2017, along with the combined total. Aggregate real dividends have grown relatively
clientele effect
Argument that stocks
attract particular groups
based on dividend yield
and the resulting tax
effects.
14.3
repurchase
Refers to a firm’s purchase
of its own stock; an
alternative to a cash
dividend. Also called stock
repurchase.
ros13952_ch14_457-486.indd 466 12/21/18 11:45 AM
C H A P T E R 1 4 Dividends and Dividend Policy 467
steadily through time, but repurchases have exploded in the last two decades. They
reached a peak of $563 billion in 2007, or about 2.75 times the size of aggregate divi-
dends. Repurchases plunged in the 2008–2009 recession as firms conserved cash, but
they rebounded in 2010.
Share repurchases are typically accomplished in one of three ways. First, compa-
nies may purchase their own stock, just as anyone would buy shares of a particular
stock. In these open market purchases, the firm does not reveal itself as the buyer. Thus,
the seller does not know whether the shares were sold back to the firm or to another
investor.
Second, the firm could institute a tender offer. Here, the firm announces to all of its
stockholders that it is willing to buy a fixed number of shares at a specific price. For
example, suppose Arts and Crafts (A&C), Inc., has 1 million shares of stock outstanding,
with a stock price of $50 per share. The firm makes a tender offer to buy back 300,000
shares at $60 per share. A&C chooses a price above $50 to induce shareholders to sell,
that is, tender, their shares. In fact, if the tender price is set high enough, shareholders
very well may want to sell more than the 300,000 shares. In the extreme case where all
outstanding shares are tendered, A&C will buy back 3 out of every 10 shares that a share-
holder has.
0
100
200
300
400
500
600
700
800
900
19
71
19
72
19
73
19
74
19
75
19
76
19
77
19
78
19
79
19
80
19
81
19
82
19
83
19
84
19
85
19
86
19
87
19
88
19
89
19
90
19
91
19
92
19
93
19
94
19
95
19
96
19
97
19
98
19
99
20
00
20
01
20
02
20
03
20
04
20
05
20
06
20
07
20
08
20
09
20
10
20
11
20
12
20
13
20
14
20
15
20
16
20
17
B
ill
io
ns
o
f r
ea
l 2
01
2
U
SD
Dividends
Repurchases
Total payout
Source: Redrawn by authors using Compustat data, following Farre-Mensa, Michaely, and Schmalz, “Payout Policy,” Annual Review of Financial
Economics, vol. 6, 2014, 75–134. Updated by authors.
Aggregate real (2012) dividends and stock repurchases by publicly held U.S. industrial
firms: 1971–2017
FIGURE 14.3
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468 P A R T 7 Long-Term Financing
Finally, firms may repurchase shares from specific individual stockholders. This proce-
dure has been called a targeted repurchase. For example, suppose the International Biotech-
nology Corporation purchased approximately 10 percent of the outstanding stock of the
Prime Robotics Company (P-R Co.) in April at around $38 per share. At that time, Interna-
tional Biotechnology announced to the Securities and Exchange Commission that it eventu-
ally might try to take control of P-R Co. In May, P-R Co. repurchased the International
Biotechnology holdings at $48 per share, well above the market price at that time. This offer
was not extended to other shareholders.
Cash Dividends versus Repurchase
Imagine an all-equity company with excess cash of $300,000. The firm pays no dividends,
and its net income for the year just ended is $49,000. The market value balance sheet at the
end of the year is represented here:
Market Value Balance Sheet
(before paying out excess cash)
Excess cash $ 3300,000 Debt $ 0
Other assets 333 333333700,000 Equity 1,000,000
Total $1,000,000 Total $1,000,000
There are 100,000 shares outstanding. The total market value of the equity is $1 million, so
the stock sells for $10 per share. Earnings per share (EPS) are $49,000/100,000 = $.49,
and the price-earnings ratio (PE) is $10/.49 = 20.4.
One option the company is considering is a $300,000/100,000 = $3 per share extra
cash dividend. Alternatively, the company is thinking of using the money to repurchase
$300,000/$10 = 30,000 shares of stock.
If commissions, taxes, and other imperfections are ignored in our example, the stock-
holders shouldn’t care which option is chosen. Does this seem surprising? It shouldn’t, re-
ally. What is happening here is that the firm is paying out $300,000 in cash. The new
balance sheet is represented here:
Market Value Balance Sheet
(after paying out excess cash)
Excess cash $ 0 Debt $33 0
Other assets 33700,000 Equity 33700,000
Total $700,000 Total $700,000
If the cash is paid out as a dividend, there are still 100,000 shares outstanding, so each is
worth $7.
The fact that the per-share value fell from $10 to $7 is not a cause for concern. Con-
sider a stockholder who owns 100 shares. At $10 per share before the dividend, the total
value is $1,000.
After the $3 dividend, this same stockholder has 100 shares worth $7 each, for a total
of $700, plus 100 × $3 = $300 in cash, for a combined total of $1,000. This illustrates what
we saw early on: A cash dividend doesn’t affect a stockholder’s wealth if there are no imper-
fections. In this case, the stock price fell by $3 when the stock went ex dividend.
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C H A P T E R 1 4 Dividends and Dividend Policy 469
Also, because total earnings and the number of shares outstanding haven’t changed,
EPS is still 49 cents. The price-earnings ratio, however, falls to $7/.49 = 14.3. Why we are
looking at accounting earnings and PE ratios will be apparent in a moment.
Alternatively, if the company repurchases 30,000 shares, there are 70,000 left outstand-
ing. The balance sheet looks the same:
Market Value Balance Sheet
(after share repurchase)
Excess cash $ 0 Debt $33 0
Other assets 33700,000 Equity 33700,000
Total $700,000 Total $700,000
The company is worth $700,000 again, so each remaining share is worth $700,000/70,000
= $10. Our stockholder with 100 shares is obviously unaffected. For example, if she was so
inclined, she could sell 30 shares and end up with $300 in cash and $700 in stock, as she
has if the firm pays the cash dividend. This is an example of a homemade dividend.
In this second case, EPS goes up because total earnings remain the same while the
number of shares goes down. The new EPS is $49,000/70,000 = $.70. However, the impor-
tant thing to notice is that the PE ratio is $10/.70 = 14.3, the same as it was following the
dividend.
This example illustrates the important point that, if there are no imperfections, a cash
dividend and a share repurchase are essentially the same thing. This is another illustration
of dividend policy irrelevance when there are no taxes or other imperfections.
Real-World Considerations in a Repurchase
The example we have described shows that a repurchase and a cash dividend are the same
thing in a world without taxes and transaction costs. In the real world, there are some ac-
counting differences between a share repurchase and a cash dividend, but the most impor-
tant difference is in the tax treatment.
Under current tax law, a repurchase has a significant tax advantage over a cash divi-
dend. A dividend is taxed, and a shareholder has no choice about whether or not to receive
the dividend. In a repurchase, a shareholder pays taxes only if (1) the shareholder actually
chooses to sell and (2) the shareholder has a capital gain on the sale.
Suppose a dividend of $1 per share is taxed at ordinary rates. Investors in the 28 per-
cent tax bracket who own 100 shares of the security pay $100 × .28 = $28 in taxes. Selling
shareholders would pay far lower taxes if $100 worth of stock were repurchased. This is be-
cause taxes are paid only on the profit from a sale. Thus, the gain on a sale would be only
$40 if shares sold at $100 were originally purchased at $60. The capital gains tax would be
.28 × $40 = $11.20. Note that the recent reductions in dividend and capital gains tax rates
do not change the fact that a repurchase has a potentially large tax edge.
To give a few examples of recent activity, as we mentioned in the chapter opener, Ap-
ple announced a $100 billion buyback in 2018. This purchase came after the company said
in May 2017 that it had completed $211 billion of its then-current $250 billion buyback
program. And IBM is well known for its aggressive buyback policies. In late 2017, the
company announced it would repurchase about $3 billion of its stock during 2018. This
amount was much lower than the more than $50 billion it spent from 2010 through 2015.
So how much of its stock has IBM repurchased? In 1995, the company had about 2.2 bil-
lion shares of stock outstanding. At the end of 2017, there were only about 918 million
ros13952_ch14_457-486.indd 469 12/21/18 11:45 AM
shares outstanding, so over a 22-year period, the company had repurchased more than
half its stock!
One cautionary note is in order concerning share repurchases, or buybacks. A company
announcing plans to buy back some of its stock has no legal obligation to actually do it, and
it turns out that many announced repurchases are never completed. Our nearby Finance
Matters discusses some recent events in stock buybacks.
Share Repurchase and EPS
You may read in the popular financial press that a share repurchase is beneficial because it
causes earnings per share to increase. As we have seen, this will happen. The reason is that
a share repurchase reduces the number of outstanding shares, but it has no effect on total
earnings. As a result, EPS rises.
However, the financial press may place undue emphasis on EPS figures in a repurchase
agreement. In our preceding example, we saw that the value of the stock wasn’t affected by
the EPS change. In fact, the PE ratio was exactly the same when we compared a cash divi-
dend to a repurchase.
Stock Buybacks: No End in Sight
Although the recent recession slowed stock buybacks, recently buybacks have begun to grow again. In fact, for
the past several years, share repurchases have been so
large that U.S. corporations bought back more shares than
they sold. In other words, aggregate net equity raised by
U.S. corporations has been negative. For example, during
2017, S&P 500 companies repurchased about $519 billion of
stock, while at the same time new equity issuance was only
$140 billion.
Some companies appear to have become serial repur-
chasers. For example, ExxonMobil had suspended its repur-
chase program in late 2017. However, from 2008 to 2017,
ExxonMobil repurchased about $180 billion of its stock. Mi-
crosoft is another serial repurchaser. During its 2014 fiscal
year, the company repurchased about $6.4 billion of its
stock and had repurchased about $117 billion over the
2008–2017 period. And Microsoft still had plans to complete
its announced $40 billion repurchase.
Stock buybacks have evolved to the point where they
are used for other purposes. For example, in January 2005,
consumer products giant Procter & Gamble (P&G) an-
nounced that it was purchasing razor manufacturer Gillette
for $54 billion. The purchase was paid for entirely with stock
in P&G. This is important because if a company acquires an-
other company for cash, the shareholders of the acquired
company may be forced to pay taxes. If shareholders re-
ceive stock, no taxes are due. What made the deal unique
was that P&G announced at the same time that it would
repurchase from $18 to $22 billion in stock. Thus, P&G es-
sentially paid about 60 percent in stock and 40 percent in
cash, but the way the deal was structured made it look like a
100 percent stock acquisition to Gillette’s stockholders.
Stock buybacks can be a large percentage of a com-
pany’s equity. For example, in May 2018, Micron Technology
announced plans to buy back $10 billion of its stock. While
this amount is not as large as many other buybacks, it repre-
sented about 17 percent of the company’s stock. Another
example in the same month is Qualcomm, which spent
about $12 billion on buybacks, or about 15 percent of the
company’s value. And MGM Resorts announced plans to
repurchase $2 billion of its stock, which would account for
about 13 percent of the company’s value.
We haven’t discussed what happens to the stock when
a company does a buyback. There are actually several
things the company can do. Many companies keep the stock
and use the shares for employee stock option plans. When
employee stock options are exercised by the employees,
new shares are created, which increases the number of
shares of stock outstanding. By using the repurchased
shares, the company does not need to issue any new
shares. A company also can keep the repurchased stock for
itself as Treasury stock. Finally, the company can cancel the
stock completely. In essence, it destroys the shares repur-
chased, which reduces the number of shares outstanding.
FINANCE MATTERS
470
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C H A P T E R 1 4 Dividends and Dividend Policy 471
WHAT WE KNOW AND DO NOT KNOW
ABOUT DIVIDEND AND PAYOUT POLICIES
Dividends and Dividend Payers
As we have discussed, there are numerous good reasons favoring a dividend policy of low
(or no) payout. Nonetheless, as we showed earlier in Figure 14.3, in the United States,
aggregate dividends paid are quite large. For example, in 1978, U.S. industrial firms listed
on the major exchanges paid $32 billion in total dividends. By 2010, that number had risen
to $199 billion (unadjusted for inflation), an increase of more than 500 percent (after
adjusting for inflation, the increase is smaller, 84 percent, but still substantial).
While we know dividends are large in the aggregate, we also know that the number of
companies that pay dividends has declined. Over the same 1978–2010 period, the number
of industrial companies paying dividends declined from more than 2,000 to 855, and the
percentage of these firms paying dividends declined 50 percent, to just under 30 percent.2
The fact that aggregate dividends grew while the number of payers fell so sharply seems
a bit paradoxical, but the explanation is straightforward. Dividend payments are heavily
concentrated in a relatively small set of large firms. In 2010, for example, more than 80
percent of aggregate dividends were paid by just 100 firms. The top 25 payers, which in-
cluded such well-known giants as ExxonMobil and General Electric, collectively paid about
54 percent of all dividends. Thus, the reason that dividends grew while dividend payers
shrank is that the decline in dividend payers is almost entirely due to smaller firms, which
tend to pay smaller dividends in the first place.
One important reason that the percentage of dividend-paying firms has declined is that the
population of firms has changed. There has been a huge increase in the number of newly listed
firms over the last 25 or so years. Newly listed firms tend to be younger and less profitable. Such
firms need their internally generated cash to fund growth and typically do not pay dividends.
Another factor at work is that firms appear to be more likely to begin making payouts
using share repurchases, which are flexible, rather than committing to making cash distribu-
tions. Such a policy seems quite sensible. However, after controlling for the changing mix of
firms and the increase in share repurchasing activity, there still appears to be a decreased
propensity to pay dividends among certain types of older, better-established firms, though
further research is needed on this subject.
The fact that the number of dividend-paying firms has declined so sharply is an interest-
ing phenomenon. Making matters even more interesting is evidence showing that the trend
may have begun to reverse itself. Take a look at Figure 14.4, which shows the percentage of
industrial firms paying dividends over the period 1971–2017, along with the percentage
of (1) firms doing repurchases and (2) firms with a positive payout of one type or the other
14.4
CONCEPT QUESTIONS
14.3a Why might a stock repurchase make more sense than an extra cash dividend?
14.3b What is the effect of a stock repurchase on a firm’s EPS? Its PE?
2These figures and those in the following two paragraphs are from H. DeAngelo, L. DeAngelo, and D. Skinner,
“Corporate Payout Policy,” Foundations and Trends in Finance 3 (2009), as updated by the authors.
ros13952_ch14_457-486.indd 471 12/21/18 11:45 AM
472 P A R T 7 Long-Term Financing
(or both). As shown, there is a pronounced downward trend of dividend payers, but that
trend appears to bottom out in 2000 and then reverse somewhat in 2002. So what’s going on?
Part of the apparent rebound in Figure 14.4 is probably an illusion. The number of
firms listed on the major stock markets dropped sharply, from over 5,000 to under 4,000,
during the period 2000–2005. About 2,000 firms delisted over this period, 98 percent of
which were not dividend payers. Thus, the percentage of firms paying dividends rose
because nonpayers dropped out in large numbers.3 By 2017, the number of listed firms had
declined to below 3,000, and the percentage of dividend payers reached 34 percent.
However, once we control for the dropout problem, there is still an increase in the pro-
portion of dividend payers, but it happens in 2003. As shown in Figure 14.5, the uptick is
concentrated in the months following May 2003. What is so special about this month? The
answer is that in May 2003, top personal tax rates on dividends were slashed from about 38
to 15 percent. Thus, consistent with our earlier tax arguments, a reduction in personal tax
rates led to increases in dividends.
However, it is important not to read too much into Figure 14.5. It seems clear that the
reduction in tax rates did have an effect, but, on balance, what we see is a few hundred firms
initiating dividends. There are still thousands of firms that did not initiate dividends, even
3These numbers and this explanation are from R. Chetty and E. Saez, “The Effects of the 2003 Dividend Tax Cut on
Corporate Behavior: Interpreting the Evidence,” American Economic Review Papers and Proceedings 96 (2006).
Firms with positive total payoutDividend payers
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
19
71
19
72
19
73
19
74
19
75
19
76
19
77
19
78
19
79
19
80
19
81
19
82
19
83
19
84
19
85
19
86
19
87
19
88
19
89
19
90
19
91
19
92
19
93
19
94
19
95
19
96
19
97
19
98
19
99
20
00
20
01
20
02
20
03
20
04
20
05
20
06
20
07
20
08
20
09
20
10
20
11
20
12
20
13
20
14
20
15
20
16
20
17
Fr
ac
tio
n
of
a
ll
pu
bl
ic
fi
rm
s
Repurchasing firms
Source: Redrawn by authors, using Compustat data, following Farre-Mensa, J., Michaely, R. and Schmalz, M. C., “Payout Policy,” Annual Review of
Financial Economics, vol. 6, 2014, 75–134. Update by authors.
Proportion of dividend payers, repurchasers, and firms with positive total payout among all
publicly held U.S. industrial firms: 1971–2017
FIGURE 14.4
ros13952_ch14_457-486.indd 472 12/21/18 11:45 AM
C H A P T E R 1 4 Dividends and Dividend Policy 473
though the tax rate reduction was very large. Thus, the evidence suggests that tax rates mat-
ter, but they are not a primary determinant of dividend policy. This interpretation is consis-
tent with the results of a 2005 survey of financial executives, more than ⅔ of whom said that
the tax rate cut probably or definitely would not affect their dividend policies.4
A second force that may be at work over time is the maturing of many of the (surviving)
newly listed firms we mentioned earlier. As these firms have become better established,
their profitability has increased (and, potentially, their investment opportunities have de-
creased), and they have begun to pay dividends.
A third factor that may be contributing to the increase in the number of dividend payers
is a little more subtle. The technology-heavy NASDAQ index plummeted in the spring of
2000 (due to the “dot-com” crash), and it became clear that many newly listed companies
were likely to fail. Shortly thereafter, major accounting scandals at companies such as Enron
and WorldCom left investors unsure of the trustworthiness of reported earnings. In such an
environment, companies may have chosen to initiate dividends in an attempt to signal to
investors that they had the cash to make dividend payments now and in the future.
The apparent reversal in the decline of dividend payers is a recent phenomenon, so its
significance remains to be seen. It may prove to be just a transient event in the middle of a
long decline. We will have to wait and see.
4See A. Brav, J. R. Graham, C. R. Harvey, and R. Michaely, “Managerial Response to the May 2003 Dividend Tax
Cut,” Financial Management 37 (2008).
FIGURE 14.5
1 Q
20
01
Year and quarter
Tax cut enacted
10
0
20
40
50
30
60
N
um
be
r o
f i
nd
us
tr
ia
l fi
rm
s
in
iti
at
in
g
di
vi
de
nd
s
(p
er
q
ua
rt
er
)
2 Q
20
01
3 Q
20
01
4 Q
20
01
1 Q
20
02
2 Q
20
02
3 Q
20
02
4 Q
20
02
1 Q
20
03
2 Q
20
03
3 Q
20
03
4 Q
20
03
1 Q
20
04
2 Q
20
04
3 Q
20
04
4 Q
20
04
1 Q
20
05
2 Q
20
05
3 Q
20
05
4 Q
20
05
1 Q
20
06
2 Q
20
06
3 Q
20
06
4 Q
20
06
Source: Brav, A., Graham, J. R., Harvey, C. R. and Michaely, R., “Managerial Response to the May 2003 Dividend Tax Cut,” Financial Management,
vol. 37, 2008.
Regular dividend initiations, 2001–2006
ros13952_ch14_457-486.indd 473 12/21/18 11:45 AM
474 P A R T 7 Long-Term Financing
Corporations Smooth Dividends
Dividend cuts are frequently viewed as very bad news by market participants. As a result,
companies only cut dividends when there is no other acceptable alternative. For the same
reason, companies are also reluctant to increase dividends unless they are sure the new divi-
dend level can be sustained.
In practice, what we observe is that dividend-paying companies tend to raise dividends
only after earnings have risen, and they don’t increase or cut dividends in response to tem-
porary earnings fluctuations. In other words, (1) dividend growth lags earnings growth and
(2) dividend growth will tend to be much smoother than earnings growth.
There are companies with extraordinarily long dividend payment histories. The S&P
500 Dividend Aristocrat list consists of 54 companies that have increased dividends for at
least 25 consecutive years. Two companies with long histories of dividend increases are tool
manufacturer Stanley Works (now Stanley Black & Decker) and Procter & Gamble. At the
end of 2017, Stanley Black & Decker had paid a dividend each year for the past 141 consecutive
years and had increased its dividend in each of the last 47 years. Procter & Gamble had in-
creased its dividend for 61 years.
Putting It All Together
Much of what we have discussed in this chapter (and much of what we know about divi-
dends from decades of research) can be pulled together and summarized in the following
five observations:5
1. Aggregate dividends and stock repurchases are massive, and they have increased
steadily in nominal and real terms over the years.
2. Dividends are heavily concentrated among a relatively small number of large, mature firms.
3. Managers are very reluctant to cut dividends, normally doing so only due to firm-
specific problems.
4. Managers smooth dividends, raising them slowly and incrementally as earnings grow.
5. Stock prices react to unanticipated changes in dividends.
The challenge now is to fit these five pieces into a reasonably coherent picture. With regard
to payouts in general, meaning the combination of stock repurchases and cash dividends, a
simple life-cycle theory fits Points 1 and 2. The key ideas are straightforward. First, relatively
young and less-profitable firms generally should not make cash distributions. They need the
cash to fund investments (and flotation costs discourage the raising of outside cash).
However, as a firm matures, it begins to generate free cash flow (which, you will recall,
is internally generated cash flow beyond that needed to fund profitable investment activi-
ties). Significant free cash flow can lead to agency problems if it is not distributed. Manag-
ers may become tempted to pursue empire building or otherwise spend the excess cash in
ways not in the shareholders’ best interests. Thus, firms come under pressure to make distri-
butions rather than hoard cash. And, consistent with what we observe, we expect large firms
with a history of profitability to make large distributions.
Thus, the life-cycle theory says that firms trade off the agency costs of excess cash re-
tention against the potential future costs of external equity financing. A firm should begin
making distributions when it generates sufficient internal cash flow to fund its investment
needs now and into the foreseeable future.
5This list is distilled in part from a longer list in DeAngelo, H. and DeAngelo, L., “Payout Policy Pedagogy: What
Matters and Why,” European Financial Management, vol. 13, 2007.
ros13952_ch14_457-486.indd 474 12/21/18 11:45 AM
C H A P T E R 1 4 Dividends and Dividend Policy 475
The more complex issue concerns the type of distribution, cash dividends versus repur-
chases. The tax argument in favor of repurchases is a clear and strong one. Further, repur-
chases are a much more flexible option (and managers greatly value financial flexibility), so
the question is: Why would firms ever choose a cash dividend?
If we are to answer this question, we have to ask a different question. What can a cash
dividend accomplish that a share repurchase cannot? One answer is that when a firm makes
a commitment to pay a cash dividend now and into the future, it sends a two-part signal to the
markets. As we already have discussed, one signal is that the firm anticipates being profitable,
with the ability to make the payments on an ongoing basis. Note that a firm cannot benefit by
trying to fool the market in this regard because the firm would ultimately be punished when
it couldn’t make the dividend payment (or couldn’t make it without relying on external
financing). Thus, a cash dividend may let a firm distinguish itself from less-profitable rivals.
A second, and more subtle, signal takes us back to the agency problem of free cash
flow. By committing to pay cash dividends now and in the future, the firm signals that it
won’t be hoarding cash (or at least not as much cash), thereby reducing agency costs and
enhancing shareholder wealth.
This two-part signaling story is consistent with Points 3–5 above, but an obvious objec-
tion remains. Why don’t firms just commit to a policy of setting aside whatever money
would be used to pay dividends and use it instead to buy back shares? After all, either way,
a firm is committing to pay out cash to shareholders.
A fixed repurchase strategy suffers from two drawbacks. The first is verifiability. A firm
could announce an open market repurchase and then not do it. By suitably fudging its
books, it would be some time before the deception was discovered. Thus, it would be neces-
sary for shareholders to develop a monitoring mechanism, meaning some sort of way for
stockholders to know for sure that the repurchase in fact was done. Such a mechanism
wouldn’t be difficult to build (it could be a simple trustee relationship such as we observe in
the bond markets), but it currently does not exist. Of course, a tender offer repurchase needs
little or no verification, but such offers have expenses associated with them. The beauty of a
cash dividend is that it needs no monitoring. A firm is forced to cut and mail checks four
times a year, year in and year out.
A second objection to a fixed repurchase strategy is more controversial. Suppose man-
agers, as insiders, are better able than stockholders to judge whether their stock price is too
high or too low. (Note that this idea does not conflict with semistrong market efficiency if
inside information is the reason.) In this case, a fixed repurchase commitment forces man-
agement to buy back stock even in circumstances when the stock is overvalued. In other
words, it forces management into making negative NPV investments.
More research on the cash dividend versus share repurchase question is needed, but the
historical trend seems to be favoring continued growth in repurchases relative to dividends.
Total corporate payouts seem to be relatively stable over time at roughly 20 percent of ag-
gregate earnings, but repurchases are becoming a larger portion of that total. The split
reached about 50–50 in the latter part of the 1990s, but it looks like aggregate repurchases
have recently passed aggregate dividends.
One aspect of aggregate cash dividends that has not received much attention is that
there may be a strong legacy effect. Before 1982, the regulatory status of stock repurchases
was somewhat murky, creating a significant disincentive. In 1982, the SEC, after years of
debate, created a clear set of guidelines for firms to follow, thereby making repurchases
much more attractive. The impact of this change is clear in Figure 14.3. Repurchases im-
mediately began growing in 1983–1984.
The legacy effect arises because many of the giant firms that pay such a large portion of
aggregate dividends were paying dividends before (and perhaps long before) 1982. To the
ros13952_ch14_457-486.indd 475 12/21/18 11:45 AM
476 P A R T 7 Long-Term Financing
extent that these firms are unwilling to cut their dividends, aggregate cash dividends will be
large, but only because of a “lock-in” effect for older firms. If locked-in, legacy payers ac-
count for much of the aggregate dividend, what we should observe is (1) a sharply reduced
tendency for maturing firms to initiate dividends and (2) a growth in repurchases relative to
cash dividends over time. We actually do see evidence of both of these trends; however,
legacy effects alone can’t account for all cash dividend payers.
THE PROS AND CONS OF PAYING DIVIDENDS
Pros Cons
1. Cash dividends can underscore good results
and provide support to the stock price.
1. Dividends are taxed to recipients.
2. Dividends may attract institutional investors
who prefer some return in the form of
dividends. A mix of institutional and individual
investors may allow a firm to raise capital at a
lower cost because of the ability of the firm to
reach a wider market.
2. Dividends can reduce internal sources
of financing. Dividends may force the
firm to forgo positive NPV projects or to
rely on costly external equity financing.
3. Stock price usually increases with the
announcement of a new or increased
dividend.
3. Once established, dividend cuts are
hard to make without adversely
affecting a firm’s stock price.
4. Dividends absorb excess cash flow and may
reduce agency costs that arise from conflicts
between management and shareholders.
Some Survey Evidence on Dividends
A recent study surveyed a large number of financial executives regarding dividend policy.
One of the questions asked was, “Do these statements describe factors that affect your com-
pany’s dividend decisions?” Table 14.1 shows some of the results.
As shown in Table 14.1, financial managers are very disinclined to cut dividends. More-
over, they are very conscious of their previous dividends and desire to maintain a relatively
steady dividend. In contrast, the cost of external capital and the desire to attract “prudent
man” investors (those with fiduciary duties) are less important.
Policy Statements
Percent Who Agree
or Strongly Agree
1. We try to avoid reducing dividends per share. 93.8%
2. We try to maintain a smooth dividend from year to year. 89.6
3. We consider the level of dividends per share that we have
paid in recent quarters.
88.2
4. We are reluctant to make dividend changes that might have to
be reversed in the future.
77.9
5. We consider the change or growth in dividends per share. 66.7
6. We consider the cost of raising external capital to be smaller
than the cost of cutting dividends.
42.8
7. We pay dividends to attract investors subject to “prudent
man” investment restrictions.
41.7
*Survey respondents were asked the question, “Do these statements describe factors that affect your company’s
dividend decisions?”
Source: Adapted from Table 4 of Brav, A., Graham, J. R., Harvey, C. R., and Michaely, R., “Payout Policy in the 21st
Century,” Journal of Financial Economics, Elsevier, 2005.
Survey responses on
dividend decisions*
TABLE 14.1
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C H A P T E R 1 4 Dividends and Dividend Policy 477
Table 14.2 is drawn from the same survey, but here the responses are to the question,
“How important are the following factors to your company’s dividend decision?” Not sur-
prisingly, given the responses in Table 14.1 and our earlier discussion, the highest priority is
maintaining a consistent dividend policy. The next several items are also consistent with our
previous analysis. Financial managers are very concerned about earnings stability and future
earnings levels in making dividend decisions, and they consider the availability of good in-
vestment opportunities. Survey respondents also believed that attracting both institutional
and individual (retail) investors was relatively important.
In contrast to our discussion of taxes and flotation costs in the earlier part of this chap-
ter, the financial managers in this survey did not think that personal taxes paid on dividends
by shareholders are very important. And even fewer think that equity flotation costs are
relevant.
STOCK DIVIDENDS AND STOCK SPLITS
Another type of dividend is paid out in shares of stock. This type of dividend is called a
stock dividend. A stock dividend is not a true dividend because it is not paid in cash. The
effect of a stock dividend is to increase the number of shares that each owner holds.
Because there are more shares outstanding, each is worth less.
A stock dividend is commonly expressed as a percentage; for example, a 20 percent
stock dividend means that a shareholder receives one new share for every five currently
owned (a 20 percent increase). Because every shareholder owns 20 percent more stock, the
total number of shares outstanding rises by 20 percent. As we will see in a moment, the
result is that each share of stock is worth about 20 percent less.
A stock split is essentially the same thing as a stock dividend, except that a split is ex-
pressed as a ratio instead of a percentage. When a split is declared, each share is split up to
create additional shares. For example, in a three-for-one stock split, each old share is split
into three new shares. As a result, the par value of each share would be reduced to one-third
of the presplit value.
By convention, stock dividends of less than 20 to 25 percent are called small stock divi-
dends. A stock dividend greater than this 20 to 25 percent is called a large stock dividend. For
14.5
stock dividend
Payment made by a firm
to its owners in the form
of stock, diluting the value
of each share outstanding.
stock split
An increase in a firm’s
shares outstanding
without any change in
owners’ equity.
Policy Statements
Percent Who Think This Is
Important or Very Important
1. Maintaining consistency with our historic dividend policy. 84.1%
2. Stability of future earnings. 71.9
3. A sustainable change in earnings. 67.1
4. Attracting institutional investors to purchase our stock. 52.5
5. The availability of good investment opportunities for
our firm to pursue.
47.6
6. Attracting retail investors to purchase our stock. 44.5
7. Personal taxes our stockholders pay when receiving
dividends.
21.1
8. Flotation costs to issuing new equity. 9.3
*Survey respondents were asked the question, “How important are the following factors to your company’s dividend
decision?”
Source: Adapted from Table 5 of Brav, A., Graham, J. R., Harvey, C. R., and Michaely, R., “Payout Policy in the 21st
Century,” Journal of Financial Economics, Elsevier, 2005. Used with permission.
Survey responses on
dividend decisions*
TABLE 14.2
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478 P A R T 7 Long-Term Financing
example, in March 2018, Aflac, known for its “spokesduck,” completed a two-for-one stock
split in the form of a stock dividend. In June 2018, Trex Company, manufacturer of decking
materials, announced its 100 percent stock dividend in the form of a two-for-one stock split.
Except for some relatively minor accounting differences, a stock dividend has the same
effect as a stock split. In fact, you can see the relationship between the two because both
companies announced the stock dividend in the same way a stock split would be
announced.
Value of Stock Splits and Stock Dividends
The laws of logic tell us that stock splits and stock dividends can (1) leave the value of the
firm unaffected, (2) increase its value, or (3) decrease its value. Unfortunately, the issues are
complex enough that one cannot easily determine which of the three relationships holds.
The Benchmark Case A strong case can be made that stock dividends and splits do
not change either the wealth of any shareholder or the wealth of the firm as a whole. The
reason is that they are just paper transactions and alter the number of shares outstanding.
For example, if a firm declares a two-for-one split, all that happens is that the number of
shares is doubled, with the result that each share is worth half as much. The total value is
not affected.
Although this simple conclusion is relatively obvious, there are reasons that often are
given to suggest that there may be some benefits to these actions. The typical financial man-
ager is aware of many real-world complexities, and, for that reason, the stock split or stock
dividend decision is not treated lightly in practice.
Popular Trading Range Proponents of stock dividends and stock splits frequently
argue that a security has a proper trading range. When the security is priced above this
level, many investors do not have the funds to buy the common trading unit of 100 shares,
called a round lot. Thus, firms will split the stock to keep the price in this trading range.
Although this argument is a popular one, its validity is questionable for a number of
reasons. Mutual funds, pension funds, and other institutions have steadily increased their
trading activity since World War II and now handle a sizable percentage of total trading
volume (e.g., on the order of 80 percent of NYSE trading volume). Because these institu-
tions buy and sell in huge amounts, the individual share price is of little concern.
Furthermore, we sometimes observe share prices that are quite large without appearing
to cause problems. For example, consider the Swiss chocolatier Lindt. In July 2018, Lindt
shares were selling for around 77,000 Swiss francs each, or about $77,600. A round lot
would have cost a cool $7.76 million. This is fairly expensive, but not compared to Berkshire
Hathaway, the U.S. company run by legendary investor Warren Buffett. In July 2018, each
share of the company’s Class A stock sold for about $285,000, down from a high of
$326,000 in January 2018 (the Class B stock was much cheaper at $186 per share).
Finally, there is evidence that stock splits actually may decrease the liquidity of the
company’s shares. Following a two-for-one split, the number of shares traded should more
than double if liquidity is increased by the split. This doesn’t appear to happen, and the op-
posite is sometimes observed.
Reverse Splits
A less frequently encountered financial maneuver is the reverse split. For example, in May
2018, shopping center owner DDR Corporation underwent a one-for-two reverse stock split,
and, in February 2018, Tenax Therapeutics, a specialty pharmaceutical company, underwent
Information on upcoming
stock splits is available
on the splits calendar at
investmenthouse.com/
splits.htm and finance
.yahoo.com.
trading range
Price range between
highest and lowest prices
at which a stock is
typically traded.
reverse split
Stock split under which a
firm’s number of shares
outstanding is reduced.
ros13952_ch14_457-486.indd 478 12/21/18 11:45 AM
C H A P T E R 1 4 Dividends and Dividend Policy 479
a 1-for-20 reverse stock split. In a 1-for-20 reverse split, each investor exchanges 20 old shares
for 1 new share. The par value is increased by a factor of 20 in the process. For small com-
panies, reverse splits can become quite large. In February 2018, dry bulk transportation
company FreeSeas, Inc., completed a whopper, a 1-for-5,000 reverse split.
Given real-world imperfections, three related reasons are cited for reverse splits. First,
transaction costs to shareholders may be less after the reverse split. Second, the liquidity
and marketability of a company’s stock might be improved when its price is raised to the
popular trading range. Third, stocks selling at prices below a certain level are not considered
respectable, meaning that investors underestimate these firms’ earnings, cash flow, growth,
and stability. Some financial analysts argue that a reverse split can help achieve instant re-
spectability. As was the case with stock splits, none of these reasons is particularly compel-
ling, especially not the third one.
There are two other reasons for reverse splits. First, stock exchanges have minimum
price per share requirements. A reverse split may bring the stock price up to such a mini-
mum. For example, NASDAQ begins the delisting process for companies whose stock price
drops below $1 per share for 30 days. Following the collapse of the Internet boom in 2001–
2002, a large number of Internet-related companies found themselves in danger of being
delisted and used reverse splits to boost their stock prices. Second, companies sometimes
perform reverse splits and, at the same time, buy out any stockholders who end up with less
than a certain number of shares.
For example, in February 2017, Lime Energy completed a reverse/forward split. In this
case, the company first did a 1-for-300 reverse stock split. The company repurchased all
shares held by stockholders with less than one share of stock, thereby eliminating small
shareholders (and reducing the total number of shareholders). The purpose of the reverse
split was to allow the company to save on administrative expenses related to shareholder
relations. What made the proposal especially imaginative was that immediately after the re-
verse split, the company did a 300-for-1 ordinary split to restore the stock to its original cost!
CONCEPT QUESTIONS
14.5a What is the effect of a stock split on stockholder wealth?
14.5b What is a reverse split?
SUMMARY AND CONCLUSIONS
In this chapter, we first discussed the types of dividends and how they are paid. We then
defined dividend policy and examined whether or not dividend policy matters. Next, we il-
lustrated how a firm might establish a dividend policy and described an important alterna-
tive to cash dividends, a share repurchase.
In covering these subjects, we saw that:
1. Dividend policy is irrelevant when there are no taxes or other imperfections.
2. Individual shareholder income taxes and new issue flotation costs are real-world
considerations that favor a low-dividend payout. With taxes and new issue costs, the
firm should pay out dividends only after all positive NPV projects have been fully
financed.
ros13952_ch14_457-486.indd 479 12/21/18 11:45 AM
480 P A R T 7 Long-Term Financing
3. There are groups in the economy that may favor a high payout. These include many
large institutions such as pension plans. Recognizing that some groups prefer a high
payout and some prefer a low payout, the clientele effect supports the idea that
dividend policy responds to the needs of stockholders. For example, if 40 percent of
the stockholders prefer low dividends and 60 percent of the stockholders prefer high
dividends, approximately 40 percent of companies will have a low-dividend payout,
while 60 percent will have a high payout. This sharply reduces the impact of any
individual firm’s dividend policy on its market price.
4. Dividend stability is usually viewed as highly desirable. We therefore discussed a
compromise strategy that provides for a stable dividend and appears to be quite
similar to the dividend policies many firms follow in practice.
5. A stock repurchase acts much like a cash dividend but has a significant tax advantage.
Stock repurchases are therefore a very useful part of overall dividend policy.
To close out our discussion of dividends, we emphasize one last time the difference
between dividends and dividend policy. Dividends are important because the value of a
share of stock is ultimately determined by the dividends that will be paid. What is less clear
is whether or not the time pattern of dividends (more now versus more later) matters. This
is the dividend policy question, and it is not easy to give a definitive answer to it.
POP QUIZ!
Can you answer the following questions? If your class is using Connect, log on to
SmartBook to see if you know the answers to these and other questions, check out
the study tools, and find out what topics require additional practice!
Section 14.1 What are the forms of cash dividends?
Section 14.2 According to the clientele effect, can a firm boost its share price by
raising dividends?
Section 14.3 When a firm authorizes a trustee to repurchase shares as they be-
come available, what purchase technique is it using?
Section 14.4 What is a firm paying cash dividends signaling?
Section 14.5 Why is a stock dividend not a true dividend?
CHAPTER REVIEW AND SELF-TEST PROBLEM
14.1 Repurchase versus Cash Dividend Trantor Corporation is deciding whether to
pay out $300 in excess cash in the form of an extra dividend or a share repurchase.
Current earnings are $1.50 per share, and the stock sells for $15. The market value
balance sheet before paying out the $300 is as follows:
Market Value Balance Sheet
(before paying out excess cash)
Excess cash $ 300 Debt $ 400
Other assets 1,600 Equity 1,500
Total $1,900 Total $1,900
Evaluate the two alternatives in terms of the effect on the price per share of the
stock, the EPS, and the PE ratio. (See Problem 12.)
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C H A P T E R 1 4 Dividends and Dividend Policy 481
■ Answer to Chapter Review and Self-Test Problem
14.1 The market value of the equity is $1,500. The price per share is $15, so there are
100 shares outstanding. The cash dividend would amount to $300/100 = $3 per
share. When the stock goes ex dividend, the price will drop by $3 per share to $12.
Put another way, the total assets decrease by $300, so the equity value goes down by
this amount to $1,200. With 100 shares, the new stock price is $12 per share. After
the dividend, EPS will be the same, $1.50, but the PE ratio will be $12/$1.50 =
8 times.
With a repurchase, $300/15 = 20 shares will be bought up, leaving 80. The
equity will again be worth $1,200 total. With 80 shares, this is $1,200/80 = $15 per
share, so the price doesn’t change. Total earnings for Trantor must be $1.50 × 100 =
$150. After the repurchase, EPS will be higher at $150/80 = $1.875. The PE ratio,
however, still will be $15/$1.875 = 8 times.
CRITICAL THINKING AND CONCEPTS REVIEW
LO 2 14.1 Dividend Policy Irrelevance How is it possible that dividends are so
important, but, at the same time, dividend policy is irrelevant?
LO 4 14.2 Stock Repurchases What is the impact of a stock repurchase on a
company’s debt ratio? Does this suggest another use for excess cash?
LO 1 14.3 Life Cycle Theory of Dividends Explain the life cycle theory of dividend
payments. How does it explain corporate dividend payments that are seen
in the stock market?
LO 1 14.4 Dividend Chronology On Friday, December 8, Hometown Power Co.’s
board of directors declares a dividend of 75 cents per share payable on
Wednesday, January 17, to shareholders of record as of Wednesday, January
3. When is the ex-dividend date? If a shareholder buys stock before that
date, who gets the dividends on those shares, the buyer or the seller?
LO 1 14.5 Alternative Dividends Some corporations, like one British company that
offers its large shareholders free crematorium use, pay dividends in kind
(i.e., offer their services to shareholders at below-market cost). Should
mutual funds invest in stocks that pay these dividends in kind? (The
fundholders do not receive these services.)
LO 2 14.6 Dividends and Stock Price If increases in dividends tend to be followed
by (immediate) increases in share prices, how can it be said that dividend
policy is irrelevant?
LO 2 14.7 Dividends and Stock Price Last month, Central Virginia Power
Company, which had been having trouble with cost overruns on a nuclear
power plant that it had been building, announced that it was “temporarily
suspending dividend payments due to the cash flow crunch associated with
its investment program.” The company’s stock price dropped from $28.50
to $25 when this announcement was made. How would you interpret this
change in the stock price (i.e., what would you say caused it)?
LO 1 14.8 Dividend Reinvestment Plans The DRK Corporation recently has
developed a dividend reinvestment plan (DRIP). The plan allows investors
to reinvest cash dividends automatically in DRK in exchange for new shares
of stock. Over time, investors in DRK will be able to build their holdings by
reinvesting dividends to purchase additional shares of the company.
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482 P A R T 7 Long-Term Financing
Over 1,000 companies offer dividend reinvestment plans. Most companies
with DRIPs charge no brokerage or service fees. In fact, the shares of DRK
will be purchased at a 10 percent discount from the market price.
A consultant for DRK estimates that about 75 percent of DRK’s
shareholders will take part in this plan. This is somewhat higher than the
average.
Evaluate DRK’s dividend reinvestment plan. Will it increase shareholder
wealth? Discuss the advantages and disadvantages involved here.
LO 2 14.9 Dividend Policy During 2017, 108 companies went public with common
stock offerings, raising a combined total of $24.5 billion. Relatively few of
these 108 companies involved paid cash dividends. Why do you think most
chose not to pay dividends?
LO 1 14.10 Investment and Dividends The Phew Charitable Trust pays no taxes on
its capital gains or on its dividend income or interest income. Would it be
irrational for it to have low-dividend, high-growth stocks in its portfolio?
Would it be irrational for it to have municipal bonds in its portfolio?
Explain.
QUESTIONS AND PROBLEMS
Select problems are available in McGraw-Hill Connect. Please see the pack-
aging options section of the Preface for more information.
BASIC (Questions 1–11)
1. Dividends and Stock Prices Your portfolio is 200 shares of Callahan, Inc.
The stock currently sells for $93 per share. The company has announced a
dividend of $1.43 per share with an ex-dividend date of April 19. Assuming
no taxes, how much will your stock be worth on April 19?
2. Dividends and Stock Prices It is April 19. Using the information in the
previous problem, what is your total portfolio value?
3. Dividends and Taxes Estes Park, Inc., has declared a dividend of $8.40
per share. Suppose capital gains are not taxed, but dividends are taxed at 15
percent. New IRS regulations require that taxes be withheld at the time the
dividend is paid. The company’s stock sells for $87 per share, and the stock
is about to go ex dividend. What do you think the ex-dividend price will be?
4. Stock Dividends The owners’ equity accounts for Masterson International
are shown here:
Common stock ($1 par value) $ 345,000
Capital surplus 157,000
Retained earnings 33333333603,000
Total owners’ equity $805,000
a. If the company’s stock currently sells for $42 per share and a 10 percent
stock dividend is declared, how many new shares will be distributed?
Show how the equity accounts would change.
b. If the company declared a 25 percent stock dividend, how would the
accounts change?
LO 2
LO 2
LO 2
LO 3
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C H A P T E R 1 4 Dividends and Dividend Policy 483
5. Stock Splits For the company in Problem 4, show how the equity accounts
will change if:
a. The company declares a two-for-one stock split. How many shares are
outstanding now? What is the new par value per share?
b. The company declares a one-for-five reverse stock split. How many
shares are outstanding now? What is the new par value per share?
6. Stock Splits and Stock Dividends Bermuda Triangle Corporation (BTC)
currently has 395,000 shares of stock outstanding that sell for $83 per share.
Assuming no market imperfections or tax effects exist, what will the share
price be after:
a. BTC has a five-for-three stock split?
b. BTC has a 15 percent stock dividend?
c. BTC has a 42.5 percent stock dividend?
d. BTC has a four-for-seven reverse stock split?
e. Determine the new number of shares outstanding in parts (a)
through (d).
7. Regular Dividends The balance sheet for Tempest, Inc., is shown here in
market value terms. There are 19,000 shares of stock outstanding.
Market Value Balance Sheet
Cash $120,000
Fixed assets 33476,600 Equity $596,600
Total $596,600 Total $596,600
The company has declared a dividend of $1.15 per share. The stock goes
ex dividend tomorrow. Ignoring any tax effects, what is the stock selling for
today? What will it sell for tomorrow? What will the balance sheet look like
after the dividends are paid?
8. Share Repurchase In the previous problem, suppose the company has
announced it is going to repurchase $21,850 worth of stock instead of paying
a dividend. What effect will this transaction have on the equity of the firm?
How many shares will be outstanding? What will the price per share be
after the repurchase? Ignoring tax effects, show how the share repurchase is
effectively the same as a cash dividend.
9. Stock Dividends The market value balance sheet for Briggs Manufacturing
is shown here. The company has declared a 20 percent stock dividend.
The stock goes ex dividend tomorrow (the chronology for a stock dividend
is similar to that for a cash dividend). There are 21,000 shares of stock
outstanding. What will the ex-dividend price be?
Market Value Balance Sheet
Cash $135,000 Debt $215,000
Fixed assets 3333730,000 Equity 3650,000
Total $865,000 Total $865,000
10. Stock Dividends The company with the common equity accounts shown
here has declared a 10 percent stock dividend at a time when the market
LO 3
LO 3
LO 1
LO 4
LO 3
LO 3
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484 P A R T 7 Long-Term Financing
value of its stock is $48 per share. What effects on the equity accounts will
the distribution of the stock dividend have?
Common stock ($1 par value) $33 225,000
Capital surplus 1,070,000
Retained earnings 3 3333332,543,000
Total owners’ equity $3,838,000
11. Stock Splits In the previous problem, suppose the company instead
decides on a two-for-one stock split. The firm’s 67-cent-per-share cash
dividend on the new (postsplit) shares represents an increase of 10 percent
over last year’s dividend on the presplit stock. What effect does this have on
the equity accounts? What was last year’s dividend per share?
INTERMEDIATE (Questions 12–13)
12. Stock Repurchase Taco Time Corporation is evaluating an extra dividend
versus a share repurchase. In either case, $7,095 would be spent. Current
earnings are $2.70 per share, and the stock currently sells for $59 per share.
There are 4,300 shares outstanding. Ignore taxes and other imperfections in
answering the first two questions.
a. Evaluate the two alternatives in terms of the effect on the price per share
of the stock and shareholder wealth.
b. What will be the effect on the company’s EPS and PE ratio under the
two different scenarios?
c. In the real world, which of these actions would you recommend? Why?
13. Dividend Policy The Quick Buck Company is an all-equity firm that has
been in existence for the past three years. Company management expects
that the company will last for two more years and then be dissolved. The firm
will generate cash flows of $450,000 next year and $790,000 in two years,
including the proceeds from the liquidation. There are 20,000 shares of stock
outstanding and shareholders require a return of 12 percent.
a. What is the current price per share of the stock?
b. The board of directors is dissatisfied with the current dividend policy
and proposes that a dividend of $580,000 be paid next year. To raise the
cash necessary for the increased dividend, the company will sell new
shares of stock. How many shares of stock must be sold? What is the
new price per share of the existing shares of stock?
CHALLENGE (Questions 14–15)
14. Expected Return, Dividends, and Taxes The Gecko Company and
the Gordon Company are two firms whose business risk is the same
while having different dividend policies. Gecko pays no dividend, whereas
Gordon has an expected dividend yield of 3.5 percent. Suppose the capital
gains tax rate is zero, whereas the income tax rate is 28 percent. Gecko has
an expected earnings growth rate of 12 percent annually, and its stock price
is expected to grow at this same rate. If the aftertax expected returns on the
two stocks are equal (because they are in the same risk class), what is the
pretax required return on Gordon’s stock?
LO 3
LO 4
LO 2
LO 2
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C H A P T E R 1 4 Dividends and Dividend Policy 485
15. Dividends and Taxes As discussed in the text, in the absence of market
imperfections and tax effects, we would expect the share price to decline
by the amount of the dividend payment when the stock goes ex dividend.
Once we consider the role of taxes, however, this is not necessarily true. One
model has been proposed that incorporates tax effects into determining the
ex-dividend price:6
(P0 − Px)/D = (1 − TP)/(1 − TG)
where P0 is the price just before the stock goes ex, Px is the ex-dividend share
price, D is the amount of the dividend per share, TP is the relevant marginal
personal tax rate on dividends, and TG is the effective marginal tax rate on
capital gains.
a. If TP = TG = 0, how much will the share price fall when the stock goes ex?
b. If TP = 15 percent and TG = 0, how much will the share price fall?
c. If TP = 15 percent and TG = 30 percent, how much will the share price
fall?
d. Suppose the only owners of stock are corporations. Recall that
corporations get at least an 80 percent exemption from taxation on the
dividend income they receive, but they do not get such an exemption on
capital gains. If the corporation’s income and capital gains tax rates are
both 21 percent, what does this model predict the ex-dividend share
price will be?
e. What does this problem tell you about real-world tax considerations and
the dividend policy of the firm?
LO 2
14.1 Dividend Reinvestment Plans Dividend reinvestment plans (DRIPs) permit
shareholders to automatically reinvest cash dividends in the company. To find out more
about DRIPs, go to www.fool.com and answer the following questions. What are the
advantages Motley Fool lists for DRIPs? What are the different types of DRIPs? What is
a direct purchase plan? How does a direct purchase plan differ from a DRIP?
14.2 Dividends Go to www.thestreet.com/dividends and find the list of dividends. How
many companies went ex dividend today? What is the largest declared dividend? For the
stocks going ex today, what is the longest time until the payable date?
14.3 Stock Splits Go to www.stocksplits.net and find the stock splits. How many stock
splits are listed? How many are reverse splits? What is the largest split and the largest
reverse split in terms of shares? Pick a company and follow the link. What type of
information do you find?
14.4 Stock Splits How many times has Procter & Gamble stock split? Go to P&G’s
webpage at www.pg.com and find the history of the company’s stock splits. When did
Procter & Gamble stock first split? What was the split? When was the most recent stock
split? If you owned 100 shares of Procter & Gamble on January 1, 1950, and never sold
any shares, how many shares would you own today?
WHAT’S ON
THE WEB?
6N. Elton and M. Gruber, “Marginal Stockholder Tax Rates and the Clientele Effect,” Review of Economics and Sta-
tistics 52 (February 1970).
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486 P A R T 7 Long-Term Financing
who provided capital for the company, is the third pri-
mary owner. Each owns 25 percent of the 1 million
shares outstanding. The company has several other
individuals, including current employees, who own the
remaining shares.
Recently, the company designed a new computer
motherboard. The company’s design is both more effi-
cient and less expensive to manufacture, and the ETI
design is expected to become standard in many per-
sonal computers. After investigating the possibility of
manufacturing the new motherboard, ETI determined
that the costs involved in building a new plant would be
prohibitive. The owners also decided that they were un-
willing to bring in another large outside owner. Instead,
ETI sold the design to an outside firm. The sale of the
motherboard design was completed for an aftertax pay-
ment of $30 million.
Electronic Timing, Inc. (ETI), is a small company founded 15 years ago by electronics engineers Tom
Miller and Jessica Kerr. ETl manufactures integrated
circuits to capitalize on the complex mixed-signal de-
sign technology and recently has entered the market
for frequency timing generators, or silicon timing de-
vices, which provide the timing signals or “clocks” nec-
essary to synchronize electronic systems. Its clock
products originally were used in PC video graphics ap-
plications, but the market subsequently expanded to
include motherboards, PC peripheral devices, and
other digital consumer electronics, such as digital tele-
vision boxes and game consoles. ETI also designs and
markets custom application-specific integrated circuits
(ASICs) for industrial customers. The ASIC’s design
combines analog and digital, or mixed-signal, technol-
ogy. In addition to Tom and Jessica, Nolan Pittman,
CHAPTER CASE
Electronic Timing, Inc.
1. Tom believes the company should use the extra
cash to pay a special one-time dividend. How will
this proposal affect the stock price? How will it
affect the value of the company?
2. Jessica believes the company should use the
extra cash to pay off debt and upgrade and
expand its existing manufacturing capability. How
would Jessica’s proposals affect the company?
3. Nolan favors a share repurchase. He argues that a
repurchase will increase the company’s PE ratio,
return on assets, and return on equity. Are his
arguments correct? How will a share repurchase
affect the value of the company?
4. Another option discussed by Tom, Jessica, and
Nolan would be to begin a regular dividend pay-
ment to shareholders. How would you evaluate
this proposal?
5. One way to value a share of stock is the dividend
growth, or growing perpetuity, model. Consider
the following: The dividend payout ratio is
1 – b, where b is the “retention” or “plowback” ra-
tio. So, the dividend next year will be the earnings
next year, E1, times (1 – b). The most commonly
used equation to calculate the sustainable growth
rate is the return on equity times the retention ra-
tio. Substituting these relationships into the divi-
dend growth model, we get the following equation
to calculate the price of a share of stock today:
P 0 =
E 1 “(1 − b”) _________ R S − ROE × b
What are the implications of this result in terms of
whether the company should pay a dividend or
upgrade and expand its manufacturing capability?
Explain.
6. Does the question of whether the company
should pay a dividend depend on whether the
company is organized as a corporation or an LLC?
Q U E S T I O N S
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Please visit us at essentialsofcorporatefinance.blogspot.com for the latest developments in the world of corporate finance.
487
Please visit us at essentialsofcorporatefinance.blogspot.com for the latest developments in the world of corporate finance.
On March 23, 2018, online backup and collaboration company Dropbox went public. Assisted by the investment banks
Goldman Sachs and JPMorgan, along with a syndicate of 10 other
banks, Dropbox sold about 26.8 million shares of stock to the public
at a price of $21. The stock price opened trading at $29 before
reaching a high for the day of $31.60. At the end of the day, the
stock closed at $28.48. The Dropbox IPO raised $563 million, not
an extremely large amount for an IPO. However, company insiders
still held about 26 percent of the company’s stock. In this chapter,
we examine the process by which companies such as Dropbox sell
stock to the public, the costs of doing so, and the role of investment
banks in the process.
Businesses large and small have one thing in common: They
need long-term capital. This chapter describes how they get it. We
pay particular attention to what is probably the most important stage in a company’s financial
life cycle, the initial public offering. Such offerings are the process by which companies con-
vert from being privately owned to being publicly owned. For many, starting a company,
growing it, and taking it public is the ultimate entrepreneurial dream.
All firms, at varying times, must obtain capital. To do so, a firm must either borrow the money (debt financing), sell a portion of the firm (equity financing), or both. How a
firm raises capital depends a great deal on the size of the firm, its life-cycle stage, and its
growth prospects.
In this chapter, we examine some of the ways in which firms actually raise capital. We
begin by looking at companies in the early stages of their lives and the importance of ven-
ture capital for such firms. We then look at the process of going public and the role of
Raising Capital15
LEARNING OBJECTIVES
After studying this chapter, you should
be able to:
LO 1 Explain the venture capital market
and its role in the financing of new,
high-risk ventures.
LO 2 Describe how securities are sold to
the public and the role of
investment banks in the process.
LO 3 Explain initial public offerings, and
identify some of the costs of going
public.
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488 P A R T 7 Long-Term Financing
investment banks. Along the way, we discuss many of the issues associated with selling secu-
rities to the public and their implications for all types of firms. We close the chapter with a
discussion of sources of debt capital.1
THE FINANCING LIFE CYCLE OF A FIRM:
EARLY-STAGE FINANCING AND VENTURE
CAPITAL
One day, you and a friend have a great idea for a new computer software product that helps
users communicate using the next generation Meganet. Filled with entrepreneurial zeal, you
christen the product MegaComm and set about bringing it to market.
Working nights and weekends, you are able to create a prototype of your product. It
doesn’t actually work, but at least you can show it around to illustrate your idea. To actually
develop the product, you need to hire programmers, buy computers, rent office space, and
so on. Unfortunately, because you are both college students, your combined assets are not
sufficient to fund a pizza party, much less a start-up company. You need what is often re-
ferred to as OPM—other people’s money.
Your first thought might be to approach a bank for a loan. You would probably dis-
cover, however, that banks are generally not interested in making loans to start-up compa-
nies with no assets (other than an idea) run by fledgling entrepreneurs with no track
record. Instead, your search for capital would very likely lead you to the venture capital
(VC) market.
Venture Capital
The term venture capital does not have a precise meaning, but it generally refers to financing
for new, often high-risk, ventures. For example, before it went public, Internet auctioneer
eBay was venture capital-financed. Individual venture capitalists invest their own money,
whereas venture capital firms specialize in pooling funds from various sources and investing
them. The underlying sources of funds for such firms include individuals, pension funds,
insurance companies, large corporations, and even university endowment funds. The broad
term private equity often is used to label the rapidly growing area of equity financing for
nonpublic companies.2
Venture capitalists and venture capital firms recognize that many, or even most, new
ventures will not fly, but the occasional one will. The potential profits are enormous in such
cases. To limit their risk, venture capitalists generally provide financing in stages. At each
stage, enough money is invested to reach the next milestone or planning stage. For example,
the first-stage (or first “round”) financing might be enough to get a prototype built and a
manufacturing plan completed. Based on the results, the second-stage financing might be a
major investment needed to actually begin manufacturing, marketing, and distribution.
There might be many such stages, each of which represents a key step in the process of
growing the company.
Venture capital firms often specialize in different stages. Some specialize in very early
“seed money,” or ground floor, financing. In contrast, financing in the later stages might
15.1
venture capital (VC)
Financing for new, often
high-risk, ventures.
1We are indebted to Jay R. Ritter of the University of Florida and M. Shane Hadden of The Currency Report
(www.globalcurrencyreport.com) for helpful comments and suggestions on this chapter.
2So-called vulture capitalists specialize in high-risk investments in established, but financially distressed, firms.
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C H A P T E R 1 5 Raising Capital 489
come from venture capitalists specializing in so-called mezzanine level financing, where
mezzanine level refers to the level just above the ground floor.
The fact that financing is available in stages and is contingent on specified goals being
met is a powerful motivating force for the firm’s founders. Often, the founders receive rela-
tively little in the way of salary and have substantial portions of their personal assets tied up
in the business. At each stage of financing, the value of the founders’ stake grows and the
probability of success rises. If goals are not met, the venture capitalist will withhold further
financing, thereby limiting future losses.
In addition to providing financing, venture capitalists generally will actively participate
in running the firm, providing the benefit of experience with previous start-ups as well as
general business expertise. This is especially true when the firm’s founders have little or no
hands-on experience running a company.
Some Venture Capital Realities
Although there is a large venture capital market, the truth is that access to venture capital is
really very limited. Venture capital companies receive huge numbers of unsolicited propos-
als, the vast majority of which end up in the circular file (the waste basket). Venture capital-
ists rely heavily on informal networks of engineers, scientists, lawyers, accountants, bankers,
and other venture capitalists to help identify potential investments. As a result, personal
contacts are important in gaining access to the venture capital market; it is very much an
“introduction” market.
Another simple fact about venture capital is that it is incredibly expensive. In a typical
deal, the venture capitalist will demand (and get) 40 percent or more of the equity in the
company. The venture capitalist frequently will hold voting convertible preferred stock,
which gives various priorities in the event that the company is sold or liquidated. The ven-
ture capitalist typically will demand (and get) several seats on the company’s board of direc-
tors and even may appoint one or more members of senior management.
Choosing a Venture Capitalist
Some start-up companies, particularly those headed by experienced, previously successful
entrepreneurs, will be in such demand that they will have the luxury of looking beyond the
money in choosing a venture capitalist. There are some key considerations in such a case,
some of which can be summarized as follows:
1. Financial strength is important. The venture capitalist needs to have the resources and
financial reserves for additional financing stages should they become necessary. This
doesn’t mean that bigger is necessarily better, however, because of our next
consideration.
2. Style is important. Some venture capitalists will wish to be very much involved in day-
to-day operations and decision making, whereas others will be content with monthly
reports. Which is better depends on the firm and also on the venture capitalists’
business skills. In addition, a large venture capital firm may be less flexible and more
bureaucratic than a smaller “boutique” firm.
3. References are important. Has the venture capitalist been successful with similar firms?
Of equal importance, how has the venture capitalist dealt with situations that didn’t
work out?
4. Contacts are important. A venture capitalist may be able to help the business in ways
other than helping with financing and management by providing introductions to
potentially important customers, suppliers, and other industry contacts. Venture
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490 P A R T 7 Long-Term Financing
capitalist firms frequently specialize in a few particular industries, and such
specialization could prove quite valuable.
5. Exit strategy is important. Venture capitalists are generally not long-term investors.
How and under what circumstances the venture capitalist will “cash out” of the
business should be carefully evaluated.
Conclusion
If a start-up succeeds, the big payoff frequently comes when the company is sold to an-
other company or goes public. Either way, investment bankers often are involved in the
process.
CONCEPT QUESTIONS
15.1a What is venture capital?
15.1b Why is venture capital often provided in stages?
SELLING SECURITIES TO THE PUBLIC:
THE BASIC PROCEDURE
We discuss the process of selling securities to the public in the next several sections, paying
particular attention to the process of going public.
There are many rules and regulations surrounding the process of selling securities.
The Securities Act of 1933 is the origin of federal regulations for all new interstate secu-
rities issues. The Securities Exchange Act of 1934 is the basis for regulating securities
already outstanding. The Securities and Exchange Commission, or SEC, administers
both acts.
There are a series of steps involved in issuing securities to the public. In general terms,
the basic procedure is as follows:
1. Management’s first step in issuing any securities to the public is to obtain approval
from the board of directors. In some cases, the number of authorized shares of
common stock must be increased. This requires a vote of the shareholders.
2. The firm must prepare a registration statement and file it with the SEC. With a few
exceptions, the registration statement is required for all public, interstate issues of
securities.
Normally, a registration statement contains many pages of financial information,
including a financial history, details of the existing business, proposed financing, and
plans for the future.
3. The SEC examines the registration statement during a waiting period. During this
time, the firm may distribute copies of a preliminary prospectus. The prospectus
contains much of the information put into the registration statement, and it is given to
potential investors by the firm. The preliminary prospectus is sometimes called a
red herring, in part because bold red letters are printed on the cover.
A registration statement becomes effective on the 20th day after its filing unless
the SEC sends a letter of comment suggesting changes. In that case, after the changes
are made, the 20-day waiting period starts again. It is important to note that the SEC
does not consider the economic merits of the proposed sale; it merely makes sure that
15.2
Find out what firms are
going public this week at
marketwatch.com.
registration
statement
A statement filed with the
SEC that discloses all
material information
concerning the
corporation making a
public offering.
prospectus
A legal document
describing details of the
issuing corporation and
the proposed offering to
potential investors.
red herring
A preliminary prospectus
distributed to prospective
investors in a new issue of
securities.
ros13952_ch15_487-520.indd 490 12/22/18 5:59 PM
C H A P T E R 1 5 Raising Capital 491
various rules and regulations are followed. Also, the SEC generally does not check the
accuracy or truthfulness of information in the prospectus.
The registration statement does not initially contain the price of the new issue.
Usually, a price amendment is filed at or near the end of the waiting period, and the
registration becomes effective.
4. The company cannot sell the securities during the waiting period. However, oral offers
can be made.
5. On the effective date of the registration statement, a price is determined and a full-
fledged selling effort gets under way. A final prospectus must accompany the delivery
of securities or confirmation of sale, whichever comes first.
Tombstone advertisements (or tombstones) are used by underwriters after the waiting
period. An example is reproduced in Figure 15.1. The tombstone contains the name of the
issuer (the World Wrestling Federation, or WWF, in this case). It provides some informa-
tion about the issue, and it lists the investment banks (the underwriters) that are involved
with selling the issue. The role of the investment banks in selling securities is discussed
more fully in the following pages.
The investment banks are divided into groups called brackets on the tombstone, based
on their participation in the issue, and the names of the banks are listed alphabetically
within each bracket. The brackets often are viewed as a kind of pecking order. In general,
the higher the bracket, the greater is the underwriter’s prestige.
Crowdfunding
On April 5, 2012, the JOBS Act was signed into law. A provision of this act allowed compa-
nies to raise money through crowdfunding, which is the practice of raising small amounts of
capital from a large number of people, typically via the Internet. Crowdfunding was first
used to underwrite the U.S. tour of British rock band Marillion, but the JOBS Act allows
companies to sell regular equity by crowdfunding. Originally, the JOBS Act allowed a com-
pany to issue up to $1 million in securities in a 12-month period, although this limit was
raised to $5 million in 2015.
We should make an important distinction about two types of crowdfunding—project crowd-
funding and equity crowdfunding. As an example of project crowdfunding, consider the card
game Exploding Kittens, which exploded on the crowdfunding website Kickstarter and raised
$8.8 million from about 220,000 backers. During the crowdfunding campaign, the company
presold card decks. Every backer was shipped a deck of cards for the game, beginning about
six months after the campaign ended. In this case, the backers were purchasers, not inves-
tors. This type of crowdfunding also has become a popular way to raise money for charitable
causes. In contrast, with equity crowdfunding, the backers receive equity in the company.
In May 2016, Regulation CF (also known as Title III of the JOBS Act) kicked in, which
allows small investors access to new crowdfunding “portals.” Previously, investors in crowd-
funding had to be “accredited.” For an individual, this requirement translates to more than
$1 million in net worth or more than $200,000 in income for two of the past three years.
Regulation CF allows investors with less than $100,000 in income or assets to invest at least
$2,000 per year, up to a maximum of $5,000.
To sell securities through Regulation CF, a company must file a form with the SEC.
This filing makes the company eligible to list its securities on a crowdfunding portal that is
approved by FINRA (the Financial Industry Regulatory Authority), the same agency we
mentioned earlier in the textbook for bond price reporting. Crowdfunding portals are al-
ready specializing. For example, there are portals that specialize in only accredited inves-
tors, all investors, or real estate, to name just a few.
tombstone
An advertisement
announcing a public
offering.
Check out two of the more
well-known project and
charitable crowdfunding
websites at www.kick
starter.com and www
.gofundme.com.
ros13952_ch15_487-520.indd 491 12/22/18 5:59 PM
An example of a
tombstone
advertisement
FIGURE 15.1
World Wrestling Federation Entertainment, Inc.
Class A Common Stock
Price $17.00 Per Share
Copies of the Prospectus may be obtained in any State in which this announcement
is circulated from only such of the Underwriters, including the undersigned,
as may lawfully offer these securities in such State.
U.S. Offering
9,200,000 Shares
This portion of the underwriting is being offered in the United States and Canada.
Bear, Stearns & Co. Inc.
Credit Suisse First Boston
Merrill Lynch & Co.
Wit Capital Corporation
International Offering
2,300,000 Shares
This portion of the underwriting is being offered outside of the United States and Canada.
Bear, Stearns International Limited
Credit Suisse First Boston
Merrill Lynch International
This announcement is neither an offer to sell nor a solicitation of an offer to buy any of these securities.
The offering is made only by the Prospectus.
New Issue
11,500,000 Shares
Allen & Company Banc of America Securities LLC Deutsche Banc Alex. Brown
Donaldson, Lufkin & Jenrette A.G. Edwards & Sons, Inc. Hambrecht & Quist ING Barings
Prudential Securities SG Cowen Wassertein Perella Securities, Inc. Advest, Inc.
Axiom Capital Management, Inc. Blackford Securities Corp. J.C. Bradford & Co.
Joseph Charles & Assoc., Inc. Chatsworth Securities LLC Gabelli & Company, Inc.
Gaines, Berland Inc. Jefferies & Company, Inc. Josephthal & Co. Inc. Neuberger Berman, LLC
Raymond James & Associates, Inc. Sanders Morris Mundy
Tucker Anthony Cleary Gull Wachovia Securities, Inc.
Incorporated
492
ros13952_ch15_487-520.indd 492 12/22/18 5:59 PM
C H A P T E R 1 5 Raising Capital 493
Initial Coin Offerings
In addition to sales of traditional debt and equity, a company can raise funds by selling
tokens. These tokens often grant the holder the right to use the company’s service in the
future. For example, a company building a railroad may issue a token that can be used as a
train ticket after the railroad is built.
Token sales occur on digital currency platforms and easily can be transferred on the
platform or converted to U.S. dollars on specialized token exchanges. This liquidity has
made tokens a popular means of funding since their introduction in 2015. Tokens are now
purchased by both customers and investors, who may never use the token for the service
being offered.
The initial sale of a token on a digital currency platform is often called an initial coin
offering or ICO (to sound like IPO). Many start-up companies are now choosing to raise
funding through an ICO rather than the traditional venture capital channels. The most com-
mon platform for issuing new tokens is Ethereum, but there are many competitors. In 2017,
there were 234 ICOs with a total value of about $3.7 billion.
Token sales are most popular among companies that are building services based on
blockchain technology. This technology is at the heart of bitcoin and other cryptocurrencies.
A blockchain is a timestamped ledger of transactions that is kept among a network of users
without centralized control. It is similar to a traditional database, except that cryptography
is used to make it infeasible to change the data once they are added to the chain. Many
industries, including finance, are now updating their recordkeeping infrastructure with
blockchain technology.
Token sales also can serve as an effective marketing tool. This is especially true if the busi-
ness benefits from network effects as the potential for price appreciation in the tokens attracts
new customers. The increase in customers increases the value of the service, which in turn
increases the value of the tokens. For example, Civic is building a blockchain-based identity
platform and its currency is used to purchase identity verification services from trusted parties.
The company raised $33 million in June 2017 through an ICO of the CVC token. The total
value of the tokens at the end of 2017 was $224 million, although in an indication of the vola-
tility of tokens, the value dropped to less than $70 million by the middle of 2018.
CONCEPT QUESTIONS
15.2a What are the basic procedures in selling a new issue?
15.2b What is a registration statement?
ALTERNATIVE ISSUE METHODS
When a company decides to issue a new security, it can sell it as a public issue or a private
issue. In the case of a public issue, the firm is required to register the issue with the SEC.
However, if the issue is to be sold to fewer than 35 investors, the sale can be carried out
privately. In this case, a registration statement is not required.3
See upcoming ICOs at
tokenmarket.net
/ico-calendar.
The SEC has some
warnings on ICOs at www
.sec.gov/news/public
-statement/statement
-clayton-2017-12-11.
See the market value of
tokens at https://coin
marketcap.com.
15.3
3A variety of different arrangements can be made for private equity issues. Selling unregistered securities avoids the
costs of complying with the Securities Exchange Act of 1934. Regulation significantly restricts the resale of unreg-
istered equity securities. For example, the purchaser may be required to hold the securities for at least two years.
Many of the restrictions were significantly eased in 1990 for very large institutional investors, however. The private
placement of bonds is discussed in a later section.
ros13952_ch15_487-520.indd 493 12/22/18 5:59 PM
494 P A R T 7 Long-Term Financing
For equity sales, there are two kinds of public issues: a general cash offer and a
rights offer (or rights offering). With a cash offer, securities are offered to the general public
on a “first come, first served” basis. With a rights offer, securities are initially offered only
to existing owners. Rights offers are fairly common in other countries, but they are relatively
rare in the United States, particularly in recent years. We therefore focus on cash offers in
this chapter.
The first public equity issue that is made by a company is referred to as an
initial public offering (IPO), or an unseasoned new issue. This issue occurs when a company
decides to go public. Obviously, all initial public offerings are cash offers. If the firm’s exist-
ing shareholders wanted to buy the shares, the firm wouldn’t have to sell them publicly in
the first place.
A seasoned equity offering (SEO) is a new issue for a company with securities that
have been previously issued. The terms secondary and follow-on offering also are commonly
used. A seasoned equity offering of common stock can be made by using a cash offer or a
rights offer.
These methods of issuing new securities are shown in Table 15.1. They are discussed
beginning in Section 15.4.
CONCEPT QUESTIONS
15.3a Why is an initial public offering necessarily a cash offer?
15.3b What is the difference between a rights offer and a cash offer?
general cash offer
An issue of securities
offered for sale to the
general public on a cash
basis.
rights offer
A public issue of securities
in which securities are first
offered to existing
shareholders. Also known
as rights offering.
initial public offering
(IPO)
A company’s first equity
issue made available to
the public. Also
unseasoned new issue.
seasoned equity
offering (SEO)
A new equity issue of
securities by a company
that has previously issued
securities to the public.
The methods of
issuing new
securities
TABLE 15.1 Method Type Definition
Public
Traditional
negotiated
cash offer
Firm commitment
cash offer
Company negotiates an agreement with an
investment banker to underwrite and distribute the
new shares. A specified number of shares are bought
by underwriters and sold at a higher price.
Best efforts cash
offer
Company has investment bankers sell as many of the
new shares as possible at the agreed-upon price. There is
no guarantee concerning how much cash will be raised.
Some best efforts offerings do not use an underwriter.
Dutch auction
cash offer
Company has investment bankers auction shares to
determine the highest offer price obtainable for a
given number of shares to be sold.
Privileged
subscription
Direct rights offer Company offers the new stock directly to its existing
shareholders.
Standby rights
offer
Like the direct rights offer, this contains a privileged
subscription arrangement with existing shareholders.
The net proceeds are guaranteed by the underwriters.
Nontraditional
cash offer
Shelf cash offer Qualifying companies can authorize all the shares
they expect to sell over a two-year period and sell
them when needed.
Competitive firm
cash offer
Company can elect to award the underwriting contract
through a public auction instead of negotiation.
Private Direct placement Securities are sold directly to the purchaser, who, at
least until recently, generally could not resell the
securities for at least two years.
ros13952_ch15_487-520.indd 494 12/22/18 5:59 PM
C H A P T E R 1 5 Raising Capital 495
UNDERWRITERS
If the public issue of securities is a cash offer, underwriters are usually involved. Underwrit-
ing is an important line of business for large investment firms such as Merrill Lynch. Under-
writers perform services such as the following for corporate issuers:
1. Formulating the method used to issue the securities.
2. Pricing the new securities.
3. Selling the new securities.
Typically, the underwriter buys the securities for less than the offering price and accepts the
risk of not being able to sell them. The difference between the underwriter’s buying price
and the offering price is called the spread, or discount. It is the basic compensation re-
ceived by the underwriter. Sometimes the underwriter will get noncash compensation in the
form of warrants and stock in addition to the spread.4
Underwriters combine to form an underwriting group called a syndicate to share the
risk and to help sell the issue. In a syndicate, one or more managers arrange the offering.
This manager is designated as the lead manager, or principal manager. The lead manager
typically has the responsibility of pricing the securities. The other underwriters in the syndi-
cate serve primarily to distribute the issue.
Choosing an Underwriter
A firm can offer its securities to the highest bidding underwriter on a competitive offer basis,
or it can negotiate directly with an underwriter. In most cases, companies usually do new
issues of debt and equity on a negotiated offer basis.
There is evidence that competitive underwriting is cheaper to use than negotiated un-
derwriting, and the underlying reasons for the dominance of negotiated underwriting in the
United States are the subject of ongoing debate.
Types of Underwriting
Two basic types of underwriting are involved in a cash offer: firm commitment and best
efforts.
Firm Commitment Underwriting In firm commitment underwriting, the issuer
sells the entire issue to the underwriters, who then attempt to resell it. This is the most prev-
alent type of underwriting in the United States. This is really a purchase-resale arrangement,
and the underwriter’s fee is the spread. For a new issue of seasoned equity, the underwriters
can look at the market price to determine what the issue should sell for, and 95 percent of
all such new issues are firm commitments.
If the underwriter cannot sell all of the issue at the agreed-upon offering price, it may
have to lower the price on the unsold shares. Nonetheless, with firm commitment under-
writing, the issuer receives the agreed-upon amount, and all the risk associated with selling
the issue is transferred to the underwriter.
Because the offering price usually isn’t set until the underwriters have investigated how
receptive the market is to the issue, this risk is usually minimal. Also, because the offering
price usually is not set until just before selling commences, the issuer doesn’t know precisely
what its net proceeds will be until that time.
15.4
underwriters
Investment firms that act
as intermediaries between
a company selling
securities and the
investing public.
spread
Compensation to the
underwriter, determined
by the difference between
the underwriter’s buying
price and offering price.
syndicate
A group of underwriters
formed to share the risk
and to help sell an issue.
firm commitment
underwriting
The underwriter buys the
entire issue, assuming full
financial responsibility for
any unsold shares.
4Warrants are essentially options to buy stock at a fixed price for some fixed period of time.
ros13952_ch15_487-520.indd 495 12/22/18 5:59 PM
496 P A R T 7 Long-Term Financing
To determine the offering price, the underwriter will meet with potential buyers, typi-
cally large institutional buyers such as mutual funds. Often, the underwriter and company
management will do presentations in multiple cities, pitching the stock in what is known as
a road show. Potential buyers provide information on the price they would be willing to pay
and the number of shares they would purchase at a particular price. This process of solicit-
ing information about buyers and the prices and quantities they would demand is known as
book building. As we will see, despite the book building process, underwriters frequently get
the price wrong, or so it seems.
Best Efforts Underwriting In best efforts underwriting, the underwriter is legally
bound to use “best efforts” to sell the securities at the agreed-upon offering price. Beyond
this, the underwriter does not guarantee any particular amount of money to the issuer.
This form of underwriting has become very uncommon; firm commitments are the
dominant form.
Dutch Auction Underwriting With Dutch auction underwriting, the underwriter
does not set a fixed price for the shares to be sold. Instead, the underwriter conducts an
auction in which investors bid for shares. The offer price is determined based on the submit-
ted bids. A Dutch auction also is known by the more descriptive name uniform price auction.
This approach to selling securities to the public is relatively new in the IPO market and has
not been widely used there, but it is very common in the bond markets. For example, it is
the sole procedure used by the U.S. Treasury to sell enormous quantities of notes, bonds,
and bills to the public.
Dutch auction underwriting was much in the news in 2004 because the web search
company Google (now known as Alphabet) elected to use this approach. The best way to
understand a Dutch or uniform price auction is to consider a simple example. Suppose
the Rial Company wants to sell 400 shares to the public. The company receives five bids
as follows:
Bidder Quantity Price
A 100 shares $16
B 100 shares 14
C 200 shares 12
D 100 shares 12
E 200 shares 10
Thus, Bidder A is willing to buy 100 shares at $16 each, Bidder B is willing to buy 100 shares
at $14, and so on. The Rial Company examines the bids to determine the highest price that
will result in all 400 shares being sold. So, for example, at $14, A and B would buy only 200
shares, so that price is too high. Working our way down, all 400 shares won’t be sold until
we hit a price of $12, so $12 will be the offer price in the IPO. Bidders A through D will
receive shares; Bidder E will not.
There are two additional important points to observe in our example: First, all the win-
ning bidders will pay $12, even Bidders A and B, who actually bid a higher price. The fact
that all successful bidders pay the same price is the reason for the name “uniform price
auction.” The idea in such an auction is to encourage bidders to bid aggressively by provid-
ing some protection against bidding a price that is too high.
Second, notice that at the $12 offer price, there are actually bids for 500 shares,
which exceeds the 400 shares Rial wants to sell. Thus, there has to be some sort of
best efforts
underwriting
The underwriter sells as
much of the issue as
possible but can return
any unsold shares to the
issuer without financial
responsibility.
Dutch auction
underwriting
The type of underwriting
in which the offer price is
set based on competitive
bidding by investors. Also
known as a uniform price
auction.
Learn all about Dutch
auction IPOs at www
.wrhambrecht.com.
ros13952_ch15_487-520.indd 496 12/22/18 5:59 PM
C H A P T E R 1 5 Raising Capital 497
allocation. How this is done varies a bit, but, in the IPO market, the approach has been to
compute the ratio of shares offered to shares bid at the offer price or better, which, in our
example, is 400/500 = .8, and allocate bidders that percentage of their bids. In other
words, Bidders A through D would each receive 80 percent of the shares they bid at a
price of $12 per share.
The Green Shoe Provision
Many underwriting contracts contain a Green Shoe provision (sometimes called the over-
allotment option), which gives the members of the underwriting group the option to purchase
additional shares from the issuer at the offering price.5 Essentially, all IPOs and SEOs
include this provision, but ordinary debt offerings generally do not. The stated reason
for the Green Shoe option is to cover excess demand and oversubscriptions. Green Shoe
options usually last for about 30 days and involve no more than 15 percent of the newly
issued shares.
The Aftermarket
The period after a new issue is initially sold to the public is referred to as the aftermar-
ket. The lead underwriter frequently will “stabilize,” or support, the market price for a
relatively short time following the offering. This is done by actually selling 115 percent
of the issue. If the price rises in the aftermarket, the underwriter will exercise the Green
Shoe option to purchase the extra 15 percent needed. If the price declines, however, the
underwriter will step in and buy the stock in the open market, thereby supporting the
price. In this second case, the underwriter allows the Green Shoe option to expire.6
This happened in the May 2012 IPO of Facebook when lead underwriter Morgan Stan-
ley was forced to step in and stabilize the stock price. Even though the stock opened at
$42.05, it quickly fell to $38 less than an hour after trading on the stock began. At that
point, Morgan Stanley stepped in and began buying shares of the stock to create a floor
of $38 per share.
Lockup Agreements
Although they are not required by law, almost all underwriting contracts contain so-called
lockup agreements. Such agreements specify how long insiders must wait after an IPO be-
fore they can sell some or all of their stock. Lockup periods have become fairly standardized
in recent years at 180 days. Thus, following an IPO, insiders can’t cash out until six months
have gone by, which ensures that they maintain a significant economic interest in the com-
pany going public.
Lockup periods are also important because it is not unusual for the number of locked-up
shares to exceed the number of shares held by the public, sometimes by a substantial multi-
ple. On the day the lockup period expires, there is the possibility that a large number of
shares will hit the market on the same day and thereby depress values. The evidence sug-
gests that, on average, venture capital-backed companies are particularly likely to experience
a loss in value on the lockup expiration day.
Green Shoe
provision
A contract provision giving
the underwriter the option
to purchase additional
shares from the issuer at
the offering price. Also
overallotment option.
lockup agreement
The part of the
underwriting contract that
specifies how long
insiders must wait after an
IPO before they can sell
stock.
Learn more about
investment banks at Merrill
Lynch’s website: www.ml
.com.
5The term Green Shoe provision sounds quite exotic, but the origin is relatively mundane. The term comes from the
name of the Green Shoe Manufacturing Company, which, in 1963, was the first issuer to grant such an option.
6Occasionally, the price of a security falls dramatically when the underwriter ceases to stabilize the price. In such
cases, Wall Street humorists (the ones who didn’t buy any of the stock) have referred to the period following the
aftermarket as the aftermath.
ros13952_ch15_487-520.indd 497 12/22/18 5:59 PM
498 P A R T 7 Long-Term Financing
The Quiet Period
From the time a company begins to seriously consider an IPO until 40 calendar days follow-
ing an IPO, the SEC requires that a firm and its managing underwriters observe a “quiet
period.” This means that all communications with the public must be limited to ordinary
announcements and other purely factual matters. The SEC’s logic is that all relevant infor-
mation should be contained in the prospectus. An important result of this requirement is
that the underwriters’ analysts are prohibited from making recommendations to investors.
As soon as the quiet period ends, however, the managing underwriters typically publish re-
search reports, usually accompanied by a favorable “buy” recommendation.
Firms that don’t stay quiet can have their IPOs delayed. For example, just before Goo-
gle’s IPO, an interview with cofounders Sergey Brin and Larry Page appeared in Playboy.
The interview almost caused a postponement of the IPO, but Google was able to amend its
prospectus in time (by including the article!). However, in May 2004, Salesforce.com’s IPO
was delayed because an interview with CEO Marc Benioff appeared in The New York Times.
Salesforce.com finally went public two months later.
Direct Listing
While firms usually use underwriters to help their stock become publicly traded, it is not
required. If it wishes to do so, and it meets the requirements of the stock exchange, a com-
pany can do a direct listing. In this case, the firm arranges for its stock to be listed on the
exchange without marketing and other help from an underwriter. Direct listings are uncom-
mon for large firms, but music-streaming giant Spotify, with a valuation well into the billions
of dollars, completed one on the NYSE in 2018. Among other things, a direct listing is
much less expensive because there are no underwriting fees and other associated costs. Such
fees are discussed in detail in a subsequent section, and they can be substantial.
CONCEPT QUESTIONS
15.4a What do underwriters do?
15.4b What is the Green Shoe provision?
IPOs AND UNDERPRICING
Determining the correct offering price is the most difficult thing an underwriter must do for
an initial public offering. The issuing firm faces a potential cost if the offering price is set too
high or too low. If the issue is priced too high, it may be unsuccessful and have to be with-
drawn. If the issue is priced below the true market value, the issuer’s existing shareholders
will experience an opportunity loss when they sell their shares for less than they are worth.
Underpricing is fairly common. It obviously helps new shareholders earn a higher re-
turn on the shares they buy. However, the existing shareholders of the issuing firm are not
helped by underpricing. To them, it is an indirect cost of issuing new securities. For exam-
ple, consider Chinese online retailer Alibaba’s IPO in September 2014. The stock was priced
at $68 in the IPO and rose to a first-day high of $99.70 before closing at $93.89, a gain of
about 38.1 percent. Based on these numbers, Alibaba was underpriced by about $25.89 per
share. Because Alibaba sold 320.1 million shares, the company missed out on an additional
$8.3 billion, a record amount “left on the table.” The previous record of $5.1 billion was
held by Visa, set in its 2008 IPO.
direct listing
A security offering in
which the company offers
securities directly to
investors, bypassing
underwriters.
15.5
ros13952_ch15_487-520.indd 498 12/22/18 5:59 PM
C H A P T E R 1 5 Raising Capital 499
Dutch auctions are supposed to eliminate this kind of “pop” in first-day prices. As we
previously discussed, Google sold 19.6 million shares at a price of $85 in a Dutch auction
IPO. However, the stock closed at $100.34 on the first day, an increase of 18 percent, so
Google missed out on an additional $300 million.
One of the largest dollar amounts “left on the table” occurred in 1999 when eToys went
public, offering 8.2 million shares. The stock jumped $57 above the offer price on the first
day, which meant eToys left about half a billion dollars on the table. eToys could have used
the money; it filed for bankruptcy less than two years later. In May 2002, the company sued
its lead underwriter, claiming the offer price was deliberately set too low.
Of course, not all IPOs increase in price on the first day. For example, security com-
pany ADT went public on January 19, 2018, at a price of $14. The company’s stock opened
at $12.65, dropped to $12.00, before closing at $12.29 by the end of the day, a drop of about
12 percent from the IPO price.
A worse fate awaited BATS Global Markets. BATS, which stands for Better Alternative
Trading System, was an electronic stock market that handled about 11 percent of the trading
on the U.S. markets. On March 23, 2012, the company went public, selling 6.3 million
shares at a price of $16 each. The IPO was the first IPO to take place on the BATS market,
an important step toward attracting other new IPOs. However, shortly after trading on
BATS stock began, things turned sour. Trades were executed at $15.25, below the initial of-
fering price. Less than nine seconds later, the stock price dropped to .0002 cent! Less than
30 seconds later, trading on BATS stock was halted, all trades in the stock were canceled,
and the IPO was withdrawn.
Evidence on Underpricing
Figure 15.2 provides a more general illustration of the underpricing phenomenon. What is
shown is the month-by-month history of underpricing for SEC-registered IPOs.7 The period
IPO information is
ubiquitous on the World
Wide Web. Two sites of
interest are www.rena
issancecapital.com and
IPO Monitor at www
.ipomonitor.com.
Average initial returns by month for SEC-registered initial public offerings: 1960–2017
−50
0
50
100
150
200
19
60
19
65
19
70
19
75
19
80
19
85
19
90
19
95
20
00
20
05
20
10
20
15
A
ve
ra
ge
fi
rs
t-d
ay
re
tu
rn
(%
)
FIGURE 15.2
Source: Ibbotson, R. G., Sindelar, J. L. and Ritter, J. R., “The Market’s Problems with the Pricing of Initial Public Offerings,” Journal of Applied
Corporate Finance, vol. 7, Spring 1994, as updated by the authors.
7The discussion in this section draws on Jay R. Ritter, “Initial Public Offerings,” Contemporary Finance Digest 2
(Spring 1998).
ros13952_ch15_487-520.indd 499 12/22/18 5:59 PM
500 P A R T 7 Long-Term Financing
covered is 1960 through 2017. Figure 15.3 presents the number of offerings in each month
for the same period.
Figure 15.2 shows that underpricing can be quite dramatic, exceeding 100 percent in
some months. In such months, the average IPO more than doubled in value, sometimes in a
matter of hours. Also, the degree of underpricing varies through time, and periods of severe
underpricing (“hot issue” markets) are followed by periods of little underpricing (“cold is-
sue” markets). For example, in the 1960s, the average IPO was underpriced by 21.2 percent.
In the 1970s, the average underpricing was much smaller (7.2 percent), and the amount of
underpricing was actually very small or even negative for much of that time. For 1990–1999,
IPOs were underpriced by 21.4 percent on average, and for 2010–2017, the average under-
pricing was 15.5 percent.
From Figure 15.3, it is apparent that the number of IPOs is also highly variable through
time. Further, there are pronounced cycles in both the degree of underpricing and the num-
ber of IPOs. Comparing Figures 15.2 and 15.3, we see that increases in the number of new
offerings tend to follow periods of significant underpricing by roughly 6 to 12 months. This
probably occurs because companies decide to go public when they perceive that the market
is highly receptive to new issues.
Table 15.2 contains a year-by-year summary of underpricing for the years 1960 to 2017.
As is indicated, a grand total of 13,079 companies were included in this analysis. The degree
of underpricing averaged 16.8 percent overall for the 58 years examined. Securities were
overpriced on average in only 5 of the 58 years; in 1973, the average decrease in value was
−17.8 percent. At the other extreme, in 1999, the 484 issues were underpriced, on average,
by a remarkable 69.7 percent. The nearby Finance Matters box shows that IPO underpricing
is not confined to the United States; instead, it seems to be a global phenomenon.
IPO Underpricing: The 1999–2000 Experience
Table 15.2, along with Figures 15.2 and 15.3, show that 1999 and 2000 were extraordinary
years in the IPO market. During these two years, 866 companies went public, and the
Number of offerings by month for SEC-registered initial public offerings: 1960–2017
0
20
40
60
80
100
120
140
19
60
19
65
19
70
19
75
19
80
19
85
19
90
19
95
20
00
20
05
20
10
20
15
N
um
be
r o
f I
PO
s
FIGURE 15.3
Source: Ibbotson, R. G., Sindelar, J. L. and Ritter, J. R., “The Market’s Problems with the Pricing of Initial Public Offerings,” Journal of Applied
Corporate Finance, vol. 7, Spring 1994, as updated by the authors.
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C H A P T E R 1 5 Raising Capital 501
Number of offerings, average first-day returns, and gross proceeds of initial public
offerings: 1960–2017
TABLE 15.2
Year
Number of
Offerings*
Average First-
Day Return, %†
Gross
Proceeds,
$ Millions‡
1960 269 17.8 553
1961 435 34.1 1,243
1962 298 −1.6 431
1963 83 3.9 246
1964 97 5.3 380
1965 146 12.7 409
1966 85 7.1 275
1967 100 37.7 641
1968 368 55.9 1,205
1969 780 12.5 2,605
1970 358 −.7 780
1971 391 21.2 1,655
1972 562 7.5 2,724
1973 105 −17.8 330
1974 9 −7.0 51
1975 12 −.2 261
1976 26 1.9 214
1977 15 3.6 128
1978 19 12.6 207
1979 39 8.5 313
1980 71 13.9 905
1981 193 6.2 2,313
1982 79 10.5 1,012
1983 521 8.9 11,418
1984 213 2.8 2,608
1985 217 6.5 4,848
1986 478 6.1 15,549
1987 337 5.7 12,623
1988 132 5.4 4,089
1989 124 7.8 5,906
1990 116 10.4 4,334
1991 293 11.8 16,431
1992 416 10.2 22,750
Year
Number of
Offerings*
Average First-
Day Return, %†
Gross
Proceeds,
$ Millions‡
1993 527 12.7 31,756
1994 410 9.8 17,418
1995 464 21.1 28,017
1996 689 17.3 42,428
1997 485 13.9 32,547
1998 308 20.3 34,400
1999 484 69.7 64,809
2000 382 56.2 64,931
2001 79 14.2 34,241
2002 70 8.6 22,136
2003 68 11.9 10,075
2004 181 12.3 31,663
2005 167 10.1 28,577
2006 162 11.9 30,648
2007 160 14.0 35,704
2008 21 5.7 22,762
2009 42 10.6 13,296
2010 100 9.2 30,708
2011 82 13.2 27,750
2012 105 17.1 32,074
2013 162 20.9 39,093
2014 225 14.9 46,967
2015 122 18.1 22,020
2016 78 14.4 12,843
2017 119 12.4 25,596
1960–1969 2,661 21.2 7,988
1970–1979 1,536 7.2 6,663
1980–1989 2,365 6.9 61,271
1990–1999 4,192 21.4 294,890
2000–2009 1,332 24.5 294,033
2010–2017 993 15.5 237,051
1960–2017 13,079 16.8 901,896
*The number of offerings excludes IPOs with an offer price of less than $5.00, ADRs, best efforts, units, Regulation A offers (small issues, raising less
than $1.5 million during the 1980s), real estate investment trusts (REITs), partnerships, and closed-end funds. Banks and S&Ls and non-CRSP-listed
IPOs are included.
†First-day returns are computed as the percentage return from the offering price to the first closing market price.
‡Gross proceeds exclude overallotment options but include the international tranche, if any. No adjustments for inflation have been made.
Source: Data from 1960–1974 is taken from Table 1 of Ibbotson, R., Sindelar, J. and Ritter, J. R., Journal of Applied Corporate Finance article, “The
Market’s Problems with the Pricing of Initial Public Offerings,” vol. 7, no. 1, Spring 1994, 66–74; Data from 1975–2017 is compiled by Ritter, Jay R.
using Thomson Financial, Dealogic, and other sources. The 1975–1992 numbers are different from those reported in the JACF article because the
published article included IPOs that did not qualify for listing on Nasdaq, the Amex, or NYSE (mainly penny stocks).
average first-day return across the two years was about 65 percent. During this time, 194
IPOs doubled, or more than doubled, in value on the first day. In contrast, only 39 did so in
the preceding 24 years combined. One company, VA Linux, shot up 698 percent!
The dollar amount raised in 2000, $64.9 billion, was a record, followed closely by 1999.
The underpricing was so severe in 1999 that companies left another $36 billion “on the ta-
ble,” which was substantially more than in 1990 through 1998 combined, and, in 2000, the
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IPO Underpricing around the World
The United States is not the only country in which initial public offerings (IPOs) of common stock are underpriced.
The phenomenon exists in every country with a stock mar-
ket, although the extent of underpricing varies from country
to country.
In general, countries with developed capital markets
have more moderate underpricing than in emerging mar-
kets. During the Internet bubble of 1999–2000, however,
underpricing in the developed capital markets increased
dramatically. In the United States, for example, the aver-
age first-day return during 1999–2000 was 65 percent.
At the same time that underpricing in the developed
capital markets increased, the underpricing of IPOs sold
to residents of China moderated. The Chinese average
has come down to a mere 118 percent, which is lower
than it had been in the early and mid-1990s. After the
bursting of the Internet bubble in mid-2000, the level of
underpricing in the United States, Germany, and other
developed capital markets has returned to more tradi-
tional levels.
The accompanying table gives a summary of the aver-
age first-day returns on IPOs in a number of countries
around the world, with the figures collected from a number
of studies by various authors.
FINANCE MATTERS
Country
Sample
Size
Time
Period
Average Initial
Return (%) Country
Sample
Size
Time
Period
Average Initial
Return (%)
Argentina 26 1991–2013 4.2% Malaysia 474 1980–2013 56.2%
Australia 1,562 1976–2011 21.8 Mauritius 40 1989–2005 15.2
Austria 103 1971–2013 6.4 Mexico 123 1987–2012 11.6
Belgium 114 1984–2006 13.5 Morocco 33 2004–2011 33.3
Brazil 275 1979–2011 33.1 Netherlands 181 1982–2006 10.2
Bulgaria 9 2004–2007 36.5 New Zealand 242 1979–2013 18.6
Canada 743 1971–2016 6.5 Nigeria 122 1989–2013 13.1
Chile 81 1982–2013 7.4 Norway 209 1984–2013 8.1
China 3,116 1990–2016 145.4 Pakistan 80 2000–2013 22.1
Cyprus 73 1997–2012 20.3 Philippines 155 1987–2013 18.1
Denmark 164 1984–2011 7.4 Poland 309 1991–2012 13.3
Egypt 62 1990–2010 10.4 Portugal 32 1992–2013 11.9
Finland 168 1971–2013 16.9 Russia 64 1999–2013 3.3
France 697 1983–2010 10.5 Saudi Arabia 80 2003–2011 239.8
Germany 779 1978–2014 23.0 Singapore 609 1973–2013 25.81
Greece 373 1976–2013 50.8 South Africa 316 1980–2013 17.4
Hong Kong 1,486 1980–2013 15.8 South Korea 1,758 1980–2014 58.8
India 2,983 1990–2014 88.0 Spain 143 1986–2013 10.3
Indonesia 464 1990–2014 24.9 Sri Lanka 105 1987–2008 33.5
Iran 279 1991–2004 22.4 Sweden 405 1980–2015 25.9
Ireland 38 1991–2013 21.6 Switzerland 164 1983–2013 27.3
Israel 348 1990–2006 13.8 Taiwan 1,620 1980–2013 38.1
Italy 312 1985–2013 15.2 Thailand 500 1987–2012 35.1
Japan 3,488 1970–2016 44.7 Turkey 355 1990–2011 10.3
Jordan 53 1999–2008 149.0 United Kingdom 4,932 1959–2012 16.0
Korea 1,720 1980–2013 59.3 United States 13,079 1960–2017 16.8
Source: Professor Jay R. Ritter, the Joseph B. Cordell Professor of Finance at the University of Florida. An outstanding scholar, he is well known for
his insightful analyses of new issues and going public.
amount was at least $27 billion. In other words, over the two-year period, companies missed
out on $63 billion because of underpricing.
October 19, 1999, was one of the more memorable days during this time. The World
Wrestling Federation (WWF) (now known as World Wrestling Entertainment, or WWE)
502
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C H A P T E R 1 5 Raising Capital 503
and Martha Stewart Omnimedia both went public, so it was Martha Stewart versus “Stone
Cold” Steve Austin in a Wall Street version of MTV’s Celebrity Deathmatch. When the clos-
ing bell rang, it was a clear smackdown as Martha Stewart gained 98 percent on the first day
compared to 48 percent for the WWF. If you’re interested in finding out how IPOs have
done recently, check out our nearby Work the Web box.
The IPO market cooled off considerably in 2001. Many observers now refer to the
1999–2000 period as the Internet “bubble” period. The word bubble in this context refers to
a situation in which prices are bid up to irrational, and unsustainable, levels. During 1999,
for example, 323 of the companies that went public were considered Internet IPOs, meaning
companies that did most (or all) of their business on the Internet, or companies whose prod-
ucts were used for computers or networks. By April 2001, of the 1999 internet IPOs, only
12, or 4 percent, were trading above their offer price, and only 4, or 1 percent, were trading
above their first-day close. Was it really a bubble? Let us say that, at a minimum, there were
instances of valuations that are very hard to reconcile with economic reality. A nearby
Finance Matters box discusses one of the most notorious, the case of Palm, Inc., maker of
handheld computers.
QUESTIONS
1. Go to www.nasdaq.com/markets/ipos/performance.aspx and find the companies that
have had the best 1-day, 30-day, 60-day, and 6-month performances. How do the most
recent gains compare with the gains shown above? Which companies had the biggest
first-day drops?
2. Go to www.ipomonitor.com and find out which companies have filed for an IPO but
have yet to start trading.
W R K T H E W E B
So, do the high returns IPOs sometimes earn have you excited? Do you wonder how recent NASDAQ IPOs have performed? You can find out at www.nasdaq.com/markets/ipos
/performance.aspx. On the website, you can sort by 1-day, 30-day, 60-day, and 6-month perfor-
mance after the IPO. We went to the website and here is part of what we found:
As you can see, TDH Holdings was up 460 percent in the 30 days after its IPO, and Genprex was
up about 204 percent in the first 30 days of trading.
Source: nasdaq.com
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The (Mis)pricing of Palm, Inc.
At one time, Palm was entirely owned by 3Com, Inc., a profitable provider of computer networking products
and services. On March 2, 2000, 3Com sold 5 percent of its
stake in Palm to the public via an IPO. This type of IPO, in
which a company sells a part of its stock (usually a minority
share) in a subsidiary, is called an equity “carve-out,” and
such carve-outs are not uncommon events.
At some point following a carve-out, the parent company
often will distribute the remaining shares in the subsidiary to its
stockholders. This transaction is called a spin-off. In Palm’s
case, 3Com planned to spin off its remaining shares to 3Com’s
shareholders before the end of the year. Under the plan, 3Com
shareholders would receive about 1.5 shares of Palm for every
share of 3Com that they owned. Thus, after the IPO, investors
could buy shares in Palm directly, or they could buy shares indi-
rectly by purchasing stock in 3Com and waiting a little while.
Here is where it gets interesting. Because the owner of
a share of 3Com will ultimately get 1.5 shares of Palm, each
share of 3Com has to be worth at least as much as 1.5 shares
of Palm, right? In fact, given that 3Com’s other businesses
were profitable, 3Com’s stock price should be well above 1.5
times that of Palm.
It didn’t happen that way. The day before the Palm IPO,
3Com closed at $104.13 per share. After the first day of trad-
ing, Palm closed at $95.06 per share, implying that the price
of 3Com should have jumped to at least $145. Instead, 3Com
fell to $81.81. The next day, the wacky pricing was promi-
nently discussed in The Wall Street Journal and elsewhere,
so it wasn’t a secret. It was easy to see, yet it persisted for
months.
Based on these prices, the stock market was placing
a negative value on 3Com’s non-Palm businesses. Be-
cause the stock sold for about $82 per share when it
should have sold for at least $145, the market was valuing
all of 3Com’s non-Palm operations at $82 − 145 = −$63
per share, or about −$22 billion in all! Of course, stock
prices can’t be negative, so a reasonable interpretation
would be that Palm’s stock price was far too high relative
to 3Com’s.
Episodes like that of Palm are rare, but there were at
least five other cases of clear negative valuations in roughly
the same time period as Palm’s IPO. In all cases, the nega-
tive values gradually disappeared, so the misvaluations
were corrected, but it took time in each case.
FINANCE MATTERS
The Partial Adjustment Phenomenon
When a company files its registration statement with the SEC, at some point in the pro-
cess it will indicate a range of stock prices within which it expects to offer shares. This range
is called the “file price range,” or words to that effect. A file price range of $10–$12 is com-
mon, but many others exist. For example, when Dropbox initially filed for its IPO, it indi-
cated an anticipated price in the $16 to $18 range.
Just before a company’s shares are sold to investors, the final IPO offer price is deter-
mined. As shown in Panel A of Table 15.3, that price can be above, within, or below the
price range originally indicated by the company. Over the period 1980–2017, 48 percent of
IPOs were within the file range, with 29 percent below and 23 percent above.
Panel B of Table 15.3 illustrates an interesting and very clear pattern. IPO underpricing
is much more severe when an offer is priced above the file range. Again over the 1980–2017
period, IPOs that priced above the file range were underpriced by 50 percent, on average,
compared to only 3 percent for firms priced below it. The 1999–2000 period again stands out.
Issues that “went off ” above the file range were underpriced, on average, by 122 percent!
This pattern is known as the “partial adjustment” phenomenon. The name refers to the
fact that when firms raise their IPO offer prices, they only do so partially, meaning that they
don’t move the price high enough. In Dropbox’s case, the final offer price was $21, much
higher than the original file range, but not high enough: The stock jumped to $31.60 on the
first day of trading on March 23, 2018, when it closed at $28.48.
504
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C H A P T E R 1 5 Raising Capital 505
IPO underpricing
and file price range
TABLE 15.3A. Percentage of IPOs Relative to File Price Range
Below Within Above
1980–1989 30% 57% 13%
1990–1998 27 49 24
1999–2000 18 38 44
2001–2017 35 44 21
1980–2017 29 48 23
B. Average First-Day Returns Relative to File Price Range
Below Within Above
1980–1989 0% 6% 20%
1990–1998 4 11 31
1999–2000 8 26 122
2001–2017 3 11 37
1980–2017 3 11 50
Source: Professor Jay R. Ritter, University of Florida.
Why does the partial adjustment phenomenon exist? The answer is unknown. The ques-
tion is related to the broader question of why IPO underpricing exists, which we consider next.
Why Does Underpricing Exist?
Based on the evidence we’ve examined, an obvious question is why does underpricing con-
tinue to exist? As we discuss, there are various explanations, but, to date, there is a lack of
complete agreement among researchers as to which is correct.
We present some pieces of the underpricing puzzle by stressing two important caveats
to our preceding discussion. First, the average figures we have examined tend to obscure the
fact that much of the apparent underpricing is attributable to the smaller, more highly
speculative issues. This point is illustrated in Table 15.4, which shows the extent of
Average first-day returns, categorized by sales, for IPOs: 1980–2017*TABLE 15.4
1980–1989 1990–1998 1999–2000 2001–2017
Annual Sales
of Issuing Firms
Number
of Firms
First-Day
Average
Return
Number
of Firms
First-Day
Average
Return
Number
of Firms
First-Day
Average
Return
Number
of Firms
First-Day
Average
Return
$0 ≤ sales ≤ $10m 425 10.3% 741 17.2% 331 68.9% 372 9.6%
$10m ≤ sales ≤ $20m 242 8.6 393 18.5 138 81.4 82 13.6
$20m ≤ sales ≤ $50m 501 7.8 789 18.8 154 75.5 217 14.8
$50m ≤ sales ≤ $100m 356 6.3 590 12.8 86 62.2 284 20.5
$100m ≤ sales ≤ $200m 234 5.1 454 11.8 56 35.8 241 17.9
$200m ≤ sales 290 3.4 646 8.7 91 25.0 647 11.8
All 2,048 7.2 3,613 14.8 856 64.6 1,843 13.9
*Sales, measured in millions, are for the last 12 months prior to going public. All sales have been converted into dollars of 2003 purchasing power,
using the Consumer Price Index. There are 8,360 IPOs, after excluding IPOs with an offer price of less than $5.00 per share. The average first-day
return is 17.8 percent.
Source: Professor Jay R. Ritter, University of Florida.
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506 P A R T 7 Long-Term Financing
underpricing for 8,360 firms over the period from 1980 through 2017. Here, the firms are
grouped based on their total sales in the 12 months prior to the IPO.
As illustrated in Table 15.4, there is a tendency for underpricing to be more pronounced
for firms with relatively small pre-IPO sales. These firms tend to be young firms, and such
young firms can be very risky investments. Arguably, they must be significantly underpriced,
on average, to attract investors, and this is one explanation for the underpricing
phenomenon.
The second caveat is that relatively few IPO buyers actually will get the initial high aver-
age returns observed in IPOs, and many actually will lose money. Although it is true that, on
average, IPOs have positive initial returns, a significant fraction of them have price drops.
Furthermore, when the price is too low, the issue is often “oversubscribed.” This means in-
vestors will not be able to buy all of the shares they want, and the underwriters will allocate
the shares among investors.
The average investor will find it difficult to get shares in a “successful” offering (one in
which the price increases) because there will not be enough shares to go around. On the
other hand, an investor blindly submitting orders for IPOs tends to get more shares in issues
that go down in price.
To illustrate, consider this tale of two investors. Smith knows very accurately what the
Bonanza Corporation is worth when its shares are offered. She is confident that the shares
are underpriced. Jones knows only that IPOs are usually underpriced. Armed with this in-
formation, Jones decides to buy 1,000 shares of every IPO. Does he actually earn an abnor-
mally high return on the initial offering?
The answer is no, and at least one reason is Smith. Knowing about the Bonanza Cor-
poration, Smith invests all her money in its IPO. When the issue is oversubscribed, the
underwriters have to somehow allocate the shares between Smith and Jones. The net re-
sult is that when an issue is underpriced, Jones doesn’t get to buy as much of it as he
wanted.
Smith also knows that the Blue Sky Corporation IPO is overpriced. In this case, she
avoids its IPO altogether, and Jones ends up with a full 1,000 shares. To summarize this tale,
Jones gets fewer shares when more knowledgeable investors swarm to buy an underpriced
issue and gets all he wants when the smart money avoids the issue.
This is an example of a “winner’s curse,” and it is thought to be another reason why
IPOs have such a large average return. When the average investor “wins” and gets the entire
allocation, it may be because those who knew better avoided the issue. The only way under-
writers can counteract the winner’s curse and attract the average investor is to underprice
new issues (on average) so that the average investor still makes a profit.
A final reason for underpricing is that the underpricing is a kind of insurance for the
investment banks. Conceivably, an investment bank could be sued successfully by angry
customers if it consistently overpriced securities. Underpricing guarantees that, at least on
average, customers will come out ahead.
CONCEPT QUESTIONS
15.5a Why is underpricing a cost to the issuing firm?
15.5b Suppose a stockbroker calls you up out of the blue and offers to sell you “all the
shares you want” of a new issue. Do you think the issue will be more, or less,
underpriced than average?
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C H A P T E R 1 5 Raising Capital 507
NEW EQUITY SALES AND
THE VALUE OF THE FIRM
We now turn to a consideration of seasoned equity offerings (SEOs), which, as we discussed
earlier, are offerings by firms that already have outstanding securities. It seems reasonable
to believe that new long-term financing is arranged by firms after positive net present value
projects are put together. As a consequence, when the announcement of external financing
is made, the firm’s market value should go up. Interestingly, this is not what happens. Stock
prices tend to decline following the announcement of a new equity issue, although they tend
to not change much following a debt announcement. A number of researchers have studied
this issue. Plausible reasons for this strange result include the following:
1. Managerial information. If management has superior information about the market
value of the firm, it may know when the firm is overvalued. If it does, it will attempt to
issue new shares of stock when the market value exceeds the correct value. This will
benefit existing shareholders. However, the potential new shareholders are not stupid,
and they will anticipate this superior information and discount it in lower market
prices at the new issue date.
2. Debt usage. A company’s issuing new equity may reveal that the company has too
much debt or too little liquidity. One version of this argument says that the equity
issue is a bad signal to the market. After all, if the new projects are favorable ones,
why should the firm let new shareholders in on them? It could just issue debt and let
the existing shareholders have all the gain.
3. Issue costs. As we discuss next, there are substantial costs associated with selling
securities.
The drop in value of the existing stock following the announcement of a new issue is an
example of an indirect cost of selling securities. This drop typically might be on the order of
3 percent for an industrial corporation (and somewhat smaller for a public utility), so, for a
large company, it can represent a substantial amount of money. We label this drop the
abnormal return in our discussion of the costs of new issues that follows.
CONCEPT QUESTIONS
15.6a What are some possible reasons the price of a stock drops on the announcement of a
new equity issue?
15.6b Explain why we might expect a firm with a positive NPV investment to finance it
with debt instead of equity.
THE COST OF ISSUING SECURITIES
Issuing securities to the public isn’t free, and the costs of different methods are important
determinants of which is used. These costs associated with floating a new issue are generi-
cally called flotation costs. In this section, we take a closer look at the flotation costs associ-
ated with equity sales to the public.
The costs of selling stock are classified in the following table and fall into six categories:
(1) the spread, (2) other direct expenses, (3) indirect expenses, (4) abnormal returns
(discussed previously), (5) underpricing, and (6) the Green Shoe option.
15.6
15.7
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508 P A R T 7 Long-Term Financing
The Costs of Issuing Securities
1. Spread The spread consists of direct fees paid by the issuer to the
underwriting syndicate—the difference between the price the
issuer receives and the offer price.
2. Other direct expenses These are direct costs incurred by the issuer that are not part
of the compensation to underwriters. These costs include
filing fees, legal fees, and taxes—all reported on the
prospectus.
3. Indirect expenses These costs are not reported on the prospectus and include the
cost of management time spent working on the new issue.
4. Abnormal returns In a seasoned issue of stock, the price of the existing stock drops
on average by 3 percent upon the announcement of the issue.
This drop is called the abnormal return.
5. Underpricing For initial public offerings, losses arise from selling the stock
below the true value.
6. Green Shoe option The Green Shoe option gives the underwriters the right
to buy additional shares at the offer price to cover
overallotments.
Table 15.5 reports direct costs as a percentage of the gross amount raised for IPOs,
SEOs, straight (ordinary) bonds, and convertible bonds sold by U.S. companies over the
19-year period from 1990 through 2008. These are direct costs only. Not included are indi-
rect expenses, the cost of the Green Shoe provision, underpricing (for IPOs), and abnormal
returns (for SEOs).
As Table 15.5 shows, the direct costs alone can be very large, particularly for smaller
issues (less than $10 million). On a smaller IPO, for example, the total direct costs amount
to 25.22 percent of the amount raised. This means that if a company sells $10 million in
stock, it will net only about $7.5 million; the other $2.5 million goes to cover the under-
writer spread and other direct expenses. Typical underwriter spreads on an IPO range from
about 5 percent for large offerings to 10 percent for small offerings, but, for about half of the
IPOs in Table 15.5, the spread is exactly 7 percent, so this is, by far, the most common
spread. The nearby Finance Matters box provides a detailed example for a particular
company.
Overall, four clear patterns emerge from Table 15.5. First of all, with the possible excep-
tion of straight debt offerings (about which we will have more to say later), there are sub-
stantial economies of scale. The underwriter spreads are smaller on larger issues, and the
other direct costs fall sharply as a percentage of the amount raised, a reflection of the
mostly fixed nature of such costs. Second, the costs associated with selling debt are substan-
tially less than the costs of selling equity. Third, IPOs have higher expenses than SEOs, but
the difference is not as great as might originally be guessed. Finally, straight bonds are
cheaper to float than convertible bonds.
As we have discussed, the underpricing of IPOs is an additional cost to the issuer.
To give a better idea of the total cost of going public, Table 15.6 combines the informa-
tion in Table 15.5 for IPOs with data on the underpricing experienced by these firms.
Comparing the total direct costs (in the fifth column) to the underpricing (in the sixth
column), we see that they tend to be similar in size, so the direct costs are only about
half of the total for small issues. Overall, across all size groups, the total direct costs
amount to 10 percent of the amount raised and the underpricing amounts to
19 percent.
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Direct costs as a percentage of gross proceeds for equity (IPOs and SEOs) and straight and convertible bonds offered by
domestic operating companies: 1990–2008
TABLE 15.5
IPOs SEOs
Proceeds
($ millions)
Number of
Issues
Gross
Spread
Other Direct
Expense
Total Direct
Cost
Number of
Issues
Gross
Spread
Other Direct
Expense
Total Direct
Cost
2.00–9.99 1,007 9.40% 15.82% 25.22% 515 8.11% 26.99% 35.11%
10.00–19.99 810 7.39 7.30 14.69 726 6.11 7.76 13.86
20.00–39.99 1,422 6.96 7.06 14.03 1,393 5.44 4.10 9.54
40.00–59.99 880 6.89 2.87 9.77 1,129 5.03 8.93 13.96
60.00–79.99 522 6.79 2.16 8.94 841 4.88 1.98 6.85
80.00–99.99 327 6.71 1.84 8.55 536 4.67 2.05 6.72
100.00–199.99 702 6.39 1.57 7.96 1,372 4.34 .89 5.23
200.00–499.99 440 5.81 1.03 6.84 811 3.72 1.22 4.94
500.00 and up 155 5.01 .49 5.50 264 3.10 .27 3.37
Total/Average 6,265 7.19 3.18 10.37 7,587 5.02 2.68 7.69
Straight Bonds Convertible Bonds
2.00–9.99 3,962 1.64 2.40 4.03 14 6.39 3.43 9.82
10.00–19.99 3,400 1.50 1.71 3.20 23 5.52 3.09 8.61
20.00–39.99 2,690 1.25 .92 2.17 30 4.63 1.67 6.30
40.00–59.99 3,345 .81 .79 1.59 35 3.49 1.04 4.54
60.00–79.99 891 1.65 .80 2.44 60 2.79 .62 3.41
80.00–99.99 465 1.41 .57 1.98 16 2.30 .62 2.92
100.00–199.99 4,949 1.61 .52 2.14 82 2.66 .42 3.08
200.00–499.99 3,305 1.38 .33 1.71 46 2.65 .33 2.99
500.00 and up 1,261 .61 .15 .76 7 2.16 .13 2.29
Total/Average 24,268 1.38 .61 2.00 313 3.07 .85 3.92
Source: Lee, I., Lochhead, S., Ritter, J. and Zhao, Quanshui, “The Costs of Raising Capital,” Journal of Financial Research, vol. 1, Spring 1996, calculations and updates by the authors.
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Anatomy of an IPO
On June 29, 2018, Domo, Inc., the corporate communica-tions company based in American Fork, Utah, went
public via an IPO. Domo issued 9.2 million shares of stock at
a price of $21 each. The lead underwriters on the IPO were
JMP Securities and William Blair & Company, assisted by a
syndicate of other investment banks. Even though the IPO
raised a gross sum of $193.2 million, Domo got to keep only
about $175.7 million after expenses. The biggest expense
was the 7 percent underwriter spread, which is ordinary for
an offering of this size. Domo sold each of the 9.2 million
shares to the underwriters for $19.53, and the underwriters
in turn sold the shares to the public for $21.00 each.
But wait—there’s more. Domo spent $28,979 in SEC
registration fees, $35,414 in other filing fees, and $152,500
to be listed on the NASDAQ Global Market. The company
also spent $1.8 million in legal fees, $1.575 million on ac-
counting to obtain the necessary audits, $4,000 for a trans-
fer agent to physically transfer the shares and maintain a
list of shareholders, $185,000 for printing and engraving
expenses, and, finally, $200,000 in miscellaneous
expenses.
As Domo’s outlays show, an IPO can be a costly under-
taking! In the end, Domo’s expenses totaled about $17.5 mil-
lion, of which $13.52 million went to the underwriters and
$3.98 million went to other parties. All told, the total direct
cost to Domo was 9.7 percent of the issue proceeds raised
by the company. This amount doesn’t include the indirect
cost of the first-day price pop. Domo’s stock closed at
$27.30 on the first day of trading, so the company left about
$60 million on the table.
FINANCE MATTERS
Direct and indirect
costs, in percentages,
of equity IPOs:
1990–2008
TABLE 15.6 Proceeds
($ in millions)
Number of
Issues
Gross
Spread
Other Direct
Expense
Total
Direct Cost Underpricing
2.00–9.99 1,007 9.40% 15.82% 25.22% 20.42%
10.00–19.99 810 7.39 7.30 14.69 10.33
20.00–39.99 1,422 6.96 7.06 14.03 17.03
40.00–59.99 880 6.89 2.87 9.77 28.26
60.00–79.99 522 6.79 2.16 8.94 28.36
80.00–99.99 327 6.71 1.84 8.55 32.92
100.00–199.99 702 6.39 1.57 7.96 21.55
200.00–499.99 440 5.81 1.03 6.84 6.19
500.00 and up 155 5.01 .49 5.50 6.64
Total/Average 6,265 7.19 3.18 10.37 19.34
Source: Inmoo Lee, Inmoo, Lochhead, Scott, Ritter, Jay and Zhao, Quanshui, “The Costs of Raising Capital,” Journal
of Financial Research, vol. 1, Spring 1996, calculations and updates by the authors.
510
Finally, with regard to debt offerings, there is a general pattern in issue costs that is
somewhat obscured in Table 15.5. Recall from Chapter 6 that bonds carry different credit
ratings. Higher-rated bonds are said to be investment grade, whereas lower-rated bonds are
noninvestment grade. Table 15.7 contains a breakdown of direct costs for bond issues after
the investment and noninvestment grades have been separated.
Table 15.7 clarifies three things regarding debt issues. First, there are substantial econ-
omies of scale here as well. Second, investment-grade issues have much lower direct costs,
particularly for straight bonds. Finally, there are relatively few noninvestment-grade issues in
the smaller size categories, reflecting the fact that such issues are more commonly handled
as private placements, which we discuss in our next section.
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Average gross spreads and total direct costs for domestic debt issues: 1990–2008TABLE 15.7
Convertible Bonds
Investment Grade Junk or Not Rated
Proceeds
($ millions)
Number of
Issues
Gross
Spread
Other Direct
Expense
Total
Direct Cost
Number of
Issues
Gross
Spread
Other Direct
Expense
Total Direct
Cost
2.00–9.99 — — — — 14 6.39% 3.43% 9.82%
10.00–19.99 1 14.12% 1.87% 15.98% 23 5.52 3.09 8.61
20.00–39.99 — — — — 30 4.63 1.67 6.30
40.00–59.99 3 1.92 .51 2.43 35 3.49 1.04 4.54
60.00–79.99 6 1.65 .44 2.09 60 2.79 .62 3.41
80.00–99.99 4 .89 .27 1.16 16 2.30 .62 2.92
100.00–199.99 27 2.22 .33 2.55 82 2.66 .42 3.08
200.00–499.99 27 2.03 .19 2.22 46 2.65 .33 2.99
500.00 and up 11 1.94 .13 2.06 7 2.16 .13 2.29
Total/Average 79 2.15 .29 2.44 313 3.31 .98 4.29
Straight Bonds
Investment Grade Junk or Not Rated
2.00–9.99 2,709 .62% 1.28% 1.90% 1,253 2.77% 2.50% 5.27%
10.00–19.99 2,564 .59 1.17 1.76 836 3.15 1.97 5.12
20.00–39.99 2,400 .63 .74 1.37 290 3.07 1.13 4.20
40.00–59.99 3,146 .40 .52 .92 199 2.93 1.20 4.14
60.00–79.99 792 .58 .38 .96 99 3.12 1.16 4.28
80.00–99.99 385 .66 .29 .96 80 2.73 .93 3.66
100.00–199.99 4,427 .54 .25 .79 522 2.73 .68 3.41
200.00–499.99 3,031 .52 .25 .76 274 2.59 .39 2.98
500.00 and up 1,207 .31 << .08 <<<.39 << 54 2.38 .25 2.63
Total/Average 20,661 .52 .35 .87 3,607 2.76 .81 3.57
Source: Lee, Inmoo, Lochhead, Scott, Ritter, Jay and Zhao, Quanshui, “The Costs of Raising Capital,” Journal of Financial Research, vol. 1, Spring 1996, calculations and updates by the authors.
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512 P A R T 7 Long-Term Financing
CONCEPT QUESTIONS
15.7a What are the different costs associated with security offerings?
15.7b What lessons do we learn from studying issue costs?
ISSUING LONG-TERM DEBT
The general procedures followed in a public issue of bonds are the same as those for stocks.
The issue must be registered with the SEC, there must be a prospectus, and so on. The reg-
istration statement for a public issue of bonds, however, is different from the one for com-
mon stock. For bonds, the registration statement must indicate an indenture.
Another important difference is that more than 50 percent of all debt is issued
privately. There are two basic forms of direct private long-term financing: term loans and
private placement.
15.8
EXAMPLE 15.1 How Much Does That IPO Cost?
The Faulk Co. has just gone public under a firm commitment agreement. Faulk received $32 for
each of the 4.1 million shares sold. The initial offering price was $34.40 per share, and the stock
rose to $41 per share in the first few minutes of trading. Faulk paid $905,000 in legal and other di-
rect costs and $250,000 in indirect costs. What was the flotation cost as a percentage of funds
raised?
The net amount raised is the number of shares offered times the price received by the company,
minus the costs associated with the offer, so:
Net amount raised = (4,100,000 shares)($32) − 905,000 − 250,000
Net amount raised = $130,045,000
Next, we can calculate the direct costs. Part of the direct costs are given in the problem, but the
company also had to pay the underwriters. The stock was offered at $34.40 per share, and the
company received $32 per share. The difference, which is the underwriters’ spread, is also a direct
cost. The total direct costs were:
Total direct costs = $905,000 + ($34.40 − 32)(4,100,000 shares)
Total direct costs = $10,745,000
We are given part of the indirect costs, but the underpricing is another indirect cost. The total indi-
rect costs were:
Total indirect costs = $250,000 + ($41 − 34.40)(4,100,000 shares)
Total indirect costs = $27,310,000
The total costs are:
Total costs = $10,745,000 + 27,310,000
Total costs = $38,055,000
The flotation costs as a percentage of the amount raised is the total cost divided by the amount
raised, or:
Flotation cost percentage = $38,055,000/$130,045,000
Flotation cost percentage = .2926, or 29.26%
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C H A P T E R 1 5 Raising Capital 513
Term loans are direct business loans. These loans have maturities of between one year
and five years. Most term loans are repayable during the life of the loan. The lenders in-
clude commercial banks, insurance companies, and other lenders that specialize in corpo-
rate finance. Private placements are very similar to term loans except that the maturities
are longer.
The important differences between direct private long-term financing and public issues
of debt are
1. A direct long-term loan avoids the cost of Securities and Exchange Commission
registration.
2. Direct placement is likely to have more restrictive covenants.
3. It is easier to renegotiate a term loan or a private placement in the event of a default.
It is harder to renegotiate a public issue because hundreds of holders are usually
involved.
4. Life insurance companies and pension funds dominate the private-placement segment
of the bond market. Commercial banks are significant participants in the term-loan
market.
5. The costs of distributing bonds are lower in the private market.
The interest rates on term loans and private placements are often higher than those on
an equivalent public issue. This difference may reflect the trade-off between a higher interest
rate and more flexible arrangements in the event of financial distress, as well as the lower
costs associated with private placements.
An additional, and very important, consideration is that the flotation costs associ-
ated with selling debt are much less than the comparable costs associated with selling
equity.
CONCEPT QUESTIONS
15.8a What is the difference between private and public bond issues?
15.8b A private placement is likely to have a higher interest rate than a public issue. Why?
SHELF REGISTRATION
To simplify the procedures for issuing securities, in March 1982, the SEC adopted Rule 415
on a temporary basis, and it was made permanent in November 1983. Rule 415 allows shelf
registration. Both debt and equity securities can be shelf registered.
Shelf registration permits a corporation to register an offering that it reasonably ex-
pects to sell within the next two years and then sell the issue whenever it wants during that
two-year period. In July 2018, information technology company Helios & Matheson an-
nounced a shelf registration to sell up to $1.2 billion of debt and equity. According to the
registration documents filed by the company, the proceeds were to be used for future acqui-
sitions of other businesses, assets, or securities.
Not all companies can use Rule 415. The primary qualifications are
1. The company must be rated investment grade.
2. The firm cannot have defaulted on its debt in the past three years.
term loans
Direct business loans of,
typically, one to five years.
private placements
Loans, usually long-term
in nature, provided
directly by a limited
number of investors.
15.9
shelf registration
Registration permitted by
SEC Rule 415, which
allows a company to
register all issues it
expects to sell within two
years at one time, with
subsequent sales at any
time within those two
years.
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514 P A R T 7 Long-Term Financing
3. The aggregate market value of the firm’s outstanding stock must be more than
$150 million.
4. The firm must not have had a violation of the Securities Act of 1934 in the past
three years.
The rule has been controversial. Arguments have been constructed against shelf
registration:
1. The costs of new issues might go up because underwriters might not be able to
provide as much current information to potential investors as they would otherwise,
so investors would pay less. The expense of selling the issue piece by piece therefore
might be higher than that of selling it all at once.
2. Some investment bankers have argued that shelf registration will cause a “market
overhang” that will depress market prices. In other words, the possibility that
the company could increase the supply of stock at any time will have a negative
impact on the current stock price. There is little evidence to support this
position, however.
In addition to shelf registrations, companies also sell stock through continuous equity
offerings, or “dribble” programs. In a dribble program, the company registers the stock
with the SEC through a variety of different methods and sells the shares in dribbles as it
sees fit. In other words, the company sells the stock on the secondary market like any other
investor would.
CONCEPT QUESTIONS
15.9a What is shelf registration?
15.9b What are the arguments against shelf registration?
SUMMARY AND CONCLUSIONS
This chapter has looked at how corporate securities are issued. The following are the main
points:
1. The venture capital market is a primary source of financing for new high-risk
companies.
2. The costs of issuing securities can be quite large. They are much lower (as a
percentage) for larger issues.
3. Firm commitment underwriting is far more prevalent for large issues than best efforts
underwriting. This is probably connected to the uncertainty of smaller issues. For a
given size offering, the direct expenses of best efforts underwriting and firm
commitment underwriting are of the same magnitude.
4. The direct and indirect costs of going public can be substantial. However, once a firm
is public, it can raise additional capital with much greater ease.
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C H A P T E R 1 5 Raising Capital 515
POP QUIZ!
Can you answer the following questions? If your class is using Connect, log on to
SmartBook to see if you know the answers to these and other questions, check out
the study tools, and find out what topics require additional practice!
Section 15.1 What are some important considerations when choosing between
venture capitalists?
Section 15.2 When is a new issue usually priced?
Section 15.3 What are the differences between general cash offers and rights
offers?
Section 15.4 What grants an underwriter the ability to purchase additional shares
of stock at the offer price?
Section 15.5 What occurs if IPO shares are sold at an offering price that is too low?
Assume the offering is a firm commitment offering.
Section 15.6 What has been presented as a reason why stock prices tend to de-
cline when a new equity issue is announced?
Section 15.7 What are the costs associated with issuing new securities?
Section 15.8 What reasons are given as potential explanations why interest rates
on private debt are higher than the interest rates paid on comparable public debt?
Section 15.9 What is offered as the primary argument against shelf registration?
CHAPTER REVIEW AND SELF-TEST PROBLEMS
CRITICAL THINKING AND CONCEPTS REVIEW
15.1 Flotation Costs The L5 Corporation is considering an equity issue to finance a
new space station. A total of $10 million in new equity is needed. If the direct costs
are estimated at 6 percent of the amount raised, how large does the issue need to be?
What is the dollar amount of the flotation cost? (See Problem 2.)
■ Answer to Chapter Review and Self-Test Problem
15.1 The firm needs to net $10 million after paying the 6 percent flotation costs. So, the
amount raised is given by:
Amount raised × (1 − .06) = $10 million
Amount raised = $10,000,000/.94 = $10.638 million
The total flotation cost is thus $638,000.
LO 2 15.1 Debt versus Equity Offering Size In the aggregate, debt offerings are much
more common than equity offerings and typically much larger as well. Why?
LO 2 15.2 Debt versus Equity Flotation Costs Why are the costs of selling equity so
much larger than the costs of selling debt?
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516 P A R T 7 Long-Term Financing
LO 2 15.3 Bond Ratings and Flotation Costs Why do noninvestment-grade bonds
have much higher direct costs than investment-grade issues?
LO 2 15.4 Underpricing in Debt Offerings Why is underpricing not a great concern
with bond offerings?
Use the following information to answer the next three questions. Zipcar, the
car-sharing company, went public in April of 2011. Assisted by the investment
bank Goldman, Sachs & Co., Zipcar sold 9.68 million shares at $18 each,
thereby raising a total of $174.24 million. By the end of the first day of trad-
ing, the stock had zipped to $28 per share, down from a high of $31.50. On
the basis of the end-of-day numbers, Zipcar shares were apparently under-
priced by about $10 each, meaning that the company missed out on an addi-
tional $96.8 million.
LO 3 15.5 IPO Pricing The Zipcar IPO was underpriced by about 56 percent.
Should Zipcar be upset at Goldman over the underpricing?
LO 3 15.6 IPO Pricing In the previous question, how would it affect your thinking to
know that the company was incorporated about 10 years earlier, had only
$186 million in revenues in 2010, and had never earned a profit? Additionally,
the viability of the company’s business model was still unproven.
LO 3 15.7 IPO Pricing In the previous two questions, how would it affect your
thinking to know that in addition to the 9.68 million shares offered in the
IPO, Zipcar had an additional 30 million shares outstanding? Of those
30 million shares, 14.1 million shares were owned by four venture capital
firms, and 15.5 million shares were owned by the 12 directors and executive
officers.
LO 3 15.8 IPO Underpricing In 1980, a certain assistant professor of finance bought
12 initial public offerings of common stock. He held each of these for
approximately one month and then sold. The investment rule he followed
was to submit a purchase order for every firm commitment initial public
offering of oil and gas exploration companies. There were 22 of these
offerings, and he submitted a purchase order for approximately $1,000 in
stock for each of the companies. With 10 of these, no shares were allocated
to this assistant professor. With 5 of the 12 offerings that were purchased,
fewer than the requested number of shares were allocated.The year 1980
was very good for oil and gas exploration company owners: On average, for
the 22 companies that went public, the stocks were selling for 80 percent
above the offering price a month after the initial offering date. The assistant
professor looked at his performance record and found that the $8,400
invested in the 12 companies had grown to $10,000, representing a return
of only about 20 percent (commissions were negligible). Did he have bad
luck, or should he have expected to do worse than the average initial public
offering investor? Explain.
LO 1 15.9 Venture Capital In the chapter, we mentioned that venture capital is very
expensive. Why do you think this is true?
LO 3 15.10 IPO Pricing The following material represents the cover page and
summary of the prospectus for the initial public offering of the Pest
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C H A P T E R 1 5 Raising Capital 517
Investigation Control Corporation (PICC), which is going public
tomorrow with a firm commitment initial public offering managed by the
investment banking firm of Erlanger and Ritter. Answer the following
questions:
a. Assume that you know nothing about PICC other than the information
contained in the prospectus. Based on your knowledge of finance, what
is your prediction for the price of PICC tomorrow? Provide a short
explanation of why you think this will occur.
b. Assume that you have several thousand dollars to invest. When
you get home from class tonight, you find that your stockbroker,
whom you have not talked to for weeks, has called. She has left a
message that PICC is going public tomorrow and that she can
get you several hundred shares at the offering price if you call
her back first thing in the morning. Discuss the merits of this
opportunity.
PROSPECTUS PICC
200,000 shares
PEST INVESTIGATION CONTROL CORPORATION
Of the shares being offered hereby, all 200,000 are being sold by the Pest Investigation Control
Corporation, Inc. (“the Company”). Before the offering, there has been no public market for the shares
of PICC, and no guarantee can be given that any such market will develop.
These securities have not been approved or disapproved by the SEC nor has the commission passed upon
the accuracy or adequacy of this prospectus. Any representation to the contrary is a criminal offense.
Price to
Public
Underwriting
Discount
Proceeds to
Company*
Per share $11.00 $1.10 $9.90
Total $2,200,000 $220,000 $1,980,000
*Before deducting expenses estimated at $27,000 and payable by the Company.
This is an initial public offering. The common shares are being offered, subject to prior sale, when, as,
and if delivered to and accepted by the Underwriters and subject to approval of certain legal matters
by their Counsel and by Counsel for the Company. The Underwriters reserve the right to withdraw,
cancel, or modify such offer and to reject offers in whole or in part.
Erlanger and Ritter, Investment Bankers
July 12, 2019
Prospectus Summary
The Company The Pest Investigation Control Corporation (PICC) breeds and markets toads
and tree frogs as ecologically safe insect-control mechanisms.
The Offering 200,000 shares of common stock, no par value.
Listing The Company will seek listing on NASDAQ and will trade over the counter.
Shares Outstanding As of June 30, 2019, 400,000 shares of common stock were outstanding. After
the offering, 600,000 shares of common stock will be outstanding.
Use of Proceeds To finance expansion of inventory and receivables and general working
capital, and to pay for country club memberships for certain finance
professors.
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518 P A R T 7 Long-Term Financing
Selected Financial Information
(amounts in thousands except per-share data)
Fiscal Year Ended June 30
2017 2018 2019
Revenues $60.00 $120.00 $240.00
Net earnings 3.80 15.90 36.10
Earnings per share .01 .04 .09
As of June 30, 2019
Actual
As Adjusted for
This Offering
Working capital $ 8 $ 1,961
Total assets 511 2,464
Stockholders’ equity 423 2,376
QUESTIONS AND PROBLEMS
Select problems are available in McGraw-Hill Connect. Please see the pack-
aging options section of the Preface for more information.
BASIC (Questions 1–7)
1. IPO Underpricing The Koepka Co. and the Johnson Co. both have
announced IPOs at $40 per share. One of these is undervalued by $12.25,
and the other is overvalued by $5.50, but you have no way of knowing
which is which. You plan on buying 1,000 shares of each issue. If an issue is
underpriced, it will be rationed, and only half your order will be filled. If you
could get 1,000 shares in Koepka and 1,000 shares in Johnson, what would
your profit be? What profit do you actually expect? What principle have you
illustrated?
2. Calculating Flotation Costs The Sullivan Co. needs to raise $78 million
to finance its expansion into new markets. The company will sell new shares
of equity via a general cash offering to raise the needed funds. If the offer
price is $31 per share and the company’s underwriters charge a spread of
7 percent, how many shares need to be sold?
3. Calculating Flotation Costs In the previous problem, if the SEC filing fee
and associated administrative expenses of the offering are $1,425,000, how
many shares need to be sold now?
4. Calculating Flotation Costs The Sugarland Co. has just gone public.
Under a firm commitment agreement, the company received $17.67 for
each of the 27 million shares sold. The initial offering price was $19 per
share, and the stock rose to $24.80 per share in the first few minutes of
trading. The company paid $1,475,000 in legal and other direct costs and
$350,000 in indirect costs. What was the flotation cost as a percentage of
funds raised?
5. Calculating Flotation Costs The Elkmont Corporation needs to raise
$63.8 million to finance its expansion into new markets. The company will
sell new shares of equity via a general cash offering to raise the needed funds.
LO 3
LO 3
LO 3
LO 3
LO 3
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C H A P T E R 1 5 Raising Capital 519
WHAT’S ON
THE WEB?
15.1 IPO Filings Go to www.ipomonitor.com and find the most recent IPO. Now go to
the SEC website at www.sec.gov and look up the company’s filings with the SEC. What
is the name of the filing the company made to sell stock to the public? What does this
company do? How does the company propose to use the funds raised by the IPO?
15.2 Secondary Offerings Go to www.ipomonitor.com and find the most recent
secondary stock offering. At what price was the stock offered for sale to the public? How
does this offer price compare to the market price of the stock on the same day?
15.3 Initial Public Offerings What was the largest IPO? Go to www.ipomonitor.com and
find out. In what country was the company located? What was the largest IPO in the
United States?
If the offer price is $22 per share and the company’s underwriters charge a
spread of 7.5 percent, how many shares need to be sold?
6. Calculating Flotation Costs In the previous problem, if the SEC filing fee
and associated administrative expenses of the offering are $1,450,000, how
many shares need to be sold now?
7. Calculating Flotation Costs The Wiley Oakley Co. has just gone public.
Under a firm commitment agreement, Wiley received $21.39 for each of
the 7.75 million shares sold. The initial offering price was $23 per share,
and the stock rose to $26.30 per share in the first few minutes of trading.
Wiley paid $1,350,000 in legal and other direct costs and $210,000
in indirect costs. What was the flotation cost as a percentage of
funds raised?
LO 3
LO 3
ros13952_ch15_487-520.indd 519 12/22/18 5:59 PM
520 P A R T 7 Long-Term Financing
underwriter fee is 7 percent on all initial stock offerings of
the size of S&S Air’s offering. Renata tells Mark and Todd
that the company can expect to pay about $1,800,000 in
legal fees and expenses, $13,500 in SEC registration fees,
and $15,000 in other filing fees. Additionally, to be listed
on the NASDAQ, the company must pay $125,000. There
are also transfer agent fees of $6,500 and engraving ex-
penses of $450,000. The company also should expect to
pay $75,000 for other expenses associated with the IPO.
Finally, Renata tells Mark and Todd that to file with
the SEC, the company must provide three years’ audited
financial statements. She is unsure about the costs of
the audit. Mark tells Renata that the company provides
audited financial statements as part of the bond cove-
nant, and the company pays $300,000 per year for the
outside auditor.
Mark Sexton and Todd Story have been discussing the future of S&S Air. The company has been expe-
riencing fast growth, and the two see only clear skies in
the company’s future. However, the fast growth can no
longer be funded by internal sources, so Mark and Todd
have decided the time is right to take the company pub-
lic. To this end, they have entered into discussions with
the investment bank of Crowe & Mallard. The company
has a working relationship with Renata Harper, the un-
derwriter who assisted with the company’s previous
bond offering. Crowe & Mallard have assisted numerous
small companies in the IPO process, so Mark and Todd
feel confident with this choice.
Renata begins by telling Mark and Todd about the
process. Although Crowe & Mallard charged an under-
writer fee of 4 percent on the bond offering, the
CHAPTER CASE
S&S Air Goes Public
1. At the end of the discussion, Mark asks Renata
about the Dutch auction IPO process. What are the
differences in the expenses to S&S Air if it uses a
Dutch auction IPO versus a traditional IPO? Should
the company go public through a Dutch auction or
use a traditional underwritten offering?
2. During the discussion of the potential IPO and
S&S Air’s future, Mark states that he feels the com-
pany should raise $90 million. However, Renata
points out that if the company needs more cash in
the near future, a secondary offering close to the
IPO would be problematic. Instead, she suggests
that the company should raise $125 million in the
IPO. How can we calculate the optimal size of the
IPO? What are the advantages and disadvantages
of increasing the size of the IPO to $125 million?
3. After deliberation, Mark and Todd have decided
that the company should use a firm commitment
offering with Crowe & Mallard as the lead under-
writer. The IPO will be for $90 million. Ignoring
underpricing, how much will the IPO cost the
company as a percentage of the funds received?
4. Many employees of S&S Air have shares of stock
in the company because of an existing employee
stock purchase plan. To sell the stock, the
employees can tender their shares to be sold in
the IPO at the offering price, or the employees
can retain their stock and sell it in the secondary
market after S&S Air goes public. Todd asks you
to advise the employees about which option is
better. What would you suggest to the
employees?
Q U E S T I O N S
ros13952_ch15_487-520.indd 520 12/22/18 5:59 PM
Please visit us at essentialsofcorporatefinance.blogspot.com for the latest developments in the world of corporate finance.
521
Please visit us at essentialsofcorporatefinance.blogspot.com for the latest developments in the world of corporate finance.
Auto inventory is a closely followed number. A high days’ sales in inventory can indicate a forthcoming production slowdown,
while a low days’ sales in inventory can indicate a need for
increased production. A 60-day supply of inventory is considered
optimal in the industry, but there is a lot of variation. For example, in
April 2018, BMW only had a 35-day supply of its 3-series sedan.
Of course, other automobile models had higher inventory levels.
Mitsubishi had a 243-day supply of the Eclipse crossover, or almost
two-thirds of a year in sales!
Short-term financial planning is one activity that concerns ev-
eryone in business. As this chapter illustrates, such planning requires,
among other things, sales projections from marketing, cost num-
bers from accounting, and inventory requirements from operations. Perhaps a particularly
good reason to study this chapter for many is that short-term planning and management are
frequently where new hires start out in a corporation, especially in finance and accounting.
Also, such planning is especially important for small businesses, and a lack of adequate
short-term financial resources is a frequently cited reason for small business failure.
To this point, we have described many of the decisions of long-term finance, includ-ing capital budgeting, dividend policy, and financial structure. In this chapter, we begin
to discuss short-term finance. Short-term finance is primarily concerned with the analysis of
decisions that affect current assets and current liabilities.
Frequently, the term net working capital is associated with short-term financial decision
making. As we describe in Chapter 2 and elsewhere, net working capital is the difference
between current assets and current liabilities. Often, short-term financial management is
called working capital management. These mean the same thing. Working capital manage-
ment can be critical for a company. According to a recent survey, if an average company
with $10 billion in sales could match the best working capital management company, it
could reduce working capital by $1.4 billion, or 14 percent of sales.
Short-Term Financial
Planning16
LEARNING OBJECTIVES
After studying this chapter, you should
be able to:
LO 1 Discuss operating and cash cycles
and why they are important.
LO 2 Differentiate between the types of
short-term financial policies.
LO 3 Identify the essentials of short-
term financial planning.
PART EIGHT Short-Term Financial Management
ros13952_ch16_521-552.indd 521 12/24/18 5:32 PM
522 P A R T 8 Short-Term Financial Management
There is no universally accepted definition of short-term finance. The most important
difference between short-term and long-term finance is the timing of cash flows. Short-term
financial decisions typically involve cash inflows and outflows that occur within a year or
less. For example, short-term financial decisions are involved when a firm orders raw mate-
rials, pays in cash, and anticipates selling finished goods in one year for cash. In contrast,
long-term financial decisions are involved when a firm purchases a special machine that will
reduce operating costs over, say, the next five years.
What types of questions fall under the general heading of short-term finance? To name
a few:
1. What is a reasonable level of cash to keep on hand (in a bank) to pay bills?
2. How much should the firm borrow in the short term?
3. How much credit should be extended to customers?
This chapter introduces the basic elements of short-term financial decisions. First, we
discuss the short-term operating activities of the firm. We then identify some alternative
short-term financial policies. Finally, we outline the basic elements of a short-term financial
plan and describe short-term financing instruments.
TRACING CASH AND NET WORKING CAPITAL
In this section, we examine the components of cash and net working capital as they change
from one year to the next. We have already discussed various aspects of this subject in Chap-
ters 2 and 3. We briefly review some of that discussion as it relates to short-term financing
decisions. Our goal is to describe the short-term operating activities of the firm and their
impact on cash and working capital.
To begin, recall that current assets are cash and other assets that are expected to con-
vert to cash within the year. Current assets are presented on the balance sheet in order of
their liquidity—the ease with which they can be converted to cash and the time it takes to
convert them. Four of the most important items found in the current asset section of a bal-
ance sheet are cash and cash equivalents, marketable securities, accounts receivable, and
inventories.
Analogous to their investment in current assets, firms use several kinds of short-term
debt, called current liabilities. Current liabilities are obligations that are expected to require
cash payment within one year. Three major items found as current liabilities are accounts
payable; expenses payable, including accrued wages and taxes; and notes payable.
Because we want to focus on changes in cash, we start off by defining cash in terms of
the other elements of the balance sheet. This lets us isolate the cash account and explore the
impact on cash from the firm’s operating and financing decisions. The basic balance sheet
identity can be written as:
Net working capital + Fixed assets = Long-term debt + Equity [16.1]
Net working capital is cash plus other current assets, less current liabilities; that is:
Net working capital = (Cash + Other current assets) − Current liabilities [16.2]
If we substitute this for net working capital in the basic balance sheet identity and rearrange
things a bit, we see that cash is:
Cash = Long-term debt + Equity + Current liabilities
− Current assets other than cash − Fixed assets
[16.3]
Interested in a career
in short-term finance?
Visit the Association for
Financial Professionals
website at
www.afponline.org.
16.1
ros13952_ch16_521-552.indd 522 12/24/18 5:32 PM
C H A P T E R 1 6 Short-Term Financial Planning 523
This tells us, in general terms, that some activities naturally increase cash and some
activities decrease it. We can list these along with an example of each as follows:
Activities That Increase Cash
Increasing long-term debt (borrowing over the long term).
Increasing equity (selling some stock).
Increasing current liabilities (getting a 90-day loan).
Decreasing current assets other than cash (selling some inventory for cash).
Decreasing fixed assets (selling some property).
Activities That Decrease Cash
Decreasing long-term debt (paying off a long-term debt).
Decreasing equity (repurchasing some stock).
Decreasing current liabilities (paying off a 90-day loan).
Increasing current assets other than cash (buying some inventory for cash).
Increasing fixed assets (buying some property).
Notice that our two lists are exact opposites. For example, floating a long-term bond issue
increases cash (at least until the money is spent). Paying off a long-term bond issue
decreases cash.
Activities that increase cash are called sources of cash. Those activities that decrease
cash are called uses of cash. Looking back at our list, we see that sources of cash always in-
volve increasing a liability (or equity) account or decreasing an asset account. This makes
sense because increasing a liability means we have raised money by borrowing it or by sell-
ing an ownership interest in the firm. A decrease in an asset means that we have sold or
otherwise liquidated an asset. In either case, there is a cash inflow.
Uses of cash are the reverse. A use of cash involves decreasing a liability by paying it
off, perhaps, or increasing assets by purchasing something. Both of these activities require
that the firm spend some cash.
EXAMPLE 16.1 Sources and Uses
Here is a quick check of your understanding of sources and uses: If accounts payable go up
by $100, is this a source or a use? If accounts receivable go up by $100, is this a source or
a use?
Accounts payable are what we owe our suppliers. This is a short-term debt. If it rises by $100,
we have effectively borrowed the money, so this is a source of cash. Receivables are what our cus-
tomers owe to us, so an increase of $100 in accounts receivable means that we have loaned the
money; this is a use of cash.
CONCEPT QUESTIONS
16.1a What is the difference between net working capital and cash?
16.1b Will net working capital always increase when cash increases?
16.1c List five potential uses of cash.
16.1d List five potential sources of cash.
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524 P A R T 8 Short-Term Financial Management
THE OPERATING CYCLE
AND THE CASH CYCLE
The primary concerns in short-term finance are the firm’s short-run operating and financ-
ing activities. For a typical manufacturing firm, these short-run activities might consist of
the following sequence of events and decisions:
Events Decisions
1. Buying raw materials 1. How much inventory to order
2. Paying cash 2. Whether to borrow or draw down cash balances
3. Manufacturing the product 3. What choice of production technology to use
4. Selling the product 4. Whether credit should be extended to a particular customer
5. Collecting cash 5. How to collect
These activities create patterns of cash inflows and cash outflows. These cash flows are
both unsynchronized and uncertain. They are unsynchronized because, for example, the
payment of cash for raw materials does not happen at the same time as the receipt of cash
from selling the product. They are uncertain because future sales and costs cannot be pre-
cisely predicted.
Defining the Operating and Cash Cycles
We can start with a simple case. One day, call it Day 0, you purchase $1,000 worth of inven-
tory on credit. You pay the bill 30 days later, and, after 30 more days, someone buys the
$1,000 in inventory for $1,400. Your buyer does not actually pay for another 45 days. We
can summarize these events chronologically as follows:
Day Activity Cash Effect
0 Acquire inventory on credit None
30 Pay for inventory −$1,000
60 Sell inventory on credit None
105 Collect on sale +$1,400
The Operating Cycle There are several things to notice in our example. First, the
entire cycle, from the time we acquire some inventory to the time we collect the cash, takes
105 days. This is called the operating cycle.
As we illustrate, the operating cycle is the length of time it takes to acquire inven-
tory, sell it, and collect for it. This cycle has two distinct components. The first part is
the time it takes to acquire and sell the inventory. This period, a 60-day span in our
example, is called the inventory period. The second part is the time it takes to collect
on the sale, 45 days in our example. This is called the accounts receivable period, or the
receivables period.
Based on our definitions, the operating cycle is obviously the sum of the inventory and
receivables periods:
Operating cycle = Inventory period + Accounts receivable period [16.4]
105 days = 60 days + 45 days
16.2
operating cycle
The time period between
the acquisition of
inventory and the
collection of cash from
receivables.
inventory period
The time it takes to
acquire and sell inventory.
accounts receivable
period
The time between sale of
inventory and collection
of the receivable.
ros13952_ch16_521-552.indd 524 12/24/18 5:32 PM
C H A P T E R 1 6 Short-Term Financial Planning 525
What the operating cycle describes is how a product moves through the current asset ac-
counts. It begins life as inventory, it is converted to a receivable when it is sold, and it is fi-
nally converted to cash when we collect from the sale. Notice that, at each step, the asset is
moving closer to cash.
The Cash Cycle The second thing to notice is that the cash flows and other events
that occur are not synchronized. For example, we don’t actually pay for the inventory until
30 days after we acquire it. The intervening 30-day period is called the accounts
payable period. Next, we spend cash on Day 30, but we don’t collect until Day 105. Some-
how, we have to arrange to finance the $1,000 for 105 − 30 = 75 days. This period is called
the cash cycle.
The cash cycle, therefore, is the number of days that pass until we collect the cash from
a sale, measured from when we actually pay for the inventory. Notice that, based on our
definitions, the cash cycle is the difference between the operating cycle and the accounts
payable period:
Cash cycle = Operating cycle − Accounts payable period
75 days = 105 days − 30 days
[16.5]
Figure 16.1 depicts the short-term operating activities and cash flows for a typical man-
ufacturing firm by looking at the cash flow time line. As is shown, the cash flow time line is
made up of the operating cycle and the cash cycle. In Figure 16.1, the need for short-term
financial management is suggested by the gap between the cash inflows and the cash out-
flows. This is related to the length of the operating cycle and the accounts payable period.
The gap between short-term inflows and outflows can be filled either by borrowing or
by holding a liquidity reserve in the form of cash or marketable securities. Alternatively, the
gap can be shortened by changing the inventory, receivables, and payables periods. These
are all managerial options that we discuss later and in a subsequent chapter.
The Operating Cycle and the Firm’s Organizational Chart
Before we examine the operating and cash cycles in greater detail, it is useful to take a look
at the people involved in managing a firm’s current assets and liabilities. As Table 16.1
illustrates, short-term financial management in a large corporation involves a number of
different financial and nonfinancial managers. Examining Table 16.1, we see that selling
accounts payable
period
The time between receipt
of inventory and payment
for it.
cash cycle
The time between cash
disbursement and cash
collection.
cash flow time line
Graphical representation
of the operating cycle and
the cash cycle.
Cash flow time line
and the short-term
operating activities
of a typical
manufacturing firm
FIGURE 16.1Inventory
purchased
Inventory
sold
Inventory period Accounts receivable period
Accounts payable
period
Cash pai d
for inventory
Cash cycl e
Cash
received
Operating cycle
The operating cycle is the time period from inventory purchase until the receipt of
cash. The cash cycle is the time period from when cash is paid out to when cash
is received.
ros13952_ch16_521-552.indd 525 12/24/18 5:32 PM
526 P A R T 8 Short-Term Financial Management
on credit involves at least three different individuals: the credit manager, the marketing man-
ager, and the controller. Of these three, only two are responsible to the vice president of fi-
nance (the marketing function is usually associated with the vice president of marketing).
Thus, there is the potential for conflict, particularly if different managers only concentrate
on part of the picture. For example, if marketing is trying to land a new account, it may seek
more liberal credit terms as an inducement. However, this may increase the firm’s invest-
ment in receivables or its exposure to bad-debt risk, and conflict can result.
Calculating the Operating and Cash Cycles
In our example, the lengths of time that made up the different periods were obvious. If all
we have is financial statement information, we will have to do a little more work. We illus-
trate these calculations next.
To begin, we need to determine various things such as how long it takes, on average, to
sell inventory and how long it takes, on average, to collect. We start by gathering some bal-
ance sheet information such as the following (in thousands):
Item Beginning Ending Average
Inventory $2,000 $3,000 $2,500
Accounts receivable 1,600 2,000 1,800
Accounts payable 750 1,000 875
Also, from the most recent income statement, we might have the following figures (in
thousands):
Net sales $11,500
Cost of goods sold 88888,200
We now need to calculate some financial ratios. We discussed these in some detail in
Chapter 3; here we define them and use them as needed.
Managers who deal
with short-term
financial problems
TABLE 16.1
Title of Manager
Duties Related to Short-Term
Financial Management Assets/Liabilities Influenced
Cash manager Collection, concentration, disbursement;
short-term investments; short-term
borrowing; banking relations
Cash, marketable securities,
short-term loans
Credit manager Monitoring and control of accounts
receivable; credit policy decisions
Accounts receivable
Marketing manager Credit policy decisions Accounts receivable
Purchasing manager Decisions on purchases, suppliers; may
negotiate payment terms
Inventory, accounts payable
Production manager Setting of production schedules and
materials requirements
Inventory, accounts payable
Payables manager Decisions on payment policies and on
whether to take discounts
Accounts payable
Controller Accounting information on cash flows;
reconciliation of accounts payable;
application of payments to accounts
receivable
Accounts receivable,
accounts payable
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C H A P T E R 1 6 Short-Term Financial Planning 527
The Operating Cycle First of all, we need the inventory period. We spent $8.2 million
on inventory (our cost of goods sold). Our average inventory was $2.5 million. We thus
turned our inventory over $8.2/$2.5 times during the year:1
Inventory turnover =
Cost of goods sold
________________
Average inventory
= $8.2 million __________
$2.5 million
= 3.28 times
Loosely speaking, this tells us that we bought and sold off our inventory 3.28 times during
the year. This means that, on average, we held our inventory for:
Inventory period
=
365 days
_____________
Inventory turnover
=
365 ____
3.28
= 111.3 days
So, the inventory period is about 111 days. On average, in other words, inventory sat for
about 111 days before it was sold.2
Similarly, receivables averaged $1.8 million, and sales were $11.5 million. Assuming
that all sales were credit sales, the receivables turnover is:3
Receivables turnover
=
Credit sales ____________________
Average accounts receivable
=
$11).)5 million __________
$1).)8 million
= 6.4 times
If we turn over our receivables 6.4 times, then the receivables period is:
Receivables period
=
365 days
_______________
Receivables turnover
=
365 ___
6.4
= 57.1 days
The receivables period also is called the days’ sales in receivables or the average collection
period. Whatever it is called, it tells us that our customers took an average of 57 days to pay.
The operating cycle is the sum of the inventory and receivables periods:
Operating cycle = Inventory period + Accounts receivable period
= 111 days + 57 days = 168 days
This tells us that, on average, 168 days elapse between the time we acquire inventory and,
having sold it, collect for the sale.
The Cash Cycle We now need the payables period. From the information given above,
average payables were $875,000, and cost of goods sold was again $8.2 million. Our pay-
ables turnover is:
Payables turnover =
Cost of goods sold
________________
Average payables
= $8.2 million ___________
$).)875 million
= 9.4 times
1Notice that in calculating inventory turnover here, we used the average inventory instead of using the ending inven-
tory as we did in Chapter 3. Both approaches are used in the real world. To gain some practice using average fig-
ures, we will stick with this approach in calculating various ratios throughout this chapter.
2This measure is conceptually identical to the days’ sales in inventory we discussed in Chapter 3.
3If less than 100 percent of our sales are credit sales, then we need a little more information, namely, credit sales
for the year. See Chapter 3 for more discussion of this measure.
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528 P A R T 8 Short-Term Financial Management
The payables period is:
Payables period
=
365 days
_____________
Payables turnover
=
365 ___
9.4
= 38.9 days
Thus, we took an average of 39 days to pay our bills.
Finally, the cash cycle is the difference between the operating cycle and the payables
period:
Cash cycle = Operating cycle − Accounts payable period
= 168 days − 39 days = 129 days
So, on average, there is a 129-day delay from the time we pay for merchandise to the time we
collect on the sale.
EXAMPLE 16.2 The Operating and Cash Cycles
You have collected the following information for the Slowpay Company:
Item Beginning Ending
Inventory $5,000 $7,000
Accounts receivable 1,600 2,400
Accounts payable 2,700 4,800
Credit sales for the year just ended were $50,000, and cost of goods sold was $30,000. How long
does it take Slowpay to collect on its receivables? How long does merchandise stay around before
it is sold? How long does Slowpay take to pay its bills?
We can first calculate the three turnover ratios:
Inventory turnover = $30,000/6,000 = 5 times
Receivables turnover = $50,000/2,000 = 25 times
Payables turnover = $30,000/3,750 = 8 times
We use these to get the various periods:
Inventory period = 365/5 = 73 days
Receivables period = 365/25 = 14.6 days
Payables period = 365/8 = 45.6 days
All told, Slowpay collects on a sale in 14.6 days, inventory sits around for 73 days, and bills get paid
after about 46 days. The operating cycle here is the sum of the inventory and receivables periods:
73 + 14.6 = 87.6 days. The cash cycle is the difference between the operating cycle and the pay-
ables period: 87.6 – 45.6 = 42 days.
Interpreting the Cash Cycle
Our examples show that the cash cycle depends on the inventory, receivables, and payables pe-
riods. The cash cycle increases as the inventory and receivables periods get longer. It decreases
if the company is able to defer payment of payables and thereby lengthen the payables period.
Most firms have a positive cash cycle, and they thus require financing for inventories
and receivables. The longer the cash cycle, the more financing is required. Also, changes in
the firm’s cash cycle often are monitored as an early-warning measure. A lengthening cycle
can indicate that the firm is having trouble moving inventory or collecting on its receivables.
Such problems can be masked, at least partially, by an increased payables cycle, so both
should be monitored.
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We easily can see the link between the firm’s cash cycle and its profitability by recalling
that one of the basic determinants of profitability and growth for a firm is its total asset
turnover, which is defined as Sales/Total assets. In Chapter 3, we saw that the higher this
ratio is, the greater are the firm’s accounting return on assets, ROA, and return on equity,
ROE. Thus, all other things being the same, the shorter the cash cycle is, the lower is the
firm’s investment in inventories and receivables. As a result, the firm’s total assets are lower,
and total turnover is higher.
Cash Cycle Comparison
In 2017, CFO magazine published its annual survey of work-ing capital for various industries. The results of this survey
highlight the differences in cash and operating cycles across
industries. The table below shows four different industries
and the operating and cash cycles for each. Of these, the
food products industry has the shortest operating and cash
cycles. The auto components industry has the shortest
inventory period, a day less than the food products industry.
The short inventory period in the auto components industry
is due to years of efficiency efforts.
FINANCE MATTERS
529
Compared to the food products industry, the auto com-
ponents, chemical services, and energy services indus-
tries all have a much longer operating cycle. The chemical
services and energy services industries have similar operat-
ing cycles, but the makeup differs. The chemical services
industry has a longer inventory period, while the energy ser-
vices industry has a longer receivables period. Notice the
receivables period is very short for the food products indus-
try as customers tend to pay in cash or use credit cards. As a
result, firms in this industry have little or no receivables.
We’ve seen that operating and cash cycles can vary quite
a bit across industries, but these cycles also can be different for
companies within the same industry. Below you will find the
operating and cash cycles for selected Internet and catalog
retail companies. As you can see, there are differences. Wayfair
and Amazon both have negative cash cycles. However, the two
companies have negative cash cycles for different reasons.
Wayfair has both a low receivables period and inventory period,
while Amazon’s is significantly larger in both cases. But
Amazon’s payables period is 114 days, or almost three months.
When you look at the operating and cash cycles, con-
sider that each is really a financial ratio. As with any financial
ratio, firm and industry characteristics will have an effect, so
take care in your interpretation. For example, in looking at
Lands’ End, we note it has a long inventory period. Is that a
bad thing? Maybe not. Lands’ End has a different business
model compared to the other three companies shown, and,
as a result, it has different inventory management strategies.
Receivables
Period
(days)
Inventory
Period
(days)
Operating
Cycle
(days)
Payables
Period
(days)
Cash
Cycle
(days)
Auto components 47 36 83 61 22
Chemical services 54 71 125 48 77
Energy services 81 56 137 35 102
Food products 6 37 8 43 27 16
Receivables
Period
(days)
Inventory
Period
(days)
Operating
Cycle
(days)
Payables
Period
(days)
Cash
Cycle
(days)
Wayfair 2 3 5 55 –50
Amazon 16 52 68 114 –46
HSN 34 61 95 46 49
Lands’ End 11 156 167 78 89
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530 P A R T 8 Short-Term Financial Management
To see how important the cash cycle is, consider the consequences of the U.S. Postal
Service’s decision to increase the standard delivery time from two days to three days. A
working capital expert estimated that as a result of this decision, a company with $10 billion
in revenue could see an increase in net working capital of $100 million. The nearby Finance
Matters box discusses the cash cycles and operating cycles for several industries, as well as
for some specific companies.
CONCEPT QUESTIONS
16.2a What does it mean to say that a firm has an inventory turnover ratio of 4?
16.2b Describe the operating cycle and cash cycle. What are the differences?
16.2c Explain the connection between a firm’s accounting-based profitability and its
cash cycle.
SOME ASPECTS OF SHORT-TERM
FINANCIAL POLICY
The short-term financial policy that a firm adopts will be reflected in at least two ways:
1. The size of the firm’s investment in current assets. This is usually measured relative to the
firm’s level of total operating revenues. A flexible, or accommodative, short-term
financial policy would maintain a relatively high ratio of current assets to sales. A
restrictive short-term financial policy would entail a low ratio of current assets to sales.4
2. The financing of current assets. This is measured as the proportion of short-term debt
(that is, current liabilities) and long-term debt used to finance current assets. A
restrictive short-term financial policy means a high proportion of short-term debt
relative to long-term financing, and a flexible policy means less short-term debt and
more long-term debt.
If we take these two areas together, we see that a firm with a flexible policy would have
a relatively large investment in current assets. It would finance this investment with rela-
tively less in short-term debt. The net effect of a flexible policy is thus a relatively high level
of net working capital. Put another way, with a flexible policy, the firm maintains a larger
overall level of liquidity.
The Size of the Firm’s Investment in Current Assets
Flexible short-term financial policies with regard to current assets include such actions as:
1. Keeping large balances of cash and marketable securities.
2. Making large investments in inventory.
3. Granting liberal credit terms, which results in a high level of accounts receivable.
Restrictive short-term financial policies would be just the opposite of the ones above:
1. Keeping low cash balances and little investment in marketable securities.
2. Making small investments in inventory.
3. Allowing few or no credit sales, thereby minimizing accounts receivable.
16.3
4Some people use the term conservative in place of flexible and the term aggressive in place of restrictive.
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C H A P T E R 1 6 Short-Term Financial Planning 531
Determining the optimal level of investment in short-term assets requires an identifica-
tion of the different costs of alternative short-term financing policies. The objective is to
trade off the cost of a restrictive policy against the cost of a flexible one to arrive at the best
compromise.
Current asset holdings are highest with a flexible short-term financial policy and low-
est with a restrictive policy. So, flexible short-term financial policies are costly in that they
require a greater investment in cash and marketable securities, inventory, and accounts
receivable. However, we expect that future cash inflows will be higher with a flexible pol-
icy. For example, sales are stimulated by the use of a credit policy that provides liberal fi-
nancing to customers. A large amount of finished inventory on hand (“on the shelf ”)
provides a quick delivery service to customers and may increase sales. Similarly, a large
inventory of raw materials may result in fewer production stoppages because of inventory
shortages.
A more restrictive short-term financial policy probably reduces future sales levels below
those that would be achieved under flexible policies. It is also possible that higher prices can
be charged to customers under flexible working capital policies. Customers may be willing
to pay higher prices for the quick delivery service and more liberal credit terms implicit in
flexible policies.
Managing current assets can be thought of as involving a trade-off between costs that
rise and costs that fall with the level of investment. Costs that rise with increases in the level
of investment in current assets are called carrying costs. The larger the investment a firm
makes in its current assets, the higher its carrying costs will be. Costs that fall with increases
in the level of investment in current assets are called shortage costs.
In a general sense, carrying costs are the opportunity costs associated with current as-
sets. The rate of return on current assets is very low when compared to that on other assets.
For example, the rate of return on U.S. Treasury bills is usually well below 5 percent. This is
very low compared to the rate of return firms would like to achieve overall. (U.S. Treasury
bills are an important component of cash and marketable securities.)
Shortage costs are incurred when the investment in current assets is low. If a firm runs
out of cash, it will be forced to sell marketable securities. Of course, if a firm runs out of
cash and cannot readily sell marketable securities, it may have to borrow or default on an
obligation. This situation is called a cash-out. A firm may lose customers if it runs out of in-
ventory (a stock-out) or if it cannot extend credit to customers.
More generally, there are two kinds of shortage costs:
1. Trading, or order, costs. Order costs are the costs of placing an order for more cash
(brokerage costs, for example) or more inventory (production setup costs, for
example).
2. Costs related to lack of safety reserves. These are costs of lost sales, lost customer
goodwill, and disruption of production schedules.
The top part of Figure 16.2 illustrates the basic trade-off between carrying costs and short-
age costs. On the vertical axis, we have costs measured in dollars, and, on the horizontal
axis, we have the amount of current assets. Carrying costs start out at zero when current
assets are zero and then climb steadily as current assets grow. Shortage costs start out very
high and then decline as we add current assets. The total cost of holding current assets is the
sum of the two. Notice how the combined costs reach a minimum at CA*. This is the opti-
mal level of current assets.
Optimal current asset holdings are highest under a flexible policy. This policy is one in
which the carrying costs are perceived to be low relative to shortage costs. This is Case A in
Figure 16.2. In comparison, under restrictive current asset policies, carrying costs are
carrying costs
Costs that rise with
increases in the level of
investment in current
assets.
shortage costs
Costs that fall with
increases in the level of
investment in current
assets.
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532 P A R T 8 Short-Term Financial Management
Carrying costs and
shortage costs
FIGURE 16.2
CA*
Shortage costs
Carrying costs
Total cost of
holding current assets
Minimum point
Amount of
current assets (CA)
Dollars
Short-term financial policy: the optimal investment in current assets
CA* represents the optimal amount of current assets.
Holding this amount minimizes total costs.
Carrying costs increase with the level of investment in current assets. They include
the costs of maintaining economic value and opportunity costs. Shortage costs
decrease with increases in the level of investment in current assets. They include
trading costs and the costs related to being short of the current asset (for example,
being short of cash). The firm’s policy can be characterized as flexible or restrictive.
Minimum point
Minimum point
Shortage costs
Carrying costs
Shortage costs
Carrying costs
Amount of
current assets (CA)
Dollars
Amount of
current assets (CA)
Dollars
Total cost
Total cost
A flexible policy is most appropriate when carrying costs
are low relative to shortage costs.
A restrictive policy is most appropriate when carrying costs
are high relative to shortage costs.
A. Flexible policy B. Restrictive policy
CA* CA*
perceived to be high relative to shortage costs, resulting in lower current asset holdings. This
is Case B in Figure 16.2.
Alternative Financing Policies for Current Assets
In previous sections, we looked at the basic determinants of the level of investment in cur-
rent assets, and we thus focused on the asset side of the balance sheet. Now we turn to the
financing side of the question. Here we are concerned with the relative amounts of short-
term and long-term debt, assuming the investment in current assets is constant.
A growing firm can be thought of as having a total asset requirement consisting of the
current assets and long-term assets needed to run the business efficiently. The total asset re-
quirement may exhibit change over time for many reasons, including (1) a general growth trend,
(2) seasonal variation around the trend, and (3) unpredictable day-to-day and month-to-month
ros13952_ch16_521-552.indd 532 12/24/18 5:32 PM
C H A P T E R 1 6 Short-Term Financial Planning 533
fluctuations. This situation is depicted in Figure 16.3. (We have not tried to show the
unpredictable day-to-day and month-to-month variations in the total asset requirement.)
The peaks and valleys in Figure 16.3 represent the firm’s total asset needs through time.
For example, for a lawn and garden supply firm, the peaks might represent inventory build-
ups prior to the spring selling season. The valleys come about because of lower off-season
inventories. There are two strategies such a firm might consider to meet its cyclical needs.
First, the firm could keep a relatively large pool of marketable securities. As the need for
inventory and other current assets begins to rise, the firm sells off marketable securities and
uses the cash to purchase whatever is needed. Once the inventory is sold and inventory
holdings begin to decline, the firm reinvests in marketable securities. This approach is the
flexible policy illustrated in Figure 16.4 as Policy F. Notice that the firm essentially uses a
pool of marketable securities as a buffer against changing current asset needs.
At the other extreme, the firm could keep relatively little in marketable securities. As
the need for inventory and other assets begins to rise, the firm borrows the needed cash on
a short-term basis. The firm repays the loans as the need for assets cycles back down. This
approach is the restrictive policy illustrated in Figure 16.4 as Policy R.
The total asset
requirement
over time
FIGURE 16.3
Seasonal
variation
General growth in
fixed assets
and permanent
current assets
Total asset
requirement
Time
Dollars
Alternative asset financing policies
Marketable
securities
Long-term
financing
Time
Dollars
Policy F
Policy F always implies a short-term cash surplus
and a large investment in cash and marketable
securities.
Short-term
financing
Total asset
requirement
Long-term
financing
Time
Dollars
Policy R
Policy R uses long-term financing for permanent
asset requirements only and short-term borrowing
for seasonal variations.
Total asset
requirement
FIGURE 16.4
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534 P A R T 8 Short-Term Financial Management
In comparing the two strategies illustrated in Figure 16.4, notice that the chief differ-
ence is the way in which the seasonal variation in asset needs is financed. In the flexible
case, the firm finances internally, using its own cash and marketable securities. In the re-
strictive case, the firm finances externally, borrowing the needed funds on a short-term ba-
sis. As we discussed earlier, all else being the same, a firm with a flexible policy will have a
greater investment in net working capital.
Which Financing Policy Is Best?
What is the most appropriate amount of short-term borrowing? There is no definitive an-
swer. Several considerations must be included in a proper analysis:
1. Cash reserves. The flexible financing policy implies surplus cash and little short-term
borrowing. This policy reduces the probability that a firm will experience financial
distress. Firms may not have to worry as much about meeting recurring short-run
obligations. However, investments in cash and marketable securities are zero net
present value investments at best.
2. Maturity hedging. Most firms attempt to match the maturities of assets and liabilities.
They finance inventories with short-term bank loans and fixed assets with long-term
financing. Firms tend to avoid financing long-lived assets with short-term borrowing.
This type of maturity mismatching would necessitate frequent refinancing and is
inherently risky because short-term interest rates are more volatile than longer-term rates.
3. Relative interest rates. Short-term interest rates are usually lower than long-term rates.
This implies that it is, on average, more costly to rely on long-term borrowing as
compared to short-term borrowing.
The two policies, F and R, that we discuss above are, of course, extreme cases. With F, the
firm never does any short-term borrowing, and, with R, the firm never has a cash reserve
(an investment in marketable securities). Figure 16.5 illustrates these two policies along
with a compromise, Policy C.
A compromise
financing policy
FIGURE 16.5
Total seasonal
variation
Short-term
financing Flexible policy (F)
Compromise policy (C)
Restrictive policy (R)
Marketable
securities
General growth in
fixed assets
and permanent
current assets
With a compromise policy, the firm keeps a reserve of liquidity that
it uses to initially finance seasonal variations in current asset needs.
Short-term borrowing is used when the reserve is exhausted.
Dollars
Time
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C H A P T E R 1 6 Short-Term Financial Planning 535
Current assets and
current liabilities as
a percentage of total
assets for selected
companies: 2018
TABLE 16.2Amazon Boeing Cisco Walmart
Cash and near cash 13.20% 8.13% 5.89% 3.85%
Marketable securities 6.56 .58 41.85 .00
Accounts receivable 9.52 11.33 8.02 2.23
Inventories 10.95 53.99 1.67 21.13
Other current assets .00 2.18 1.46 88 1.70
Total current assets 40.22% 76.22% 58.89% 28.91%
Accounts payable 33.13% 64.77% 4.81% 34.51%
Short-term borrowings .00 1.74 6.79 4.90
Other short-term liabilities 4.89 .00 13.53 .00
Total current liabilities 38.02% 66.52% 25.12% 39.41%
With this compromise approach, the firm borrows in the short term to cover peak fi-
nancing needs, but it maintains a cash reserve in the form of marketable securities during
slow periods. As current assets build up, the firm draws down this reserve before doing any
short-term borrowing. This allows for some run-up in current assets before the firm has to
resort to short-term borrowing.
Current Assets and Liabilities in Practice
Short-term assets represent a significant portion of a typical firm’s overall assets. For U.S.
manufacturing, mining, and trade corporations, current assets were about 50 percent of to-
tal assets in the 1960s. Today, this figure is closer to 40 percent. Most of the decline is due
to more efficient cash and inventory management. Over this same period, current liabilities
rose from about 20 percent of total liabilities and equity to almost 30 percent. The result is
that liquidity (as measured by the ratio of net working capital to total assets) has declined,
signaling a move to more restrictive short-term policies.
The cash cycle is longer in some industries than in others because of different products
and industry practices. Table 16.2 illustrates this point by comparing the current asset and
liability percentages for four different companies. Of the four, Boeing has the highest level
of inventories. Does this mean Boeing is less efficient? Probably not; instead, the relatively
high inventory levels are consistent with the industry. Boeing manufactures airplanes, and
manufacturing a jetliner can take one to two years. During this time, the partially completed
plane is on Boeing’s balance sheet as inventory. Walmart also needs a higher level of inven-
tory on hand to satisfy customers who walk into its stores. In contrast, Cisco is mostly soft-
ware and information technology, so its inventory levels are lower. Notice also that Walmart
has the lowest levels of current assets to total assets, implying that fixed assets are large, as
you would expect from such a capital-intensive company. Walmart does have a somewhat
unique feature in its working capital. If you notice, current liabilities exceed current assets,
which means Walmart has a negative net working capital.
CONCEPT QUESTIONS
16.3a What considerations determine the optimal size of the firm’s investment in current
assets?
16.3b What considerations determine the optimal compromise between flexible and
restrictive net working capital policies?
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536 P A R T 8 Short-Term Financial Management
THE CASH BUDGET
The cash budget is a primary tool in short-run financial planning. It allows the financial
manager to identify short-term financial needs and opportunities. Importantly, the cash
budget will help the manager explore the need for short-term borrowing. The idea of the
cash budget is simple: It records estimates of cash receipts (cash in) and disbursements
(cash out). The result is an estimate of the cash surplus or deficit.
Sales and Cash Collections
We start with an example for the Fun Toys Corporation. We will prepare a quarterly cash
budget. We could just as well use a monthly, weekly, or even daily basis. We choose quarters
for convenience and also because a quarter is a common short-term business planning
period.
All of Fun Toys’ cash inflows come from the sale of toys. Cash budgeting for Fun Toys
therefore must start with a sales forecast for the coming year, by quarter:
Q1 Q2 Q3 Q4
Sales (in millions) $200 $300 $250 $400
Note that these are predicted sales, so there is forecasting risk here; actual sales could
be more or less. Also, Fun Toys started the year with accounts receivable equal
to $120.
Fun Toys has a 45-day receivables, or average collection, period. This means that half of
the sales in a given quarter will be collected the following quarter. This happens because
sales made during the first 45 days of a quarter will be collected in that quarter. Sales made
in the second 45 days will be collected in the next quarter. Note that we are assuming that
each quarter has 90 days, so the 45-day collection period is the same as a half-quarter collec-
tion period.
Based on the sales forecasts, we now need to estimate Fun Toys’s projected cash collec-
tions. First, any receivables that we have at the beginning of a quarter will be collected
within 45 days, so all of them will be collected sometime during the quarter. Second, as we
discussed, any sales made in the first half of the quarter will be collected within the quarter,
so total cash collections are:
Cash collections = Beginning accounts receivable + ½ × Sales [16.6]
For example, in the first quarter, cash collections would be the beginning receivables of
$120 plus half of sales, ½ × $200 = $100, for a total of $220.
Because beginning receivables all are collected along with half of sales, ending receiv-
ables for a particular quarter would be the other half of sales. First-quarter sales are pro-
jected at $200, so ending receivables will be $100. This will be the beginning receivables in
the second quarter. Cash collections in the second quarter will thus be $100 plus half of the
projected $300 in sales, or $250 total.
Continuing this process, we can summarize Fun Toys’s projected cash collections in
Table 16.3 as the only source of cash. Of course, this might not be the case. Other sources
of cash could include asset sales, investment income, and receipts from planned long-term
financing.
16.4
coverage online
Excel
Master
cash budget
A forecast of cash receipts
and disbursements for the
next planning period.
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C H A P T E R 1 6 Short-Term Financial Planning 537
Cash Outflows
Next, we consider the cash disbursements, or payments. These come in four basic
categories:
1. Payments of accounts payable. These are payments for goods or services rendered by
suppliers, such as raw materials. Generally, these payments will be made sometime
after purchases.
2. Wages, taxes, and other expenses. This category includes all other regular costs of doing
business that require actual expenditures. Depreciation, for example, is often thought
of as a regular cost of business, but it requires no cash outflow and is not included.
3. Capital expenditures. These are payments of cash for long-lived assets.
4. Long-term financing expenses. This category, for example, includes interest payments
on long-term debt outstanding and dividend payments to shareholders.
Fun Toys’s purchases from suppliers (in dollars) in a quarter are equal to 60 percent of the
next quarter’s predicted sales. Fun Toys’s payments to suppliers are equal to the previous
quarter’s purchases, so the accounts payable period is 90 days. For example, in the quarter
just ended, Fun Toys ordered .60 × $200 = $120 in supplies. This will actually be paid in
the first quarter (Q1) of the coming year.
Wages, taxes, and other expenses are routinely 20 percent of sales; interest and divi-
dends are currently $20 per quarter. In addition, Fun Toys plans a major plant expansion
(a capital expenditure) of $100 in the second quarter. If we put all this information together,
the cash outflows are as shown in Table 16.4.
The Cash Balance
The predicted net cash inflow is the difference between cash collections and cash disburse-
ments. The net cash inflow for Fun Toys is shown in Table 16.5. What we see immediately
is that there is a net cash inflow in the first and third quarters and a net outflow in the
second and fourth.
Cash collections for
Fun Toys (in millions)
TABLE 16.3Q1
$120
200
–220
100
Q2 Q3 Q4
Beginning receivables
Sales
Cash collections
Ending receivables
Collections = Beginning receivables + ½ × Sales
Ending receivables = Beginning receivables + Sales – Collections
= ½ × Sales
$100
300
–250
150
$150
250
–275
125
$125
400
–325
200
Cash disbursements
for Fun Toys (in
millions)
TABLE 16.4
Wages, taxes, other expenses
Payment of accounts (60% of sales)
Capital expenditures
Long-term financing expenses
(interest and dividends)
Total cash disbursements
Q1 Q2 Q3 Q4
$120
40
0
20
$180
$180
60
100
20
$360
$150
50
0
20
$220
$240
80
0
20
$340
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538 P A R T 8 Short-Term Financial Management
Net cash inflow for
Fun Toys (in millions)
TABLE 16.5
Total cash collections
Total cash disbursements
Net cash inflow
Q1 Q2 Q3 Q4
$220
180
$ 40
$250
360
–$110
$275
220
$ 55
$325
340
–$ 15
Cash balance for Fun
Toys (in millions)
TABLE 16.6 Q1 Q2 Q3 Q4
Beginning cash balance
Net cash inflow
Ending cash balance
Minimum cash balance
Cumulative surplus (deficit)
$20
40
$60
– 10
$50
$60
–110
–$50
– 10
–$60
–$50
55
$ 5
– 10
–$ 5
$ 5
– 15
–$10
– 10
–$20
We will assume that Fun Toys starts the year with a $20 cash balance. Further-
more, Fun Toys maintains a $10 minimum cash balance to guard against unforeseen
contingencies and forecasting errors. So, we start the first quarter with $20 in cash.
This rises by $40 during the quarter, and the ending balance is $60. Of this, $10 is re-
served as a minimum, so we subtract it out and find that the first-quarter surplus is
$60 − 10 = $50.
Fun Toys starts the second quarter with $60 in cash (the ending balance from the pre-
vious quarter). There is a net cash inflow of −$110, so the ending balance is $60 − 110 =
−$50. We need another $10 as a buffer, so the total deficit is −$60. These calculations and
those for the last two quarters are summarized in Table 16.6.
Beginning in the second quarter, Fun Toys has a cash shortfall of $60. This occurs be-
cause of the seasonal pattern of sales (higher toward the end of the second quarter), the
delay in collections, and the planned capital expenditure.
The cash situation at Fun Toys is projected to improve to a $5 deficit in the third
quarter, but, by year’s end, Fun Toys is showing a $20 deficit. Without some sort of
financing, this deficit will carry over into the next year. We explore this subject in the
next section.
For now, we can make the following general comments on Fun Toys’s cash needs:
1. Fun Toys’s large outflow in the second quarter is not necessarily a sign of trouble. It
results from delayed collections on sales and a planned capital expenditure
(presumably a worthwhile one).
2. The figures in our example are based on a forecast. Sales could be much worse (or
better) than the forecast figures.
CONCEPT QUESTIONS
16.4a How would you do a sensitivity analysis (discussed in Chapter 9) for Fun Toys’s net
cash balance?
16.4b What could you learn from a sensitivity analysis?
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C H A P T E R 1 6 Short-Term Financial Planning 539
SHORT-TERM BORROWING
Fun Toys has a short-term financing problem. It cannot meet the forecast cash outflows in
the second quarter from internal sources. How it will finance the shortfall depends on its
financial policy. With a very flexible policy, Fun Toys might seek up to $60 million in long-
term debt financing.
In addition, note that much of the cash deficit comes from the large capital expendi-
ture. Arguably, this is a candidate for long-term financing. Nonetheless, because we have
discussed long-term financing elsewhere, we will concentrate here on two short-term bor-
rowing options: (1) unsecured borrowing and (2) secured borrowing.
Unsecured Loans
The most common way to finance a temporary cash deficit is to arrange a short-term, unse-
cured bank loan. Firms that use short-term bank loans often arrange a line of credit. A
line of credit is an agreement under which a firm is authorized to borrow up to a specified
amount. To ensure that the line is used for short-term purposes, the borrower will some-
times be required to pay the line down to zero and keep it there for some period during the
year, typically 60 days (called a cleanup period).
Short-term lines of credit are classified as either committed or noncommitted. The latter
is an informal arrangement that allows firms to borrow up to a previously specified limit
without going through the normal paperwork (much as you would with a credit card). A re-
volving credit arrangement (or revolver) is similar to a line of credit, but it is usually open for
two or more years, whereas a line of credit would usually be evaluated on an annual basis.
Committed lines of credit are more formal legal arrangements and often involve a com-
mitment fee paid by the firm to the bank. The interest rate on the line of credit will usually
float. A firm that pays a commitment fee for a committed line of credit is essentially buying
insurance to guarantee that the bank can’t back out of the agreement (absent some material
change in the borrower’s status).
Secured Loans
Banks and other finance companies often require security for a short-term loan as they do
for a long-term loan. Security for short-term loans usually consists of accounts receivable,
inventories, or both.
Accounts Receivable Financing Accounts receivable financing involves either
assigning receivables or factoring receivables. Under assignment, the lender has the receiv-
ables as security, but the borrower is still responsible if a receivable can’t be collected. With
conventional factoring, the receivable is discounted and sold to the lender (the factor). Once
it is sold, collection is the factor’s problem, and the factor assumes the full risk of default on
bad accounts. With maturity factoring, the factor forwards the money on an agreed-upon
future date.
16.5
line of credit
A formal (committed) or
informal (noncommitted)
prearranged, short-term
bank loan.
accounts receivable
financing
A secured short-term loan
that involves either the
assignment or factoring of
receivables.
EXAMPLE 16.3 Cost of Factoring
For the year just ended, LuLu’s Pies had an average of $50,000 in accounts receivable. Credit sales
were $500,000. LuLu’s factors its receivables by discounting them 3 percent, in other words, by
selling them for 97 cents on the dollar. What is the effective interest rate on this source of short-term
financing?
(continued)
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540 P A R T 8 Short-Term Financial Management
Inventory Loans Inventory loans, short-term loans to purchase inventory, come in
three basic forms: blanket inventory liens, trust receipts, and field warehouse financing:
1. Blanket inventory lien. A blanket lien gives the lender a lien against all the borrower’s
inventories (the blanket “covers” everything).
2. Trust receipt. A trust receipt is a device by which the borrower holds specific inventory
in “trust” for the lender. Automobile dealer financing, for example, is done by use of
trust receipts. This type of secured financing also is called floor planning, in reference
to inventory on the showroom floor. However, it is somewhat cumbersome to use trust
receipts for, say, wheat grain.
3. Field warehouse financing. In field warehouse financing, a public warehouse company
(an independent company that specializes in inventory management) acts as a control
agent to supervise the inventory for the lender.
Other Sources
There are a variety of other sources of short-term funds employed by corporations. Two of
the most important are commercial paper and trade credit.
Commercial paper consists of short-term notes issued by large and highly rated firms.
Typically, these notes are of short maturity, ranging up to 270 days (beyond that limit, the
firm must file a registration statement with the SEC). Because the firm issues these directly,
the interest rate the borrowing firm obtains can be significantly below the rate a bank would
charge for a direct loan.
Another option available to a firm is to increase the accounts payable period; in other
words, it may take longer to pay its bills. This amounts to borrowing from suppliers in the
form of trade credit. This is an extremely important form of financing for smaller businesses
in particular. As we discuss in Chapter 17, a firm using trade credit may end up paying a
much higher price for what it purchases, so this can be a very expensive source of
financing.
CONCEPT QUESTIONS
16.5a What are the two basic forms of short-term financing?
16.5b Describe two types of secured loans.
inventory loan
A secured short-term loan
to purchase inventory.
To determine the interest rate, we first have to know the accounts receivable, or average col-
lection, period. During the year, LuLu’s turned over its receivables $500,000/$50,000 = 10 times.
The average collection period is therefore 365/10 = 36.5 days.
The interest paid here is a form of “discount interest.” In this case, LuLu’s is paying 3 cents in
interest on every 97 cents of financing. The interest rate per 36.5 days is thus .03/.97 = .0309, or
3.09%. The APR is 10 × 3.09% = 30.9%, but the effective annual rate is:
EAR = 1.030910 − 1 = .356, or 35.6%
The factoring is a relatively expensive source of money in this case.
We should note that if the factor takes on the risk of default by a buyer, then the factor is pro-
viding insurance as well as immediate cash. More generally, the factor essentially takes over the
firm’s credit operations. This can result in a significant saving. The interest rate we calculated is
therefore overstated, particularly if default is a significant possibility.
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C H A P T E R 1 6 Short-Term Financial Planning 541
A SHORT-TERM FINANCIAL PLAN
To illustrate a completed short-term financial plan, we will assume that Fun Toys arranges
to borrow any needed funds on a short-term basis. The interest rate is 20 percent APR, and
it is calculated on a quarterly basis. From Chapter 5, we know that the rate is 20%/4 = 5%
per quarter. We will assume that Fun Toys starts the year with no short-term debt.
From Table 16.6, we see that Fun Toys has a second-quarter deficit of $60 million. We
will have to borrow this amount. Net cash inflow in the following quarter is $55 million. We
now have to pay $60 × .05 = $3 million in interest out of that, leaving $52 million to reduce
the borrowing.
We still owe $60 − 52 = $8 million at the end of the third quarter. Interest in the last
quarter thus will be $8 × .05 = $.4 million. In addition, net inflows in the last quarter are
−$15 million, so we have to borrow a total of $15.4 million, bringing our total borrowing up
to $15.4 + 8 = $23.4 million. Table 16.7 extends Table 16.6 to include these calculations.
Notice that the ending short-term debt is equal to the cumulative deficit for the entire
year, $20 million, plus the interest paid during the year, $3 + .4 = $3.4 million, for a total
of $23.4 million.
Our plan is very simple. For example, we ignored the fact that the interest paid on the
short-term debt is tax deductible. We also ignored the fact that the cash surplus in the first quar-
ter would earn some interest (which would be taxable). We could add on a number of refine-
ments. Even so, our plan highlights the fact that in about 90 days Fun Toys will need to borrow
$60 million or so on a short-term basis. It’s time to start lining up the source of the funds.
Our plan also illustrates that financing the firm’s short-term needs will cost about
$3.4 million in interest (before taxes) for the year. This is a starting point for Fun Toys to begin
evaluating alternatives to reduce this expense. For example, can the $100 million planned ex-
penditure be postponed or spread out? At 5 percent per quarter, short-term credit is expensive.
Also, if Fun Toys’s sales are expected to keep growing, then the $20 million plus deficit
will probably also keep growing, and the need for additional financing is permanent. Fun
Toys may wish to think about raising money on a long-term basis to cover this need.
CONCEPT QUESTIONS
16.6a In Table 16.7, does Fun Toys have a projected deficit or surplus?
16.6b In Table 16.7, what would happen to Fun Toys’s deficit or surplus if the minimum
cash balance was reduced to $5?
16.6
Short-term financial
plan for Fun Toys
(in millions)
TABLE 16.7Q1 Q2 Q3 Q4
Beginning cash balance $20 $60 $10 $10.0
Net cash inflow 40 −110 55 − 15.0
New short-term borrowing — 60 — 15.4
Interest on short-term borrowing — — − 3 − .4
Short-term borrowing repaid — 8 — − 52 —
Ending cash balance $60 $10 $10 $10.0
Minimum cash balance − 88810 − 10 − 10 − 10.0
Cumulative surplus (deficit) $50 $ 0 $ 0 $ .0
Beginning short-term borrowing 0 0 60 8.0
Change in short-term debt 0 60 − 52 15.4
Ending short-term debt $ 0 $60 $ 8 $23.4
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542 P A R T 8 Short-Term Financial Management
SUMMARY AND CONCLUSIONS
1. This chapter has introduced the management of short-term finance. Short-term
finance involves short-lived assets and liabilities. We traced and examined the short-
term sources and uses of cash as they appear on the firm’s financial statements. We
saw how current assets and current liabilities arise in the short-term operating
activities and the cash cycle of the firm.
2. Managing short-term cash flows involves the minimizing of costs. The two major costs
are carrying costs, the returns foregone by keeping too much invested in short-term
assets such as cash, and shortage costs, the costs of running out of short-term assets.
The objective of managing short-term finance and doing short-term financial planning
is to find the optimal trade-off between these two costs.
3. In an “ideal” economy, the firm could perfectly predict its short-term uses and sources
of cash, and net working capital could be kept at zero. In the real world we live in, cash
and net working capital provide a buffer that lets the firm meet its ongoing obligations.
The financial manager seeks the optimal level of each of the current assets.
4. The financial manager can use the cash budget to identify short-term financial needs. The
cash budget tells the manager what borrowing is required or what lending will be possible
in the short run. The firm has available to it a number of possible ways of acquiring funds
to meet short-term shortfalls, including the use of unsecured and secured loans.
POP QUIZ!
Can you answer the following questions? If your class is using Connect, log on to
SmartBook to see if you know the answers to these and other questions, check out
the study tools, and find out what topics require additional practice!
Section 16.1 Will decreasing accounts payable decrease cash?
Section 16.2 If the inventory period is 40 days and the accounts receivable period
is 60 days, then how long is the operating cycle?
Section 16.3 What are the opportunity costs of holding current assets called?
Section 16.5 Under what type of loan does the lender have a lien against all of the
borrower’s inventory?
CHAPTER REVIEW AND SELF-TEST PROBLEMS
16.1 The Operating and Cash Cycles Consider the following financial statement
information for the Glory Road Company:
Item Beginning Ending
Inventory $1,543 $1,669
Accounts receivable 4,418 3,952
Accounts payable 2,551 2,673
Net sales $11,500
Cost of goods sold 8,200
Calculate the operating and cash cycles. (See Problem 6.)
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C H A P T E R 1 6 Short-Term Financial Planning 543
16.2 Cash Balance for Masson Corporation The Masson Corporation has a 60-day
average collection period and wishes to maintain a $5 million minimum cash
balance. Based on this and the information below, complete the following cash
budget. What conclusions do you draw? (See Problem 16.)
MASSON CORPORATION
Cash Budget
(in millions)
Q1 Q2 Q3 Q4
Beginning receivables $120
Sales 90 $120 $150 $120
Cash collections
Ending receivables
Total cash collections
Total cash disbursements 80 160 180 160
Net cash inflow
Beginning cash balance $ 5
Net cash inflow
Ending cash balance
Minimum cash balance
Cumulative surplus (deficit)
■ Answers to Chapter Review and Self-Test Problems
16.1 We first need the turnover ratios. Note that we use the average values for all balance
sheet items and that we base the inventory and payables turnover measures on cost
of goods sold.
Inventory turnover = $8,200/[($1,543 + 1,669)/2]
= 5.11 times
Receivables turnover = $11,500/[($4,418 + 3,952)/2]
= 2.75 times
Payables turnover = $8,200/[($2,551 + 2,673)/2]
= 3.14 times
We can now calculate the various periods:
Inventory period = 365 days/5.11 times = 71.49 days
Receivables period = 365 days/2.75 times = 132.83 days
Payables period = 365 days/3.14 times = 116.27 days
So, the time it takes to acquire inventory and sell it is about 71 days. Collection takes
another 133 days, so the operating cycle is thus 71 + 133 = 204 days. The cash cycle
is this 204 days less the payables period, 204 − 116 = 88 days.
16.2 Since Masson has a 60-day collection period, only those sales made in the first
30 days of the quarter will be collected in the same quarter. Total cash collections
in the first quarter will thus equal 30/90 = ⅓ of sales plus beginning receivables,
or $120 + ⅓ × $90 = $150. Ending receivables for the first quarter (and the
second-quarter beginning receivables) are the other ⅔ of sales, or ⅔ × $90 = $60.
The remaining calculations are straightforward, and the completed budget follows.
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544 P A R T 8 Short-Term Financial Management
MASSON CORPORATION
Cash Budget
(in millions)
Q1 Q2 Q3 Q4
Beginning receivables $120 $ 60 $ 80 $100
Sales 90 120 150 120
Cash collections 150 100 130 140
Ending receivables $ 60 $ 80 $100 $ 80
Total cash collections $150 $100 $130 $140
Total cash disbursements 80 160 180 160
Net cash inflow $ 70 −$ 60 −$ 50 −$ 20
Beginning cash balance $ 5 $ 75 $ 15 −$ 35
Net cash inflow 70 − 60 − 50 − 20
Ending cash balance $ 75 $ 15 −$ 35 −$ 55
Minimum cash balance −$ 5 −$ 5 −$ 5 −$ 5
Cumulative surplus (deficit) $ 70 $ 10 −$ 40 −$ 60
The primary conclusion from this schedule is that, beginning in the third quarter,
Masson’s cash surplus becomes a cash deficit. By the end of the year, Masson will
need to arrange for $60 million in cash beyond what will be available.
CRITICAL THINKING AND CONCEPTS REVIEW
LO 1 16.1 Operating Cycle What are some of the characteristics of a firm with a
long operating cycle?
LO 1 16.2 Cash Cycle What are some of the characteristics of a firm with a long
cash cycle?
LO 3 16.3 Sources and Uses For the year just ended, you have gathered the
following information on the Holly Corporation:
a. A $200 dividend was paid.
b. Accounts payable increased by $500.
c. Fixed asset purchases were $900.
d. Inventories increased by $625.
e. Long-term debt decreased by $1,200.
Label each item as a source or use of cash and describe its effect on the
firm’s cash balance.
LO 2 16.4 Cost of Current Assets Kane Manufacturing, Inc., has recently installed
a just-in-time (JIT) inventory system. Describe the effect this is likely to
have on the company’s carrying costs, shortage costs, and operating cycle.
LO 1 16.5 Cycles Is it possible for a firm’s cash cycle to be longer than its operating
cycle? Explain why or why not.
Use the following information to answer Questions 16.6–16.10. Last month,
BlueSky Airline announced that it would stretch out its bill payments to 45 days
from 30 days. The reason given was that the company wanted to “control costs
and optimize cash flow.” The increased payables period will be in effect for all of
the company’s 4,000 suppliers.
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C H A P T E R 1 6 Short-Term Financial Planning 545
LO 1 16.6 Operating and Cash Cycles What impact did this change in payables
policy have on BlueSky’s operating cycle? Its cash cycle?
LO 1 16.7 Operating and Cash Cycles What impact did the announcement have on
BlueSky’s suppliers?
LO 1 16.8 Corporate Ethics Is it ethical for large firms to unilaterally lengthen their
payables periods, particularly when dealing with smaller suppliers?
LO 1 16.9 Payables Period Why don’t all firms increase their payables periods to
shorten their cash cycles?
LO 1 16.10 Payables Period BlueSky lengthened its payables period to “control costs
and optimize cash flow.” Exactly what is the cash benefit to BlueSky from
this change?
QUESTIONS AND PROBLEMS
Select problems are available in McGraw-Hill Connect. Please see the pack-
aging options section of the Preface for more information.
BASIC (Questions 1–12)
1. Changes in the Cash Account Indicate the impact of the following
corporate actions on cash, using the letter I for an increase, D for a decrease,
or N when no change occurs.
a. A dividend is paid with funds received from a sale of debt.
b. Real estate is purchased and paid for with short-term debt.
c. Inventory is bought on credit.
d. A short-term bank loan is repaid.
e. Next year’s taxes are prepaid.
f. Preferred stock is repurchased.
g. Sales are made on credit.
h. Interest on long-term debt is paid.
i. Payments for previous sales are collected.
j. The accounts payable balance is reduced.
k. A dividend is paid.
l. Production supplies are purchased and paid for with a short-term note.
m. Utility bills are paid.
n. Cash is paid for raw materials purchased for inventory.
o. Marketable securities are purchased.
2. Cash Equation Peeples, Inc., has a book value of equity of $14,325.
Long-term debt is $8,200. Net working capital, other than cash, is $2,340.
Fixed assets are $19,260. How much cash does the company have? If current
liabilities are $1,840, what are current assets?
3. Changes in the Operating Cycle Indicate the effect that the following will
have on the operating cycle. Use the letter I to indicate an increase, the letter
D for a decrease, and the letter N for no change.
a. Average receivables go up.
b. Credit payment times for customers are increased.
LO 3
LO 3
LO 1
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546 P A R T 8 Short-Term Financial Management
c. Inventory turnover goes from 3 times to 7 times.
d. Payables turnover goes from 6 times to 11 times.
e. Receivables turnover goes from 7 times to 9 times.
f. Payments to suppliers are accelerated.
4. Changes in Cycles Indicate the impact of the following on the cash and
operating cycles, respectively. Use the letter I to indicate an increase, the
letter D for a decrease, and the letter N for no change.
a. The terms of cash discounts offered to customers are made less
favorable.
b. The cash discounts offered by suppliers are increased; thus, payments
are made earlier.
c. An increased number of customers begin to pay in cash instead of with
credit.
d. Fewer raw materials than usual are purchased.
e. A greater percentage of raw material purchases are paid for with credit.
f. More finished goods are produced for inventory instead of for order.
5. Calculating Cash Collections The Geller Company has projected the
following quarterly sales amounts for the coming year:
Q1 Q2 Q3 Q4
Sales $615 $705 $660 $925
a. Accounts receivable at the beginning of the year are $360. The company
has a 45-day collection period. Calculate cash collections in each of the
four quarters by completing the following:
Q1 Q2 Q3 Q4
Beginning receivables
Sales
Cash collections
Ending receivables
b. Rework part (a) assuming a collection period of 60 days.
c. Rework part (a) assuming a collection period of 30 days.
6. Calculating Cycles Consider the following financial statement information
for the Sourstone Corporation:
Item Beginning Ending
Inventory $7,203 $9,041
Accounts receivable 3,069 3,995
Accounts payable 3,617 4,599
Net sales $95,982
Cost of goods sold 59,814
Assume all sales are on credit. Calculate the operating and cash cycles. How
do you interpret your answer?
LO 1
LO 3
LO 1
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C H A P T E R 1 6 Short-Term Financial Planning 547
7. Factoring Receivables Your firm has an average collection period of
43 days. Current practice is to factor all receivables immediately at a
2 percent discount. What is the effective cost of borrowing in this case?
Assume that default is extremely unlikely.
8. Calculating Payments Wentworth Products has projected the following
sales for the coming year:
Q1 Q2 Q3 Q4
Sales $650 $740 $875 $805
Sales in the year following this one are projected to be 15 percent greater
in each quarter.
a. Calculate payments to suppliers assuming that the company places
orders during each quarter equal to 30 percent of projected sales for the
next quarter. Assume that the company pays immediately. What is the
payables period in this case?
Q1 Q2 Q3 Q4
Payment of accounts
b. Rework part (a) assuming a 90-day payables period.
c. Rework part (a) assuming a 60-day payables period.
9. Calculating Payments The MacDonald Corporation’s purchases from
suppliers in a quarter are equal to 75 percent of the next quarter’s forecast
sales. The payables period is 60 days. Wages, taxes, and other expenses are
30 percent of sales, and interest and dividends are $110 per quarter. No
capital expenditures are planned. Projected quarterly sales are:
Q1 Q2 Q3 Q4
Sales $1,640 $1,920 $2,215 $2,355
Sales for the first quarter of the following year are projected at $2,050.
Calculate the company’s cash outlays by completing the following:
Q1 Q2 Q3 Q4
Payment of accounts
Wages, taxes, other expenses
Long-term financing expenses
(interest and dividends)
Total
10. Calculating Cash Collections The following is the sales budget for Coore,
Inc., for the first quarter of 2019.
January February March
Sales budget $168,000 $186,000 $199,000
LO 3
LO 3
LO 3
LO 3
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548 P A R T 8 Short-Term Financial Management
Credit sales are collected as follows:
65 percent in the month of the sale
20 percent in the month after the sale
15 percent in the second month after the sale
The accounts receivable balance at the end of the previous quarter was
$107,000 ($78,100 of which was uncollected December sales).
a. Compute the sales for November.
b. Compute the sales for December.
c. Compute the cash collections from sales for each month from January
through March.
11. Calculating the Cash Budget Here are some important figures from the
budget of Crenshaw, Inc., for the second quarter of 2019.
April May June
Credit sales $689,000 $598,000 $751,000
Credit purchases 302,000 282,000 338,000
Cash disbursements
Wages, taxes, and expenses 137,000 129,000 179,000
Interest 15,600 15,600 15,600
Equipment purchases 53,500 6,600 248,000
The company predicts that 5 percent of its credit sales will never be collected,
35 percent of its sales will be collected in the month of the sale, and the re-
maining 60 percent will be collected in the following month. Credit purchases
will be paid in the month following the purchase.
In March 2019, credit sales were $561,000. Using this information, com-
plete the following cash budget:
April May June
Beginning cash balance $182,000
Cash receipts
Cash collections from credit sales
Total cash available
Cash disbursements
Purchases 289,000
Wages, taxes, and expenses
Interest
Equipment purchases
Total cash disbursements
Ending cash balance
12. Calculating Cash Collections The Doak Company has projected the
following quarterly sales amounts for the coming year:
Q1 Q2 Q3 Q4
Sales $3,900 $4,700 $4,300 $3,600
LO 3
LO 3
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C H A P T E R 1 6 Short-Term Financial Planning 549
a. Accounts receivable at the beginning of the year are $1,700.
The company has a 45-day collection period. Calculate cash
collections in each of the four quarters by completing the
following:
Q1 Q2 Q3 Q4
Beginning receivables
Sales
Cash collections
Ending receivables
b. Rework part (a) assuming a collection period of 60 days.
c. Rework part (a) assuming a collection period of 30 days.
INTERMEDIATE (Questions 13–16)
13. Costs of Borrowing You’ve worked out a line of credit arrangement that
allows you to borrow up to $40 million at any time. The interest rate is
.527 percent per month. In addition, 4 percent of the amount that you
borrow must be deposited in a noninterest-bearing account. Assume that
your bank uses compound interest on its line-of-credit loans.
a. What is the effective annual interest rate on this lending arrangement?
b. Suppose you need $15 million today and you repay it in six months.
How much interest will you pay?
14. Costs of Borrowing A bank offers your firm a revolving credit arrangement
for up to $75 million at an interest rate of 1.54 percent per quarter. The bank
also requires you to maintain a compensating balance of 4 percent against
the unused portion of the credit line, to be deposited in a noninterest-bearing
account. Assume you have a short-term investment account at the bank
that pays .53 percent per quarter, and assume that the bank uses compound
interest on its revolving credit loans.
a. What is your effective annual interest rate (an opportunity cost) on
the revolving credit arrangement if your firm does not use it during
the year?
b. What is your effective annual interest rate on the lending arrangement if
you borrow $40 million immediately and repay it in one year?
c. What is your effective annual interest rate if you borrow $75 million
immediately and repay it in one year?
15. Cash and Operating Cycles Hanse, Inc., has a cash cycle of 38.5 days,
an operating cycle of 62.4 days, and an inventory period of 24.4 days. The
company reported cost of goods sold in the amount of $445,000, and credit
sales were $724,000. What is the company’s average balance in accounts
payable and accounts receivable?
16. Cash Budget Hurzdan, Inc., has a 32-day average collection period and
wants to maintain a minimum cash balance of $20 million, which is what the
company currently has on hand. The company currently has a receivables
LO 3
LO 3
LO 3
LO 3
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550 P A R T 8 Short-Term Financial Management
balance of $236 million and has developed the following sales and cash
disbursement budgets (in millions):
Q1 Q2 Q3 Q4
Sales $390 $493 $595 $545
Total cash disbursement 321 432 767 463
Complete the following cash budget for the company. What conclusions
do you draw?
HURZDAN, INC.
Cash Budget
(in millions)
Q1 Q2 Q3 Q4
Beginning receivables
Sales
Cash collections
Ending receivables
Total cash collections
Total cash disbursements
Net cash inflow
Beginning cash balance
Net cash inflow
Ending cash balance
Minimum cash balance
Cumulative surplus (deficit)
CHALLENGE (Questions 17–18)
17. Costs of Borrowing In exchange for a $400 million fixed commitment line
of credit, your firm has agreed to do the following:
1. Pay 1.58 percent per quarter on any funds actually borrowed.
2. Maintain a 5 percent compensating balance on any funds actually
borrowed.
3. Pay an up-front commitment fee of .25 percent of the amount of the
line.
Based on this information, answer the following:
a. Ignoring the commitment fee, what is the effective annual interest rate
on this line of credit?
b. Suppose your firm immediately uses $210 million of the line and pays
it off in one year. What is the effective annual interest rate on this
$210 million loan?
18. Costs of Borrowing Come and Go Bank offers your firm a discount
interest loan with an interest rate of 7.3 percent for up to $20 million, and in
addition requires you to maintain a 4 percent compensating balance against
the face amount borrowed. What is the effective annual interest rate on this
lending arrangement?
LO 3
LO 3
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C H A P T E R 1 6 Short-Term Financial Planning 551
WHAT’S ON
THE WEB?
16.1 Cash Cycle Go to www.reuters.com. You will need to find the most recent
annual income statement and the two most recent balance sheets for McKesson
(MCK) and Newmont Mining (NEM). McKesson is involved in pharmaceuticals
and consumer health care, while Newmont Mining is a leading gold mining company.
Calculate the cash cycle for each company and comment on any similarities
or differences.
16.2 Operating Cycle Using the information you gathered in the previous problem,
calculate the operating cycle for each company. What are the similarities or differences?
Is this what you would expect from companies in each of these industries?
16.3 Sources and Uses of Cash Find the two most recent balance sheets for 3M at
the “Investor Relations” link on the website www.3m.com. For each account in the
balance sheet, show the change during the most recent year and note whether this
was a source or use of cash. Do your numbers add up and make sense? Explain
your answer for total assets as compared to your answer for total liabilities and
owners’ equity.
EXCEL MASTER IT! PROBLEM
coverage online
Excel
MasterHeidi Pedersen, the treasurer for Wood Products, Inc., has just been asked by Justin Wood, the company’s president, to prepare a memo detailing the company’s ending cash
balance for the next three months. Following, you will see the relevant estimates for
this period.
July August September
Credit sales $1,275,800 $1,483,500 $1,096,300
Credit purchases 765,480 890,160 657,780
Cash disbursements
Wages, taxes, and expenses 348,600 395,620 337,150
Interest 29,900 29,900 29,900
Equipment 0 158,900 96,300
Credit sales collections:
Collected in month of sale 35%
Collected month after sale 60%
Never collected 5%
June credit sales $1,135,020
June credit purchases $ 681,012
Beginning cash balance $ 425,000
All credit purchases are paid in the month after the purchase.
a. Complete the cash budget for Wood Products for the next three months.
b. Heidi knows that the cash budget will become a standard report completed before
each quarter. To help reduce the time preparing the report each quarter, she
would like a memo with the appropriate information in Excel linked to the memo.
Prepare a memo to Justin that will automatically update when the values are
changed in Excel.
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552 P A R T 8 Short-Term Financial Management
Q1 Q2 Q3 Q4
Gross sales $777,500 $826,500 $896,000 $832,000
Gross sales for the first quarter of next year are pro-
jected at $815,000.
Piepkorn typically orders 50 percent of next quar-
ter’s projected gross sales in the current quarter, and
suppliers are typically paid in 53 days. Wages, taxes,
and other costs run about 30 percent of gross sales.
The company has a quarterly interest payment of
$105,000 on its long-term debt.
The company uses a local bank for its short-term fi-
nancial needs. It pays 1.5 percent per quarter on all short-
term borrowing and maintains a money market account
that pays 1 percent per quarter on all short-term deposits.
Gary has asked you to prepare a cash budget and
short-term financial plan for the company under the cur-
rent policies. He also has asked you to prepare addi-
tional plans based on changes in several inputs.
You recently have been hired by Piepkorn Manufac-turing to work in its newly established treasury de-
partment. Piepkorn Manufacturing is a small company
that produces cardboard boxes in a variety of sizes.
Gary Piepkorn, the owner of the company, works primar-
ily in the sales and production areas. Currently, the com-
pany puts all receivables in one shoe box and all
payables in another. Because of the disorganized sys-
tem, the finance area needs work, and that’s what
you’ve been brought in to do.
The company currently has a cash balance of
$138,000 and plans to purchase new box-folding ma-
chinery in the fourth quarter at a cost of $275,000.
The purchase of the machinery will be made with cash
because of the discount offered. The company’s pol-
icy is to maintain a target cash balance of $100,000.
All sales are in cash and all purchases are made on
credit.
Gary Piepkorn has projected the following gross
sales for each of the next four quarters:
CHAPTER CASE
Piepkorn Manufacturing Working Capital Management, Part 1
1. Use the numbers given to complete the cash
budget and short-term financial plan.
2. Rework the cash budget and short-term financial
plan assuming Piepkorn changes to a target bal-
ance of $80,000.
PIEPKORN MANUFACTURING
Cash Budget
Q1 Q2 Q3 Q4
Beginning cash balance
Net cash inflow
Ending cash balance
Minimum cash balance
Cumulative surplus
(deficit)
PIEPKORN MANUFACTURING
Short-Term Financial Plan
Q1 Q2 Q3 Q4
Target cash balance
Net cash inflow
New short-term investments
Income from short-term
investments
Short-term investments sold
New short-term borrowing
Interest on short-term borrowing
Short-term borrowing repaid
Ending cash balance
Minimum cash balance
Cumulative surplus (deficit)
Beginning short-term
investments
Ending short-term investments
Beginning short-term debt
Ending short-term debt
Q U E S T I O N S
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Please visit us at essentialsofcorporatefinance.blogspot.com for the latest developments in the world of corporate finance.
553
Most often, when news breaks about a firm’s bank accounts, it’s because the company is running low on cash. However,
that wasn’t the case for many companies in the middle of 2018. For
example, Apple had a cash balance of about $285 billion, or $57
per share! Other companies also had large cash balances. For
example, Microsoft had a cash hoard of about $147 billion, while
Alphabet had about $102 billion. Why would firms such as these
hold such large quantities of cash? We examine cash management
in this chapter to find out.
This chapter considers various aspects of working capital man-
agement. Commonly, responsibility for working capital is spread
across several different disciplines. Accounting is frequently
responsible for payables and receivables, operations is in charge of
inventory, and finance handles cash management. Marketing also
plays an important role because sales forecasts are a key determi-
nant of working capital needs. So, an understanding of working
capital management is important for just about everyone in the firm.
Working Capital
Management17
LEARNING OBJECTIVES
After studying this chapter, you should be
able to:
LO 1 Explain how firms manage their
cash, and identify some of the
collection, concentration, and
disbursement techniques used.
LO 2 Analyze how firms manage their
receivables and the basic
components of a firm’s credit
policies.
LO 3 Differentiate between the types of
inventory and inventory
management systems used by
firms, and explain what determines
the optimal inventory level.
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This chapter examines working capital management. Recall from Chapter 1 that working capital management deals with a firm’s short-term, or current, assets and liabilities. A
firm’s current liabilities consist largely of short-term borrowing. We discussed short-term
borrowing in our previous chapter, so this chapter mainly focuses on current assets, in par-
ticular, cash, accounts receivable, and inventory.
FLOAT AND CASH MANAGEMENT
We begin our analysis of working capital management by looking at how firms manage cash.
The basic objective in cash management is to keep the investment in cash as low as possible
while still operating the firm’s activities efficiently and effectively. This goal usually reduces
17.1
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554 P A R T 8 Short-Term Financial Management
to the dictum “Collect early and pay late.” Accordingly, we discuss ways of accelerating col-
lections and managing disbursements.
In addition, firms must invest temporarily idle cash in short-term marketable securities.
As we discuss in various places, these securities can be bought and sold in the financial
markets. As a group, they have very little default risk, and most are highly liquid. There are
different types of these so-called money market securities, and we discuss a few of the most
important ones a bit later.
Reasons for Holding Cash
John Maynard Keynes, in his great work The General Theory of Employment, Interest, and
Money, identified three reasons why liquidity is important: the speculative motive, the pre-
cautionary motive, and the transaction motive. We discuss these next.
The Speculative and Precautionary Motives The speculative motive is the
need to hold cash in order to be able to take advantage of, for example, bargain purchase
opportunities that might arise, attractive interest rates, and (in the case of international
firms) favorable exchange rate fluctuations.
For most firms, reserve borrowing ability and marketable securities can be used to sat-
isfy speculative motives. Thus, for a modern firm, there might be a speculative motive for
liquidity, but not necessarily for cash per se. Think of it this way: If you have a credit card
with a very large credit limit, then you can probably take advantage of any unusual bargains
that come along without carrying any cash.
This is also true, to a lesser extent, for precautionary motives. The precautionary motive
is the need for a safety supply to act as a financial reserve. Once again, there probably is a
precautionary motive for liquidity. However, given that the value of money market instru-
ments is relatively certain and that instruments such as T-bills are extremely liquid, there is
no real need to hold substantial amounts of cash for precautionary purposes.
The Transaction Motive Cash is needed to satisfy the transaction motive, the need
to have cash on hand to pay bills. Transaction-related needs come from the normal disburse-
ment and collection activities of the firm. The disbursement of cash includes the payment
of wages and salaries, trade debts, taxes, and dividends.
Cash is collected from sales, the selling of assets, and new financing. The cash inflows
(collections) and outflows (disbursements) are not perfectly synchronized, and some level
of cash holdings is necessary to serve as a buffer. Perfect liquidity is the characteristic of
cash that allows it to satisfy the transaction motive.
As electronic funds transfers and other high-speed, “paperless” payment mechanisms
continue to develop, even the transaction demand for cash may all but disappear. Even
if it does, however, there will still be a demand for liquidity and a need to manage
it efficiently.
Benefits of Holding Cash When a firm holds cash in excess of some necessary
minimum, it incurs an opportunity cost. The opportunity cost of excess cash (held in cur-
rency or bank deposits) is the interest income that could be earned in the next best use, such
as investing in marketable securities.
Given the opportunity cost of holding cash, why would a firm hold excess cash? The
answer is that a cash balance must be maintained to provide the liquidity necessary for
speculative motive
The need to hold cash to
take advantage of
additional investment
opportunities, such as
bargain purchases.
precautionary
motive
The need to hold cash as
a safety margin to act as a
financial reserve.
transaction motive
The need to hold cash to
satisfy normal
disbursement and
collection activities
associated with a firm’s
ongoing operations.
ros13952_ch17_553-588.indd 554 12/22/18 6:03 PM
C H A P T E R 1 7 Working Capital Management 555
transaction needs—paying bills. If the firm maintains too small a cash balance, it may run
out of cash. If this happens, the firm may have to raise cash on a short-term basis. This
could involve, for example, selling marketable securities or borrowing.
Activities such as selling marketable securities and borrowing involve various costs. As
we’ve discussed, holding cash has an opportunity cost. To determine the appropriate cash
balance, the firm must weigh the benefits of holding cash against these costs. We discuss
this subject in more detail in the sections that follow.
Understanding Float
As you no doubt know, the amount of money you have according to your checkbook can be
very different from the amount of money that your bank thinks you have. The reason is that
some of the checks you have written haven’t yet been presented to the bank for payment.
The same thing is true for a business. The cash balance that a firm shows on its books is
called the firm’s book, or ledger, balance. The balance shown in its bank account as available
to spend is called its available, or collected, balance. The difference between the available
balance and the ledger balance is called the float, and it represents the net effect of checks
in the process of clearing (moving through the banking system).
Disbursement Float Checks written by a firm generate disbursement float, causing a
decrease in the firm’s book balance but no change in its available balance. For example, sup-
pose General Mechanics, Inc. (GMI), currently has $100,000 on deposit with its bank. On
June 8, it buys some raw materials and pays with a check for $100,000. The company’s book
balance is immediately reduced by $100,000 as a result.
GMI’s bank, however, will not find out about this check until it is presented to GMI’s
bank for payment on, say, June 14. Until the check is presented, the firm’s available balance
is greater than its book balance by $100,000. In other words, before June 8, GMI has a zero
float:
Float = Firm’s available balance − Firm’s book balance
= $100,000 − 100,000
= $0
GMI’s position from June 8 to June 14 is:
Disbursement float = Firm’s available balance − Firm’s book balance
= $100,000 − 0
= $100,000
During this period of time while the check is clearing, GMI has a balance with the bank of
$100,000. It can obtain the benefit of this cash while the check is clearing. For example, the
available balance could be temporarily invested in marketable securities and thus earn some
interest. We will return to this subject a little later.
Collection Float and Net Float Checks received by the firm create collection float.
Collection float increases book balances but does not immediately change available bal-
ances. Suppose GMI receives a check from a customer for $100,000 on October 8. Assume,
as before, that the company has $100,000 deposited at its bank and a zero float. It deposits
the check and increases its book balance by $100,000, to $200,000. However, the additional
cash is not available to GMI until its bank has presented the check to the customer’s bank
and received $100,000. This will occur on, say, October 14. In the meantime, the cash
float
The difference between
book cash and bank cash,
representing the net effect
of checks in the process of
clearing.
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556 P A R T 8 Short-Term Financial Management
position at GMI will reflect a collection float of $100,000. We can summarize these events.
Before October 8, GMI’s position is:
Float = Firm’s available balance − Firm’s book balance
= $100,000 − 100,000
= $0
GMI’s position from October 8 to October 14 is:
Collection float = Firm’s available balance − Firm’s book balance
= $100,000 − 200,000
= −$100,000
In general, a firm’s payment (disbursement) activities generate disbursement float, and its
collection activities generate collection float. The net effect—that is, the sum of the total col-
lection and disbursement floats—is the net float. The net float at any point in time is the
overall difference between the firm’s available balance and its book balance. If the net float
is positive, then the firm’s disbursement float exceeds its collection float and its available
balance exceeds its book balance. If the available balance is less than the book balance, then
the firm has a negative net float.
A firm should be concerned with its net float and available balance more than its book
balance. If a financial manager knows that a check written by the company will not clear for
several days, that manager will be able to keep a lower cash balance at the bank than might
be true otherwise. This can generate a great deal of money.
For example, take the case of retail giant Walmart. The average daily sales for Walmart
were about $1.37 billion in 2017. If Walmart’s collections could have been sped up by a
single day, then the company could have freed up $1.37 billion for investing. At a relatively
modest .01 percent daily rate, the interest earned would have been on the order of
$137,000 per day.
EXAMPLE 17.1 Staying Afloat
Suppose you have $5,000 on deposit. One day you write a check for $1,000 to pay for books, and
you deposit $2,000. What are your disbursement, collection, and net floats?
After you write the $1,000 check, you show a balance of $4,000 on your books, but the bank
shows $5,000 while the check is clearing. This means you have a disbursement float of $1,000.
After you deposit the $2,000 check, you show a balance of $6,000. Your available balance
doesn’t rise until the check clears. This means you have a collection float of −$2,000. Your net float
is the sum of the collection and disbursement floats, or −$1,000.
Overall, you show $6,000 on your books. The bank shows a $7,000 balance, but only $5,000
is available because your deposit has not cleared. The discrepancy between your available bal-
ance and your book balance is the net float (−$1,000), and it is bad for you. If you write another
check for $5,500, there may not be sufficient available funds to cover it, and it might bounce. This
is the reason the financial manager has to be more concerned with available balances than book
balances.
Float Management Float management involves controlling the collection and dis-
bursement of cash. The objective in cash collection is to speed up collections and reduce the
lag between the time customers pay their bills and the time the cash becomes available. The
objective in cash disbursement is to control payments and minimize the firm’s costs associ-
ated with making payments.
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C H A P T E R 1 7 Working Capital Management 557
Total collection or disbursement times can be broken down into three parts: mailing
time, processing delay, and availability delay:
1. Mailing time is the part of the collection and disbursement process during which
checks are trapped in the postal system.
2. Processing delay is the time it takes the receiver of a check to process the payment and
deposit it in a bank for collection.
3. Availability delay refers to the time required to clear a check through the banking system.
Speeding up collections involves reducing one or more of these components. Slowing dis-
bursements involves increasing one or more of them. We describe some procedures for
managing collection and disbursement times below.
Ethical and Legal Questions The cash manager must work with collected bank
cash balances and not the firm’s book balance (which reflects checks that have been depos-
ited but not collected). If this is not done, a cash manager could be drawing on uncollected
cash as a source of funds for short-term investing. Most banks charge a penalty rate for the
use of uncollected funds. However, banks may not have good enough accounting and con-
trol procedures to be fully aware of the use of uncollected funds. This raises some ethical
and legal questions for the firm.
For example, in May 1985, E. F. Hutton (a large investment bank), pleaded guilty to
2,000 charges of mail and wire fraud in connection with a scheme the firm had operated
from 1980 to 1982. E. F. Hutton employees wrote checks totaling hundreds of millions of
dollars against uncollected cash. The proceeds were then invested in short-term money mar-
ket assets. This type of systematic overdrafting of accounts (or check kiting, as it is some-
times called) is neither legal nor ethical and is apparently not a widespread practice among
corporations. Also, the particular inefficiencies in the banking system that Hutton was ex-
ploiting have been largely eliminated.
For its part, E. F. Hutton paid a $2 million fine, reimbursed the government (the U.S.
Department of Justice) $750,000, and reserved an additional $8 million for restitution to
defrauded banks. We should note that the key issue in the case against Hutton was not its
float management per se, but, rather, its practice of writing checks for no economic reason
other than to exploit float. Unfortunately, check kiting is still not dead. In March 2018, a
Nebraska business owner pleaded guilty to a check kiting scheme that involved four differ-
ent banks. His plea agreement helped avoid a potential 30-year federal prison term, but he
faced five years of probation, incurred a $1 million fine, and had to pay about $835,000 in
restitution.
Electronic Data Interchange and Check 21: The End of Float? Electronic
data interchange (EDI) is a general term that refers to the growing practice of direct, elec-
tronic information exchange between all types of businesses. One important use of EDI,
often called financial EDI, or FEDI, is to electronically transfer financial information and
funds between parties, thereby eliminating paper invoices, paper checks, mailing, and han-
dling. For example, it is possible to arrange to have your checking account directly debited
each month to pay many types of bills, and corporations now routinely directly deposit
paychecks into employee accounts. More generally, EDI allows a seller to send a bill elec-
tronically to a buyer, thereby avoiding the mail. The buyer can then authorize payment,
which also occurs electronically. Its bank then transfers the funds to the seller’s account at
a different bank. The net effect is that the length of time required to initiate and complete a
business transaction is shortened considerably, and much of what we normally think of as
ros13952_ch17_553-588.indd 557 12/22/18 6:03 PM
558 P A R T 8 Short-Term Financial Management
float is sharply reduced or eliminated. As the use of FEDI increases (which it will), float
management will evolve to focus much more on issues surrounding computerized informa-
tion exchange and funds transfers.
On October 29, 2004, the Check Clearing Act for the 21st Century, also known as
Check 21, took effect. Before Check 21, a bank receiving a check was required to send the
physical check to the customer’s bank before payment could be made. Now a bank can
transmit an electronic image of the check to the customer’s bank and receive payment im-
mediately. Previously, an out-of-state check might take three days to clear, but with Check
21, the clearing time is typically one day, and often, a check can clear the same day it is writ-
ten. Thus, Check 21 has significantly reduced float.
CONCEPT QUESTIONS
17.1a What is the transaction motive for holding cash?
17.1b What is the cost to the firm of holding excess cash?
17.1c Which of these would a firm be more interested in reducing: collection float or
disbursement float? Why?
17.1d What is the benefit from reducing or eliminating float?
CASH MANAGEMENT: COLLECTION,
DISBURSEMENT, AND INVESTMENT
As a part of managing its cash, a firm must make arrangements to collect from its custom-
ers, pay its suppliers, and invest any excess cash on hand. We begin by examining how firms
collect and concentrate cash.
Cash Collection and Concentration
From our previous discussion, we know that collection delays work against the firm. All
other things being the same, then, a firm will adopt procedures to speed up collections and
thereby decrease collection times. In addition, even after cash is collected, firms need pro-
cedures to funnel, or concentrate, that cash where it can be best used. We discuss some
common collection and concentration procedures next.
Components of Collection Time Based on our discussion above, we can depict
the basic parts of the cash collection process as follows: The total time in this process is
made up of mailing time, check-processing delay, and the bank’s availability delay.
17.2
Customer
mails
payment
Company
receives
payment
Company
deposits
payment
Cash
becomes
available
Availability
delay
Processing
delay
Mailing
time
Collection time
Time
ros13952_ch17_553-588.indd 558 12/22/18 6:03 PM
C H A P T E R 1 7 Working Capital Management 559
The amount of time that cash spends in each part of the cash collection process de-
pends on where the firm’s customers and banks are located and how efficient the firm is at
collecting cash.
Cash Collection How a firm collects from its customers depends in large part on the
nature of the business. The simplest case would be a business such as a restaurant chain.
Most of its customers will pay with cash, check, or credit card at the point of sale (this is
called over-the-counter collection), so there is no problem with mailing delay. Normally, the
funds would be deposited in a local bank, and the firm would have some means (discussed
next) of gaining access to the funds.
When some or all of the payments a company receives are checks that arrive through
the mail, all three components of collection time become relevant. The firm may choose to
have all the checks mailed to one location, or, more commonly, the firm might have a num-
ber of different mail collection points to reduce mailing times. Also, the firm may run its
collection operation itself or might hire an outside firm that specializes in cash collection.
We discuss these issues in more detail later.
Other approaches to cash collection exist. One that is becoming more common is the
preauthorized payment system. With this arrangement, the payment amounts and payment
dates are fixed in advance. When the agreed-upon date arrives, the amount is automatically
transferred from the customer’s bank account to the firm’s bank account, sharply reducing
or even eliminating collection delays. The same approach is used by firms that have online
terminals, meaning that when a sale is rung up, the money is immediately transferred to the
firm’s accounts.
Lockboxes When a firm receives its payments by mail, it must decide where the checks
will be mailed and how the checks will be picked up and deposited. Careful selection of the
number and locations of collection points can greatly reduce collection times. Many firms
use special post office boxes called lockboxes to intercept payments and speed cash
collection.
Figure 17.1 illustrates a lockbox system. The collection process is started by customers
mailing their checks to a post office box instead of sending them to the firm. The lockbox is
maintained by a local bank. A large corporation may actually have more than 20 lockboxes
around the country.
In the typical lockbox system, the local bank collects the lockbox checks from the post
office several times a day. The bank deposits the checks directly to the firm’s account. De-
tails of the operation are recorded (in some computer-usable form) and sent to the firm.
A lockbox system reduces mailing time because checks are received at a nearby post
office instead of at corporate headquarters. Lockboxes also reduce the processing time be-
cause the corporation doesn’t have to open the envelopes and deposit checks for collection.
In all, a bank lockbox should enable a firm to get its receipts processed, deposited, and
cleared faster than if it were to receive checks at its headquarters and deliver them itself to
the bank for deposit and clearing.
Cash Concentration As we discussed earlier, a firm will typically have a number of
cash collection points, and, as a result, cash collections may end up in many different banks
and bank accounts. From here, the firm needs procedures to move the cash into its main
accounts. This is called cash concentration. By routinely pooling its cash, the firm greatly
simplifies its cash management by reducing the number of accounts that must be tracked.
Also, by having a larger pool of funds available, a firm may be able to negotiate a better rate
on any short-term investments.
lockboxes
Special post office boxes
set up to intercept and
speed up accounts
receivable collections.
cash concentration
The practice of and
procedures for moving
cash from multiple banks
into the firm’s main
accounts.
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560 P A R T 8 Short-Term Financial Management
In setting up a concentration system, firms typically will use one or more concentration
banks. A concentration bank pools the funds obtained from local banks contained
within some geographic region. Concentration systems often are used in conjunction with
lockbox systems. Figure 17.2 illustrates how an integrated cash collection and cash concen-
tration system might look.
Managing Cash Disbursements
From the firm’s point of view, disbursement float is desirable, so the goal in managing dis-
bursement float is to slow down disbursements as much as possible. To do this, the firm
may develop strategies to increase mail float, processing float, and availability float on the
checks it writes. Beyond this, firms have developed procedures for minimizing cash held for
payment purposes. We now discuss the most common of these procedures.
Increasing Disbursement Float As we have seen, float in terms of slowing down
payments comes from the time involved in mail delivery, check processing, and collection of
funds. Disbursement float can be increased by writing a check on a geographically distant
bank. For example, a New York supplier might be paid with checks drawn on a Los Angeles
bank. This will increase the time required for the checks to clear through the banking sys-
tem. Mailing checks from remote post offices is another way firms slow down
disbursement.
The flow starts when a customer mails remittances to a post office box instead of to the
corporation. Several times a day the bank collects the lockbox receipts from the post
office. The checks are then put into the company bank accounts.
Local bank
collects funds from
post office boxes
Envelopes opened;
separation of
checks and receipts
Bank check-
clearing process
Details of receivables
go to firm
Firm processes
receivables
Deposit of checks
into bank accounts
Customer
payments
Customer
payments
Customer
payments
Customer
payments
Post office
box 1
Post office
box 2
FIGURE 17.1
Overview of lockbox
processing
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C H A P T E R 1 7 Working Capital Management 561
Tactics for maximizing disbursement float are debatable on both ethical and economic
grounds. First, as we discuss later, payment terms very frequently offer a substantial dis-
count for early payment. The discount is usually much larger than any possible savings from
“playing the float game.” In such cases, increasing mailing time will be of no benefit if the
recipient dates payments based on the date received (as is common) as opposed to the post-
mark date.
Beyond this, suppliers are not likely to be fooled by attempts to slow down disburse-
ment. The negative consequences from poor relations with suppliers can be costly. In
broader terms, intentionally delaying payments by taking advantage of mailing times or un-
sophisticated suppliers may amount to avoiding paying bills when they are due, an unethical
business procedure.
Controlling Disbursements We have seen that maximizing disbursement float is
probably poor business practice. However, a firm still will wish to tie up as little cash as pos-
sible in disbursements. Firms therefore have developed systems for efficiently managing the
disbursement process. The general idea in such systems is to have no more than the mini-
mum amount necessary to pay bills on deposit in the bank. We discuss some approaches to
accomplishing this goal next.
Statements are sent by mail to
firm for receivables processing
Funds are transferred
to concentration bank
Cash manager analyzes bank balance and deposit
information and makes cash allocation revision
Firm sales
office
Local bank
deposits
Post office
lockbox receipts
Customer
payments
Customer
payments
Customer
payments
Customer
payments
Concentration
bank
Firm cash
manager
Short-term
investment of cash
Maintenance of
cash reserves
Disbursements
activity
Lockboxes and
concentration banks
in a cash
management system
FIGURE 17.2
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562 P A R T 8 Short-Term Financial Management
Zero-balance accounts With a zero-balance account, the firm, in cooperation with its
bank, maintains a master account and a set of subaccounts. When a check written on
one of the subaccounts must be paid, the necessary funds are transferred in from the
master account. Figure 17.3 illustrates how such a system might work. In this case, the
firm maintains two disbursement accounts, one for suppliers and one for payroll. As is
shown, if the firm does not use zero-balance accounts, then each of these accounts must
have a safety stock of cash to meet unanticipated demands. If the firm does use zero-
balance accounts, then it can keep one safety stock in a master account and transfer the
funds to the two subsidiary accounts as needed. The key is that the total amount of cash
held as a buffer is smaller under the zero-balance arrangement, which frees up cash to be
used elsewhere.
Controlled disbursement accounts Almost all payments that must be made in a given day
are known in the morning. With a controlled disbursement account, the bank informs the
firm of the day’s total, and the firm transfers (usually by wire) the amount needed.
Investing Idle Cash
If a firm has a temporary cash surplus, it can invest in short-term securities. As we have
mentioned at various times, the market for short-term financial assets is called the money
market. The maturity of short-term financial assets that trade in the money market is one
year or less.
Most large firms manage their own short-term financial assets, transacting through
banks and dealers. Some large firms and many small firms use money market mutual funds.
These are funds that invest in short-term financial assets for a management fee. The manage-
ment fee is compensation for the professional expertise and diversification provided by the
fund manager.
Among the many money market mutual funds, some specialize in corporate customers.
In addition, banks offer arrangements in which the bank takes all excess available funds at
the close of each business day and invests them for the firm.
controlled
disbursement
account
A disbursement practice
under which the firm
transfers an amount to a
disbursing account that is
sufficient to cover
demands for payment.
Safety stock
Cash
transfers
Cash
transfers
Master account
Payroll account Supplier account
Two zero-balance accounts
Safety stocks
Payroll account Supplier account
No zero-balance account
Without zero-balance accounts, separate safety stocks must
be maintained, which ties up cash unnecessarily. With
zero-balance accounts, the firm keeps a single safety stock
of cash in a master account. Funds are transferred into
disbursement accounts as needed.
Zero-balance accountsFIGURE 17.3
zero-balance
account
A disbursement account in
which the firm maintains a
zero balance, transferring
funds in from a master
account only as needed to
cover checks presented
for payment.
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C H A P T E R 1 7 Working Capital Management 563
Temporary Cash Surpluses Firms have temporary cash surpluses for various rea-
sons. Two of the most important are the financing of seasonal or cyclical activities of the
firm and the financing of planned or possible expenditures.
Seasonal or cyclical activities Some firms have a predictable cash flow pattern. They
have surplus cash flows during part of the year and deficit cash flows the rest of the year.
For example, MasterCraft, known for its sport boats, has a seasonal cash flow pattern
influenced by summer.
A firm such as MasterCraft may buy marketable securities when surplus cash flows oc-
cur and sell marketable securities when deficits occur. Of course, bank loans are another
short-term financing device. The use of bank loans and marketable securities to meet tempo-
rary financing needs is illustrated in Figure 17.4. In this case, the firm is following a compro-
mise working capital policy in the sense we discussed in the previous chapter.
Planned or possible expenditures Firms frequently accumulate temporary investments in
marketable securities to provide the cash for a plant construction program, dividend
payment, or other large expenditure. Thus, firms may issue bonds and stocks before the
cash is needed, investing the proceeds in short-term marketable securities and then selling
the securities to finance the expenditures. Also, firms may face the possibility of having to
make a large cash outlay. An obvious example would be the possibility of losing a large
lawsuit. Firms may build up cash surpluses against such a contingency.
Characteristics of Short-Term Securities Given that a firm has some temporar-
ily idle cash, there are a variety of short-term securities available for investing. The most
important characteristics of these short-term marketable securities are their maturity, de-
fault risk, marketability, and taxability.
Maturity Maturity refers to the time period over which interest and principal payments are
made. From Chapter 6, we know that for a given change in the level of interest rates, the
prices of longer-maturity securities will change more than those of shorter-maturity
Marketable
securities
Bank
loans
Total financing
needs
Short-term
financing
Long-term
financing
10 32
Time 1: A surplus cash position exists. Seasonal demand for current assets is low. The
surplus is invested in short-term marketable securities.
Time 2: A deficit cash position exists. Seasonal demand for current assets is high. The
financial deficit is financed by selling marketable securities and by bank
borrowing.
Dollars
Time (quarters)
Seasonal cash
demands
FIGURE 17.4
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564 P A R T 8 Short-Term Financial Management
securities. As a consequence, firms often limit their investments in marketable securities to
those maturing in less than 90 days to avoid the risk of losses in value from changing
interest rates.
Default risk Default risk refers to the probability that interest and principal will not be
paid in the promised amounts on the due dates (or not paid at all). Of course, some
securities have negligible default risk, such as U.S. Treasury bills. Given the purposes of
investing idle corporate cash, firms typically avoid investing in marketable securities with
significant default risk.
Marketability Marketability refers to how easy it is to convert an asset to cash; so,
marketability and liquidity mean much the same thing. Some money market instruments are
much more marketable than others. At the top of the list are U.S. Treasury bills, which can
be bought and sold very cheaply and very quickly.
Taxability Interest earned on money market securities that are not some kind of
government obligation (either federal or state) is taxable at the local, state, and federal
levels. U.S. Treasury obligations such as T-bills are exempt from state taxation, but other
government-backed debt is not. Municipal securities are exempt from federal taxes, but they
may be taxed at the state level.
Some Different Types of Money Market Securities Money market securities
are generally highly marketable and short term. They usually have low risk of default. They
are issued by the U.S. government (e.g., U.S. Treasury bills), domestic and foreign banks
(e.g., certificates of deposit), and business corporations (e.g., commercial paper). There are
many types in all, and we only illustrate a few of the most common here.
U.S. Treasury bills are obligations of the U.S. government that mature in 4, 13, 26, or
52 weeks. The 4-, 13-, and 26-week bills are sold by auction every week, and 52-week bills are
sold every four weeks.
Short-term tax-exempts are short-term securities issued by states, municipalities, and
certain other agencies. Because these are all considered municipal securities, they are ex-
empt from federal taxes. Short-term tax-exempts have more default risk than U.S. Treasury
issues and are less marketable. Because the interest is exempt from federal income tax, the
pretax yield on tax-exempts is lower than that on comparable securities such as U.S. Treasury
bills. Also, corporations face some restrictions on holding tax-exempts as investments.
Commercial paper refers to short-term securities issued by finance companies, banks,
and corporations. Typically, commercial paper is unsecured. Maturities range from a few
weeks to 270 days.
There is no especially active secondary market in commercial paper. As a consequence,
the marketability can be low; however, firms that issue commercial paper often will repur-
chase it directly before maturity. The default risk of commercial paper depends on the finan-
cial strength of the issuer.
Certificates of deposit (CDs) are short-term loans to commercial banks. These are
normally jumbo CDs—those in excess of $100,000. There are active markets in CDs of
3-month, 6-month, 9-month, and 12-month maturities.
Because 70 to 80 percent of the dividends received by one corporation from another
are exempt from taxation, the relatively high dividend yields on preferred stock provide a
strong incentive for investment. The only problem is that the dividend is fixed with ordinary
preferred stock, so the price can fluctuate more than is desirable in a short-term investment.
Check out short-term
rates online at
www.bloomberg.com.
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C H A P T E R 1 7 Working Capital Management 565
So-called money market preferred stock is a recent innovation featuring a floating dividend.
The dividend is reset fairly often (usually every 49 days), so this type of preferred has much
less price volatility than ordinary preferred, and it has become a popular short-term
investment.
CONCEPT QUESTIONS
17.2a What is a lockbox? What purpose does it serve?
17.2b What is a concentration bank? What purpose does it serve?
17.2c Is maximizing disbursement float a sound business practice?
17.2d What are some types of money market securities?
CREDIT AND RECEIVABLES
When a firm sells goods and services, it can demand cash on or before the delivery date, or
it can extend credit to customers and allow some delay in payment.
Why would firms grant credit? The obvious reason is that offering credit is a way of
stimulating sales. The costs associated with granting credit are not trivial. First, there is the
chance that the customer will not pay. Second, the firm has to bear the costs of carrying the
receivables. The credit policy decision thus involves a trade-off between the benefits of in-
creased sales and the costs of granting credit.
From an accounting perspective, when credit is granted, an account receivable is cre-
ated. These receivables include credit to other firms, called trade credit, and credit granted
to consumers, called consumer credit, and they represent a major investment of financial re-
sources by U.S. businesses. Furthermore, trade credit is a very important source of financ-
ing for corporations. However we look at it, receivables and receivables management are
very important aspects of a firm’s short-term financial policy.
Components of Credit Policy
If a firm decides to grant credit to its customers, then it must establish procedures for ex-
tending credit and collecting. In particular, the firm will have to deal with the following
components of credit policy:
1. Terms of sale: The terms of sale establish how the firm proposes to sell its goods and
services. If the firm grants credit to a customer, the terms of sale will specify (perhaps
implicitly) the credit period, the cash discount and discount period, and the type of
credit instrument.
2. Credit analysis: In granting credit, a firm determines how much effort to expend
trying to distinguish between customers who will pay and customers who will not pay.
Firms use a number of devices and procedures to determine the probability that
customers will not pay, and, put together, these are called credit analysis.
3. Collection policy: After credit has been granted, the firm has the potential problem of
collecting the cash when it becomes due, for which it must establish a collection
policy.
In the next several sections, we will discuss these components of credit policy that
collectively make up the decision to grant credit.
17.3
terms of sale
Conditions under which a
firm sells its goods and
services for cash or credit.
credit analysis
The process of
determining the
probability that customers
will or will not pay.
collection policy
Procedures followed by a
firm in collecting accounts
receivable.
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566 P A R T 8 Short-Term Financial Management
Terms of Sale
As we described earlier, the terms of a sale are made up of three distinct elements:
1. The period for which credit is granted (the credit period).
2. The cash discount and the discount period.
3. The type of credit instrument.
Within a given industry, the terms of sale are usually fairly standard, but these terms vary
quite a bit across industries. In many cases, the terms of sale are remarkably archaic and
literally date to previous centuries. Organized systems of trade credit that resemble current
practice can be traced easily to the great fairs of medieval Europe, and they almost surely
existed long before then.
The Basic Form The easiest way to understand the terms of sale is to consider an ex-
ample. For bulk candy, terms of 2/10, net 60 might be quoted.1 This means that customers
have 60 days from the invoice date (discussed next) to pay the full amount. However, if pay-
ment is made within 10 days, a 2 percent cash discount can be taken.
Consider a buyer who places an order for $1,000, and assume that the terms of the sale
are 2/10, net 60. The buyer has the option of paying $1,000 × (1 − .02) = $980 in 10 days
or paying the full $1,000 in 60 days. If the terms were stated as net 30, then the customer
would have 30 days from the invoice date to pay the entire $1,000, and no discount would
be offered for early payment.
In general, credit terms are interpreted in the following way:
(take this discount off the invoice price)/(if you pay in this many days), (else pay the full
invoice amount in this many days)
Thus, 5/10, net 45 means take a 5 percent discount from the full price if you pay within 10
days, or else pay the full amount in 45 days.
The Credit Period The credit period is the basic length of time for which credit is
granted. The credit period varies widely from industry to industry, but it is almost always
between 30 and 120 days. If a cash discount is offered, then the credit period has two com-
ponents: the net credit period and the cash discount period.
The net credit period is the length of time the customer has to pay. The cash discount
period, as the name suggests, is the time during which the discount is available. With 2/10,
net 30, for example, the net credit period is 30 days and the cash discount period is 10 days.
The invoice date The invoice date is the beginning of the credit period. An invoice is a
written account of merchandise shipped to the buyer. For individual items, by convention,
the invoice date is usually the shipping date or the billing date, not the date that the buyer
receives the goods or the bill.
Length of the credit period A number of factors influence the length of the credit
period. Two of the most important are the buyer’s inventory period and the operating
cycle. All other things being equal, the shorter these are, the shorter the credit period
normally will be.
credit period
The length of time for
which credit is granted.
invoice
Bill for goods or services
provided by the seller to
the purchaser.
1The terms of sale cited from specific industries in this section and elsewhere are drawn from Theodore N. Beck-
man, Credits and Collections: Management and Theory (New York: McGraw-Hill, 1962).
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C H A P T E R 1 7 Working Capital Management 567
Based on our discussion in Chapter 16, the operating cycle has two components: the
inventory period and the receivables period. The inventory period is the time it takes the
buyer to acquire inventory (from us), process it, and sell it. The receivables period is the
time it then takes the buyer to collect on the sale. Note that the credit period that we offer
is effectively the buyer’s payables period.
By extending credit, we finance a portion of our buyer’s operating cycle and thereby
shorten the buyer’s cash cycle. If our credit period exceeds the buyer’s inventory period,
then we are financing not only the buyer’s inventory purchases, but part of the buyer’s re-
ceivables as well.
Furthermore, if our credit period exceeds our buyer’s operating cycle, then we are ef-
fectively providing financing for aspects of our customer’s business beyond the immediate
purchase and sale of our merchandise. The reason is that the buyer effectively has a loan
from us even after the merchandise is resold, and the buyer can use that credit for other
purposes. For this reason, the length of the buyer’s operating cycle is often cited as an ap-
propriate upper limit to the credit period.
There are a number of other factors that influence the credit period. Many of these also
influence our customers’ operating cycles; so, once again, these are related subjects. Among
the most important are:
1. Perishability and collateral value. Perishable items have relatively rapid turnover and
relatively low collateral value. Credit periods are thus shorter for such goods.
2. Consumer demand. Products that are well established generally have more rapid
turnover. Newer or slow-moving products often will have longer credit periods
associated with them to entice buyers.
3. Cost, profitability, and standardization. Relatively inexpensive goods tend to have
shorter credit periods. The same is true for relatively standardized goods and raw
materials. These all tend to have lower markups and higher turnover rates, both of
which lead to shorter credit periods.
4. Credit risk. The greater the credit risk of the buyer, the shorter the credit period is
likely to be (assuming that credit is granted at all).
5. The size of the account. If the account is small, the credit period may be shorter
because small accounts are more costly to manage and the customers are less
important.
6. Competition. When the seller is in a highly competitive market, longer credit periods
may be offered as a way of attracting customers.
7. Customer type. A single seller might offer different credit terms to different buyers. A
food wholesaler, for example, might supply groceries, bakeries, and restaurants. Each
group would probably have different credit terms. More generally, sellers often have
both wholesale and retail customers, and they frequently quote different terms to the
two types.
Cash Discounts As we have seen, cash discounts are often part of the terms of sale.
The practice of granting discounts for cash purchases in the United States dates to the Civil
War and is widespread today. One reason discounts are offered is to speed up the collection
of receivables. This will have the effect of reducing the amount of credit being offered, and
the firm must trade this off against the cost of the discount.
Notice that when a cash discount is offered, the credit is essentially free during the dis-
count period. The buyer only pays for the credit after the discount expires. With 2/10, net
30, a rational buyer either pays in 10 days to make the greatest possible use of the free credit
cash discount
A discount given to induce
prompt payment. Also
sales discount.
For more on the credit
process for small
businesses, see
www.newyorkfed.org
/smallbusiness/index.html.
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568 P A R T 8 Short-Term Financial Management
or pays in 30 days to get the longest possible use of the money in exchange for giving up the
discount. So, by giving up the discount, the buyer effectively gets 30 − 10 = 20 days’ credit.
Another reason for cash discounts is that they are a way of charging higher prices to
customers that have had credit extended to them. In this sense, cash discounts are a con-
venient way of charging for the credit granted to customers.
In our examples, it might seem that the discounts are rather small. With 2/10, net 30,
for example, early payment only gets the buyer a 2 percent discount. Does this provide a
significant incentive for early payment? The answer is “yes” because the implicit interest
rate is extremely high.
To see why the discount is important, we will calculate the cost to the buyer of not pay-
ing early. To do this, we will find the interest rate that the buyer is effectively paying for the
trade credit. Suppose the order is for $1,000. The buyer can pay $980 in 10 days or wait
another 20 days and pay $1,000. It’s obvious that the buyer is effectively borrowing $980 for
20 days and that the buyer pays $20 in interest on the “loan.” What’s the interest rate?
With $20 in interest on $980 borrowed, the rate is $20/$980 = .020408, or 2.0408%. This is
relatively low, but remember that this is the rate per 20-day period. There are 365/20 = 18.25 such
periods in a year, so, by not taking the discount, the buyer is paying an effective annual rate of:
EAR = 1.020408 18.25 − 1 = .446, or 44.6%
From the buyer’s point of view, this is an expensive source of financing!
Given that the interest rate is so high here, it is unlikely that the seller benefits from
early payment. Ignoring the possibility of default by the buyer, the decision by a customer to
forgo the discount almost surely works to the seller’s advantage.
Visit the National
Association of Credit
Management at
www.nacm.org.
EXAMPLE 17.2 What’s the Rate?
Ordinary tiles are often sold with terms of 3/30, net 60. What effective annual rate does a buyer pay
by not taking the discount? What would the APR be if one were quoted?
Here we have 3 percent discount interest on 60 – 30 = 30 days’ credit. The rate per 30 days
is .03/.97 = .03093, or 3.093%. There are 365/30 = 12.17 such periods in a year, so the effective
annual rate is:
EAR = 1.03093 12.17 − 1 = .449, or 44.9%
The APR, as always, would be calculated by multiplying the rate per period by the number of
periods:
APR = .03093 × 12.17 = .376, or 37.6%
An interest rate calculated like this APR is often quoted as the cost of the trade credit, and, as this
example illustrates, this seriously can understate the true cost.
Credit Instruments The credit instrument is the basic evidence of indebtedness.
Most trade credit is offered on open account. This means that the only formal instrument of
credit is the invoice, which is sent with the shipment of goods and which the customer signs
as evidence that the goods have been received. Afterwards, the firm and its customers re-
cord the exchange on their books of account.
At times, the firm may require that the customer sign a promissory note. This is a basic
IOU and might be used when the order is large or when the firm anticipates a problem in
collections. Promissory notes are uncommon, but they can eliminate possible controversies
later about the existence of debt.
One problem with promissory notes is that they are signed after delivery of the goods.
One way to obtain a credit commitment from a customer before the goods are delivered is
credit instrument
The evidence of
indebtedness.
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C H A P T E R 1 7 Working Capital Management 569
to arrange a commercial draft. Typically, the firm draws up a commercial draft calling for the
customer to pay a specific amount by a specified date. The draft is then sent to the custom-
er’s bank with the shipping invoices.
If immediate payment on the draft is required, it is called a sight draft. If immediate pay-
ment is not required, then the draft is a time draft. When the draft is presented and the buyer
“accepts” it, meaning that the buyer promises to pay it in the future, then it is called a trade ac-
ceptance and is sent back to the selling firm. The seller then can keep the acceptance or sell it to
someone else. If a bank accepts the draft, meaning that the bank is guaranteeing payment, then
the draft becomes a banker’s acceptance. This arrangement is common in international trade.
Optimal Credit Policy
In principle, the optimal amount of credit is determined by the point at which the incremen-
tal cash flows from increased sales are exactly equal to the incremental costs of carrying the
increased investment in accounts receivable.
The Total Credit Cost Curve The trade-off between granting credit and not grant-
ing credit isn’t hard to identify, but it is difficult to quantify precisely. As a result, we
only can describe an optimal credit policy.
To begin, the carrying costs associated with granting credit come in three forms:
1. The required return on receivables.
2. The losses from bad debts.
3. The cost of managing credit and credit collections.
We already have discussed the first and second of these. The third cost, the cost of manag-
ing credit, is the expense associated with running the credit department. Firms that don’t
grant credit have no such department and no such expense. These three costs all will in-
crease as credit policy is relaxed.
If a firm has a very restrictive credit policy, then all of the above costs will be low. In
this case, the firm will have a “shortage” of credit, so there will be an opportunity cost. This
opportunity cost is the extra potential profit from credit sales that is lost because credit is
refused. This forgone benefit comes from two sources: the increase in quantity sold and,
potentially, a higher price. These costs go down as credit policy is relaxed.
The sum of the carrying costs and the opportunity costs of a particular credit policy is
called the total credit cost curve. We have drawn such a curve in Figure 17.5. As Figure 17.5
illustrates, there is a point, C*, where the total credit cost is minimized. This point corresponds
to the optimal amount of credit, or, equivalently, the optimal investment in receivables.
If the firm extends more credit than this amount, the additional net cash flow from new
customers will not cover the carrying costs of the investment in receivables. If the level of
receivables is below this amount, then the firm is forgoing valuable profit opportunities.
In general, the costs and benefits from extending credit will depend on characteristics
of particular firms and industries. All other things being equal, for example, it is likely that
firms with (1) excess capacity, (2) low variable operating costs, and (3) repeat customers
will extend credit more liberally than other firms. See if you can explain why each of these
contributes to a more liberal credit policy.
Organizing the Credit Function Firms that grant credit have the expense of run-
ning a credit department. In practice, firms often choose to contract out all or part of the
credit function to a factor, an insurance company, or a captive finance company. Chapter 16
discussed factoring, an arrangement in which the firm sells its receivables. Depending on
credit cost curve
Graphical representation
of the sum of the carrying
costs and the opportunity
costs of a credit policy.
ros13952_ch17_553-588.indd 569 12/22/18 6:03 PM
570 P A R T 8 Short-Term Financial Management
the specific arrangement, the factor may have full responsibility for credit checking, authori-
zation, and collection. Smaller firms may find such an arrangement cheaper than running a
credit department.
Firms that manage internal credit operations are self-insured against default, meaning
that they bear all the risk of nonpayment. An alternative is to buy credit insurance through
an insurance company. The insurance company offers coverage up to a preset dollar limit
for accounts. As you would expect, accounts with a higher credit rating merit higher insur-
ance limits. This type of insurance is particularly important for exporters, and government
insurance is available for certain types of exports.
Large firms often extend credit through a captive finance company, which is a partially
or wholly owned subsidiary that handles the credit function for the parent company. Toyota
Financial Services, or TFS, is a well-known example. Toyota sells to car dealers, who in turn
sell to customers. TFS finances the dealer’s inventory of cars and also finances customers
who buy the cars.
Credit Analysis
Thus far, we have focused on establishing credit terms. Once a firm decides to grant credit
to its customers, it then must establish guidelines for determining who will and who will not
be allowed to buy on credit. Credit analysis refers to the process of deciding whether or not
to extend credit to a particular customer. It usually involves two steps: gathering relevant
information and determining creditworthiness.
Credit Information If a firm does want credit information on customers, there are a
number of sources. Information sources commonly used to assess creditworthiness include
the following:
1. Financial statements. A firm can ask a customer to supply financial statements such as
balance sheets and income statements. Minimum standards and rules of thumb based
captive finance
company
A partially or wholly
owned subsidiary that
handles the credit function
for the parent company.
The costs of granting
credit
Optimal
amount
of credit
Total costs
Carrying costs
Opportunity costs
Cost
($)
Amount of credit
extended ($)C*
Carrying costs are the cash flows that must be incurred when credit is granted.
They are positively related to the amount of credit extended.
Opportunity costs are the lost sales from refusing credit. These costs go down
when credit is granted.
FIGURE 17.5
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C H A P T E R 1 7 Working Capital Management 571
on financial ratios like the ones we discussed in Chapter 3 then can be used as a basis
for extending or refusing credit.
2. Credit reports on the customer’s payment history with other firms. Quite a few
organizations sell information on the credit strength and credit history of business
firms. The best-known and largest firm of this type is Dun & Bradstreet, which
provides subscribers with a credit reference book and credit reports on individual
firms. Experian is another well-known credit-reporting firm. Ratings and information
are available for a huge number of firms, including very small ones. Equifax,
TransUnion, and Experian are the major suppliers of consumer credit information.
3. Banks. Banks generally will provide some assistance to their business customers in
acquiring information on the creditworthiness of other firms.
4. The customer’s payment history with the firm. The most obvious way to obtain
information about the likelihood of a customer’s not paying is to examine whether
they have settled past obligations and how quickly they have met these obligations.
Credit Evaluation and Scoring There are no magical formulas for assessing the
probability that a customer will not pay. In very general terms, the classic five Cs of credit
are the basic factors to be evaluated:
1. Character. The customer’s willingness to meet credit obligations.
2. Capacity. The customer’s ability to meet credit obligations out of operating cash flows.
3. Capital. The customer’s financial reserves.
4. Collateral. Assets pledged by the customer for security in case of default.
5. Conditions. General economic conditions in the customer’s line of business.
Credit scoring refers to the process of calculating a numerical rating for a customer based
on information collected; credit is then granted or refused based on the result. For example,
a firm might rate a customer on a scale of 1 (very poor) to 10 (very good) on each of the
five Cs of credit using all the information available about the customer. A credit score could
then be calculated based on the total. From experience, a firm might choose to grant credit
only to customers with a score above, say, 30.
Firms such as credit card issuers have developed elaborate statistical models for credit
scoring. Usually, all of the legally relevant and observable characteristics of a large pool of
customers are studied to find their historic relation to default rates. Based on the results, it
is possible to determine the variables that best predict whether or not a customer will pay
and then calculate a credit score based on those variables.
Because credit-scoring models and procedures determine who is and who is not credit-
worthy, it is not surprising that they have been the subject of government regulation. In
particular, the kinds of background and demographic information that can be used in the
credit decision are limited.
Collection Policy
Collection policy is the final element in credit policy. Collection policy involves monitoring
receivables to spot trouble and obtaining payment on past-due accounts.
Monitoring Receivables To keep track of payments by customers, most firms will
monitor outstanding accounts. First, a firm normally will keep track of its average collection
period, ACP, through time. If a firm is in a seasonal business, the ACP will fluctuate during
the year, but unexpected increases in the ACP are a cause for concern. Either customers in
five Cs of credit
The five basic credit
factors to be evaluated:
character, capacity,
capital, collateral, and
conditions.
credit scoring
The process of quantifying
the probability of default
when granting consumer
credit.
Web-surfing students
should visit the Dun &
Bradstreet home page—
this major supplier of
credit information can be
found at www.dnb.com.
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572 P A R T 8 Short-Term Financial Management
general are taking longer to pay, or some percentage of accounts receivable is seriously
overdue.
The aging schedule is a second basic tool for monitoring receivables. To prepare one,
the credit department classifies accounts by age.2 Suppose a firm has $100,000 in receiv-
ables. Some of these accounts are only a few days old, but others have been outstanding for
quite some time. The following is an example of an aging schedule.
Aging Schedule
Age of Account Amount
Percentage of Total Value
of Accounts Receivable
0–10 days $ 50,000 50%
11–60 days 25,000 25
61–80 days 20,000 20
Over 80 days 5,000 5
$100,000 100%
If this firm has a credit period of 60 days, then 25 percent of its accounts are late. Whether
or not this is a serious problem depends on the nature of the firm’s collections and custom-
ers. It is often the case that accounts beyond a certain age are almost never collected. Moni-
toring the age of accounts is very important in such cases.
Firms with seasonal sales will find the percentages on the aging schedule changing dur-
ing the year. For example, if sales in the current month are very high, then total receivables
also will increase sharply. This means that the older accounts, as a percentage of total re-
ceivables, become smaller and might appear less important. Some firms have refined the
aging schedule so that they have an idea of how it should change with peaks and valleys in
their sales.
Collection Effort A firm usually goes through the following sequence of procedures
for customers whose payments are overdue:
1. It sends out a delinquency letter informing the customer of the past-due status of the
account.
2. It makes a telephone call to the customer.
3. It employs a collection agency.
4. It takes legal action against the customer.
At times, a firm may refuse to grant additional credit to customers until arrearages are
cleared up. This may antagonize a normally good customer, and it points to a potential con-
flict of interest between the collections department and the sales department.
CONCEPT QUESTIONS
17.3a What are the basic components of credit policy?
17.3b Explain what terms of “3/45, net 90” mean. What is the effective interest rate?
17.3c What are the five Cs of credit?
aging schedule
A compilation of accounts
receivable by the age of
each account.
2Aging schedules are used elsewhere in business. For example, aging schedules often are prepared for
inventory items.
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C H A P T E R 1 7 Working Capital Management 573
INVENTORY MANAGEMENT
Like receivables, inventories represent a significant investment for many firms. For a typical
manufacturing operation, inventories often will exceed 15 percent of assets. For a retailer, in-
ventories could represent more than 25 percent of assets. From our discussion in Chapter 16,
we know that a firm’s operating cycle is made up of its inventory period and its receivables
period. This is one reason for considering credit and inventory policy in the same chapter.
Beyond this, both credit and inventory policies are used to drive sales, and the two must be
coordinated to ensure that the process of acquiring inventory, selling it, and collecting on the
sale proceeds smoothly. For example, changes in credit policy designed to stimulate sales
must be simultaneously accompanied by planning for adequate inventory.
The Financial Manager and Inventory Policy
Despite the size of a typical firm’s investment in inventories, the financial manager of a firm
normally will not have primary control over inventory management. Instead, other func-
tional areas such as purchasing, production, and marketing usually will share decision-
making authority. Inventory management has become an increasingly important specialty
in its own right, and financial management often only will have input into the decision.
However, inventory policy can have dramatic financial effects. We therefore survey some
basics of inventory and inventory policy in the sections ahead.
Inventory Types
For a manufacturer, inventory normally is classified into one of three categories. The first
category is raw material. This is whatever the firm uses as a starting point in its production
process. Raw materials might be something as basic as iron ore for a steel manufacturer or
something as sophisticated as disk drives for a computer manufacturer.
The second type of inventory is work-in-progress, which is what the name suggests—
unfinished product. How big this portion of inventory is depends in large part on the length
of the production process. For an airframe manufacturer, for example, work-in-progress can
be substantial. The third and final type of inventory is finished goods, that is, products ready
to ship or sell.
There are three things to keep in mind concerning inventory types. First, the names for
the different types can be a little misleading because one company’s raw materials could be
another’s finished goods. For example, going back to our steel manufacturer, iron ore would
be a raw material, and steel would be the final product. An auto body panel stamping opera-
tion will have steel as its raw material and auto body panels as its finished goods, and an
automobile assembler will have body panels as raw materials and automobiles as finished
products.
The second thing to keep in mind is that the various types of inventory can be quite
different in terms of their liquidity. Raw materials that are commodity-like or relatively
standardized can be easy to convert to cash. Work-in-progress, on the other hand, can be
quite illiquid and have little more than scrap value. As always, the liquidity of finished goods
depends on the nature of the product.
Finally, a very important distinction between finished goods and other types of invento-
ries is that the demand for an inventory item that becomes a part of another item usu-
ally is termed derived, or dependent, demand because the firm’s need for these inventory
types depends on its need for finished items. In contrast, the firm’s demand for finished
goods is not derived from demand for other inventory items, so it is sometimes said to be
independent.
17.4
Visit the Society for
Inventory Management
Benchmarking Analysis at
www.simba.org.
ros13952_ch17_553-588.indd 573 12/22/18 6:03 PM
574 P A R T 8 Short-Term Financial Management
Inventory Costs
As we discussed in Chapter 16, there are two basic types of costs associated with current
assets in general and with inventory in particular. The first of these are carrying costs. Here,
carrying costs represent all of the direct and opportunity costs of keeping inventory on
hand. These include:
1. Storage and tracking costs.
2. Insurance and taxes.
3. Losses due to obsolescence, deterioration, or theft.
4. The opportunity cost of capital for the invested amount.
The sum of these costs can be substantial, roughly ranging from 20 to 40 percent of inven-
tory value per year.
The other types of costs associated with inventory are shortage costs. These are costs as-
sociated with having inadequate inventory on hand. The two components of shortage costs
are restocking costs and costs related to safety reserves. Depending on the firm’s business,
order, or restocking, costs are either the costs of placing an order with suppliers or the cost of
setting up a production run. The costs related to safety reserves are opportunity losses such
as lost sales and loss of customer goodwill that result from having inadequate inventory.
A basic trade-off in inventory management exists because carrying costs increase with
inventory levels while shortage, or restocking, costs decline with inventory levels. The basic
goal of inventory management thus is to minimize the sum of these two costs. We consider
ways to reach this goal in the next section.
CONCEPT QUESTIONS
17.4a What are the different types of inventory?
17.4b What are three things to remember when examining inventory types?
17.4c What is the basic goal of inventory management?
INVENTORY MANAGEMENT TECHNIQUES
As we described earlier, the goal of inventory management is usually framed as cost minimi-
zation. Three techniques are discussed in this section, ranging from the relatively simple to
the very complex.
The ABC Approach
The ABC approach is a simple approach to inventory management where the basic idea is to
divide inventory into three (or more) groups. The underlying rationale is that a small portion of
inventory in terms of quantity might represent a large portion in terms of inventory value. For
example, this situation would exist for a manufacturer that uses some relatively expensive, high-
tech components and some relatively inexpensive basic materials in producing its products.3
Figure 17.6 illustrates an ABC comparison of items in terms of the percentage of inventory
value represented by each group versus the percentage of items represented. As Figure 17.6
shows, the A Group constitutes only 10 percent of inventory by item count, but it represents
17.5
3The ABC approach to inventory should not be confused with activity-based costing, a common topic in mana-
gerial accounting.
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C H A P T E R 1 7 Working Capital Management 575
over half of the value of inventory. The A Group items are thus monitored closely, and inven-
tory levels are kept relatively low. At the other end, basic inventory items, such as nuts and bolts,
also will exist, but because these are crucial and inexpensive, large quantities are ordered and
kept on hand. These would be C Group items. The B Group is made up of in-between items.
The Economic Order Quantity Model
The economic order quantity, or EOQ, model is the best-known approach to explicitly
establishing an optimal inventory level. The basic idea is illustrated in Figure 17.7, which
economic order
quantity (EOQ)
The restocking quantity
that minimizes the total
inventory costs.
100
80
60
40
20
0
20
40
60
80
100
Percentage of
inventory
value
Percentage of
inventory
items
57%
10%
27%
40%
16%
50%
A Group
B Group
C Group
ABC inventory
analysis
FIGURE 17.6
Total costs of holding inventory
Carrying costs
Restocking costs
Q*
Optimal size
of inventory order
Size of inventory
orders (Q)
Cost of holding
inventory ($)
Restocking costs are greatest when the firm holds a small quantity of inventory.
Carrying costs are greatest when there is a large quantity of inventory on hand.
Total costs are the sum of the carrying and restocking costs.
Costs of holding
inventory
FIGURE 17.7
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576 P A R T 8 Short-Term Financial Management
plots the various costs associated with holding inventory (on the vertical axis) against
inventory levels (on the horizontal axis). As is shown, inventory carrying costs rise and
restocking costs decrease as inventory levels increase. From our discussion of the total
credit cost curve in this chapter, the general shape of the total inventory cost curve is
familiar. With the EOQ model, we will attempt to specifically locate the minimum total
cost point, Q*.
In our discussion below, an important point to keep in mind is that the actual cost of
the inventory itself is not included. The reason is that the total amount of inventory the firm
needs in a given year is dictated by sales. What we are analyzing here is how much the firm
should have on hand at any particular time. More precisely, we are trying to determine what
order size the firm should use when it restocks its inventory.
Inventory Depletion To develop the EOQ, we will assume that the firm’s inventory is
sold at a steady rate until it hits zero. At that point, the firm restocks its inventory back to
some optimal level. Suppose the Eyssell Corporation starts out today with 3,600 units of a
particular item in inventory. Annual sales of this item are 46,800 units, which is 900 per
week. If Eyssell sells 900 units in inventory each week, then, after four weeks, all the available
inventory will be sold, and Eyssell will restock by ordering (or manufacturing) another
3,600 and will start over. This selling and restocking process produces a sawtooth pattern
for inventory holdings; this pattern is illustrated in Figure 17.8. As the figure shows, Eyssell
always starts with 3,600 units in inventory and ends up at zero. On average, then, inventory
is half of 3,600, or 1,800 units.
Carrying Costs As Figure 17.7 illustrates, carrying costs are normally assumed to be
directly proportional to inventory levels. Suppose we let Q be the quantity of inventory that
10 432 765 8
Starting inventory:
Q = 3,600
Q/2 = 1,800
Ending inventory: 0
Average inventory
Weeks
The Eyssell Corporation starts with inventory of 3,600 units. The quantity drops to zero by
the end of the fourth week. The average inventory is Q/2 = 3,600/2 = 1,800 over the period.
Inventory holdings
for the Eyssell
Corporation
FIGURE 17.8
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C H A P T E R 1 7 Working Capital Management 577
Eyssell orders each time (3,600 units); we will call this the restocking quantity. Average in-
ventory would then be Q/2, or 1,800 units. If we let CC be the carrying cost per unit per
year, Eyssell’s total carrying costs will be:
Total carrying costs = Average inventory × Carrying costs per unit
= (Q/2) × CC
[17.1]
In Eyssell’s case, if carrying costs were $.75 per unit per year, then total carrying costs
would be the average inventory of 1,800 multiplied by $.75, or $1,350 per year.
Shortage Costs For now, we will focus only on the restocking costs. In essence, we
will assume that the firm never actually runs short on inventory, so that costs relating to
safety reserves are not important. We return to this issue later.
Restocking costs are normally assumed to be fixed. In other words, every time we place
an order, there are fixed costs associated with that order (remember that the cost of the in-
ventory itself is not considered here). Suppose we let T be the firm’s total unit sales per year.
If the firm orders Q units each time, then it will need to place a total of T/Q orders. For Eys-
sell, annual sales were 46,800, and the order size was 3,600. Eyssell thus places a total of
46,800/3,600 = 13 orders per year. If the fixed cost per order is F, the total restocking cost
for the year would be:
Total restocking cost = Fixed cost per order × Number of orders
= F × (T/Q)
[17.2]
For Eyssell, order costs might be $50 per order, so the total restocking cost for 13 orders
would be $50 × 13 = $650 per year.
Total Costs The total costs associated with holding inventory are the sum of the carry-
ing costs and the restocking costs:
Total costs = Carrying costs + Restocking costs
= (Q/2) × CC + F × (T/Q)
[17.3]
Our goal is to find the value of Q, the restocking quantity, that minimizes this cost. To see
how we might go about this, we can calculate total costs for some different values of Q. For
the Eyssell Corporation, we had carrying costs (CC) of $.75 per unit per year, fixed costs
(F) of $50 per order, and total unit sales (T) of 46,800 units. With these numbers, some
possible total costs are (check some of these for practice):
Restocking
Quantity (Q)
Total Carrying
Costs
(Q/2 × CC)
+
Restocking
Costs
(F × T/Q)
= Total
Costs
500 $ 187.5 $4,680.0 $4,867.5
1,000 375.0 2,340.0 2,715.0
1,500 562.5 1,560.0 2,122.5
2,000 750.0 1,170.0 1,920.0
2,500 937.5 936.0 1,873.5
3,000 1,125.0 780.0 1,905.0
3,500 1,312.5 668.6 1,981.1
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578 P A R T 8 Short-Term Financial Management
Inspecting the numbers, we see that total costs start out at almost $5,000, and they
decline to just under $1,900. The cost-minimizing quantity appears to be approxi-
mately 2,500.
To find the precise cost-minimizing quantity, we can take a look back at Figure 17.7.
What we notice is that the minimum point occurs right where the two lines cross. At this
point, carrying costs and restocking costs are the same. For the particular types of costs we
have assumed here, this always will be true, so we can find the minimum point by setting
these costs equal to each other and solving for Q*:
Carrying costs = Restocking costs
(Q*/2) × CC = F × (T/Q*)
[17.4]
With a little algebra, we get:
(Q*)2 = 2T × F _____ CC [17.5]
To solve for Q*, we take the square root of both sides to find:
Q* = √
_______
2T × F ______ CC [17.6]
This reorder quantity, which minimizes the total inventory cost, is called the economic or-
der quantity. For the Eyssell Corporation, the EOQ is:
Q* = √
_______
2T × F ______ CC
= √
___________________
(2 × 46,800() × $50 _________________ .75
= √
__________
6,240,000
= 2,498 units
Thus, for Eyssell, the economic order quantity is actually 2,498 units. At this level, verify
that the restocking costs and carrying costs are identical (they’re both $936.75).
EXAMPLE 17.3 Carrying Costs
Thiewes Shoes begins each period with 100 pairs of hiking boots in stock. This stock is depleted
each period and reordered. If the carrying cost per pair of boots per year is $3, what are the total
carrying costs for the hiking boots?
Inventories always start at 100 items and end up at 0, so average inventory is 50 items. At an
annual cost of $3 per item, total carrying costs are $150.
EXAMPLE 17.4 Restocking Costs
In Example 17.3, suppose Thiewes sells a total of 600 pairs of boots in a year. How many times per
year does Thiewes restock? Suppose the restocking cost is $20 per order. What are total restock-
ing costs?
Thiewes orders 100 items each time. Total sales are 600 items per year, so Thiewes restocks
six times per year, or about every two months. The restocking costs would be 6 orders × $20 per
order = $120.
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C H A P T E R 1 7 Working Capital Management 579
Extensions to the EOQ Model
Thus far, we have assumed that a company will let its inventory run down to zero and then
reorder. In reality, a company will wish to reorder before its inventory goes to zero for two
reasons. First, by always having at least some inventory on hand, the firm minimizes the risk
of a stockout and the resulting losses of sales and customers. Second, when a firm does re-
order, there will be some time lag before the inventory arrives. Thus, to finish our discussion
of the EOQ, we consider two extensions: safety stocks and reorder points.
Safety Stocks A safety stock is the minimum level of inventory that a firm keeps on
hand. Inventories are reordered whenever the level of inventory falls to the safety stock level.
Part A of Figure 17.9 illustrates how a safety stock can be incorporated into an EOQ model.
Notice that adding a safety stock means that the firm does not run its inventory all the way
down to zero. Other than this, the situation here is identical to that considered in our earlier
discussion of the EOQ.
Reorder Points To allow for delivery time, a firm will place orders before inventories
reach a critical level. The reorder points are the times at which the firm will actually place its
inventory orders. These points are illustrated in Part B of Figure 17.9. As is shown, the reor-
der points occur some fixed number of days (or weeks or months) before inventories are
projected to reach zero.
One of the reasons that a firm will keep a safety stock is to allow for uncertain delivery
times. We therefore can combine our reorder point and safety stock discussions in Part C of
Figure 17.9. The result is a generalized EOQ model in which the firm orders in advance of
anticipated needs and also keeps a safety stock of inventory to guard against unforeseen
fluctuations in demand and delivery times.
Managing Derived-Demand Inventories
A third type of inventory management technique is used to manage derived-demand inven-
tories. As we described previously, demand for some inventory types is derived from, or
dependent on, other inventory needs. A good example is given by the auto manufacturing
industry, where the demand for finished products derives from consumer demand, market-
ing programs, and other factors related to projected unit sales. The demand for inventory
EXAMPLE 17.5 The EOQ
Based on our previous two examples, what size orders should Thiewes place to minimize costs?
How often will Thiewes restock? What are the total carrying and restocking costs? The total costs?
We have that the total number of pairs of boots ordered for the year (T) is 600. The restocking cost
(F) is $20 per order, and the carrying cost (CC) is $3. We can calculate the EOQ for Thiewes as follows:
EOQ = √
_______
2T × F ______ CC
= √
___________________
(2 × 600") × $20 _________________ $3
= √
__________
8,000
= 89.44 units
Because Thiewes sells 600 pairs per year, it will restock 600/89.44 = 6.71 times. The total restock-
ing costs will be $20 × 6.71 = $134.16. Average inventory will be 89.44/2 = 44.72. The carrying
costs will be $3 × 44.72 = $134.16, the same as the restocking costs. The total costs are thus
$268.33.
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580 P A R T 8 Short-Term Financial Management
items such as tires, batteries, headlights, and other components is then completely deter-
mined by the number of autos planned. Materials requirements planning and just-in-time
inventory management are two methods for managing demand-dependent inventories.
Materials Requirements Planning Production and inventory specialists have
developed computer-based systems for ordering and/or scheduling production of demand-
dependent types of inventories. These systems fall under the general heading of
materials requirements planning (MRP). The basic idea behind MRP is that, once finished
goods inventory levels are set, it is possible to determine what levels of work-in-progress
inventories must exist to meet the need for finished goods. From there, it is possible to
calculate the quantity of raw materials that must be on hand. This ability to schedule back-
wards from finished goods inventories stems from the dependent nature of work-in-progress
and raw materials inventories. MRP is particularly important for complicated products for
which a variety of components are needed to create the finished product.
materials
requirements
planning (MRP)
A set of procedures used
to determine inventory
levels for demand-
dependent inventory
types, such as work-in-
progress and raw
materials.
Delivery time Delivery time Delivery time Delivery time
Safety
stock
Safety
stock
Reorder
point
Minimum
inventory
level
Time
Minimum
inventory
level
Time
Reorder
point
Time
Inventory
(units)
With a safety stock, the firm reorders when inventory reaches
a minimum level.
A. Safety stock
Inventory
(units)
B. Reorder points
Inventory
(units)
C. Combined reorder points and safety stock
When there are lags in delivery or production times, the
firm reorders when inventory reaches the reorder point.
By combining safety stock and reorder points, the firm
maintains a buffer against unforeseen events.
FIGURE 17.9
Safety stocks and
reorder points
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Just-in-Time Inventory Just-in-time, or JIT, inventory is a modern approach to man-
aging dependent inventories. The goal of JIT is essentially to minimize such inventories,
thereby maximizing turnover. The approach began in Japan, and it is a fundamental part of
much of Japanese manufacturing philosophy. As the name suggests, the basic goal of JIT is
to have only enough inventory on hand to meet immediate production needs.
The result of the JIT system is that inventories are reordered and restocked frequently.
Making such a system work and avoiding shortages require a high degree of cooperation
among suppliers. Japanese manufacturers often have a relatively small, tightly integrated
group of suppliers with whom they work closely to achieve the needed coordination. These
suppliers are a part of a large manufacturer’s (such as Toyota’s) industrial group, or keiretsu.
Each large manufacturer tends to have its own keiretsu. It also helps to have suppliers lo-
cated nearby, a situation that is common in Japan.
The kanban is an integral part of a JIT inventory system, and JIT systems are some-
times called kanban systems. The literal meaning of kanban is “card” or “sign,” but, broadly
speaking, a kanban is a signal to a supplier to send more inventory. For example, a kanban
literally could be a card attached to a bin of parts. When a worker pulls that bin, the card is
detached and routed back to the supplier, who then supplies a replacement bin.
A JIT inventory system is an important part of a larger production planning process. A
full discussion of it would necessarily shift our focus away from finance to production and
operations management, so we will leave it here. The nearby Finance Matters box discusses
some of the potential problems with a JIT inventory system.
just-in-time (JIT)
inventory
A system for managing
demand-dependent
inventories that minimizes
inventory holdings.
Supply Chain Management
J IT inventory has been widely adopted because of the potential savings in inventory. And JIT inventory systems
have led to the increased importance of supply chain man-
agement (SCM). SCM deals with all movement and storage
of raw materials, work-in-process inventory, and finished
goods from the raw material phase until the point of sale.
Because JIT relies on little or no inventory, SCM is critical,
especially when there is a disruption in the flow of raw mate-
rials necessary for production.
In March 2011, the powerful earthquake and resulting
tsunami in Japan caused tremendous damage locally, but the
supply chain effects were felt around the world. For example,
less than a week after the earthquake, a GM plant in Shreve-
port, Louisiana, was forced to shut down entirely because of a
shortage in a single part that was supplied from a Japanese
manufacturer. GM also was forced to slow down production in
its Tonawanda, New York, engine plant less than a week later.
Other companies and industries were affected as well.
For example, Toyota shut down its 13 U.S. plants temporarily,
and John Deere announced that it was delaying delivery of
excavators and mining equipment. Even domestic Japanese
companies weren’t immune from supply chain problems.
Famed camera maker Canon was forced to halt production
at its Japanese plants because of parts shortages, not earth-
quake-related damages.
While natural catastrophes can be one cause of SCM
problems, smaller events also can have a dramatic impact.
For example, in May 2018, a fire occurred at the Meridian
Magnesium Products plant in Eaton Rapids, Michigan. This
plant produces die-cast parts for the auto industry. Ford was
the hardest hit as the plant made parts for Ford’s highly prof-
itable F-150 pickup truck. As a result of the parts shortage
caused by the fire, Ford was forced to idle the company’s
Missouri plant, sending 3,600 workers home. Other auto
manufactures also were affected as General Motors shut
down production of its full-size van production lines at its
Missouri plant and Fiat Chrysler was forced to adjust the pro-
duction schedule at its Windsor, Ontario, plant.
FINANCE MATTERS
CONCEPT QUESTIONS
17.5a What does the EOQ model determine for the firm?
17.5b Which cost component of the EOQ model does JIT inventory minimize?
581
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582 P A R T 8 Short-Term Financial Management
SUMMARY AND CONCLUSIONS
This chapter has covered cash, receivables, and inventory management. Along the way, we
have touched on a large number of subjects. Some of the more important issues we exam-
ined are:
1. Firms seek to manage their cash by keeping no more than is needed on hand. The
reason is that holding cash has an opportunity cost, namely, the returns that could be
earned by investing the money.
2. Float is an important consideration in cash management, and firms seek to manage
collections and disbursements in ways designed to optimize the firm’s net float.
3. A firm’s credit policy includes the terms of sale, credit analysis, and collection policy.
The terms of sale cover three related subjects: credit period, cash discount, and credit
instrument.
4. The optimal credit policy for a firm depends on many specific factors, but generally
involves trading off the costs of granting credit, such as the carrying costs of
receivables and the possibility of nonpayment, against the benefits in terms of
increased sales.
5. There are different types of inventories that differ greatly in their liquidity and
management. The basic trade-off in inventory management is the cost of carrying
inventory versus the cost of restocking. We developed the famous EOQ model, which
explicitly balances these costs.
6. Firms use different inventory management techniques; we described a few of the
better known, including the ABC approach and just-in-time, or JIT, inventory
management.
POP QUIZ!
Can you answer the following questions? If your class is using Connect, log on to
SmartBook to see if you know the answers to these and other questions, check out
the study tools, and find out what topics require additional practice!
Section 17.2 What are the components of total collection time?
Section 17.3 What are the components of credit policy?
Section 17.4 What are shortage costs?
Section 17.5 If the reorder quantity Q equals 4,000 units and carrying costs are
$2.00 per unit per year, what will the total annual carrying costs be?
CHAPTER REVIEW AND SELF-TEST PROBLEMS
17.1 Calculating Float You have $10,000 on deposit with no outstanding checks or
uncleared deposits. One day you write a check for $4,000 and then deposit a check
for $3,000. What are your disbursement, collection, and net floats? (See Problem 3.)
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C H A P T E R 1 7 Working Capital Management 583
17.2 The EOQ Heusen Computer Manufacturing starts each period with 4,000 central
processing units (CPUs) in stock. This stock is depleted each month and reordered.
If the carrying cost per CPU is $1 and the fixed order cost is $10, is Heusen
following an economically advisable strategy? (See Problem 13.)
■ Answers to Chapter Review and Self-Test Problems
17.1 First, after you write the check for $4,000, you show a balance of $6,000. However,
while the check is clearing, your bank shows a balance of $10,000. This is a $4,000
disbursement float, and it is good for you. Next, when you deposit the $3,000, you
show a balance of $9,000, but your account will not be credited for the $3,000 until
it clears. This is a −$3,000 collection float, and it is bad for you.
The sum of the disbursement float and the collection float is your net float of
$1,000. In other words, you show a balance of $9,000, but your bank shows a
$10,000 balance, so, in net terms, you are benefiting from the float.
17.2 We can answer by first calculating Heusen’s carrying and restocking costs. The
average inventory is 2,000 CPUs, and, because the carrying costs are $1 per CPU,
total carrying costs are $2,000. Heusen restocks every month at a fixed order cost of
$10, so the total restocking costs are $120. What we see is that carrying costs are
large relative to reorder costs, so Heusen is carrying too much inventory.
To determine the optimal inventory policy, we can use the EOQ model. Because
Heusen orders 4,000 CPUs 12 times per year, total needs (T) are 48,000 CPUs. The
fixed order cost is $10, and the carrying cost per unit (CC) is $1. The EOQ is therefore:
EOQ = √
_______
2T × F ______ CC
= √
___________________
(2 × 48,000 ) × $10 _________________ $1
= √
__________
960,000
= 979.80 units
We can check this by noting that, at the EOQ, the average inventory is about 490
CPUs, so the carrying cost is $490. Heusen will have to reorder 48,000/979.8 =
49 times. The fixed order cost is $10, so the total restocking cost is also $490.
CRITICAL THINKING AND CONCEPTS REVIEW
LO 1 17.1 Cash Management Is it possible for a firm to have too much cash? Why
would shareholders care if a firm accumulates large amounts of cash?
LO 1 17.2 Cash Management What options are available to a firm if it believes it
has too much cash? How about too little?
LO 1 17.3 Agency Issues Are stockholders and creditors likely to agree on how
much cash a firm should keep on hand?
LO 1 17.4 Motivations for Holding Cash In the chapter opening, we discussed the cash
positions of several companies. Automobile manufacturers also have enormous
cash reserves. In the middle of 2018, Ford Motor Co. had about $27.5 billion
in cash, General Motors had about $17.2 billion, and Toyota had about $53.8
billion. Why would firms such as these hold such large quantities of cash?
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584 P A R T 8 Short-Term Financial Management
LO 1 17.5 Short-Term Investments Why is a preferred stock with a dividend tied to
short-term interest rates an attractive short-term investment for
corporations with excess cash?
LO 2 17.6 Collection and Disbursement Floats Which would a firm prefer: a net
collection float or a net disbursement float? Why?
LO 1 17.7 Float Suppose a firm has a book balance of $2 million. At the automatic
teller machine (ATM), the cash manager finds out that the bank balance is
$2.5 million. What is the situation here? If this is an ongoing situation,
what ethical dilemma arises?
LO 1 17.8 Short-Term Investments For each of the short-term marketable securities
given here, provide an example of the potential disadvantages the
investment has for meeting a corporation’s cash management goals.
a. U.S. Treasury bills
b. Ordinary preferred stock
c. Negotiable certificates of deposit (NCDs)
d. Commercial paper
LO 1 17.9 Agency Issues It is sometimes argued that excess cash held by a firm can
aggravate agency problems (discussed in Chapter 1) and, more generally,
reduce incentives for shareholder wealth maximization. How would you
frame the issue here?
LO 1 17.10 Use of Excess Cash One option a firm usually has with any excess cash is
to pay its suppliers more quickly. What are the advantages and
disadvantages of this use of excess cash?
LO 1 17.11 Use of Excess Cash Another option usually available for dealing with
excess cash is to reduce the firm’s outstanding debt. What are the
advantages and disadvantages of this use of excess cash?
LO 1 17.12 Float An unfortunately common practice goes like this: (Warning: Don’t
try this at home.) Suppose you are out of money in your checking account;
however, your local grocery store, as a convenience to you as a customer,
will cash a check for you. So you cash a check for $200. Of course, this
check will bounce unless you do something. To prevent this, you go to the
grocery the next day and cash another check for $200. You take this $200
and deposit it. You repeat this process every day, and, in doing so, you
make sure that no checks bounce. Eventually, manna from heaven arrives
(perhaps in the form of money from home) and you are able to cover your
outstanding checks.
To make it interesting, suppose you are absolutely certain that no checks
will bounce along the way. Assuming this is true, and ignoring any question
of legality (what we have described is probably illegal check kiting), is there
anything unethical about this? If you say yes, then why? In particular, who is
harmed?
LO 2 17.13 Credit Instruments Describe each of the following:
a. Sight draft
b. Time draft
c. Banker’s acceptance
d. Promissory note
e. Trade acceptance
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C H A P T E R 1 7 Working Capital Management 585
LO 2 17.14 Trade Credit Forms In what form is trade credit most commonly offered?
What is the credit instrument in this case?
LO 2 17.15 Receivables Costs What are the costs associated with carrying
receivables? What are the costs associated with not granting credit? What
do we call the sum of the costs for different levels of receivables?
LO 2 17.16 Five Cs of Credit What are the five Cs of credit? Explain why each is
important.
LO 2 17.17 Credit Period Length What are some of the factors that determine the
length of the credit period? Why is the length of the buyer’s operating cycle
often considered an upper bound on the length of the credit period?
LO 2 17.18 Credit Period Length In each of the following pairings, indicate which
firm would probably have a longer credit period and explain your
reasoning.
a. Firm A sells a miracle cure for baldness; Firm B sells toupees.
b. Firm A specializes in products for landlords; Firm B specializes in
products for renters.
c. Firm A sells to customers with an inventory turnover of 10 times; Firm
B sells to customers with an inventory turnover of 20 times.
d. Firm A sells fresh fruit; Firm B sells canned fruit.
e. Firm A sells and installs carpeting; Firm B sells rugs.
LO 3 17.19 Inventory Types What are the different inventory types? How do the
types differ? Why are some types said to have dependent demand whereas
other types are said to have independent demand?
LO 3 17.20 Just-in-Time Inventory If a company moves to a JIT inventory
management system, what will happen to inventory turnover? What will
happen to total asset turnover? What will happen to return on equity, ROE?
(Hint: Remember the DuPont equation from Chapter 3.)
BASIC (Questions 1–14)
1. Calculating Float You have $85,000 on deposit with no outstanding checks
or uncleared deposits. One day you write a check for $21,600. Does this
create a disbursement float or a collection float? What is your available
balance? Book balance?
2. Calculating Float You have $11,900 on deposit with no outstanding checks
or uncleared deposits. If you deposit a check for $2,200, does this create
a disbursement float or a collection float? What is your available balance?
Book balance?
3. Calculating Float You have $21,400 on deposit with no outstanding
checks or uncleared deposits. One day you write a check for $4,300 and
then deposit a check for $4,900. What are your disbursement, collection,
and net floats?
LO 1
LO 1
LO 1
QUESTIONS AND PROBLEMS
Select problems are available in McGraw-Hill Connect. Please see the pack-
aging options section of the Preface for more information.
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586 P A R T 8 Short-Term Financial Management
4. Cash Discounts You place an order for 560 units of Good X at a unit price
of $67. The supplier offers terms of 1/10, net 30.
a. How long do you have to pay before the account is overdue? If you take
the full period, how much should you remit?
b. What is the discount being offered? How quickly must you pay to get the
discount? If you do take the discount, how much should you remit?
c. If you don’t take the discount, how much interest are you paying
implicitly? How many days’ credit are you receiving?
5. Calculating Float In a typical month, the Pier Corporation receives 100
checks totaling $57,400. These are delayed three days on average. What is the
average daily float? Assume 30 days in a month.
6. Calculating Net Float Each business day, on average, a company writes
checks totaling $26,700 to pay its suppliers. The usual clearing time for the
checks is four days. Meanwhile, the company is receiving payments from its
customers each day, in the form of checks, totaling $39,600. The cash from
the payments is available to the firm after two days.
a. Calculate the company’s disbursement float, collection float, and net float.
b. How would your answer to part (a) change if the collected funds were
available in one day instead of two?
7. Size of Accounts Receivable Essence of Skunk Fragrances, Ltd., sells
6,700 units of its perfume collection each year at a price per unit of $215.
All sales are on credit with terms of 1/10, net 30. The discount is taken
by 60 percent of the customers. What is the amount of the company’s
accounts receivable? In reaction to sales by its main competitor, Sewage
Spray, Essence of Skunk is considering a change in its credit policy to terms
of 3/10, net 30 to preserve its market share. How will this change in policy
affect accounts receivable?
8. Size of Accounts Receivable The Malibu Corporation has annual credit
sales of $29.5 million. The average collection period is 34 days. What is the
average investment in accounts receivable as shown on the balance sheet?
9. ACP and Accounts Receivable Miyagi Data, Inc., sells earnings forecasts
for Japanese securities. Its credit terms are 1/10, net 30. Based on
experience, 65 percent of all customers will take the discount.
a. What is the average collection period?
b. If the company sells 1,100 forecasts every month at a price of $1,950
each, what is its average balance sheet amount in accounts receivable?
10. Size of Accounts Receivable Four Doors Down, Inc., has weekly credit
sales of $36,500, and the average collection period is 31 days. What is the
company’s average accounts receivable figure?
11. Terms of Sale A firm offers terms of 1/10, net 30. What effective annual
interest rate does the firm earn when a customer does not take the discount?
Without doing any calculations, explain what will happen to this effective
rate if:
a. The discount is changed to 2 percent.
b. The credit period is increased to 40 days.
c. The discount period is decreased to 20 days.
d. What is the EAR for each scenario?
LO 2
LO 1
LO 1
LO 2
LO 2
LO 2
LO 2
LO 2
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C H A P T E R 1 7 Working Capital Management 587
12. ACP and Receivables Turnover Rose, Inc., has an average collection period
of 29 days. Its average daily investment in receivables is $91,300. What are
annual credit sales? What is the receivables turnover?
13. EOQ Clap Off Manufacturing uses 975 switch assemblies per week and
then reorders another 975. If the relevant carrying cost per switch assembly
is $6.25 and the fixed order cost is $430, is the company’s inventory policy
optimal? Why or why not?
14. EOQ The Trektronics store begins each month with 735 phasers in stock.
This stock is depleted each month and reordered. If the carrying cost per
phaser is $26 per year and the fixed order cost is $365, what is the total
carrying cost? What is the restocking cost? Should the company increase
or decrease its order size? Describe an optimal inventory policy for the
company in terms of order size and order frequency.
INTERMEDIATE (Question 15)
15. EOQ Derivation Prove that when carrying costs and restocking costs are
as described in the chapter, the EOQ must occur at the point where the
carrying costs and restocking costs are equal.
CHALLENGE (Question 16)
16. Safety Stocks and Order Points Saché, Inc., expects to sell 700 of its
designer suits every week. The store is open seven days a week and expects
to sell the same number of suits every day. The company has an EOQ
of 500 suits and a safety stock of 100 suits. Once an order is placed, it
takes three days for Saché to get the suits in. How many orders does the
company place per year? Assume that it is Monday morning before the
store opens, and a shipment of suits has just arrived. When will Saché
place its next order?
LO 2
LO 3
LO 3
LO 3
LO 3
17.1 Commercial Paper Chevron sells commercial paper to interested institutional
investors. Go to the Chevron website at www.chevron.com to find information on
Chevron’s commercial paper. What is the credit rating for Chevron’s commercial paper?
What is the minimum size Chevron will sell? What size does it require for one- to four-
day commercial paper?
17.2 Commercial Paper Rates What were the highest and lowest historical interest rates
for commercial paper? Go to www.stlouisfed.org, find the “FRED®” data link, then the
“Interest Rates” link. What were the highest and lowest interest rates for one-, two-, and
three-month AA nonfinancial commercial paper? What about for financial commercial
paper? Did these occur at the same time? Why might the nonfinancial and financial
commercial paper rates be different?
WHAT’S ON
THE WEB?
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588 P A R T 8 Short-Term Financial Management
plan for next year. Additionally, he would like you to
inquire as to the possibility of getting improved credit
terms for the company’s purchases.
To analyze the possible switch to the new credit
terms, Gary has asked you to investigate industry stand-
ard credit terms and rework the short-term financial plan
assuming Piepkorn Manufacturing offers credit to its
customers. He also would like to investigate how better
credit terms from the company’s suppliers would affect
the short-term financial plan.
After completing the short-term financial plan for next year (at the end of Chapter 16), Gary Piepkorn
approaches you and asks about the company’s credit
policy. In looking at the competition, most companies in
the industry offer credit to customers, so Piepkorn Man-
ufacturing appears to be one of the few companies that
does not. Several customers have expressed the possi-
bility of changing to a different supplier because of the
lack of credit. Gary is interested in knowing how imple-
menting a credit policy will affect the short-term financial
CHAPTER CASE
Piepkorn Manufacturing Working
Capital Management, Part 2
1. You have looked at the credit policy offered by
your competitors and have determined that the
industry standard credit policy is 1/10, net 45. The
discount will begin to be offered on the first day of
the year. You want to examine how this credit pol-
icy would affect the cash budget and short-term
financial plan. If this credit policy is implemented,
you believe that 60 percent of customers will take
advantage of the credit offer and the accounts re-
ceivable period will be 24 days. Rework the cash
budget and short-term financial plan under the
new credit policy and a target cash balance of
$80,000. What interest rate are you effectively of-
fering customers?
2. You have talked to the company’s suppliers about
the credit terms Piepkorn receives. Currently, the
company receives terms of net 45. Your suppliers
have stated that they would offer new credit terms
of 2/25, net 40. The discount would begin to be
offered on the first day of the year. What interest
rate are the suppliers offering the company? Re-
work your cash budget and short-term financial
plan from the previous question assuming you take
advantage of the discount offered.
Q U E S T I O N S
ros13952_ch17_553-588.indd 588 12/22/18 6:03 PM
Please visit us at essentialsofcorporatefinance.blogspot.com for the latest developments in the world of corporate finance.
589
Please visit us at essentialsofcorporatefinance.blogspot.com for the latest developments in the world of corporate finance.
In Chapter 17, we mentioned the cash balances held by several large companies, but we didn’t mention that much of that cash
was held overseas. For example, Apple led the way with over
$250 billion in overseas cash, followed by Microsoft ($130 billion)
and Alphabet ($94 billion). Before 2018, companies like Apple had a
strong tax incentive to keep huge cash hoards outside the
United States. All of that changed with the signing of the Tax Cuts and
Jobs Act of 2017, which ushered in big changes in the way U.S. corpo-
rations are taxed on their overseas operations. In this chapter, we dis-
cuss this topic, along with the important roles played by currencies,
exchange rates, and other features of the international finance
landscape.
As businesses of all types have increased their reliance on in-
ternational operations, all areas of business have been strongly af-
fected. Human resources, production, marketing, accounting, and
strategy, for example, all become much more complex when nondo-
mestic considerations come into play. This chapter discusses one of
the most important aspects of international business: the impact of shifting exchange rates
and what companies (and individuals) can do to protect themselves against adverse
exchange rate movements.
PART NINE Topics in Business Finance
Companies with significant foreign operations often are called international corporations, or multinationals. Such companies must consider many financial factors that do not
directly affect purely domestic firms. These include foreign exchange rates, differing interest
rates from country to country, complex accounting methods for foreign operations, foreign
tax rates, and foreign government intervention.
The basic principles of corporate finance still apply to international corporations; like
domestic companies, they seek to invest in projects that create more value for the
International Aspects of
Financial Management18
LEARNING OBJECTIVES
After studying this chapter, you should
be able to:
LO 1 Explain how exchange rates are
quoted, assess what they mean,
and differentiate between spot
and forward exchange rates.
LO 2 Discuss purchasing power parity
and interest rate parity, and
analyze their implications for
exchange rate changes.
LO 3 Identify the different types of
exchange rate risk and ways firms
manage exchange rate risk.
LO 4 Discuss the impact of political risk
on international business
investing.
ros13952_ch18_589-615.indd 589 12/22/18 6:04 PM
590 P A R T 9 Topics in Business Finance
shareholders (or owners) than they cost and to arrange financing that raises cash at the
lowest possible cost. In other words, the net present value principle holds for both foreign
and domestic operations, but it is usually more complicated to apply the NPV rule to for-
eign investments.
We won’t have much to say here about the role of cultural and social differences in in-
ternational business. We also will not be discussing the implications of differing political
and economic systems. These factors are of great importance to international businesses,
but it would take another book to do them justice. Consequently, we will focus only on some
purely financial considerations in international finance and some key aspects of foreign ex-
change markets.
TERMINOLOGY
A common buzzword for the student of business finance is globalization. The first step in
learning about the globalization of financial markets is to conquer the new vocabulary. As
with any specialty, international finance is rich in jargon. Accordingly, we get started on the
subject with a highly eclectic vocabulary exercise.
The terms that follow are presented alphabetically, and they are not all of equal im-
portance. We choose these particular ones because they appear frequently in the finan-
cial press or because they illustrate some of the colorful language of international
finance.
1. An American Depositary Receipt, or ADR, is a security issued in the United States
that represents shares of a foreign stock, allowing that stock to be traded in the
United States. Foreign companies use ADRs, which are issued in U.S. dollars, to
expand the pool of potential U.S. investors. ADRs are available in two forms:
company sponsored, which are listed on an exchange, and unsponsored, which
usually are held by the investment bank that deals in the ADR. Both forms are
available to individual investors, but only company-sponsored issues are quoted daily
in newspapers.
2. The cross-rate is the implicit exchange rate between two currencies (usually non-U.S.)
when both are quoted in some third currency, usually the U.S. dollar.
3. A Eurobond is a bond issued in multiple countries but denominated in a single
currency, usually the issuer’s home currency. Such bonds have become an important
way to raise capital for many international companies and governments. Eurobonds
are issued outside the restrictions that apply to domestic offerings and are syndicated
and traded mostly from London. Trading can and does take place anywhere there is a
buyer and a seller.
4. Eurocurrency is money deposited in a financial center outside of the country whose
currency is involved. For instance, Eurodollars—the most widely used Eurocurrency—
are U.S. dollars deposited in banks outside the U.S. banking system.
5. Foreign bonds, unlike Eurobonds, are issued in a single country and are usually
denominated in that country’s currency. Often, the country in which these bonds are
issued will draw distinctions between them and bonds issued by domestic issuers,
including different tax laws, restrictions on the amount issued, and tougher
disclosure rules.
Foreign bonds often are nicknamed for the country where they are issued: Yankee
bonds (United States), Samurai bonds (Japan), Rembrandt bonds (the Netherlands),
Bulldog bonds (Britain), and dim sum bonds (Chinese yuan-denominated bonds issued
18.1
See www.adr.com
for more.
American Depositary
Receipt (ADR)
A security issued in the
United States representing
shares of a foreign stock
and allowing that stock to
be traded in the United
States.
cross-rate
The implicit exchange rate
between two currencies
(usually non-U.S.) quoted
in some third currency
(usually the U.S. dollar).
Eurobonds
International bonds issued
in multiple countries but
denominated in a single
currency (usually the
issuer’s currency).
Eurocurrency
Money deposited in a
financial center outside
the country whose
currency is involved.
foreign bonds
International bonds issued
in a single country, usually
denominated in that
country’s currency.
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C H A P T E R 1 8 International Aspects of Financial Management 591
in Hong Kong). Partly because of tougher regulations and disclosure requirements,
the foreign-bond market hasn’t grown in past years with the vigor of the Eurobond
market. A substantial portion of all foreign bonds are issued in Switzerland.
6. Gilts, technically, are British and Irish government securities, although the term also
includes issues of local British authorities and some overseas public-sector offerings.
7. The London Interbank Offered Rate (LIBOR) is the rate that most international banks
charge one another for loans of Eurodollars overnight in the London market. LIBOR
is a cornerstone in the pricing of money market issues and other debt issues by both
government and corporate borrowers. Interest rates are frequently quoted as some
spread over LIBOR, and they then float with the LIBOR rate.
8. There are two basic kinds of swaps: interest rate and currency. An interest rate swap
occurs when two parties exchange a floating-rate payment for a fixed-rate payment or
vice versa. Currency swaps are agreements to deliver one currency in exchange for
another. Often, both types of swaps are used in the same transaction when debt
denominated in different currencies is swapped.
CONCEPT QUESTIONS
18.1a What are the differences between a Eurobond and a foreign bond?
18.1b What are Eurodollars?
FOREIGN EXCHANGE MARKETS
AND EXCHANGE RATES
The foreign exchange market is undoubtedly the world’s largest financial market. It is the mar-
ket where one country’s currency is traded for another’s. Most of the trading takes place in a
few currencies such as the U.S. dollar ($), the British pound sterling (£), the Japanese yen (¥),
and the euro (€). Table 18.1 lists some of the more common currencies and their symbols.
The foreign exchange market is an over-the-counter market, so there is no single location
where traders get together. Instead, market participants are located in the major commercial
and investment banks around the world. They communicate using computer terminals, tele-
phones, and other telecommunications devices. For example, one communications network
for foreign transactions is the Society for Worldwide Interbank Financial Telecommunica-
tion (SWIFT), a Belgian not-for-profit cooperative. Using data transmission lines, a bank in
New York can send messages to a bank in London via SWIFT regional processing centers.
The many different types of participants in the foreign exchange market include the
following:
1. Importers who pay for goods in foreign currencies.
2. Exporters who receive foreign currency and may want to convert to their domestic
currency.
3. Portfolio managers who buy or sell foreign stocks and bonds.
4. Foreign exchange brokers who match buy and sell orders.
5. Traders who “make a market” in foreign currencies.
6. Speculators who try to profit from changes in exchange rates.
gilts
British and Irish
government securities.
London Interbank
Offered Rate (LIBOR)
The rate most
international banks charge
one another for overnight
Eurodollar loans.
swaps
Agreements to exchange
two securities or
currencies.
For current LIBOR rates,
see www.global-rates.com.
18.2
foreign exchange
market
The market in which one
country’s currency is
traded for another’s.
coverage online
Excel
Master
Visit SWIFT at www.swift
.com.
Information on doing
business globally can
be found at www
.internationalist.com.
For online currency rates,
go to www.bloomberg
.com/markets/currencies.
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592 P A R T 9 Topics in Business Finance
Exchange Rates
An exchange rate is the price of one country’s currency expressed in terms of another
country’s currency. In practice, almost all trading of currencies takes place in terms of the
U.S. dollar. For example, both the Swiss franc and the Japanese yen are traded with their
prices quoted in U.S. dollars. Exchange rates are constantly changing. Our nearby Work the
Web box shows you how to get up-to-the-minute rates.
exchange rate
The price of one country’s
currency expressed in
terms of another country’s
currency.
International
currency symbols
TABLE 18.1 Country Currency Symbol
Australia Dollar A$
Brazil Real R$
Canada Dollar Can$
China Yuan (Renminbi) π̄̄
Denmark Kroner DKr
EMU (Eurozone) Euro €
India Rupee Rs
Iran Rial RI
Japan Yen ¥
Kuwait Dinar KD
Mexico Peso Ps
New Zealand Dollar NZ$
Norway Kroner NKr
Saudi Arabia Riyal SR
Singapore Dollar S$
South Africa Rand R
South Korea Won ₩
Sweden Krona SKr
Switzerland Franc SF
Thailand Baht B|
Turkey Lira
United Kingdom Pound £
United States Dollar $
You just returned from your dream vacation to Jamaica and feel rich because you have 10,000 Jamaican dollars left over. You now need to convert this to U.S. dollars. How much
will you have? You can look up the current exchange rate and do the conversion yourself, or
work the web. We went to www.xe.com and used the currency converter on the site. This is is
what we found:
W R K T H E W E B
Looks like you left Jamaica just before you ran out of money.
Source: xe.com
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C H A P T E R 1 8 International Aspects of Financial Management 593
Exchange rates: July 9, 2018TABLE 18.2
Country/Currency USD equiv
Currency
per USD
Americas
Argentina peso .0358 27.9173
Brazil real .2582 3.8730
Canada dollar .7628 1.3110
Chile peso .001537 605.6000
Ecuador US dollar 1 1
Mexico peso .0521 19.2036
Uruguay peso .031870 31.380
Venezuela bolivar .00000871 114,855.0001
Asia-Pacific
Australia dollar .7467 1.3392
1-mo forward .7464 1.3397
3-mos forward .7464 1.3397
6-mos forward .7469 1.3389
China yuan .1511 6.6161
Hong Kong dollar .1274 7.8485
India rupee .01457 68.6567
Indonesia rupiah .0000699 14308
Japan yen .00902 110.84
1-mo forward .00900 111.06
3-mos forward .00904 110.58
6-mos forward .00911 109.73
Malaysia ringgit .2482 4.0295
New Zealand dollar .6838 1.4624
Pakistan rupee .00821 121.740
Philippines peso .0187 53.393
Singapore dollar .7371 1.3566
South Korea won .0008982 1,113.32
Taiwan dollar .03298 30.320
Thailand baht .03025 33.060
Vietnam dong .0000434 23040
Country/Currency USD equiv
Currency
per USD
Europe
Czech Rep. koruna .04545 22
Denmark krone .1577 6.3431
Euro area euro 1.1733 .8523
Hungary forint .00363135 275.38
Norway krone .1246 8.0244
Poland zloty .2725 3.6701
Romania leu .2522 3.9653
Russia ruble .01602 62.414
Sweden krona .1146 8.7241
Switzerland franc 1.0086 .9915
1-mo forward 1.0104 .9897
3-mos forward 1.0156 .9846
6-mos forward 1.0249 .9757
Turkey lira .2112 4.7342
UK pound 1.3258 .7543
1-mo forward 1.3284 .7528
3-mos forward 1.3319 .7508
6-mos forward 1.3380 .7474
Middle East/Africa
Bahrain dinar 2.6345 .3796
Egypt pound .0558 17.918
Israel shekel .2754 3.6306
Kuwait dinar 3.3049 .3026
Oman sul rial 2.59703 .3900
Qatar rial .2743 3.6453
Saudi Arabia riyal .2666 3.7506
South Africa rand .0746 13.4128
Exchange Rate Quotations Table 18.2 reproduces exchange rate quotations from
www.wsj.com and www.hsbcnet.com. The first column (labeled “USD equiv”) gives the
number of dollars it takes to buy one unit of foreign currency. For example, the Australian
dollar is quoted at .7467, which means that you can buy one Australian dollar with .7467
U.S. dollar.
The second column shows the amount of foreign currency per U.S. dollar. The Austra-
lian dollar is quoted here at 1.3392, so you can get 1.3392 Australian dollars for one U.S.
dollar. Naturally, this second exchange rate is just the reciprocal of the first one; 1/1.3392 =
.7467, allowing for a possible rounding error.
Cross-Rates and Triangle Arbitrage Using the U.S. dollar as the common de-
nominator in quoting exchange rates greatly reduces the number of necessary cross-
currency quotes. For example, with five major currencies, there would potentially be 10 ex-
change rates instead of 4. Also, the fact that the dollar is used throughout cuts down on in-
consistencies in the exchange rate quotations.
Get up-to-the-minute
exchange rates at www
.xe.com and www
.exchangerate.com.
Current and historical
foreign exchange data
are available at many
websites. A particularly
good site is maintained
by the Federal Reserve
Bank of St. Louis. Go to
www.stlouisfed.org and
find their “FRED®” link
for up-to-date exchange
rate data.
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594 P A R T 9 Topics in Business Finance
Earlier, we defined the cross-rate as the exchange rate for a non-U.S. currency expressed
in terms of another non-U.S. currency. Suppose we observed the following for the Mexican
peso (Ps) and the Swiss franc (SF):
Ps per $1 = 10.00
SF per $1 = 2.00
Suppose the cross-rate is quoted as:
Ps per SF = 4.00
What do you think?
The cross-rate here is inconsistent with the exchange rates. To see this, suppose you
have $100. If you convert this to Swiss francs, you will receive:
$100 × SF 2 per $1 = SF 200
If you convert this to pesos at the cross-rate, you will have:
SF 200 × Ps 4 per SF 1 = Ps 800
However, if you convert your dollars to pesos without going through francs, you will have:
$100 × Ps 10 per $1 = Ps 1,000
What we see is that the peso has two prices, Ps 10 per $1 and Ps 8 per $1, depending on
how we get the pesos.
To make money, we want to buy low, sell high. The important thing to note is that pesos
are cheaper if you buy them with dollars because you get 10 pesos instead of 8. You should
proceed as follows:
1. Buy 1,000 pesos for $100.
2. Use the 1,000 pesos to buy Swiss francs at the cross-rate. Because it takes four pesos
to buy a franc, you will receive Ps 1,000/4 = SF 250.
3. Use the SF 250 to buy dollars. Because the exchange rate is SF 2 per dollar, you
receive SF 250/2 = $125, for a round-trip profit of $25.
4. Repeat Steps 1 through 3.
This particular activity is called triangle arbitrage because the arbitrage involves moving
through three different exchange rates:
Ps 10/$1
SF 2/$1 = $.50/SF 1 Ps 4/SF 1 = SF .25/Ps 1
For international news
and events, visit www
.ft.com.
EXAMPLE 18.1 A Yen for Euros
Suppose you have $1,000. Based on the rates in Table 18.2, how many Japanese yen can you get?
Alternatively, if a Porsche costs €200,000 (€ is the symbol for the euro), how many dollars will you
need to buy it?
The exchange rate in terms of yen per dollar is 110.84. Your $1,000 will thus get you:
$1,000 × 110.84 yen per $1 = 110,840 yen
Because the exchange rate in terms of dollars per euro is 1.1733, you will need:
€200,000 × 1.1733 $ per euro = $234,660
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C H A P T E R 1 8 International Aspects of Financial Management 595
To prevent such opportunities, it is not difficult to see that because a dollar will buy you
either 10 pesos or two francs, the cross-rate must be:
(Ps 10/$1()(/(SF 2 / $1() = Ps 5 / SF 1
That is, five pesos per franc. If it were anything else, there would be a triangle arbitrage
opportunity.
EXAMPLE 18.2 Shedding Some Pounds
Suppose the exchange rates for the British pound and Swiss franc are:
Pounds per $1 = .60
SF per $1 = 2.00
The cross-rate is three francs per pound. Is this consistent? Explain how to go about making some
money.
The cross-rate should be SF 2.00/£.60 = SF 3.33 per pound. You can buy a pound for SF 3
in one market, and you can sell a pound for SF 3.33 in another. So, we want to first get some
francs, then use the francs to buy some pounds, and then sell the pounds. Assuming you had
$100, you could:
1. Exchange dollars for francs: $100 × 2 = SF 200.
2. Exchange francs for pounds: SF 200/3 = £66.67.
3. Exchange pounds for dollars: £66.67/.60 = $111.11.
This would result in an $11.11 round-trip profit.
Types of Transactions
There are two basic types of trades in the foreign exchange market: spot and forward. A
spot trade is an agreement to exchange currency “on the spot,” which actually means that
the transaction will be completed, or settled, within two business days. The exchange rate on
a spot trade is called the spot exchange rate. Implicitly, all of the exchange rates and trans-
actions we have discussed so far have referred to the spot market.
A forward trade is an agreement to exchange currency at some time in the future. The
exchange rate that will be used is agreed upon today and is called the forward exchange rate.
A forward trade will normally be settled sometime in the next 12 months.
If you look back at Table 18.2, you will see forward exchange rates quoted for some of
the major currencies. For example, the spot exchange rate for the Swiss franc is SF 1 =
$1.0086. The six-month forward exchange rate is SF 1 = $1.0249. This means that you can
buy a Swiss franc today for $1.0086, or you can agree to take delivery of a Swiss franc in six
months and pay $1.0249 at that time.
Notice that the Swiss franc is more expensive in the forward market ($1.0249 versus
$1.0086). Because the Swiss franc is more expensive in the future than it is today, it is said
to be selling at a premium relative to the dollar. For the same reason, the dollar is said to be
selling at a discount relative to the Swiss franc.
Why does the forward market exist? One answer is that it allows businesses and individ-
uals to lock in a future exchange rate today, thereby eliminating any risk from unfavorable
shifts in the exchange rate.
spot trade
An agreement to trade
currencies based on the
exchange rate today for
settlement within two
business days.
spot exchange rate
The exchange rate on a
spot trade.
forward trade
Agreement to exchange
currency at some time in
the future.
forward exchange
rate
The agreed-upon
exchange rate to be used
in a forward trade.
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596 P A R T 9 Topics in Business Finance
As we mentioned earlier, it is standard practice around the world (with a few excep-
tions, including the euro) to quote exchange rates in terms of the U.S. dollar. This means
that rates are quoted as the amount of currency per U.S. dollar. For the remainder of this
chapter, we will stick with this form. Things can get extremely confusing if you forget this.
Thus, when we say things like “the exchange rate is expected to rise,” it is important to
remember that we are talking about the exchange rate quoted as units of foreign currency
per U.S. dollar.
CONCEPT QUESTIONS
18.2a What is triangle arbitrage?
18.2b What do we mean by the three-month forward exchange rate?
18.2c If we say that the exchange rate is SF 1.12, what do we mean?
PURCHASING POWER PARITY
Now that we have discussed what exchange rate quotations mean, we can address an obvi-
ous question: What determines the level of the spot exchange rate? In addition, we know
that exchange rates change through time. A related question is thus: What determines the
rate of change in exchange rates? At least part of the answer in both cases goes by the name
of purchasing power parity (PPP), and it is the idea that the exchange rate adjusts to keep
purchasing power constant among currencies. As we discuss next, there are two forms of
PPP: absolute and relative.
Absolute Purchasing Power Parity
The basic idea behind absolute purchasing power parity is that a commodity costs the
same regardless of what currency is used to purchase it or where it is selling. This is a
very straightforward concept. If a beer costs £2 in London, and the exchange rate is
£.60 per dollar, then a beer costs £2/.60 = $3.33 in New York. In other words, abso-
lute PPP says that $1 will buy you the same number of, say, cheeseburgers anywhere in
the world.
More formally, let S0 be the spot exchange rate between the British pound and the U.S.
dollar today (Time 0), and remember that we are quoting exchange rates as the amount of
18.3
purchasing power
parity (PPP)
The idea that the
exchange rate adjusts to
keep purchasing power
constant among
currencies.
EXAMPLE 18.3 Looking Forward
Suppose you are expecting to receive 100 million Japanese yen in one month, and you agree to a
forward trade to exchange your yen for dollars. Based on Table 18.2, how many dollars will you get
in six months? Is the yen selling at a discount or a premium relative to the dollar?
In Table 18.2, the spot exchange rate and the one-month forward rate in terms of dollars per
yen are $.00902 = ¥1 and $.00900 = ¥1, respectively. If you expect ¥100 million in six months,
then you will get ¥100 million × $.00900 per ¥ = $900,000. Because it is less expensive to buy
yen in the forward market than in the spot market ($.00902 versus $.00900), the yen is selling at a
discount relative to the dollar.
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C H A P T E R 1 8 International Aspects of Financial Management 597
foreign currency per dollar. Let PUS and PUK be the current U.S. and British prices, respec-
tively, on a particular commodity, say, apples. Absolute PPP says that:
PUK = S0 × PUS
This tells us that the British price for something is equal to the U.S. price for that same
something, multiplied by the exchange rate.
The rationale behind PPP is similar to that behind triangle arbitrage. If PPP did not
hold, arbitrage would be possible (in principle) if apples were moved from one country to
another. For example, suppose apples in New York are selling for $4 per bushel, while in
London the price is £2.40 per bushel. Absolute PPP implies that:
PUK = S0 × PUS
£2.40 = S0 × $4
S0 = £2.40/$4 = $.60
That is, the implied spot exchange rate is £.60 per dollar. Equivalently, a pound is worth
$1/£.60 = $1.67.
Suppose, instead, that the actual exchange rate is £.50. Starting with $4, a trader could
buy a bushel of apples in New York, ship it to London, and sell it there for £2.40. Our trader
could then convert the £2.40 into dollars at the prevailing exchange rate, S0 = £.50, yielding
a total of £2.40/.50 = $4.80. The round-trip gain is 80 cents.
Because of this profit potential, forces are set in motion to change the exchange
rate and/or the price of apples. In our example, apples would begin moving from New
York to London. The reduced supply of apples in New York would raise the price of
apples there, and the increased supply in Britain would lower the price of apples in
London.
In addition to moving apples around, apple traders would be busily converting pounds
back into dollars to buy more apples. This activity increases the supply of pounds and simul-
taneously increases the demand for dollars. We would expect the value of a pound to fall.
This means that the dollar is getting more valuable, so it will take more pounds to buy one
dollar. Because the exchange rate is quoted as pounds per dollar, we would expect the ex-
change rate to rise from £.50.
For absolute PPP to hold absolutely, several things must be true:
1. The transaction costs of trading apples—shipping, insurance, spoilage, and so on—
must be zero.
2. There must be no barriers to trading apples, such as tariffs, taxes, or other political
barriers such as VRAs (voluntary restraint agreements).
3. Finally, an apple in New York must be identical to an apple in London. It won’t do for
you to send red apples to London if the English eat only green apples.
Given the fact that the transaction costs are not zero and that the other conditions are rarely
exactly met, it is not surprising that absolute PPP is really applicable only to traded goods,
and then only to very uniform ones.
For this reason, absolute PPP does not imply that a Mercedes costs the same as a Ford
or that a nuclear power plant in France costs the same as one in New York. In the case of
the cars, they are not identical. In the case of the power plants, even if they were identical,
they are expensive and very difficult to ship. On the other hand, we would be very surprised
to see a significant violation of absolute PPP for gold. See our nearby Finance Matters box
for an interesting example of PPP violations.
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Relative Purchasing Power Parity
As a practical matter, a relative version of purchasing power parity has evolved.
Relative purchasing power parity does not tell us what determines the absolute level
of the exchange rate. Instead, it tells what determines the change in the exchange rate
over time.
The Basic Idea Suppose the British pound-U.S. dollar exchange rate is currently S0 =
£.50. Further suppose that the inflation rate in Britain is predicted to be 10 percent over the
coming year and (for the moment) the inflation rate in the United States is predicted to be
zero. What do you think the exchange rate will be in a year?
If you think about it, a dollar currently costs .50 pound in Britain. With 10 percent
inflation, we expect prices in Britain to generally rise by 10 percent. So we expect that
the price of a dollar will go up by 10 percent, and the exchange rate should rise to
£.50 × 1.1 = £.55.
If the inflation rate in the United States is not zero, then we need to worry about the
relative inflation rates in the two countries. Suppose the U.S. inflation rate is predicted to be
4 percent. Relative to prices in the United States, prices in Britain are rising at a rate of 10%
− 4% = 6% per year. So we expect the price of the dollar to rise by 6 percent, and the pre-
dicted exchange rate is £.50 × 1.06 = £.53.
McPricing
As we discussed in the chapter, absolute purchasing power parity (PPP) does not seem to hold in practice.
One of the more famous violations of absolute PPP is the Big
Mac Index constructed by The Economist. To construct the
index, prices for a Big Mac in different countries are gath-
ered from McDonald’s. We went to www.economist.com to
find the January 2018 Big Mac index (we will leave it to you
to find the most recent index).
According to the index on that day, absolute PPP does
not seem to hold, at least for the Big Mac. In fact, in only 6 of
the 42 currencies surveyed by The Economist is the ex-
change rate within 10 percent of that predicted by absolute
PPP. The largest disparity was in Ukraine, where the cur-
rency was apparently undervalued by 69 percent. And 14 of
the 42 currencies were “incorrectly” priced by more than 40
percent. Why?
There are several reasons. First, a Big Mac is not really
transportable. Yes, you can load a ship with Big Macs and
send it to a country where the currency is supposedly over-
valued. But do you really think people would buy your Big
Macs? Probably not. Even though it is relatively easy to
transport a Big Mac, it would be relatively expensive, and
the hamburger would suffer in quality along the way.
Also, if you look in the index, the price of the Big Mac in
the United States is the average price from five cities. The
reason is that the Big Mac does not sell for the same price in
different parts of the United States, where presumably they
are all purchased with the dollar. The cost of living and com-
petition are only a few of the factors that will affect the price
of a Big Mac in the United States. If Big Macs are not priced
the same in the same currency, would we expect absolute
PPP to hold across currencies?
Finally, differing tastes can account for the apparent
discrepancy. In the United States, hamburgers and fast food
have become a staple of the American diet. In other coun-
tries, hamburgers have not become as entrenched. We
would expect the price of the Big Mac to be lower in the
United States because there is more fast-food competition.
In fact, when calculating PPP for the Indian rupee/U.S. dollar,
the price of the Maharaja Mac, which is made with chicken,
is used because beef is not sold at McDonald’s in India.
Having examined the Big Mac prices, we should say
that absolute PPP should hold more closely for more easily
transportable items. For instance, there are many companies
with stock listed on both the NYSE and the stock exchange
of another country. If you examine the share prices on the
two exchanges, you will find that the price of the stock is al-
most exactly what absolute PPP would predict. The reason is
that a share of stock in a particular company is (usually) the
same wherever you buy it and whatever currency is used.
FINANCE MATTERS
598
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C H A P T E R 1 8 International Aspects of Financial Management 599
The Result In general, relative PPP says that the change in the exchange rate is deter-
mined by the difference in the inflation rates of the two countries. To be more specific, we
will use the following notation:
S0 = Current (Time 0) spot exchange rate (foreign currency per dollar)
E(St) = Expected exchange rate in t periods
hUS = Inflation rate in the United States
hFC = Foreign country inflation rate
Based on our preceding discussion, relative PPP says that the expected percentage change in
the exchange rate over the next year, [E(S1) − S0]/S0, is:
[E(S1) − S0]/S0 = hFC − hUS [18.1]
In words, relative PPP says that the expected percentage change in the exchange rate is
equal to the difference in inflation rates. If we rearrange this slightly, we get:
E(S1) = S0[1 + (hFC − hUS)] [18.2]
This result makes a certain amount of sense, but care must be used in quoting the exchange
rate.
In our example involving Britain and the United States, relative PPP tells us that the
exchange rate will rise by hFC − hUS = 10% − 4% = 6% per year. Assuming that the differ-
ence in inflation rates doesn’t change, the expected exchange rate in two years, E(S2), there-
fore will be:
E(S2) = E(S1) × (1 + .06)
= .53 × 1.06
= .562
Notice that we could have written this as:
E(S2) = .53 × 1.06
= (.50 × 1.06) × 1.06
= .50 × 1.062
In general, relative PPP says that the expected exchange rate at some time in the future,
E(St), is:
E(St) = S0 × [1 + (hFC − hUS)]
t [18.3]
Because we don’t really expect absolute PPP to hold for most goods, we will focus on
relative PPP in any future discussion. Henceforth, when we refer to PPP without further
qualification, we mean relative PPP.
EXAMPLE 18.4 It’s All Relative
Suppose the Japanese exchange rate is currently 105 yen per dollar. The inflation rate in Japan
over the next three years will run, say, 2 percent per year, while the U.S. inflation rate will be 6 per-
cent. Based on relative PPP, what will the exchange rate be in three years?
Because the U.S. inflation rate is higher, we expect that a dollar will become less valuable. The
exchange rate change will be 2% – 6% = –4% per year. Over three years, the exchange rate will fall
to:
E(S3) = S0 × [1 + (hFC − hUS)]
3
= 105 × [1 + (−.04)]3
= 92.90 yen per dollar
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Currency Appreciation and Depreciation We frequently hear things like “the
dollar strengthened (or weakened) in financial markets today” or “the dollar is expected to
appreciate (or depreciate) relative to the pound.” When we say that the dollar strengthens,
or appreciates, we mean that the value of a dollar rises, so it takes more foreign currency to
buy a dollar.
What happens to exchange rates as currencies fluctuate in value depends on how ex-
change rates are quoted. Because we are quoting them as units of foreign currency per dol-
lar, the exchange rate moves in the same direction as the value of the dollar: It rises as the
dollar strengthens, and it falls as the dollar weakens.
Relative PPP tells us that the exchange rate will rise if the U.S. inflation rate is lower
than the foreign country’s. This happens because the foreign currency depreciates in value
and therefore weakens relative to the dollar.
CONCEPT QUESTIONS
18.3a What does absolute PPP say? Why might it not hold for many types of goods?
18.3b According to relative PPP, what determines the change in exchange rates?
EXCHANGE RATES AND INTEREST RATES
The next issue we need to address is the relationship between spot exchange rates, forward
exchange rates, and nominal interest rates. To get started, we need some additional
notation:
Ft = Forward exchange rate for settlement at Time t
RUS = U.S. nominal risk-free interest rate
RFC = Foreign country nominal risk-free interest rate
As before, we will use S0 to stand for the spot exchange rate. You can take the U.S. nominal
risk-free rate, RUS, to be the T-bill rate.
Covered Interest Arbitrage
Suppose we observe the following information about U.S. and Swiss currency in the
market:
S0 = SF 2.00 RUS = 10%
F1 = SF 1.90 RS = 5%
where RS is the nominal risk-free rate in Switzerland. The period is one year, so F1 is the 360-
day forward rate.
Do you see an arbitrage opportunity here? There is one. Suppose you have $1 to invest,
and you want a riskless investment. One option you have is to invest the $1 in a riskless U.S.
investment such as a 360-day T-bill. We will call this Strategy 1. If you do this, then, in one
period, your $1 will be worth:
$ value in 1 period = $1(1 + RUS)
= $1.10
Alternatively, you can invest in the Swiss risk-free investment. To do this, you need to
convert your $1 to francs and simultaneously execute a forward trade to convert francs
18.4
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C H A P T E R 1 8 International Aspects of Financial Management 601
back to dollars in one year. We will call this Strategy 2. The necessary steps would be
as follows:
1. Convert your $1 to $1 × S0 = SF 2.00.
2. At the same time, enter into a forward agreement to convert francs back to dollars in
one year. Because the forward rate is SF 1.90, you get $1 for every SF 1.90 that you
have in one year.
3. Invest your SF 2.00 in Switzerland at RS. In one year, you will have:
SF value in 1 year = SF 2.00 × (1 + RS)
= SF 2.00 × 1.05
= SF 2.10
4. Convert your SF 2.10 back to dollars at the agreed-upon rate of SF 1.90 = $1. You
end up with:
$ value in 1 year = SF 2.10/1.90
= $1.1053
Notice that the value in one year from this strategy can be written as:
$ value in 1 year = $1 × S0 × (1 + RS)/F1
= $1 × 2.00 × 1.05/1.90
= $1.1053
The return on this investment is apparently 10.53 percent. This is higher than the 10 percent
we get from investing in the United States. Because both investments are risk-free, there is
an arbitrage opportunity.
To exploit the difference in interest rates, you need to borrow, say, $5 million at the
lower U.S. rate and invest it at the higher Swiss rate. What is the round-trip profit from do-
ing this? To find out, we can work through the preceding steps:
1. Convert the $5 million at SF 2.00 = $1 to get SF 10 million.
2. Agree to exchange francs for dollars in one year at SF 1.90 to the dollar.
3. Invest the SF 10 million for one year at RS = 5%. You end up with SF 10.5 million.
4. Convert the SF 10.5 million back to dollars to fulfill the forward contract. You receive
SF 10.5 million/1.90 = $5,526,316.
5. Repay the loan with interest. You owe $5 million plus 10 percent interest, for a total of
$5.5 million. You have $5,526,316, so your round-trip profit is a risk-free $26,316.
The activity that we have illustrated here goes by the name of covered interest arbitrage.
The term covered refers to the fact that we are covered in the event of a change in the
exchange rate because we lock in the forward exchange rate today.
Interest Rate Parity
If we assume that significant covered interest arbitrage opportunities do not exist, then there
must be some relationship between spot exchange rates, forward exchange rates, and relative
interest rates. To see what this relationship is, note that, in general, Strategy 1, investing in a
riskless U.S. investment, gives us (1 + RUS) for every dollar we invest. Strategy 2, investing
in a foreign risk-free investment, gives us S0 × (1 + RFC)/F1 for every dollar we invest. Be-
cause these have to be equal to prevent arbitrage, it must be the case that:
1 + RUS = S0 × (1 + RFC)/F1
For exchange rates and
even pictures of non-U.S.
currencies, see www
.travlang.com/money.
How are the international
markets doing? Find out
at marketwatch.com.
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602 P A R T 9 Topics in Business Finance
Rearranging this a bit gets us the famous interest rate parity (IRP) condition:
F1/S0 = (1 + RFC)/(1 + RUS) [18.4]
There is a very useful approximation for IRP that illustrates very clearly what is going
on and is not difficult to remember. If we define the percentage forward premium or dis-
count as (F1 − S0)/S0, then IRP says that this percentage premium or discount is approxi-
mately equal to the difference in interest rates:
(F1 − S0)/S0 = RFC − RUS [18.5]
Very loosely, what IRP says is that any difference in interest rates between two coun-
tries for some period is offset by the change in the relative value of the currencies, thereby
eliminating any arbitrage possibilities. Notice that we also could write:
F1 = S0 × [1 + (RFC − RUS)] [18.6]
In general, if we have t periods instead of one, the IRP approximation will be written as:
Ft = S0 × [1 + (RFC − RUS)]
t [18.7]
interest rate parity
(IRP)
The condition stating that
the interest rate
differential between two
countries is equal to the
percentage difference
between the forward
exchange rate and the
spot exchange rate.
CONCEPT QUESTIONS
18.4a What is interest rate parity?
18.4b Do you expect that interest rate parity will hold more closely than purchasing power
parity? Why?
EXCHANGE RATE RISK
Exchange rate risk is the natural consequence of international operations in a world where
relative currency values move up and down. As we discuss next, there are three different
types of exchange rate risk, or exposure: short-run exposure, long-run exposure, and transla-
tion exposure.
Short-Run Exposure
The day-to-day fluctuations in exchange rates create short-run risks for international firms.
Most such firms have contractual agreements to buy and sell goods in the near future at
18.5
exchange rate risk
The risk related to having
international operations in
a world where relative
currency values vary.
EXAMPLE 18.5 Parity Check
Suppose the exchange rate for Japanese yen, S0, is currently ¥120 = $1. If the interest rate in the
United States is RUS = 10% and the interest rate in Japan is RJ = 5%, then what must the one-year
forward rate be to prevent covered interest arbitrage?
F1 = S0 × [1 + (RJ − RUS)]
= ¥120 × [1 + (.05 − .10)]
= ¥120 × .95
= ¥114
Notice that the yen will sell at a premium relative to the dollar (why?).
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C H A P T E R 1 8 International Aspects of Financial Management 603
set prices. When different currencies are involved, such transactions have an extra element
of risk.
Imagine that you are importing imitation pasta from Italy and reselling it in the United
States under the Impasta brand name. Your largest customer has ordered 10,000 cases of
Impasta. You place the order with your supplier today, but you won’t pay until the goods
arrive in 60 days. Your selling price is $6 per case. Your cost is €4.48 per case, and the ex-
change rate is currently €.80, so it takes €.80 to buy $1.
At the current exchange rate, your cost in dollars from filling the order is €4.48/€.80 =
$5.60 per case, so your pretax profit on the order is 10,000 × ($6 − 5.60) = $4,000. How-
ever, the exchange rate in 60 days probably will be different, so your profit will depend on
what the exchange rate in the future turns out to be.
For example, if the rate goes to €.85, your cost is €4.48/€.85 = $5.27 per case. Your
profit goes to $7,294. If the exchange rate goes to, say, €.747, then your cost is €4.48/€.747 =
$6 per case, and your profit is zero.
The short-run exposure in our example can be reduced or eliminated in several
ways. The most obvious way is to enter into a forward exchange agreement to lock in
an exchange rate. Suppose the 60-day forward rate is €.82. What will your profit be if
you hedge?
If you hedge, you lock in an exchange rate of €.82. Your cost in dollars thus will be
€4.48/€.82 = $5.46 per case, so your profit will be 10,000 × ($6 − 5.46) = $5,366.
Long-Run Exposure
In the long run, the value of a foreign operation can fluctuate because of unanticipated
changes in relative economic conditions. Imagine that we own a labor-intensive assembly
operation located in another country to take advantage of lower wages. Through time, unex-
pected changes in economic conditions can raise the foreign wage levels to the point where
the cost advantage is eliminated or even becomes negative.
Hedging long-run exposure is more difficult than hedging short-term risks. For one
thing, organized forward markets don’t exist for such long-term needs. Instead, the primary
option that firms have is to try to match up foreign currency inflows and outflows. The
same thing goes for matching foreign currency-denominated assets and liabilities. For exam-
ple, a firm that sells in a foreign country might try to concentrate its raw material purchases
and labor expense in that country. That way, the dollar values of its revenues and costs will
move up and down together.
Similarly, a firm can reduce its long-run exchange rate risk by borrowing in the foreign
country. Fluctuations in the value of the foreign subsidiary’s assets then will be at least par-
tially offset by changes in the value of its liabilities.
One of the more common methods used to reduce long-term exchange rate expo-
sure is to build a plant in the country that imports the products. This method of-
ten is used in the automotive industry. Honda, Toyota, and BMW, to name a few, have
built plants in the United States. BMW’s situation is particularly interesting. It pro-
duces about 400,000 cars per year in South Carolina and exports about 280,000 of
them. The costs of manufacturing the cars are mostly paid in dollars, and when BMW
exports the cars to Europe, it receives euros. So, when the dollar weakens, these vehi-
cles become more profitable for BMW. At the same time, BMW imports about 200,000
more cars to the United States each year. The costs of manufacturing these imported
cars are mostly in euros, so they become less profitable when the dollar weakens. Taken
together, these gains and losses tend to offset each other and provide BMW with a nat-
ural hedge.
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Translation Exposure
When a U.S. company calculates its accounting net income and EPS for some period, it
must “translate” everything into dollars. This can create some problems for the accountants
when there are significant foreign operations. In particular, two issues arise:
1. What is the appropriate exchange rate to use for translating each balance sheet
account?
2. How should balance sheet accounting gains and losses from foreign currency
translation be handled?
To illustrate the accounting problem, suppose that we started a small foreign subsidiary
in Lilliputia a year ago. The local currency is the gulliver, abbreviated GL. At the beginning
of the year, the exchange rate was GL 2 = $1, and the balance sheet in gullivers looked
like this:
Assets GL 1,000 Liabilities GL 500
Equity 500
At two gullivers to the dollar, the beginning balance sheet in dollars was:
Assets $500 Liabilities $250
Equity 250
Lilliputia is a quiet place, and nothing at all actually happened during the year. As a result,
net income was zero (before consideration of exchange rate changes). However, the ex-
change rate did change to 4 gullivers = $1, perhaps because the Lilliputian inflation rate is
much higher than the U.S. inflation rate.
Because nothing happened, the accounting ending balance sheet in gullivers is the
same as the beginning one. However, if we convert it to dollars at the new exchange rate,
we get:
Assets $250 Liabilities $125
Equity 125
Notice that the value of the equity has gone down by $125, even though net income was
exactly zero. Despite the fact that absolutely nothing really happened, there is a $125
accounting loss. How to handle this $125 loss has been a controversial accounting
question.
One obvious and consistent way to handle this loss is to report the loss on the par-
ent’s income statement. During periods of volatile exchange rates, this kind of treatment
can dramatically impact an international company’s reported EPS. This is purely an ac-
counting phenomenon, but, even so, such fluctuations are disliked by some financial
managers.
The current approach to translation gains and losses is based on rules set out in Fi-
nancial Accounting Standards Board (FASB) Statement Number 52, issued in December
1981. For the most part, FASB 52 requires that all assets and liabilities be translated
from the subsidiary’s currency into the parent’s currency using the exchange rate that
currently prevails.
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C H A P T E R 1 8 International Aspects of Financial Management 605
Any translation gains and losses that occur are accumulated in a special account within
the shareholders’ equity section of the balance sheet. This account might be labeled some-
thing like “unrealized foreign exchange gains (losses).” These gains and losses are not re-
ported on the income statement. As a result, the impact of translation gains and losses will
not be recognized explicitly in net income until the underlying assets and liabilities are sold
or otherwise liquidated.
Managing Exchange Rate Risk
For a large multinational firm, the management of exchange rate risk is complicated by the
fact that there can be many different currencies involved for many different subsidiaries. It
is very likely that a change in some exchange rate will benefit some subsidiaries and hurt
others. The net effect on the overall firm depends on its net exposure.
Suppose a firm has two divisions. Division A buys goods in the United States for
dollars and sells them in Britain for pounds. Division B buys goods in Britain for pounds
and sells them in the United States for dollars. If these two divisions are of roughly equal
size in terms of their inflows and outflows, then the overall firm obviously has little
exchange rate risk.
In our example, the firm’s net position in pounds (the amount coming in less the
amount going out) is small, so the exchange rate risk is small. However, if one division,
acting on its own, were to start hedging its exchange rate risk, then the overall firm’s
exchange rate risk would go up. The moral of the story is that multinational firms
have to be conscious of the overall position that the firm has in a foreign currency.
For this reason, management of exchange rate risk is probably best handled on a
centralized basis.
CONCEPT QUESTIONS
18.5a What are the different types of exchange rate risk?
18.5b How can a firm hedge short-run exchange rate risk? Long-run exchange rate risk?
POLITICAL RISK
One final element of risk in international investing is political risk. Political risk refers to
changes in value that arise as a consequence of political actions. For example, in June 2016,
British voters shocked the rest of Europe when they voted in favor of “Brexit,” the U.K. exit
from the European Union. Although the treaty that tied the U.K. to the rest of Europe re-
quired a two-year process to complete the withdrawal, financial markets didn’t take that long
to react. The British pound dropped 11 percent against the U.S. dollar on the day, and Lon-
don’s FTSE and Stoxx Europe 600 stock market indexes dropped about 8 percent. Preemi-
nent British banks Barclays and Lloyds Banking Group both were hit even harder, as they
saw stock price drops of more than 30 percent on the day. Unfortunately (or fortunately,
depending on your view), the drop in the British pound wasn’t finished. It continued to fall
against the U.S. dollar, reaching its lowest level since 1985. Political risk is not a problem
faced exclusively by international firms. As we discuss next, for example, changes in U.S. tax
18.6
political risk
Risk related to changes in
value that arise because
of political actions.
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606 P A R T 9 Topics in Business Finance
laws and regulations may benefit some U.S. firms and hurt others, so political risk exists
nationally as well as internationally.
The Tax Cuts and Jobs Act
In our chapter opener, we described the large cash balances held “overseas” by U.S. corpo-
rations. As we noted, the reason Apple and other large U.S. corporations held such large
balances overseas has to do with U.S. tax law. Tax laws are a form of political risk faced by
multinational firms.
Specifically, before the signing of the Tax Cuts and Jobs Act of 2017, the U.S. had cor-
porate tax rates that were among the highest in the developed world. At the same time, the
U.S. was somewhat unique in that it taxed corporate profits wherever they were earned, but
only after the profits were brought back, or “repatriated,” to the U.S. But what does this
mean, exactly?
To answer, let’s go back to Lilliputia, which has a 20 percent corporate tax rate, com-
pared to what would have been 35 percent in the U.S. If we earned a profit in our Lilliputian
subsidiary, that subsidiary would pay taxes to Lilliputia at the 20 percent rate. If we had left
the profits in Lilliputia, then no additional taxes were owed. But if we had brought the prof-
its back to the U.S., we would have owed additional taxes of 15 percent, the difference be-
tween the U.S. and Lilliputian tax rates. Avoiding this extra tax gave U.S. companies a
strong incentive not to repatriate profits.
Here is where it gets confusing. In the media, companies like Apple are depicted as
having huge piles of cash sitting outside the borders of the U.S., but that’s not what is really
going on. Apple’s cash is actually mostly in dollars, and it is mostly invested in various U.S.
financial assets. So, the money isn’t really “outside” the U.S.
Instead, because Apple has chosen not to pay the extra tax on its overseas profits, it is
prohibited from using that cash inside the U.S. to do things like pay dividends or build new
facilities. Note that Apple easily can get around this limitation by, for example, borrowing
against its cash and securities portfolio if it chooses to do so.
The Tax Cuts and Jobs Act of 2017 changed things in a number of ways. First, the new
flat 21 percent tax rate (down from a maximum of 35 percent) reduced the incentive to
leave cash overseas. Second, the law imposed a one-time tax of 15.5 percent on cash, securi-
ties, and receivables and a one-time tax of 8 percent on other, less-liquid assets purchased
with untaxed overseas dollars (e.g., plant, property, and equipment). Finally, broadly speak-
ing, repatriated earnings are no longer subject to additional U.S. taxes, thereby eliminating
the repatriation issue.
Managing Political Risk
Some countries do have more political risk than others, however. When firms have opera-
tions in these riskier countries, the extra political risk may lead them to require higher re-
turns on overseas investments to compensate for the risk that funds will be blocked, critical
operations interrupted, or contracts abrogated. In the most extreme case, the possibility of
outright confiscation may be a concern in countries with relatively unstable political
environments.
Political risk also depends on the nature of the business; some businesses are less likely
to be confiscated because they are not particularly valuable in the hands of a different
owner. An assembly operation supplying subcomponents that only the parent company uses
would not be an attractive “takeover” target, for example. Similarly, a manufacturing
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C H A P T E R 1 8 International Aspects of Financial Management 607
operation that requires the use of specialized components from the parent is of little value
without the parent company’s cooperation.
Natural resource developments, such as copper mining or oil drilling, are the opposite.
Once the operation is in place, much of the value is in the commodity. The political risk for
such investments is much higher for this reason. Also, the issue of exploitation is more pro-
nounced with such investments, again increasing the political risk.
Political risk can be hedged in several ways, particularly when confiscation or national-
ization is a concern. The use of local financing, perhaps from the government of the foreign
country in question, reduces the possible loss because the company can refuse to pay on the
debt in the event of unfavorable political activities. Based on our discussion above, structur-
ing the operation in such a way that it requires significant parent company involvement to
function is another way to reduce political risk.
CONCEPT QUESTIONS
18.6a What is political risk?
18.6b What are some ways of hedging political risk?
SUMMARY AND CONCLUSIONS
The international firm has a more complicated life than the purely domestic firm. Manage-
ment must understand the connection between interest rates, foreign currency exchange
rates, and inflation, and it must become aware of a large number of different financial mar-
ket regulations and tax systems. This chapter was intended to be a concise introduction to
some of the financial issues that come up in international investing.
Our coverage was necessarily brief. The main topics we discussed included:
1. Some basic vocabulary. We briefly defined some exotic terms such as LIBOR and
Eurocurrency.
2. The basic mechanics of exchange rate quotations. We discussed the spot and forward
markets and how exchange rates are interpreted.
3. The fundamental relationships between international financial variables:
a. Absolute and relative purchasing power parity, or PPP.
b. Interest rate parity, or IRP.
Absolute purchasing power parity states that $1 should have the same purchasing
power in each country. This means that an orange costs the same whether you buy it
in New York or in Tokyo.
Relative purchasing power parity means that the expected percentage change in
exchange rates between the currencies of two countries is equal to the difference in
their inflation rates.
Interest rate parity implies that the percentage difference between the
forward exchange rate and the spot exchange rate is equal to the interest rate
differential. We showed how covered interest arbitrage forces this relationship
to hold.
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CHAPTER REVIEW AND SELF-TEST PROBLEMS
POP QUIZ!
Can you answer the following questions? If your class is using Connect, log on to
SmartBook to see if you know the answers to these and other questions, check out
the study tools, and find out what topics require additional practice!
Section 18.1 A cross-rate between two currencies is usually quoted in what
currency?
Section 18.2 If $1 will buy Can$.99 and A$.95, how many Canadian dollars are
needed to buy one Australian dollar?
Section 18.3 What do you call the condition in which a commodity costs the same
regardless of the currency used or where it is purchased?
Section 18.4 Suppose the euro currently costs $1.37 and the nominal risk-free inter-
est rate in France is 3 percent while only 2 percent in the United States. What does
interest rate parity imply the forward rate for the euro will be?
Section 18.5 What are some strategies for hedging long-term exchange rate risk?
Section 18.6 Is a change in translation exposure a good example of political risk?
18.1 Relative Purchasing Power Parity The inflation rate in the United States is
projected at 6 percent per year for the next several years. The Australian inflation
rate is projected to be 2 percent during that time. The exchange rate is currently
A$2.2. Based on relative PPP, what is the expected exchange rate in two years? (See
Problem 12.)
18.2 Covered Interest Arbitrage The spot and 360-day forward rates on the Swiss franc
are SF 1.8 and SF 1.7, respectively. The risk-free interest rate in the United States is 8
percent, and the risk-free rate in Switzerland is 5 percent. Is there an arbitrage
opportunity here? How would you exploit it? (See Problem 7.)
■ Answers to Chapter Review and Self-Test Problems
18.1 From relative PPP, the expected exchange rate in two years, E(S2), is:
E(S2) = S0 × [1 + (hA − hUS)]
2
where hA is the Australian inflation rate. The current exchange rate is A$2.2, so the
expected exchange rate is:
E(S2) = A$ 2.2 × [1 + (.02 − .06)]
2
= A$ 2.2 × .962
= A$ 2.03
4. Exchange rate and political risk. We described the various types of exchange rate risk
and discussed some commonly used approaches to managing the effect of fluctuating
exchange rates on the cash flows and value of the international firm. We also
discussed political risk and some ways of managing exposure to it.
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C H A P T E R 1 8 International Aspects of Financial Management 609
18.2 From interest rate parity, the forward rate should be (approximately):
F1 = S0 × [1 + (RS − RUS)]
= 1.8 × [1 + .05 − .08]
= 1.75
Because the forward rate is actually SF 1.7, there is an arbitrage opportunity.
To exploit the arbitrage opportunity, we first note that dollars are selling for
SF 1.7 each in the forward market. From IRP, this is too cheap because they should
be selling for SF 1.75. So, we want to arrange to buy dollars with Swiss francs in the
forward market. To do this, we can:
1. Today: Borrow, say, $10 million for 360 days. Convert it to SF 18 million in the
spot market, and buy a forward contract at SF 1.7 to convert it back to dollars in
360 days. Invest the SF 18 million at 5 percent.
2. In one year: Your investment has grown to SF 18 × 1.05 = SF 18.9 million.
Convert this to dollars at the rate of SF 1.7 = $1. You will have SF
18.9 million/1.7 = $11,117,647. Pay off your loan with 8 percent interest
at a cost of $10 million × 1.08 = $10,800,000 and pocket the difference
of $317,647.
CRITICAL THINKING AND CONCEPTS REVIEW
LO 1 18.1 Spot and Forward Rates Suppose the exchange rate for the Swiss franc
is quoted as SF 1.10 in the spot market and SF 1.13 in the 90-day forward
market.
a. Is the dollar selling at a premium or a discount relative to the franc?
b. Does the financial market expect the franc to strengthen relative to the
dollar? Explain.
c. What do you suspect is true about relative economic conditions in the
United States and Switzerland?
LO 2 18.2 Purchasing Power Parity Suppose the rate of inflation in Russia will run
about 3 percent higher than the U.S. inflation rate over the next several
years. All other things being the same, what will happen to the ruble
versus dollar exchange rate? What relationship are you relying on in
answering?
LO 2 18.3 Exchange Rates The exchange rate for the Australian dollar is currently
A$1.40. This exchange rate is expected to rise by 10 percent over the next
year.
a. Is the Australian dollar expected to get stronger or weaker?
b. What do you think about the relative inflation rates in the United
States and Australia?
c. What do you think about the relative nominal interest rates in the
United States and Australia? Relative real rates?
LO 3 18.4 Yankee Bonds Which of the following most accurately describes a Yankee
bond?
a. A bond issued by General Motors in Japan with the interest payable in
U.S. dollars.
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b. A bond issued by General Motors in Japan with the interest payable
in yen.
c. A bond issued by Toyota in the United States with the interest payable
in yen.
d. A bond issued by Toyota in the United States with the interest payable
in dollars.
e. A bond issued by Toyota worldwide with the interest payable
in dollars.
LO 1 18.5 Exchange Rates Are exchange rate changes necessarily good or bad for a
particular company?
LO 4 18.6 International Risks At one point, Duracell International confirmed that it
was planning to open battery-manufacturing plants in China and India.
Manufacturing in these countries would allow Duracell to avoid import
duties of between 30 and 35 percent that have made alkaline batteries
prohibitively expensive for some consumers. What additional advantages
might Duracell see in this proposal? What are some of the risks to
Duracell?
LO 3 18.7 Multinational Corporations Given that many multinationals based in
many countries have much greater sales outside their domestic markets
than within them, what is the particular relevance of their domestic
currency?
LO 2 18.8 Exchange Rate Movements Are the following statements true or false?
Explain why.
a. If the general price index in Great Britain rises faster than that in the
United States, we would expect the pound to appreciate relative to
the dollar.
b. Suppose you are a German machine tool exporter and you invoice
all of your sales in foreign currency. Further suppose that the
European monetary authorities begin to undertake an expansionary
monetary policy. If it is certain that the easy money policy will result
in higher inflation rates in “Euroland” relative to those in other
countries, then you should use the forward markets to protect yourself
against future losses resulting from the deterioration in the value of
the euro.
c. If you could accurately estimate differences in the relative inflation
rates of two countries over a long period of time while other market
participants were unable to do so, you could successfully speculate in
spot currency markets.
LO 2 18.9 Exchange Rate Movements Some countries encourage movements in
their exchange rate relative to those of some other country as a short-term
means of addressing foreign trade imbalances. For each of the following
scenarios, evaluate the impact the announcement would have on an
American importer and an American exporter doing business with the
foreign country.
a. Officials in the administration of the U.S. government announce
that they are comfortable with a rising Mexican peso relative to
the dollar.
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C H A P T E R 1 8 International Aspects of Financial Management 611
b. British monetary authorities announce that they feel the pound has
been driven too low by currency speculators relative to the dollar.
c. The Brazilian government announces that it will print billions of new
reais and inject them into the economy in an effort to reduce the
country’s 40 percent unemployment rate.
LO 3 18.10 International Investment If financial markets are perfectly competitive
and the Eurodollar rate is above that offered in the U.S. loan market, you
would immediately want to borrow money in the United States and invest it
in Eurodollars. True or false? Explain.
QUESTIONS AND PROBLEMS
Select problems are available in McGraw-Hill Connect. Please see the pack-
aging options section of the Preface for more information.
BASIC (Questions 1–10)
1. Using Exchange Rates Take a look back at Table 18.2 to answer the
following questions:
a. If you have $100, how many Polish zlotys can you get?
b. How much is one euro worth?
c. If you have five million euros, how many dollars do you have?
d. Which is worth more, a New Zealand dollar or a Singapore dollar?
e. Which is worth more, a Mexican peso or a Chilean peso?
f. How many Swiss francs can you get for a euro? What do you call
this rate?
g. Per unit, what is the most valuable currency of those listed? The least
valuable?
2. Using the Cross-Rate Use the information in Table 18.2 to answer the
following questions:
a. Which would you rather have, $100 or £100? Why?
b. Which would you rather have, $100 Canadian or £100? Why?
c. What is the cross-rate for Canadian dollars in terms of British pounds?
For British pounds in terms of Canadian dollars?
3. Forward Exchange Rates Use the information in Table 18.2 to answer the
following questions:
a. What is the six-month forward rate for the Japanese yen in yen
per U.S. dollar? Is the yen selling at a premium or a discount?
Explain.
b. What is the three-month forward rate for the Australian dollar in U.S.
dollars per Australian dollar? Is the dollar selling at a premium or a
discount? Explain.
c. What do you think will happen to the value of the dollar relative to the
yen and the Australian dollar, based on the information in the table?
Explain.
LO 1
LO 1
LO 1
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4. Using Spot and Forward Exchange Rates Suppose the spot exchange
rate for the Canadian dollar is Can$1.12 and the six-month forward rate is
Can$1.17.
a. Which is worth more, a U.S. dollar or a Canadian dollar?
b. Assuming absolute PPP holds, what is the cost in the United States of
an Elkhead beer if the price in Canada is Can$2.49? Why might the beer
actually sell at a different price in the United States?
c. Is the U.S. dollar selling at a premium or a discount relative to the
Canadian dollar?
d. Which currency is expected to appreciate in value?
e. Which country do you think has higher interest rates—the United States
or Canada? Explain.
5. Cross-Rates and Arbitrage Suppose the Japanese yen exchange rate is ¥119
= $1 and the British pound exchange rate is £1 = $1.39.
a. What is the cross-rate in terms of yen per pound?
b. Suppose the cross-rate is ¥168 = £1. Is there an arbitrage opportunity
here? If there is, explain how to take advantage of the mispricing.
6. Interest Rate Parity Use Table 18.2 to answer the following questions.
Suppose interest rate parity holds, and the current risk-free rate in the United
States is 2.1 percent per six months. What must the six-month risk-free rate
be in Australia? In Japan? In Great Britain?
7. Interest Rates and Arbitrage The treasurer of a major U.S. firm has $30
million to invest for three months. The interest rate in the United States is
.24 percent per month. The interest rate in Great Britain is .31 percent per
month. The spot exchange rate is £.73, and the three-month forward rate is
£.75. Ignoring transaction costs, in which country would the treasurer want
to invest the company’s funds? Why?
8. Inflation and Exchange Rates Suppose the current exchange rate for the
Russian ruble is RUB 64.18. The expected exchange rate in three years is RUB
69.32. What is the difference in the annual inflation rates for the United States
and Russia over this period? Assume that the anticipated rate is constant for
both countries. What relationship are you relying on in answering?
9. Exchange Rate Risk Suppose your company imports computer
motherboards from Singapore. The exchange rate is given in Table 18.2.
You have just placed an order for 30,000 motherboards at a cost to you
of 185.50 Singapore dollars each. You will pay for the shipment when it
arrives in 90 days. You can sell the motherboards for $150 each. Calculate
your profit if the exchange rate goes up or down by 10 percent over the
next 90 days. What is the break-even exchange rate? What percentage
rise or fall does this represent in terms of the Singapore dollar versus the
U.S. dollar?
10. Exchange Rates and Arbitrage Suppose the spot and six-month forward
rates on the South Korean won are ₩1,118.33 and ₩1,120.87, respectively.
The annual risk-free rate in the United States is 2.5 percent, and the annual
risk-free rate in South Korea is 3.1 percent.
a. Is there an arbitrage opportunity here? If so, how would you exploit it?
b. What must the six-month forward rate be to prevent arbitrage?
LO 1
LO 1
LO 2
LO 2
LO 2
LO 3
LO 2
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C H A P T E R 1 8 International Aspects of Financial Management 613
INTERMEDIATE (Questions 11–15)
11. Spot versus Forward Rates Suppose the spot and three-month forward
rates for the yen are ¥108.46 and ¥107.13, respectively.
a. Is the yen expected to get stronger or weaker?
b. What would you estimate is the difference between the inflation rates of
the United States and Japan?
12. Expected Spot Rates Suppose the spot exchange rate for the Hungarian
forint is HUF 287. Interest rates in the United States are 2.7 percent per year.
They are 4.8 percent in Hungary.
a. What do you predict the exchange rate will be in one year?
b. In two years?
c. In five years? What relationship are you using?
13. Cross-Rates and Arbitrage The British pound trades at $1.3679 in London
and $1.3668 in New York. How much profit could you earn on each trade
with $10,000?
14. Purchasing Power Parity and Exchange Rates According to purchasing
power parity, if a Big Mac sells for $4.89 in the United States and króna
522.50 in Iceland, what is the króna/$ exchange rate?
15. Translation Exposure Betancourt International has operations in Arrakis.
The balance sheet for this division in Arrakeen solaris shows assets of 40,000
solaris, debt in the amount of 12,500 solaris, and equity of 27,500 solaris.
a. If the current exchange ratio is 1.35 solaris per dollar, what does the
balance sheet look like in dollars?
b. Assume that one year from now the balance sheet in solaris is exactly
the same as at the beginning of the year. If the exchange rate is 1.45
solaris per dollar, what does the balance sheet look like in dollars now?
c. Rework part (b) assuming the exchange rate is 1.26 solaris per dollar.
CHALLENGE (Question 16)
16. Translation Exposure In the previous problem, assume the equity increases
by 2,200 solaris due to retained earnings. If the exchange rate at the end of
the year is 1.29 solaris per dollar, what does the balance sheet look like?
LO 2
LO 2
LO 2
LO 2
LO 3
LO 3
WHAT’S ON
THE WEB?
18.1 Purchasing Power Parity As we discussed in the chapter, one of the more famous
examples of a violation of absolute purchasing power parity is the Big Mac index
calculated by The Economist. This index calculates the dollar price of a McDonald’s Big
Mac in different countries. You can find the Big Mac index by going to www.economist
.com. Using the most recent index, which country has the most expensive Big Macs?
Which country has the cheapest Big Macs? Why is the price of a Big Mac not the same
in every country?
18.2 Interest Rate Parity Go to the Financial Times site at www.ft.com, and find the
current exchange rate between the U.S. dollar and the euro. Next, find the U.S. dollar
LIBOR and the euro LIBOR interest rates. What must the one-year forward rate be to
prevent arbitrage? What principle are you relying on in your answer?
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EXCEL MASTER IT! PROBLEM
The Federal Reserve Bank of St. Louis has historical exchange rates on its website, www
.stlouisfed.org. Go to the website and look for the “FRED®” data. Then, download the ex-
change rate with the U.S. dollar over the past five years for the following currencies: Brazil-
ian real, Canadian dollar, Hong Kong dollar, Japanese yen, Mexican new peso, South
Korean won, Indian rupee, Swiss franc, Australian dollar, and euro. Graph the exchange
rate for each of these currencies in a dashboard that can be printed on one page.
coverage online
Excel
Master
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C H A P T E R 1 8 International Aspects of Financial Management 615
Mark and Todd are confident they can handle the
extra volume with their existing facilities, but they are
unsure about the potential financial risks of selling their
aircraft in Europe. In their discussion with Amalie, they
found out that the current exchange rate is $1.25/€. This
means that they can convert the €78,400 per airplane
paid by Amalie to $98,000. Thus, the profit on the inter-
national sales is the same as the profit on dollar-
denominated sales.
Mark and Todd decided to ask Chris Guthrie, their
financial analyst, to prepare an analysis of the proposed
international sales. Specifically, they ask Chris to answer
the following questions.
Mark Sexton and Todd Story, the owners of S&S Air, have been in discussions with an aircraft dealer in
Europe about selling the company’s Eagle airplane. The
Eagle sells for $98,000 and has a variable cost of
$81,000 per airplane. Amalie Diefenbaker, the dealer,
wants to add the Eagle to her current retail line. Amalie
has told Mark and Todd that she feels she will be able to
sell 15 airplanes per month in Europe. All sales will be
made in euros, and Amalie will pay the company
€78,400 for each plane. Amalie proposes that she order
15 aircraft today for the first month’s sales. She will pay
for all 15 aircraft in 90 days. This order and payment
schedule will continue each month.
CHAPTER CASE
S&S Air Goes International
1. What are the pros and cons of the international
sales? What additional risks will the company
face?
2. What happens to the company’s profits if the dol-
lar strengthens? What if the dollar weakens?
3. Ignoring taxes, what are S&S Air’s projected gains
or losses from this proposed arrangement at the
current exchange rate of $1.25/€? What happens
to profits if the exchange rate changes to $1.39/€?
At what exchange rate will the company break
even?
4. How could the company hedge its exchange rate
risk? What are the implications of this approach?
5. Taking all factors into account, should the com-
pany pursue the international sales deal further?
Why or why not?
Q U E S T I O N S
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616
A
APPENDIX A.1
Mathematical Tables
Interest Rate
Number of
Periods 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 12% 14% 15% 16% 18% 20% 24% 28% 32% 36%
1 1.0100 1.0200 1.0300 1.0400 1.0500 1.0600 1.0700 1.0800 1.0900 1.1000 1.1200 1.1400 1.1500 1.1600 1.1800 1.2000 1.2400 1.2800 1.3200 1.3600
2 1.0201 1.0404 1.0609 1.0816 1.1025 1.1236 1.1449 1.1664 1.1881 1.2100 1.2544 1.2996 1.3225 1.3456 1.3924 1.4400 1.5376 1.6384 1.7424 1.8496
3 1.0303 1.0612 1.0927 1.1249 1.1576 1.1910 1.2250 1.2597 1.2950 1.3310 1.4049 1.4815 1.5209 1.5609 1.6430 1.7280 1.9066 2.0972 2.3000 2.5155
4 1.0406 1.0824 1.1255 1.1699 1.2155 1.2625 1.3108 1.3605 1.4116 1.4641 1.5735 1.6890 1.7490 1.8106 1.9388 2.0736 2.3642 2.6844 3.0360 3.4210
5 1.0510 1.1041 1.1593 1.2167 1.2763 1.3382 1.4026 1.4693 1.5386 1.6105 1.7623 1.9254 2.0114 2.1003 2.2878 2.4883 2.9316 3.4360 4.0075 4.6526
6 1.0615 1.1262 1.1941 1.2653 1.3401 1.4185 1.5007 1.5869 1.6771 1.7716 1.9738 2.1950 2.3131 2.4364 2.6996 2.9860 3.6352 4.3980 5.2899 6.3275
7 1.0721 1.1487 1.2299 1.3159 1.4071 1.5036 1.6058 1.7138 1.8280 1.9487 2.2107 2.5023 2.6600 2.8262 3.1855 3.5832 4.5077 5.6295 6.9826 8.6054
8 1.0829 1.1717 1.2668 1.3686 1.4775 1.5938 1.7182 1.8509 1.9926 2.1436 2.4760 2.8526 3.0590 3.2784 3.7589 4.2998 5.5895 7.2058 9.2170 11.703
9 1.0937 1.1951 1.3048 1.4233 1.5513 1.6895 1.8385 1.9990 2.1719 2.3579 2.7731 3.2519 3.5179 3.8030 4.4355 5.1598 6.9310 9.2234 12.166 15.917
10 1.1046 1.2190 1.3439 1.4802 1.6289 1.7908 1.9672 2.1589 2.3674 2.5937 3.1058 3.7072 4.0456 4.4114 5.2338 6.1917 8.5944 11.806 16.060 21.647
11 1.1157 1.2434 1.3842 1.5395 1.7103 1.8983 2.1049 2.3316 2.5804 2.8531 3.4785 4.2262 4.6524 5.1173 6.1759 7.4301 10.657 15.112 21.199 29.439
12 1.1268 1.2682 1.4258 1.6010 1.7959 2.0122 2.2522 2.5182 2.8127 3.1384 3.8960 4.8179 5.3503 5.9360 7.2876 8.9161 13.215 19.343 27.983 40.037
13 1.1381 1.2936 1.4685 1.6651 1.8856 2.1329 2.4098 2.7196 3.0658 3.4523 4.3635 5.4924 6.1528 6.8858 8.5994 10.699 16.386 24.759 36.937 54.451
14 1.1495 1.3195 1.5126 1.7317 1.9799 2.2609 2.5785 2.9372 3.3417 3.7975 4.8871 6.2613 7.0757 7.9875 10.147 12.839 20.319 31.691 48.757 74.053
15 1.1610 1.3459 1.5580 1.8009 2.0789 2.3966 2.7590 3.1722 3.6425 4.1772 5.4736 7.1379 8.1371 9.2655 11.974 15.407 25.196 40.565 64.359 100.71
16 1.1726 1.3728 1.6047 1.8730 2.1829 2.5404 2.9522 3.4259 3.9703 4.5950 6.1304 8.1372 9.3576 10.748 14.129 18.488 31.243 51.923 84.954 136.97
17 1.1843 1.4002 1.6528 1.9479 2.2920 2.6928 3.1588 3.7000 4.3276 5.0545 6.8660 9.2765 10.761 12.468 16.672 22.186 38.741 66.461 112.14 186.28
18 1.1961 1.4282 1.7024 2.0258 2.4066 2.8543 3.3799 3.9960 4.7171 5.5599 7.6900 10.575 12.375 14.463 19.673 26.623 48.039 85.071 148.02 253.34
19 1.2081 1.4568 1.7535 2.1068 2.5270 3.0256 3.6165 4.3157 5.1417 6.1159 8.6128 12.056 14.232 16.777 23.214 31.948 59.568 108.89 195.39 344.54
20 1.2202 1.4859 1.8061 2.1911 2.6533 3.2071 3.8697 4.6610 5.6044 6.7275 9.6463 13.743 16.367 19.461 27.393 38.338 73.864 139.38 257.92 468.57
21 1.2324 1.5157 1.8603 2.2788 2.7860 3.3996 4.1406 5.0338 6.1088 7.4002 10.804 15.668 18.822 22.574 32.324 46.005 91.592 178.41 340.45 637.26
22 1.2447 1.5460 1.9161 2.3699 2.9253 3.6035 4.4304 5.4365 6.6586 8.1403 12.100 17.861 21.645 26.186 38.142 55.206 113.57 228.36 449.39 866.67
23 1.2572 1.5769 1.9736 2.4647 3.0715 3.8197 4.7405 5.8715 7.2579 8.9543 13.552 20.362 24.891 30.376 45.008 66.247 140.83 292.30 593.20 1178.7
24 1.2697 1.6084 2.0328 2.5633 3.2251 4.0489 5.0724 6.3412 7.9111 9.8497 15.179 23.212 28.625 35.236 53.109 79.497 174.63 374.14 783.02 1603.0
25 1.2824 1.6406 2.0938 2.6658 3.3864 4.2919 5.4274 6.8485 8.6231 10.835 17.000 26.462 32.919 40.874 62.669 95.396 216.54 478.90 1033.6 2180.1
30 1.3478 1.8114 2.4273 3.2434 4.3219 5.7435 7.6123 10.063 13.268 17.449 29.960 50.950 66.212 85.850 143.37 237.38 634.82 1645.5 4142.1 10143.
40 1.4889 2.2080 3.2620 4.8010 7.0400 10.286 14.974 21.725 31.409 45.259 93.051 188.88 267.86 378.72 750.38 1469.8 5455.9 19427. 66521. *
50 1.6446 2.6916 4.3839 7.1067 11.467 18.420 29.457 46.902 74.358 117.39 289.00 700.23 1083.7 1670.7 3927.4 9100.4 46890. * * *
60 1.8167 3.2810 5.8916 10.520 18.679 32.988 57.946 101.26 176.03 304.48 897.60 2595.9 4384.0 7370.2 20555. 56348. * * * *
Future value of $1 at the end of t periods = (1 + r)t
ros13952_appa_616-623.indd 616 12/21/18 12:35 PM
A P P E N D I X A Mathematical Tables 617
Interest Rate
Number of
Periods 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 12% 14% 15% 16% 18% 20% 24% 28% 32% 36%
1 1.0100 1.0200 1.0300 1.0400 1.0500 1.0600 1.0700 1.0800 1.0900 1.1000 1.1200 1.1400 1.1500 1.1600 1.1800 1.2000 1.2400 1.2800 1.3200 1.3600
2 1.0201 1.0404 1.0609 1.0816 1.1025 1.1236 1.1449 1.1664 1.1881 1.2100 1.2544 1.2996 1.3225 1.3456 1.3924 1.4400 1.5376 1.6384 1.7424 1.8496
3 1.0303 1.0612 1.0927 1.1249 1.1576 1.1910 1.2250 1.2597 1.2950 1.3310 1.4049 1.4815 1.5209 1.5609 1.6430 1.7280 1.9066 2.0972 2.3000 2.5155
4 1.0406 1.0824 1.1255 1.1699 1.2155 1.2625 1.3108 1.3605 1.4116 1.4641 1.5735 1.6890 1.7490 1.8106 1.9388 2.0736 2.3642 2.6844 3.0360 3.4210
5 1.0510 1.1041 1.1593 1.2167 1.2763 1.3382 1.4026 1.4693 1.5386 1.6105 1.7623 1.9254 2.0114 2.1003 2.2878 2.4883 2.9316 3.4360 4.0075 4.6526
6 1.0615 1.1262 1.1941 1.2653 1.3401 1.4185 1.5007 1.5869 1.6771 1.7716 1.9738 2.1950 2.3131 2.4364 2.6996 2.9860 3.6352 4.3980 5.2899 6.3275
7 1.0721 1.1487 1.2299 1.3159 1.4071 1.5036 1.6058 1.7138 1.8280 1.9487 2.2107 2.5023 2.6600 2.8262 3.1855 3.5832 4.5077 5.6295 6.9826 8.6054
8 1.0829 1.1717 1.2668 1.3686 1.4775 1.5938 1.7182 1.8509 1.9926 2.1436 2.4760 2.8526 3.0590 3.2784 3.7589 4.2998 5.5895 7.2058 9.2170 11.703
9 1.0937 1.1951 1.3048 1.4233 1.5513 1.6895 1.8385 1.9990 2.1719 2.3579 2.7731 3.2519 3.5179 3.8030 4.4355 5.1598 6.9310 9.2234 12.166 15.917
10 1.1046 1.2190 1.3439 1.4802 1.6289 1.7908 1.9672 2.1589 2.3674 2.5937 3.1058 3.7072 4.0456 4.4114 5.2338 6.1917 8.5944 11.806 16.060 21.647
11 1.1157 1.2434 1.3842 1.5395 1.7103 1.8983 2.1049 2.3316 2.5804 2.8531 3.4785 4.2262 4.6524 5.1173 6.1759 7.4301 10.657 15.112 21.199 29.439
12 1.1268 1.2682 1.4258 1.6010 1.7959 2.0122 2.2522 2.5182 2.8127 3.1384 3.8960 4.8179 5.3503 5.9360 7.2876 8.9161 13.215 19.343 27.983 40.037
13 1.1381 1.2936 1.4685 1.6651 1.8856 2.1329 2.4098 2.7196 3.0658 3.4523 4.3635 5.4924 6.1528 6.8858 8.5994 10.699 16.386 24.759 36.937 54.451
14 1.1495 1.3195 1.5126 1.7317 1.9799 2.2609 2.5785 2.9372 3.3417 3.7975 4.8871 6.2613 7.0757 7.9875 10.147 12.839 20.319 31.691 48.757 74.053
15 1.1610 1.3459 1.5580 1.8009 2.0789 2.3966 2.7590 3.1722 3.6425 4.1772 5.4736 7.1379 8.1371 9.2655 11.974 15.407 25.196 40.565 64.359 100.71
16 1.1726 1.3728 1.6047 1.8730 2.1829 2.5404 2.9522 3.4259 3.9703 4.5950 6.1304 8.1372 9.3576 10.748 14.129 18.488 31.243 51.923 84.954 136.97
17 1.1843 1.4002 1.6528 1.9479 2.2920 2.6928 3.1588 3.7000 4.3276 5.0545 6.8660 9.2765 10.761 12.468 16.672 22.186 38.741 66.461 112.14 186.28
18 1.1961 1.4282 1.7024 2.0258 2.4066 2.8543 3.3799 3.9960 4.7171 5.5599 7.6900 10.575 12.375 14.463 19.673 26.623 48.039 85.071 148.02 253.34
19 1.2081 1.4568 1.7535 2.1068 2.5270 3.0256 3.6165 4.3157 5.1417 6.1159 8.6128 12.056 14.232 16.777 23.214 31.948 59.568 108.89 195.39 344.54
20 1.2202 1.4859 1.8061 2.1911 2.6533 3.2071 3.8697 4.6610 5.6044 6.7275 9.6463 13.743 16.367 19.461 27.393 38.338 73.864 139.38 257.92 468.57
21 1.2324 1.5157 1.8603 2.2788 2.7860 3.3996 4.1406 5.0338 6.1088 7.4002 10.804 15.668 18.822 22.574 32.324 46.005 91.592 178.41 340.45 637.26
22 1.2447 1.5460 1.9161 2.3699 2.9253 3.6035 4.4304 5.4365 6.6586 8.1403 12.100 17.861 21.645 26.186 38.142 55.206 113.57 228.36 449.39 866.67
23 1.2572 1.5769 1.9736 2.4647 3.0715 3.8197 4.7405 5.8715 7.2579 8.9543 13.552 20.362 24.891 30.376 45.008 66.247 140.83 292.30 593.20 1178.7
24 1.2697 1.6084 2.0328 2.5633 3.2251 4.0489 5.0724 6.3412 7.9111 9.8497 15.179 23.212 28.625 35.236 53.109 79.497 174.63 374.14 783.02 1603.0
25 1.2824 1.6406 2.0938 2.6658 3.3864 4.2919 5.4274 6.8485 8.6231 10.835 17.000 26.462 32.919 40.874 62.669 95.396 216.54 478.90 1033.6 2180.1
30 1.3478 1.8114 2.4273 3.2434 4.3219 5.7435 7.6123 10.063 13.268 17.449 29.960 50.950 66.212 85.850 143.37 237.38 634.82 1645.5 4142.1 10143.
40 1.4889 2.2080 3.2620 4.8010 7.0400 10.286 14.974 21.725 31.409 45.259 93.051 188.88 267.86 378.72 750.38 1469.8 5455.9 19427. 66521. *
50 1.6446 2.6916 4.3839 7.1067 11.467 18.420 29.457 46.902 74.358 117.39 289.00 700.23 1083.7 1670.7 3927.4 9100.4 46890. * * *
60 1.8167 3.2810 5.8916 10.520 18.679 32.988 57.946 101.26 176.03 304.48 897.60 2595.9 4384.0 7370.2 20555. 56348. * * * *
Future value of $1 at the end of t periods = (1 + r)t
*The factor is greater than 99,999.
ros13952_appa_616-623.indd 617 12/21/18 12:35 PM
618 A P P E N D I X A Mathematical Tables
Present value of $1 to be received after t periods = 1/(1 + r)tAPPENDIX A.2
Interest Rate
Number of
Periods 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 12% 14% 15% 16% 18% 20% 24% 28% 32% 36%
1 .9901 .9804 .9709 .9615 .9524 .9434 .9346 .9259 .9174 .9091 .8929 .8772 .8696 .8621 .8475 .8333 .8065 .7813 .7576 .7353
2 .9803 .9612 .9426 .9246 .9070 .8900 .8734 .8573 .8417 .8264 .7972 .7695 .7561 .7432 .7182 .6944 .6504 .6104 .5739 .5407
3 .9706 .9423 .9151 .8890 .8638 .8396 .8163 .7938 .7722 .7513 .7118 .6750 .6575 .6407 .6086 .5787 .5245 .4768 .4348 .3975
4 .9610 .9238 .8885 .8548 .8227 .7921 .7629 .7350 .7084 .6830 .6355 .5921 .5718 .5523 .5158 .4823 .4230 .3725 .3294 .2923
5 .9515 .9057 .8626 .8219 .7835 .7473 .7130 .6806 .6499 .6209 .5674 .5194 .4972 .4761 .4371 .4019 .3411 .2910 .2495 .2149
6 .9420 .8880 .8375 .7903 .7462 .7050 .6663 .6302 .5963 .5645 .5066 .4556 .4323 .4104 .3704 .3349 .2751 .2274 .1890 .1580
7 .9327 .8706 .8131 .7599 .7107 .6651 .6227 .5835 .5470 .5132 .4523 .3996 .3759 .3538 .3139 .2791 .2218 .1776 .1432 .1162
8 .9235 .8535 .7894 .7307 .6768 .6274 .5820 .5403 .5019 .4665 .4039 .3506 .3269 .3050 .2660 .2326 .1789 .1388 .1085 .0854
9 .9143 .8368 .7664 .7026 .6446 .5919 .5439 .5002 .4604 .4241 .3606 .3075 .2843 .2630 .2255 .1938 .1443 .1084 .0822 .0628
10 .9053 .8203 .7441 .6756 .6139 .5584 .5083 .4632 .4224 .3855 .3220 .2697 .2472 .2267 .1911 .1615 .1164 .0847 .0623 .0462
11 .8963 .8043 .7224 .6496 .5847 .5268 .4751 .4289 .3875 .3505 .2875 .2366 .2149 .1954 .1619 .1346 .0938 .0662 .0472 .0340
12 .8874 .7885 .7014 .6246 .5568 .4970 .4440 .3971 .3555 .3186 .2567 .2076 .1869 .1685 .1372 .1122 .0757 .0517 .0357 .0250
13 .8787 .7730 .6810 .6006 .5303 .4688 .4150 .3677 .3262 .2897 .2292 .1821 .1625 .1452 .1163 .0935 .0610 .0404 .0271 .0184
14 .8700 .7579 .6611 .5775 .5051 .4423 .3878 .3405 .2992 .2633 .2046 .1597 .1413 .1252 .0985 .0779 .0492 .0316 .0205 .0135
15 .8613 .7430 .6419 .5553 .4810 .4173 .3624 .3152 .2745 .2394 .1827 .1401 .1229 .1079 .0835 .0649 .0397 .0247 .0155 .0099
16 .8528 .7284 .6232 .5339 .4581 .3936 .3387 .2919 .2519 .2176 .1631 .1229 .1069 .0930 .0708 .0541 .0320 .0193 .0118 .0073
17 .8444 .7142 .6050 .5134 .4363 .3714 .3166 .2703 .2311 .1978 .1456 .1078 .0929 .0802 .0600 .0451 .0258 .0150 .0089 .0054
18 .8360 .7002 .5874 .4936 .4155 .3503 .2959 .2502 .2120 .1799 .1300 .0946 .0808 .0691 .0508 .0376 .0208 .0118 .0068 .0039
19 .8277 .6864 .5703 .4746 .3957 .3305 .2765 .2317 .1945 .1635 .1161 .0829 .0703 .0596 .0431 .0313 .0168 .0092 .0051 .0029
20 .8195 .6730 .5537 .4564 .3769 .3118 .2584 .2145 .1784 .1486 .1037 .0728 .0611 .0514 .0365 .0261 .0135 .0072 .0039 .0021
21 .8114 .6598 .5375 .4388 .3589 .2942 .2415 .1987 .1637 .1351 .0926 .0638 .0531 .0443 .0309 .0217 .0109 .0056 .0029 .0016
22 .8034 .6468 .5219 .4220 .3418 .2775 .2257 .1839 .1502 .1228 .0826 .0560 .0462 .0382 .0262 .0181 .0088 .0044 .0022 .0012
23 .7954 .6342 .5067 .4057 .3256 .2618 .2109 .1703 .1378 .1117 .0738 .0491 .0402 .0329 .0222 .0151 .0071 .0034 .0017 .0008
24 .7876 .6217 .4919 .3901 .3101 .2470 .1971 .1577 .1264 .1015 .0659 .0431 .0349 .0284 .0188 .0126 .0057 .0027 .0013 .0006
25 .7798 .6095 .4776 .3751 .2953 .2330 .1842 .1460 .1160 .0923 .0588 .0378 .0304 .0245 .0160 .0105 .0046 .0021 .0010 .0005
30 .7419 .5521 .4120 .3083 .2314 .1741 .1314 .0994 .0754 .0573 .0334 .0196 .0151 .0116 .0070 .0042 .0016 .0006 .0002 .0001
40 .6717 .4529 .3066 .2083 .1420 .0972 .0668 .0460 .0318 .0221 .0107 .0053 .0037 .0026 .0013 .0007 .0002 .0001 * *
50 .6080 .3715 .2281 .1407 .0872 .0543 .0339 .0213 .0134 .0085 .0035 .0014 .0009 .0006 .0003 .0001 * * * *
ros13952_appa_616-623.indd 618 12/21/18 12:35 PM
A P P E N D I X A Mathematical Tables 619
Present value of $1 to be received after t periods = 1/(1 + r)t
Interest Rate
Number of
Periods 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 12% 14% 15% 16% 18% 20% 24% 28% 32% 36%
1 .9901 .9804 .9709 .9615 .9524 .9434 .9346 .9259 .9174 .9091 .8929 .8772 .8696 .8621 .8475 .8333 .8065 .7813 .7576 .7353
2 .9803 .9612 .9426 .9246 .9070 .8900 .8734 .8573 .8417 .8264 .7972 .7695 .7561 .7432 .7182 .6944 .6504 .6104 .5739 .5407
3 .9706 .9423 .9151 .8890 .8638 .8396 .8163 .7938 .7722 .7513 .7118 .6750 .6575 .6407 .6086 .5787 .5245 .4768 .4348 .3975
4 .9610 .9238 .8885 .8548 .8227 .7921 .7629 .7350 .7084 .6830 .6355 .5921 .5718 .5523 .5158 .4823 .4230 .3725 .3294 .2923
5 .9515 .9057 .8626 .8219 .7835 .7473 .7130 .6806 .6499 .6209 .5674 .5194 .4972 .4761 .4371 .4019 .3411 .2910 .2495 .2149
6 .9420 .8880 .8375 .7903 .7462 .7050 .6663 .6302 .5963 .5645 .5066 .4556 .4323 .4104 .3704 .3349 .2751 .2274 .1890 .1580
7 .9327 .8706 .8131 .7599 .7107 .6651 .6227 .5835 .5470 .5132 .4523 .3996 .3759 .3538 .3139 .2791 .2218 .1776 .1432 .1162
8 .9235 .8535 .7894 .7307 .6768 .6274 .5820 .5403 .5019 .4665 .4039 .3506 .3269 .3050 .2660 .2326 .1789 .1388 .1085 .0854
9 .9143 .8368 .7664 .7026 .6446 .5919 .5439 .5002 .4604 .4241 .3606 .3075 .2843 .2630 .2255 .1938 .1443 .1084 .0822 .0628
10 .9053 .8203 .7441 .6756 .6139 .5584 .5083 .4632 .4224 .3855 .3220 .2697 .2472 .2267 .1911 .1615 .1164 .0847 .0623 .0462
11 .8963 .8043 .7224 .6496 .5847 .5268 .4751 .4289 .3875 .3505 .2875 .2366 .2149 .1954 .1619 .1346 .0938 .0662 .0472 .0340
12 .8874 .7885 .7014 .6246 .5568 .4970 .4440 .3971 .3555 .3186 .2567 .2076 .1869 .1685 .1372 .1122 .0757 .0517 .0357 .0250
13 .8787 .7730 .6810 .6006 .5303 .4688 .4150 .3677 .3262 .2897 .2292 .1821 .1625 .1452 .1163 .0935 .0610 .0404 .0271 .0184
14 .8700 .7579 .6611 .5775 .5051 .4423 .3878 .3405 .2992 .2633 .2046 .1597 .1413 .1252 .0985 .0779 .0492 .0316 .0205 .0135
15 .8613 .7430 .6419 .5553 .4810 .4173 .3624 .3152 .2745 .2394 .1827 .1401 .1229 .1079 .0835 .0649 .0397 .0247 .0155 .0099
16 .8528 .7284 .6232 .5339 .4581 .3936 .3387 .2919 .2519 .2176 .1631 .1229 .1069 .0930 .0708 .0541 .0320 .0193 .0118 .0073
17 .8444 .7142 .6050 .5134 .4363 .3714 .3166 .2703 .2311 .1978 .1456 .1078 .0929 .0802 .0600 .0451 .0258 .0150 .0089 .0054
18 .8360 .7002 .5874 .4936 .4155 .3503 .2959 .2502 .2120 .1799 .1300 .0946 .0808 .0691 .0508 .0376 .0208 .0118 .0068 .0039
19 .8277 .6864 .5703 .4746 .3957 .3305 .2765 .2317 .1945 .1635 .1161 .0829 .0703 .0596 .0431 .0313 .0168 .0092 .0051 .0029
20 .8195 .6730 .5537 .4564 .3769 .3118 .2584 .2145 .1784 .1486 .1037 .0728 .0611 .0514 .0365 .0261 .0135 .0072 .0039 .0021
21 .8114 .6598 .5375 .4388 .3589 .2942 .2415 .1987 .1637 .1351 .0926 .0638 .0531 .0443 .0309 .0217 .0109 .0056 .0029 .0016
22 .8034 .6468 .5219 .4220 .3418 .2775 .2257 .1839 .1502 .1228 .0826 .0560 .0462 .0382 .0262 .0181 .0088 .0044 .0022 .0012
23 .7954 .6342 .5067 .4057 .3256 .2618 .2109 .1703 .1378 .1117 .0738 .0491 .0402 .0329 .0222 .0151 .0071 .0034 .0017 .0008
24 .7876 .6217 .4919 .3901 .3101 .2470 .1971 .1577 .1264 .1015 .0659 .0431 .0349 .0284 .0188 .0126 .0057 .0027 .0013 .0006
25 .7798 .6095 .4776 .3751 .2953 .2330 .1842 .1460 .1160 .0923 .0588 .0378 .0304 .0245 .0160 .0105 .0046 .0021 .0010 .0005
30 .7419 .5521 .4120 .3083 .2314 .1741 .1314 .0994 .0754 .0573 .0334 .0196 .0151 .0116 .0070 .0042 .0016 .0006 .0002 .0001
40 .6717 .4529 .3066 .2083 .1420 .0972 .0668 .0460 .0318 .0221 .0107 .0053 .0037 .0026 .0013 .0007 .0002 .0001 * *
50 .6080 .3715 .2281 .1407 .0872 .0543 .0339 .0213 .0134 .0085 .0035 .0014 .0009 .0006 .0003 .0001 * * * *
*The factor is zero to four decimal places.
ros13952_appa_616-623.indd 619 12/21/18 12:35 PM
620 A P P E N D I X A Mathematical Tables
Present value of an annuity of $1 per period for t periods = [1 − 1/(1 + r)t]/rAPPENDIX A.3
Interest Rate
Number of
Periods 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 12% 14% 15% 16% 18% 20% 24% 28% 32%
1 .9901 .9804 .9709 .9615 .9524 .9434 .9346 .9259 .9174 .9091 .8929 .8772 .8696 .8621 .8475 .8333 .8065 .7813 .7576
2 1.9704 1.9416 1.9135 1.8861 1.8594 1.8334 1.8080 1.7833 1.7591 1.7355 1.6901 1.6467 1.6257 1.6052 1.5656 1.5278 1.4568 1.3916 1.3315
3 2.9410 2.8839 2.8286 2.7751 2.7232 2.6730 2.6243 2.5771 2.5313 2.4869 2.4018 2.3216 2.2832 2.2459 2.1743 2.1065 1.9813 1.8684 1.7663
4 3.9020 3.8077 3.7171 3.6299 3.5460 3.4651 3.3872 3.3121 3.2397 3.1699 3.0373 2.9137 2.8550 2.7982 2.6901 2.5887 2.4043 2.2410 2.0957
5 4.8534 4.7135 4.5797 4.4518 4.3295 4.2124 4.1002 3.9927 3.8897 3.7908 3.6048 3.4331 3.3522 3.2743 3.1272 2.9906 2.7454 2.5320 2.3452
6 5.7955 5.6014 5.4172 5.2421 5.0757 4.9173 4.7665 4.6229 4.4859 4.3553 4.1114 3.8887 3.7845 3.6847 3.4976 3.3255 3.0205 2.7594 2.5342
7 6.7282 6.4720 6.2303 6.0021 5.7864 5.5824 5.3893 5.2064 5.0330 4.8684 4.5638 4.2883 4.1604 4.0386 3.8115 3.6046 3.2423 2.9370 2.6775
8 7.6517 7.3255 7.0197 6.7327 6.4632 6.2098 5.9713 5.7466 5.5348 5.3349 4.9676 4.6389 4.4873 4.3436 4.0776 3.8372 3.4212 3.0758 2.7860
9 8.5660 8.1622 7.7861 7.4353 7.1078 6.8017 6.5152 6.2469 5.9952 5.7590 5.3282 4.9464 4.7716 4.6065 4.3030 4.0310 3.5655 3.1842 2.8681
10 9.4713 8.9826 8.5302 8.1109 7.7217 7.3601 7.0236 6.7101 6.4177 6.1446 5.6502 5.2161 5.0188 4.8332 4.4941 4.1925 3.6819 3.2689 2.9304
11 10.3676 9.7868 9.2526 8.7605 8.3064 7.8869 7.4987 7.1390 6.8052 6.4951 5.9377 5.4527 5.2337 5.0286 4.6560 4.3271 3.7757 3.3351 2.9776
12 11.2551 10.5753 9.9540 9.3851 8.8633 8.3838 7.9427 7.5361 7.1607 6.8137 6.1944 5.6603 5.4206 5.1971 4.7932 4.4392 3.8514 3.3868 3.0133
13 12.1337 11.3484 10.6350 9.9856 9.3936 8.8527 8.3577 7.9038 7.4869 7.1034 6.4235 5.8424 5.5831 5.3423 4.9095 4.5327 3.9124 3.4272 3.0404
14 13.0037 12.1062 11.2961 10.5631 9.8986 9.2950 8.7455 8.2442 7.7862 7.3667 6.6282 6.0021 5.7245 5.4675 5.0081 4.6106 3.9616 3.4587 3.0609
15 13.8651 12.8493 11.9379 11.1184 10.3797 9.7122 9.1079 8.5595 8.0607 7.6061 6.8109 6.1422 5.8474 5.5755 5.0916 4.6755 4.0013 3.4834 3.0764
16 14.7179 13.5777 12.5611 11.6523 10.8378 10.1059 9.4466 8.8514 8.3126 7.8237 6.9740 6.2651 5.9542 5.6685 5.1624 4.7296 4.0333 3.5026 3.0882
17 15.5623 14.2919 13.1661 12.1657 11.2741 10.4773 9.7632 9.1216 8.5436 8.0216 7.1196 6.3729 6.0472 5.7487 5.2223 4.7746 4.0591 3.5177 3.0971
18 16.3983 14.9920 13.7535 12.6593 11.6896 10.8276 10.0591 9.3719 8.7556 8.2014 7.2497 6.4674 6.1280 5.8178 5.2732 4.8122 4.0799 3.5294 3.1039
19 17.2260 15.6785 14.3238 13.1339 12.0853 11.1581 10.3356 9.6036 8.9501 8.3649 7.3658 6.5504 6.1982 5.8775 5.3162 4.8435 4.0967 3.5386 3.1090
20 18.0456 16.3514 14.8775 13.5903 12.4622 11.4699 10.5940 9.8181 9.1285 8.5136 7.4694 6.6231 6.2593 5.9288 5.3527 4.8696 4.1103 3.5458 3.1129
21 18.8570 17.0112 15.4150 14.0292 12.8212 11.7641 10.8355 10.0168 9.2922 8.6487 7.5620 6.6870 6.3125 5.9731 5.3837 4.8913 4.1212 3.5514 3.1158
22 19.6604 17.6580 15.9369 14.4511 13.1630 12.0416 11.0612 10.2007 9.4424 8.7715 7.6446 6.7429 6.3587 6.0113 5.4099 4.9094 4.1300 3.5558 3.1180
23 20.4558 18.2922 16.4436 14.8568 13.4886 12.3034 11.2722 10.3741 9.5802 8.8832 7.7184 6.7921 6.3988 6.0442 5.4321 4.9245 4.1371 3.5592 3.1197
24 21.2434 18.9139 16.9355 15.2470 13.7986 12.5504 11.4693 10.5288 9.7066 8.9847 7.7843 6.8351 6.4338 6.0726 5.4509 4.9371 4.1428 3.5619 3.1210
25 22.0232 19.5235 17.4131 15.6221 14.0939 12.7834 11.6536 10.6748 9.8226 9.0770 7.8431 6.8729 6.4641 6.0971 5.4669 4.9476 4.1474 3.5640 3.1220
30 25.8077 22.3965 19.6004 17.2920 15.3725 13.7648 12.4090 11.2578 10.2737 9.4269 8.0552 7.0027 6.5660 6.1772 5.5168 4.9789 4.1601 3.5693 3.1242
40 32.8347 27.3555 23.1148 19.7928 17.1591 15.0463 13.3317 11.9246 10.7574 9.7791 8.2438 7.1050 6.6418 6.2335 5.5482 4.9966 4.1659 3.5712 3.1250
50 39.1961 31.4236 25.7298 21.4822 18.2559 15.7619 13.8007 12.2335 10.9617 9.9148 8.3045 7.1327 6.6605 6.2463 5.5541 4.9995 4.1666 3.5714 3.1250
ros13952_appa_616-623.indd 620 12/21/18 12:35 PM
A P P E N D I X A Mathematical Tables 621
Present value of an annuity of $1 per period for t periods = [1 − 1/(1 + r)t]/r
Interest Rate
Number of
Periods 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 12% 14% 15% 16% 18% 20% 24% 28% 32%
1 .9901 .9804 .9709 .9615 .9524 .9434 .9346 .9259 .9174 .9091 .8929 .8772 .8696 .8621 .8475 .8333 .8065 .7813 .7576
2 1.9704 1.9416 1.9135 1.8861 1.8594 1.8334 1.8080 1.7833 1.7591 1.7355 1.6901 1.6467 1.6257 1.6052 1.5656 1.5278 1.4568 1.3916 1.3315
3 2.9410 2.8839 2.8286 2.7751 2.7232 2.6730 2.6243 2.5771 2.5313 2.4869 2.4018 2.3216 2.2832 2.2459 2.1743 2.1065 1.9813 1.8684 1.7663
4 3.9020 3.8077 3.7171 3.6299 3.5460 3.4651 3.3872 3.3121 3.2397 3.1699 3.0373 2.9137 2.8550 2.7982 2.6901 2.5887 2.4043 2.2410 2.0957
5 4.8534 4.7135 4.5797 4.4518 4.3295 4.2124 4.1002 3.9927 3.8897 3.7908 3.6048 3.4331 3.3522 3.2743 3.1272 2.9906 2.7454 2.5320 2.3452
6 5.7955 5.6014 5.4172 5.2421 5.0757 4.9173 4.7665 4.6229 4.4859 4.3553 4.1114 3.8887 3.7845 3.6847 3.4976 3.3255 3.0205 2.7594 2.5342
7 6.7282 6.4720 6.2303 6.0021 5.7864 5.5824 5.3893 5.2064 5.0330 4.8684 4.5638 4.2883 4.1604 4.0386 3.8115 3.6046 3.2423 2.9370 2.6775
8 7.6517 7.3255 7.0197 6.7327 6.4632 6.2098 5.9713 5.7466 5.5348 5.3349 4.9676 4.6389 4.4873 4.3436 4.0776 3.8372 3.4212 3.0758 2.7860
9 8.5660 8.1622 7.7861 7.4353 7.1078 6.8017 6.5152 6.2469 5.9952 5.7590 5.3282 4.9464 4.7716 4.6065 4.3030 4.0310 3.5655 3.1842 2.8681
10 9.4713 8.9826 8.5302 8.1109 7.7217 7.3601 7.0236 6.7101 6.4177 6.1446 5.6502 5.2161 5.0188 4.8332 4.4941 4.1925 3.6819 3.2689 2.9304
11 10.3676 9.7868 9.2526 8.7605 8.3064 7.8869 7.4987 7.1390 6.8052 6.4951 5.9377 5.4527 5.2337 5.0286 4.6560 4.3271 3.7757 3.3351 2.9776
12 11.2551 10.5753 9.9540 9.3851 8.8633 8.3838 7.9427 7.5361 7.1607 6.8137 6.1944 5.6603 5.4206 5.1971 4.7932 4.4392 3.8514 3.3868 3.0133
13 12.1337 11.3484 10.6350 9.9856 9.3936 8.8527 8.3577 7.9038 7.4869 7.1034 6.4235 5.8424 5.5831 5.3423 4.9095 4.5327 3.9124 3.4272 3.0404
14 13.0037 12.1062 11.2961 10.5631 9.8986 9.2950 8.7455 8.2442 7.7862 7.3667 6.6282 6.0021 5.7245 5.4675 5.0081 4.6106 3.9616 3.4587 3.0609
15 13.8651 12.8493 11.9379 11.1184 10.3797 9.7122 9.1079 8.5595 8.0607 7.6061 6.8109 6.1422 5.8474 5.5755 5.0916 4.6755 4.0013 3.4834 3.0764
16 14.7179 13.5777 12.5611 11.6523 10.8378 10.1059 9.4466 8.8514 8.3126 7.8237 6.9740 6.2651 5.9542 5.6685 5.1624 4.7296 4.0333 3.5026 3.0882
17 15.5623 14.2919 13.1661 12.1657 11.2741 10.4773 9.7632 9.1216 8.5436 8.0216 7.1196 6.3729 6.0472 5.7487 5.2223 4.7746 4.0591 3.5177 3.0971
18 16.3983 14.9920 13.7535 12.6593 11.6896 10.8276 10.0591 9.3719 8.7556 8.2014 7.2497 6.4674 6.1280 5.8178 5.2732 4.8122 4.0799 3.5294 3.1039
19 17.2260 15.6785 14.3238 13.1339 12.0853 11.1581 10.3356 9.6036 8.9501 8.3649 7.3658 6.5504 6.1982 5.8775 5.3162 4.8435 4.0967 3.5386 3.1090
20 18.0456 16.3514 14.8775 13.5903 12.4622 11.4699 10.5940 9.8181 9.1285 8.5136 7.4694 6.6231 6.2593 5.9288 5.3527 4.8696 4.1103 3.5458 3.1129
21 18.8570 17.0112 15.4150 14.0292 12.8212 11.7641 10.8355 10.0168 9.2922 8.6487 7.5620 6.6870 6.3125 5.9731 5.3837 4.8913 4.1212 3.5514 3.1158
22 19.6604 17.6580 15.9369 14.4511 13.1630 12.0416 11.0612 10.2007 9.4424 8.7715 7.6446 6.7429 6.3587 6.0113 5.4099 4.9094 4.1300 3.5558 3.1180
23 20.4558 18.2922 16.4436 14.8568 13.4886 12.3034 11.2722 10.3741 9.5802 8.8832 7.7184 6.7921 6.3988 6.0442 5.4321 4.9245 4.1371 3.5592 3.1197
24 21.2434 18.9139 16.9355 15.2470 13.7986 12.5504 11.4693 10.5288 9.7066 8.9847 7.7843 6.8351 6.4338 6.0726 5.4509 4.9371 4.1428 3.5619 3.1210
25 22.0232 19.5235 17.4131 15.6221 14.0939 12.7834 11.6536 10.6748 9.8226 9.0770 7.8431 6.8729 6.4641 6.0971 5.4669 4.9476 4.1474 3.5640 3.1220
30 25.8077 22.3965 19.6004 17.2920 15.3725 13.7648 12.4090 11.2578 10.2737 9.4269 8.0552 7.0027 6.5660 6.1772 5.5168 4.9789 4.1601 3.5693 3.1242
40 32.8347 27.3555 23.1148 19.7928 17.1591 15.0463 13.3317 11.9246 10.7574 9.7791 8.2438 7.1050 6.6418 6.2335 5.5482 4.9966 4.1659 3.5712 3.1250
50 39.1961 31.4236 25.7298 21.4822 18.2559 15.7619 13.8007 12.2335 10.9617 9.9148 8.3045 7.1327 6.6605 6.2463 5.5541 4.9995 4.1666 3.5714 3.1250
ros13952_appa_616-623.indd 621 12/21/18 12:35 PM
622 A P P E N D I X A Mathematical Tables
Future value of an annuity of $1 per period for t periods = [(1 + r)t − 1]/rAPPENDIX A.4
Interest Rate
Number of
Periods 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 12% 14% 15% 16% 18% 20% 24% 28% 32% 36%
1 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
2 2.0100 2.0200 2.0300 2.0400 2.0500 2.0600 2.0700 2.0800 2.0900 2.1000 2.1200 2.1400 2.1500 2.1600 2.1800 2.2000 2.2400 2.2800 2.3200 2.3600
3 3.0301 3.0604 3.0909 3.1216 3.1525 3.1836 3.2149 3.2464 3.2781 3.3100 3.3744 3.4396 3.4725 3.5056 3.5724 3.6400 3.7776 3.9184 4.0624 4.2096
4 4.0604 4.1216 4.1836 4.2465 4.3101 4.3746 4.4399 4.5061 4.5731 4.6410 4.7793 4.9211 4.9934 5.0665 5.2154 5.3680 5.6842 6.0156 6.3624 6.7251
5 5.1010 5.2040 5.3091 5.4163 5.5256 5.6371 5.7507 5.8666 5.9847 6.1051 6.3528 6.6101 6.7424 6.8771 7.1542 7.4416 8.0484 8.6999 9.3983 10.146
6 6.1520 6.3081 6.4684 6.6330 6.8019 6.9753 7.1533 7.3359 7.5233 7.7156 8.1152 8.5355 8.7537 8.9775 9.4420 9.9299 10.980 12.136 13.406 14.799
7 7.2135 7.4343 7.6625 7.8983 8.1420 8.3938 8.6540 8.9228 9.2004 9.4872 10.089 10.730 11.067 11.414 12.142 12.916 14.615 16.534 18.696 21.126
8 8.2857 8.5830 8.8932 9.2142 9.5491 9.8975 10.260 10.637 11.028 11.436 12.300 13.233 13.727 14.240 15.327 16.499 19.123 22.163 25.678 29.732
9 9.3685 9.7546 10.159 10.583 11.027 11.491 11.978 12.488 13.021 13.579 14.776 16.085 16.786 17.519 19.086 20.799 24.712 29.369 34.895 41.435
10 10.462 10.950 11.464 12.006 12.578 13.181 13.816 14.487 15.193 15.937 17.549 19.337 20.304 21.321 23.521 25.959 31.643 38.593 47.062 57.352
11 11.567 12.169 12.808 13.486 14.207 14.972 15.784 16.645 17.560 18.531 20.655 23.045 24.349 25.733 28.755 32.150 40.238 50.398 63.122 78.998
12 12.683 13.412 14.192 15.026 15.917 16.870 17.888 18.977 20.141 21.384 24.133 27.271 29.002 30.850 34.931 39.581 50.895 65.510 84.320 108.44
13 13.809 14.680 15.618 16.627 17.713 18.882 20.141 21.495 22.953 24.523 28.029 32.089 34.352 36.786 42.219 48.497 64.110 84.853 112.30 148.47
14 14.947 15.974 17.086 18.292 19.599 21.015 22.550 24.215 26.019 27.975 32.393 37.581 40.505 43.672 50.818 59.196 80.496 109.61 149.24 202.93
15 16.097 17.293 18.599 20.024 21.579 23.276 25.129 27.152 29.361 31.772 37.280 43.842 47.580 51.660 60.965 72.035 100.82 141.30 198.00 276.98
16 17.258 18.639 20.157 21.825 23.657 25.673 27.888 30.324 33.003 35.950 42.753 50.980 55.717 60.925 72.939 87.442 126.01 181.87 262.36 377.69
17 18.430 20.012 21.762 23.698 25.840 28.213 30.840 33.750 36.974 40.545 48.884 59.118 65.075 71.673 87.068 105.93 157.25 233.79 347.31 514.66
18 19.615 21.412 23.414 25.645 28.132 30.906 33.999 37.450 41.301 45.599 55.750 68.394 75.836 84.141 103.74 128.12 195.99 300.25 459.45 700.94
19 20.811 22.841 25.117 27.671 30.539 33.760 37.379 41.446 46.018 51.159 63.440 78.969 88.212 98.603 123.41 154.74 244.03 385.32 607.47 954.28
20 22.019 24.297 26.870 29.778 33.066 36.786 40.995 45.762 51.160 57.275 72.052 91.025 102.44 115.38 146.63 186.69 303.60 494.21 802.86 1298.8
21 23.239 25.783 28.676 31.969 35.719 39.993 44.865 50.423 56.765 64.002 81.699 104.77 118.81 134.84 174.02 225.03 377.46 633.59 1060.8 1767.4
22 24.472 27.299 30.537 34.248 38.505 43.392 49.006 55.457 62.873 71.403 92.503 120.44 137.63 157.41 206.34 271.03 469.06 812.00 1401.2 2404.7
23 25.716 28.845 32.453 36.618 41.430 46.996 53.436 60.893 69.532 79.543 104.60 138.30 159.28 183.60 244.49 326.24 582.63 1040.4 1850.6 3271.3
24 26.973 30.422 34.426 39.083 44.502 50.816 58.177 66.765 76.790 88.497 118.16 158.66 184.17 213.98 289.49 392.48 723.46 1332.7 2443.8 4450.0
25 28.243 32.030 36.459 41.646 47.727 54.865 63.249 73.106 84.701 98.347 133.33 181.87 212.79 249.21 342.60 471.98 898.09 1706.8 3226.8 6053.0
30 34.785 40.568 47.575 56.085 66.439 79.058 94.461 113.28 136.31 164.49 241.33 356.79 434.75 530.31 790.95 1181.9 2640.9 5873.2 12941. 28172.3
40 48.886 60.402 75.401 95.026 120.80 154.76 199.64 259.06 337.88 442.59 767.09 1342.0 1779.1 2360.8 4163.2 7343.9 22729. 69377. * *
50 64.463 84.579 112.80 152.67 209.35 290.34 406.53 573.77 815.08 1163.9 2400.0 4994.5 7217.7 10436. 21813. 45497. * * * *
60 81.670 114.05 163.05 237.99 353.58 533.13 813.52 1253.2 1944.8 3034.8 7471.6 18535. 29220. 46058. * * * * * *
ros13952_appa_616-623.indd 622 12/21/18 12:35 PM
A P P E N D I X A Mathematical Tables 623
Future value of an annuity of $1 per period for t periods = [(1 + r)t − 1]/r
Interest Rate
Number of
Periods 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 12% 14% 15% 16% 18% 20% 24% 28% 32% 36%
1 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
2 2.0100 2.0200 2.0300 2.0400 2.0500 2.0600 2.0700 2.0800 2.0900 2.1000 2.1200 2.1400 2.1500 2.1600 2.1800 2.2000 2.2400 2.2800 2.3200 2.3600
3 3.0301 3.0604 3.0909 3.1216 3.1525 3.1836 3.2149 3.2464 3.2781 3.3100 3.3744 3.4396 3.4725 3.5056 3.5724 3.6400 3.7776 3.9184 4.0624 4.2096
4 4.0604 4.1216 4.1836 4.2465 4.3101 4.3746 4.4399 4.5061 4.5731 4.6410 4.7793 4.9211 4.9934 5.0665 5.2154 5.3680 5.6842 6.0156 6.3624 6.7251
5 5.1010 5.2040 5.3091 5.4163 5.5256 5.6371 5.7507 5.8666 5.9847 6.1051 6.3528 6.6101 6.7424 6.8771 7.1542 7.4416 8.0484 8.6999 9.3983 10.146
6 6.1520 6.3081 6.4684 6.6330 6.8019 6.9753 7.1533 7.3359 7.5233 7.7156 8.1152 8.5355 8.7537 8.9775 9.4420 9.9299 10.980 12.136 13.406 14.799
7 7.2135 7.4343 7.6625 7.8983 8.1420 8.3938 8.6540 8.9228 9.2004 9.4872 10.089 10.730 11.067 11.414 12.142 12.916 14.615 16.534 18.696 21.126
8 8.2857 8.5830 8.8932 9.2142 9.5491 9.8975 10.260 10.637 11.028 11.436 12.300 13.233 13.727 14.240 15.327 16.499 19.123 22.163 25.678 29.732
9 9.3685 9.7546 10.159 10.583 11.027 11.491 11.978 12.488 13.021 13.579 14.776 16.085 16.786 17.519 19.086 20.799 24.712 29.369 34.895 41.435
10 10.462 10.950 11.464 12.006 12.578 13.181 13.816 14.487 15.193 15.937 17.549 19.337 20.304 21.321 23.521 25.959 31.643 38.593 47.062 57.352
11 11.567 12.169 12.808 13.486 14.207 14.972 15.784 16.645 17.560 18.531 20.655 23.045 24.349 25.733 28.755 32.150 40.238 50.398 63.122 78.998
12 12.683 13.412 14.192 15.026 15.917 16.870 17.888 18.977 20.141 21.384 24.133 27.271 29.002 30.850 34.931 39.581 50.895 65.510 84.320 108.44
13 13.809 14.680 15.618 16.627 17.713 18.882 20.141 21.495 22.953 24.523 28.029 32.089 34.352 36.786 42.219 48.497 64.110 84.853 112.30 148.47
14 14.947 15.974 17.086 18.292 19.599 21.015 22.550 24.215 26.019 27.975 32.393 37.581 40.505 43.672 50.818 59.196 80.496 109.61 149.24 202.93
15 16.097 17.293 18.599 20.024 21.579 23.276 25.129 27.152 29.361 31.772 37.280 43.842 47.580 51.660 60.965 72.035 100.82 141.30 198.00 276.98
16 17.258 18.639 20.157 21.825 23.657 25.673 27.888 30.324 33.003 35.950 42.753 50.980 55.717 60.925 72.939 87.442 126.01 181.87 262.36 377.69
17 18.430 20.012 21.762 23.698 25.840 28.213 30.840 33.750 36.974 40.545 48.884 59.118 65.075 71.673 87.068 105.93 157.25 233.79 347.31 514.66
18 19.615 21.412 23.414 25.645 28.132 30.906 33.999 37.450 41.301 45.599 55.750 68.394 75.836 84.141 103.74 128.12 195.99 300.25 459.45 700.94
19 20.811 22.841 25.117 27.671 30.539 33.760 37.379 41.446 46.018 51.159 63.440 78.969 88.212 98.603 123.41 154.74 244.03 385.32 607.47 954.28
20 22.019 24.297 26.870 29.778 33.066 36.786 40.995 45.762 51.160 57.275 72.052 91.025 102.44 115.38 146.63 186.69 303.60 494.21 802.86 1298.8
21 23.239 25.783 28.676 31.969 35.719 39.993 44.865 50.423 56.765 64.002 81.699 104.77 118.81 134.84 174.02 225.03 377.46 633.59 1060.8 1767.4
22 24.472 27.299 30.537 34.248 38.505 43.392 49.006 55.457 62.873 71.403 92.503 120.44 137.63 157.41 206.34 271.03 469.06 812.00 1401.2 2404.7
23 25.716 28.845 32.453 36.618 41.430 46.996 53.436 60.893 69.532 79.543 104.60 138.30 159.28 183.60 244.49 326.24 582.63 1040.4 1850.6 3271.3
24 26.973 30.422 34.426 39.083 44.502 50.816 58.177 66.765 76.790 88.497 118.16 158.66 184.17 213.98 289.49 392.48 723.46 1332.7 2443.8 4450.0
25 28.243 32.030 36.459 41.646 47.727 54.865 63.249 73.106 84.701 98.347 133.33 181.87 212.79 249.21 342.60 471.98 898.09 1706.8 3226.8 6053.0
30 34.785 40.568 47.575 56.085 66.439 79.058 94.461 113.28 136.31 164.49 241.33 356.79 434.75 530.31 790.95 1181.9 2640.9 5873.2 12941. 28172.3
40 48.886 60.402 75.401 95.026 120.80 154.76 199.64 259.06 337.88 442.59 767.09 1342.0 1779.1 2360.8 4163.2 7343.9 22729. 69377. * *
50 64.463 84.579 112.80 152.67 209.35 290.34 406.53 573.77 815.08 1163.9 2400.0 4994.5 7217.7 10436. 21813. 45497. * * * *
60 81.670 114.05 163.05 237.99 353.58 533.13 813.52 1253.2 1944.8 3034.8 7471.6 18535. 29220. 46058. * * * * * *
*The factor is greater than 99,999.
ros13952_appa_616-623.indd 623 12/21/18 12:35 PM
624
B Key Equations
CHAPTER 2
1. The balance sheet identity, or equation:
Assets = Liabilities + Shareholders’ equity [2.1]
2. The income statement equation:
Revenues − Expenses = Income [2.2]
3. The cash flow identity:
Cash flow from assets = Cash flow to creditors
+ Cash flow to stockholders [2.3]
where:
a. Cash flow from assets = Operating cash flow (OCF) − Net
capital spending − Change in net working capital (NWC)
(1) Operating cash flow = Earnings before interest and
taxes (EBIT) + Depreciation − Taxes
(2) Net capital spending = Ending net fixed assets −
Beginning net fixed assets + Depreciation
(3) Change in net working capital = Ending NWC −
Beginning NWC
b. Cash flow to creditors = Interest paid − Net new
borrowing
c. Cash flow to stockholders = Dividend paid − Net new
equity raised
CHAPTER 3
1. The current ratio:
Current ratio = Current assets ____________ Current liabilities [3.1]
2. The quick, or acid-test, ratio:
Quick ratio =
Current assets − Inventory
___________________ Current liabilities [3.2]
3. The cash ratio:
Cash ratio = Cash ____________ Current liabilities [3.3]
4. The total debt ratio:
Total debt ratio =
Total assets − Total equity
___________________ Total assets [3.4]
5. The debt-equity ratio:
Debt-equity ratio = Total debt/Total equity [3.5]
6. The equity multiplier:
Equity multiplier = Total assets/Total equity [3.6]
7. The times interest earned (TIE) ratio:
Times interest earned ratio = EBIT ______ Interest [3.7]
8. The cash coverage ratio:
Cash coverage ratio =
EBIT + Depreciation
______________ Interest [3.8]
9. The inventory turnover ratio:
Inventory turnover =
Cost of goods sold
_____________ Inventory [3.9]
10. The average days’ sales in inventory:
Days’ sales in inventory =
365 days
_____________ Inventory turnover [3.10]
11. The receivables turnover ratio:
Receivables turnover = Sales ______________ Accounts receivable [3.11]
12. The days’ sales in receivables:
Days’ sales in receivables =
365 days
_______________ Receivables turnover [3.12]
13. The total asset turnover ratio:
Total asset turnover = Sales _________ Total assets [3.13]
14. Profit margin:
Profit margin = Net income ________ Sales [3.14]
15. Return on assets (ROA):
Return on assets = Net income _________ Total assets [3.15]
16. Return on equity (ROE):
Return on equity = Net income _________ Total equity [3.16]
17. Earnings per share (EPS):
EPS = Net income ______________ Shares outstanding [3.17]
18. The price-earnings (PE) ratio:
PE ratio =
Price per share
______________ Earnings per share [3.18]
19. The price-sales ratio:
Price-sales ratio =
Price per share
___________ Sales per share [3.19]
20. The market-to-book ratio:
Market-to-book ratio =
Market value per share
________________ Book value per share [3.20]
21. The enterprise value:
Enterprise value = Total market value of the stock
+ Book value of all liabilities − Cash [3.21]
22. The EBITDA ratio:
EBITDA ratio =
Enterprise value
____________ EBITDA [3.22]
23. The DuPont identity:
ROE = Net income __________ Sales ×
Sales ______ Assets ×
Assets ___________ Total equity
Return on assets (ROA)
ROE = Profit margin [3.23]
× Total asset turnover
× Equity multiplier
24. The dividend payout ratio:
Dividend payout ratio = Cash dividends ___________ Net income [3.24]
25. The retention ratio:
Retention ratio =
Addition to retained earnings
____________________ Net income [3.25]
26. The internal growth rate:
Internal growth rate = ROA × b ________ 1 − ROA × b [3.26]
27. The sustainable growth rate:
Sustainable growth rate = ROE × b ________ 1 − ROE × b [3.27]
CHAPTER 4
1. The future value of $1 invested for t periods at a rate of r per period:
Future value = $1 × (1 + r)t [4.1]
2. The present value of $1 to be received t periods in the future at
a discount rate of r:
PV = $1 × [1 / (1 + r) t ] = $1/ (1 + r) t [4.2]
ros13952_appb_624-626.indd 624 12/21/18 12:37 PM
A P P E N D I X B Key Equations 625
3. The relationship between future value and present value (the
basic present value equation):
PV × (1 + r)t = FVt
PV = FVt /(1 + r)
t = FVt × [1/(1 + r)
t] [4.3]
CHAPTER 5
1. The present value of an annuity of C dollars per period for t
periods when the rate of return, or interest rate, is r:
Annuity present value
=
C × ( 1 − Present value factor _____________________ r )
=
C × { 1 − [1/ (1 + r ) t ] _______________ r }
[5.1]
2. The future value factor for an annuity:
Annuity FV factor
=
(Future value factor − 1)/r
=
[ (1 + r ) t − 1]/r
[5.2]
3. The present and future factor for an annuity due:
Annuity due value = Ordinary annuity value × (1 + r) [5.3]
4. Present value for a perpetuity:
PV for a perpetuity = C / r = C × (1/r) [5.4]
5. Effective annual rate (EAR), where m is the number of times
the interest is compounded during the year:
EAR = (1 + Quoted rate/m) m − 1 [5.5]
CHAPTER 6
1. Bond value if bond has (1) a face value of F paid at maturity,
(2) a coupon of C paid per period, (3) t periods to maturity,
and (4) a yield of r per period:
Bond value = C × [1 − 1/(1 + r)t]/r + F/(1 + r)t
Bond value = Present value of
the coupons
+ Present value of
the face amount
[6.1]
2. The Fisher effect:
1 + R = (1 + r) × (1 + h) [6.2]
where h is the inflation rate
3. R = r + h + r × h [6.3]
4. R ≈ r + h [6.4]
CHAPTER 7
1. P0 = (D1 + P1)/(1 + R) [7.1]
2. P0 = D/R [7.2]
3. P 0 =
D 0 × ( 1 + g ) ________ R − g =
D 1 ____ R − g
[7.3]
4. P t =
D t × ( 1 + g ) _______ R − g =
D t+1 ____ R − g
[7.4]
5. R = D1 ⁄P0 + g [7.5]
6. Price at Time t = Benchmark PE ratio × EPSt [7.6]
CHAPTER 8
1. Net present value (NPV):
NPV = Present value of future cash flows − Investment cost
2. Payback period:
Payback period = Number of years that pass before the sum of
an investment’s cash flows equals the cost of the investment
3. The average accounting return (AAR):
AAR =
Average net income
______________ Average book value
4. Internal rate of return (IRR):
IRR = Discount rate of required return such that the net
present value of an investment is zero
5. Profitability index:
Profitability index = PV of cash flows _____________ Cost of investment
CHAPTER 9
1. Project cash flow = Project operating cash flow
− Project change in net working capital
− Project capital spending
2. Operating cash flow = EBIT + Depreciation − Taxes
3. The tax shield approach to operating cash flow:
OCF = (Sales − Costs) × (1 − TC) + Depreciation × TC
4. Total cash flow = Operating cash flow − Change in NWC
− Capital spending
5. Cash flow = Cash inflow − Cash outflow
CHAPTER 10
1. Total dollar return = Dividend income
+ Capital gain (or loss) [10.1]
2. Total cash if stock is sold = Initial investment + Total return
[10.2]
3. Variance of returns, Var(R), or σ2:
Var(R) = 1 ___ T − 1 [ ( R 1 − R
¯ ) 2 + · · · + ( R T − R ¯ ) 2 ] [10.3]
4. Geometric average return = [(1 + R1) × (1 + R2)
× · · · × (1 + RT)]
1/T − 1 [10.4]
CHAPTER 11
1. Risk premium = Expected return − Risk-free rate
= E(R) − Rf
[11.1]
2. Expected return on a portfolio:
E(RP) = x1 × E(R1) + x2 × E(R2) + · · · + xn × E(Rn) [11.2]
3. Total return = Expected return + Unexpected return
R = E(R) + U
[11.3]
4. Announcement = Expected part + Surprise [11.4]
5. R = E(R) + Systematic portion + Unsystematic portion [11.5]
6. Total risk = Systematic risk + Unsystematic risk [11.6]
7. The capital asset pricing model (CAPM):
E(Ri) = Rf + [E(RM) − Rf] βi
[11.7]
CHAPTER 12
1. RE = D 1 ⁄ P0 + g [12.1]
2. RE = Rf + βE × (RM − Rf) [12.2]
3. RP = D ⁄ P0 [12.3]
4. V = E + D [12.4]
5. 100% = E ⁄ V + D ⁄ V [12.5]
6. Weighted average cost of capital (WACC)
= (E ⁄ V ) × RE + (D ⁄ V) × RD × (1 − TC) [12.6]
ros13952_appb_624-626.indd 625 12/21/18 12:37 PM
626 A P P E N D I X B Key Equations
7. WACC = (E ⁄ V) × RE + (P ⁄ V) × RP + (D ⁄ V)
× RD × (1 − TC) [12.7]
8. Taxes* = EBIT × TC [12.8]
9. CFA* = EBIT + Depreciation − Taxes*
− Change in NWC − Capital spending
= EBIT + Depreciation − EBIT × TC
− Change in NWC − Capital spending [12.9]
10. CFA* = EBIT × (1 − TC) + Depreciation − Change in NWC
− Capital spending [12.10]
11. V 0 =
CFA 1 * _______ 1 + WACC +
CFA 2 * _________ ( 1 + WACC ) 2 +
CFA 3 * _________ ( 1 + WACC ) 3 + ⋅ ⋅ ⋅
+
CFA t * + V t ________ ( 1 + WACC ) t [12.11]
12. V t =
CFA t * +1 _______ WACC − g [12.12]
CHAPTER 13
1. Modigliani-Miller Proposition II, no taxes:
RE = RA + (RA − RD) × (D ⁄ E) [13.1]
2. Modigliani-Miller propositions, with taxes:
a. Present value of the interest tax shield:
= (TC × D × RD) ⁄ RD
= TC × D [13.2]
b. Proposition I:
VL = VU + TC × D [13.3]
CHAPTER 16
1. Net working capital + Fixed assets
= Long-term debt + Equity [16.1]
2. Net working capital = (Cash + Other current assets)
− Current liabilities [16.2]
3. Cash = Long-term debt + Equity + Current liabilities
− Current assets other than cash − Fixed assets [16.3]
4. The operating cycle:
Operating cycle = Inventory period
+ Accounts receivable period [16.4]
5. The cash cycle:
Cash cycle = Operating cycle
− Accounts payable period [16.5]
6. Total cash collections:
Cash collections = Beginning accounts receivable
+ ½ × Sales [16.6]
CHAPTER 17
1. The economic order quantity (EOQ) model:
Total carrying costs = Average inventory
× Carrying costs per unit = (Q ⁄ 2) × CC
[17.1]
2. Total restocking cost = Fixed cost per order
× Number of orders = F × (T ⁄ Q) [17.2]
3. Total costs = Carrying costs + Restocking costs
= (Q ⁄ 2) × CC + F × (T ⁄ Q) [17.3]
4. Carrying costs = Restocking costs
(Q* ⁄ 2) × CC = F × (T ⁄ Q*) [17.4]
5. (Q *) 2 = 2T × F _____ CC [17.5]
6. The optimal order size Q*:
Q * = √
_____
2T × F _____ CC [17.6]
CHAPTER 18
1. [E(S1) − S0] ⁄S0 = hFC − hUS [18.1]
2. E(S1) = S0 × [1 + (hFC − hUS)] [18.2]
3. Relative purchasing power parity (PPP):
E(St) = S0 × [1 + (hFC − hUS)]
t [18.3]
4. Interest rate parity (IRP), exact, single period:
F1 ⁄ S0 = (1 + RFC) ⁄ (1 + RUS) [18.4]
5. (F1 − S0) ⁄ S0 = RFC − RUS [18.5]
6. F1 = S0 × [1 + (RFC − RUS)] [18.6]
7. IRP, approximate, multiperiod:
Ft = S0 × [1 + (RFC − RUS)]
t [18.7]
ros13952_appb_624-626.indd 626 12/21/18 12:37 PM
627
CHAPTER 2
1. Owners’ equity = $5,690
NWC = $380
3. $86,050
5. $42,170
7. $21,290.20
9. $105
11. −$146,500
13. Book value = $4,190,000
Total NWC and market value = $5,550,000
15. $5,911
17. a. $1,200
b. $0
19. $160,000
21. a. $8,399; $7,543
b. −$427
c. $3,468; $14,469
d. −$28; $1,311
CHAPTER 3
1. Current ratio = 1.40 times
Quick ratio = .94 time
3. Receivables turnover = 12.88 times
Days’ sales in receivables = 28.35 days
5. Debt-equity ratio = .75
Equity multiplier = 1.75
7. 14.29%
9. 87.37 days
11. 6.21%
13. 11.63%
17. 18.73%
19. 7.77%
21. 15.53%
23. 10.92%
25. 5.53%
27. $529.76
29. Child profit margin = 4.00%
Store profit margin = 2.00%
Store ROE = 10.13%
31. 4.40 times
33. 6.61%
37. PE ratio = 26.40 times
P/S ratio = 3.18 times
DPS = $1.60
Market-to-book = 7.92 times
39. 6.61%
41. 1.23 times
43. 10.98%; $7,466.35; 6.09%
CHAPTER 4
1. $2,110.50
3. $7,036.89; $20,560.31; $90,426.27; $29,645.07
5. 19.48; 4.87; 20.16; 12.22
7. 13.42 years; 26.84 years
9. 56.30 years
11. $1,519.27
13. 8.10%; $22,319,707.83
15. −13.17%
17. $60,532.72
19. $15,433.02
21. $63,176.81; $55,948.50
23. 175.63 months
25. $7,765.45; $82,532.61
CHAPTER 5
1. $2,344.76; $1,937.54; $1,700.16
3. $5,080.91; $5,281.28; $6,232.93
5. $3,545.65; $3,583.81; $16,975.33; $28,334.98
7. $2,282.94; $7,513.71; $7,112.97; $5,936.19
9. $289,647.54; $2,273,988.16
11. 3.88%
13. 14.76%; 8.37%; 8.99%; 13.89%
15. 13.02%
17. $6,008.23; $7,599.74; $12,159.18
19. APR = 145.20%
EAR = 293.79%
21. 67.03 months
23. .69%; 8.25%; 8.57%
25. $1,598,270.55
27. $3,121.03
29. 5.01%
Answers to Selected
End-of-Chapter Problems C
ros13952_appc_627-630.indd 627 12/21/18 12:39 PM
628 A P P E N D I X C Answers to Selected End-of-Chapter Problems
31. $1,010.81
33. $1.18; $1.39
35. PV: $136,244.11; $138,909.01
37. G: 13.75%
H: 14.06%
39. 127.52
41. $38,443,284.41
43. APR = 5.04%
EAR = 5.16%
45. 4.15%
47. $36,317.13
49. $17,234.85
51. $111,497.16
53. APR = 29.52%
EAR = 33.86%
CHAPTER 6
3. $891.74
5. 6.50%
7. 4.78%
9. 2.80%; 2.75%
11. 2.75%
13. Previous asked = $1,206.015
17. $4,700.15
19. +2%: −8.15%; −21.86%
−2%: 9.03%; 32.09%
21. 5.88%; 5.95%; 6.03%
23. $1,039.08
25. 8.74%; 8.29%
31. 6.31%
33. 6.12%
CHAPTER 7
1. P0 = $40.76
P3 = $45.72
P15 = $72.36
3. Dividend yield = 6.14%
Capital gains yield = 4.50%
5. 9.90%
7. $90.69
9. Straight voting = $9,975,038
Cumulative voting = $3,990,038
11. $71.83
13. $66.24; $77.28
15. $118.49
17. $75.11
19. $136.78
21. 4.95%; 3.88%
23. 2.30%
25. $98.82; 5.61%
27. $90.27
CHAPTER 8
1. 2.68 years
3. 2.32 years; 3.12 years
5. 16.26%
7. $5,626.19; −$466.40; 22.19%
9. $7,220; $2,941.10; −$268.06; −$2,744.56
11. a. 14.58%; 13.94%
b. 9.25%
13. 1.113; 1.032; .934
15. a. 3.34 years; 1.97 years
b. $58,136.83; $14,228.22
c. 20.54%; 27.38%
d. 1.237; 1.268
17. a. 1.264; 1.180
b. $12,579.51; $14,564.04
19. 0%; <0%
21. a. 2.13 years; 3.05 years
b. $116,496.82; $168,215.71
23. Discounting approach = 14.52%
Reinvestment approach = 10.98%
Combination approach = 10.98%
25. 7.27%; $3,983.47; −$12,000; $20,896.98
CHAPTER 9
1. $38,410,000
3. $100,100
5. Year 7 allowance = $66,528.50
7. $1,394,459.20
9. $919,433
11. $31,981.29
13. $83,070.88
15. $82,288.43
17. NPV @ $135,000 cost savings = $100,160.15
NPV @ $95,000 cost savings = −$19,628.71
21. Base-case NPV = $3,020,917.19
Worst-case NPV = −$2,089,860.22
23. $37,447.31
CHAPTER 10
1. Total return = 15.11%
Dividend yield = 2.47%
Capital gains yield = 12.64%
3. $2,917.50
5. 12.10%; 8.83%
7. X: Average return = 7.6%
X: Variance = .01463
X: Standard deviation = 12.10%
Y: Average return = 16.80%
Y: Variance = .07032
Y: Standard deviation = 26.52%
9. a. 10.80%
b. .01797; 13.41%
11. .97%; 6.50%
13. 6.58%
ros13952_appc_627-630.indd 628 12/21/18 12:39 PM
A P P E N D I X C Answers to Selected End-of-Chapter Problems 629
15. 31.91%; 35.93%
17. −1.90% to 14.70%
−10.20% to 23.00%
19. 18%; 15.72%
21. 10.09%; 9.71%
23. 2.92%
25. .422%; .00000035%
CHAPTER 11
1. A: .6775
B: .3225
3. 13.05%
5. 10.80%
7. A: 10.55%; 4.25%
B: 15.35%; 19.94%
9. a. 11.67%
b. .01598
11. 1.08
13. 11.92%
15. 11.80%
17. a. 7.45%
b. Weight of stock = .6087
c. .801
d. Weight of stock = 200%
19. Reward-to-risk ratios:
Market = 7.00%
Y: 7.42%
Z: 6.88%
21. 9.25%; 9.95%
23. J: .4103
E(R) = 11.69%
27. C = $173,035.71
Rf = $76,964.29
CHAPTER 12
1. 10.61%
3. 11.13%; 11.11%
5. 4.59%; 3.63%
7. $200,000,000; $190,295,000; 3.99%
9. 8.67%
11. a. .2732; .7268
b. .7375; .2625
13. a. 4.73%
b. 10.90%
17. 8.09%
19. 12.16%
21. Cost < $49,263,502.45
23. a. 5.41%
b. 12.31%
CHAPTER 13
1. a. $1.24; $1.91; $2.29
b. $1.15; $1.95; $2.40
3. a. 4.39%; 6.75%; 8.10%
b. 4.08%; 6.89%; 8.50%
c. 3.47%; 5.33%; 6.40%
3.22%; 5.44%; 6.71%
5. $28.40; $9,088,000; $9,088,000
7. $47.50; $47.50
9. a. $1,846.91
b. $2,065.88
c. Sell 85 shares
11. a. 10.90%
b. 12.83%
c. 17.65%
d. 10.90%; 10.90%
13. $3,146,000
15. .64; .56
CHAPTER 14
1. $18,314
3. $79.86
5. a. New shares = 90,000; Par value = $.50
b. New shares = 9,000; Par value = $5.00
7. $31.40; $30.25
11. Par value = $.50; Dividend per share last year = $1.22
13. a. $51.58
b. $51.58
CHAPTER 15
1. $6,750; $625
3. 2,754,943 shares
5. 3,135,135 shares
CHAPTER 16
1. a. No change
b. No change
c. No change
d. Decrease
e. Decrease
f. Decrease
g. No change
h. Decrease
i. Increase
j. Decrease
k. Decrease
l. No change
m. Decrease
n. Decrease
o. Decrease
3. a. Increase
b. Increase
c. Decrease
d. No change
e. Decrease
f. No change
5. a. $668; $660; $683; $793
b. $565; $645; $690; $748
c. $770; $675; $675; $837
ros13952_appc_627-630.indd 629 12/21/18 12:39 PM
630 A P P E N D I X C Answers to Selected End-of-Chapter Problems
7. 18.71%
9. $1,902.00; $2,199.75; $2,470.75; $2,506.50
11. $264,650; $434,150; $331,200
13. a. 6.78%
b. $500,617.69
15. Average payables = $29,138.36
Average receivables = $75,375.34
CHAPTER 17
1. $85,000; $63,400
3. $4,300; −$4,900; −$600
5. $5,740
7. $71,038.36
9. a. 17 days
b. $1,198,849.32
11. d. 20.13%; 44.59%; 13.01%; 44.32%
13. 2,641.27
CHAPTER 18
1. a. Z 367.01
b. $1.1733
c. $5,866,500
d. Singapore dollar
e. Mexican peso
f. Fr/€ = $.8596
g. Kuwait dinar; Venezuelan bolivar
3. a. ¥109.73; premium
b. A$1.3397; discount
5. a. ¥/£ = 165.41
b. arbitrage profit per $ = $.0157
7. Invest in U.S. = $30,216,518.81
Invest in Great Britain = $29,472,402.71
9. Current = $397,832.82
+10% = $770,757.11
−10% = −$57,963.54
Break-even = $1.2367; −8.84%
11. −4.82%
13. $8.05
15. a. Equity = $20,370.37
b. Equity = $18,965.52
c. Equity = $21,825.40
ros13952_appc_627-630.indd 630 12/21/18 12:39 PM
631
This appendix is intended to help you use your Hewlett-Packard HP-
10B or Texas Instruments BA II Plus financial calculator to solve
problems encountered in the introductory finance course. It describes
the various calculator settings and provides keystroke solutions for
nine selected problems from this book. Please see your owner’s man-
ual for more complete instructions. For more examples and problem-
solving techniques, please see Financial Analysis with an Electronic
Calculator, 6th edition, by Mark A. White (New York: McGraw-
Hill, 2007).
CALCULATOR SETTINGS
Most calculator errors in the introductory finance course are the re-
sult of inappropriate settings. Before beginning a calculation, you
should ask yourself the following questions:
1. Did I clear the financial registers?
2. Is the compounding frequency set to once per period?
3. Is the calculator in END mode?
4. Did I enter negative numbers using the +/− key?
Clearing the Registers
All calculators have areas of memory, called registers, where variables
and intermediate results are stored. There are two sets of financial
registers, the time value of money (TVM) registers and the cash flow
(CF) registers. These must be cleared before beginning a new calcula-
tion. On the Hewlett-Packard HP-10B, pressing {CLEAR ALL}
clears both the TVM and the CF registers.1 To clear the TVM registers
on the BA II Plus, press 2nd {CLR TVM}. Press 2nd {CLR
Work} from within the cash flow worksheet to clear the CF
registers.
Compounding Frequency
Both the HP-10B and the BA II Plus are hardwired to assume monthly
compounding, that is, compounding 12 times per period. Because
very few problems in the introductory finance course make this
assumption, you should change this default setting to once per period.
On the HP-10B, press 1 {P/YR}. To verify that the default has
been changed, press the key, then press and briefly hold the
INPUT key.2 The display should read “1P_Yr”.
On the BA II Plus, you can specify both payment frequency and
compounding frequency, although they should normally be set to the
same number. To set both to once per period, press the key sequence
2nd {P/Y} 1 ENTER , then press ↓ 1 ENTER . Press-
ing 2nd {QUIT} returns you to standard calculator mode.
Using the HP-10B and TI BA
II Plus Financial Calculators D
1 The key is colored orange and serves as a Shift key for the functions in
curly brackets.
2 This is the same keystroke used to clear all registers; pretty handy, eh?
END Mode and Annuities Due
In most problems, payment is made at the end of a period, and this is
the default setting (end mode) for both the HP-10B and the BA II
Plus. Annuities due assume payments are made at the beginning of
each period (begin mode). On the HP-10B, pressing {BEG/
END} toggles between begin and end mode. Press the key sequence
2nd {BGN} 2nd {SET} 2nd {QUIT} to accomplish
the same task on the BA II Plus. Both calculators will indicate on the
display that your calculator is set for begin mode.
Sign Changes
Sign changes are used to identify the direction of cash inflows and
outflows. Generally, cash inflows are entered as positive numbers and
cash outflows are entered as negative numbers. To enter a negative
number on either the HP-10B or the BA II Plus, first press the appro-
priate digit keys and then press the change sign key, +/− . Do not
use the minus sign key, − , as its effects are quite unpredictable.
SAMPLE PROBLEMS
This section provides keystroke solutions for selected problems from
the text illustrating the nine basic financial calculator skills.
1. Future Value or Present Value of a Single Sum
Compute the future value of $2,250 at a 17 percent annual rate for
30 years.
HP-10B BA II PLUS
–2,250.00 PV –2,250.00 PV
30.00 N 30.00 N
17.00 I/YR 17.00 I/Y
FV 249,895.46 CPT FV 249,895.46
The future value is $249,895.46.
2. Present Value or Future Value of an Ordinary
Annuity
Betty’s Bank offers you a $20,000, seven-year term loan at 11 percent
annual interest. What will your annual loan payment be?
HP-10B BA II PLUS
–20,000.00 PV –20,000.00 PV
7.00 N 7.00 N
11.00 I/YR 11.00 I/Y
PMT 4,244.31 CPT PMT 4,244.31
Your annual loan payment will be $4,244.31.
ros13952_appd_631-633.indd 631 12/21/18 12:40 PM
632 A P P E N D I X D Using the HP-10B and TI BA II Plus Financial Calculators
3. Finding an Unknown Interest Rate
Assume that the total cost of a college education will be $75,000
when your child enters college in 18 years. You presently have $7,000
to invest. What rate of interest must you earn on your investment to
cover the cost of your child’s college education?
HP-10B BA II PLUS
–7,000.00 PV –7,000.00 PV
18.00 N 18.00 N
75,000.00 FV 75,000.00 FV
I/YR 14.08 CPT I/Y 14.08
You must earn an annual interest rate of at least 14.08 percent to
cover the expected future cost of your child’s education.
4. Finding an Unknown Number of Periods
One of your customers is delinquent on his accounts payable balance.
You’ve mutually agreed to a repayment schedule of $374 per month.
You will charge 1.4 percent per month interest on the overdue bal-
ance. If the current balance is $12,000, how long will it take for the
account to be paid off?
HP-10B BA II PLUS
–12,000.00 PV –12,000.00 PV
1.40 I/YR 1.40 I/Y
374.00 PMT 374.00 PMT
N 42.90 CPT N 42.90
The loan will be paid off in 42.90 months.
5. Simple Bond Pricing
Mullineaux Co. issued 11-year bonds one year ago at a coupon rate
of 8.25 percent. The bonds make semiannual payments. If the
YTM on these bonds is 7.10 percent, what is the current bond
price?
HP-10B BA II PLUS
41.25 PMT 41.25 PMT
1,000.00 FV 1,000.00 FV
20.00 N 20.00 N
3.55 I/YR 3.55 I/Y
PV − 1,081.35 CPT PV − 1,081.35
Because the bonds make semiannual payments, we must halve the
coupon payment (8.25 ÷ 2 = 4.125 ==> $41.25), halve the YTM
(7.10 ÷ 2 ==> 3.55), and double the number of periods (10 years
remaining × 2 = 20 periods). Then, the current bond price is
$1,081.35.
6. Simple Bond Yields to Maturity
Vasicek Co. has 12.5 percent coupon bonds on the market with
eight years left to maturity. The bonds make annual payments.
If one of these bonds currently sells for $1,145.68, what is its
YTM?
HP-10B BA II PLUS
–1,145.68 PV –1,145.68 PV
125.00 PMT 125.00 PMT
1,000.00 FV 1,000.00 FV
8.00 N 8.00 N
I/YR 9.79 CPT I/Y 9.79
The bond has a yield to maturity of 9.79 percent.
7. Cash Flow Analysis
What are the IRR and NPV of the following set of cash flows? As-
sume a discount rate of 10 percent.
Year Cash Flow
0 −$1,300
1 400
2 300
3 1,200
HP-10B BA II PLUS
–1,300.00 CFj CF
400.00 CFj 2ND {CLR Work}
1.00 {Nj} –1,300.00 ENTER ↓
300.00 CFj 400.00 ENTER ↓
1.00 {Nj} 1.00 ENTER ↓
1,200.00 CFj 300.00 ENTER ↓
1.00 {Nj} 1.00 ENTER ↓
{IRR/YR} 17.40 1,200.00 ENTER ↓
10.00 I/YR 1.00 ENTER ↓
{NPV} 213.15 IRR CPT 17.40
NPV
10.00 ENTER
↓ CPT 213.15
The project has an IRR of 17.40 percent and an NPV of $213.15.
8. Loan Amortization
Prepare an amortization schedule for a three-year loan of $24,000.
The interest rate is 16 percent per year, and the loan calls for equal
annual payments. How much interest is paid in the third year? How
much total interest is paid over the life of the loan?
To prepare a complete amortization schedule, you must amortize
each payment one at a time:
ros13952_appd_631-633.indd 632 12/21/18 12:40 PM
A P P E N D I X D Using the HP-10B and TI BA II Plus Financial Calculators 633
HP-10B BA II PLUS
− 24,000.00 PV –24,000.00 PV
16.00 I/YR 16.00 I/Y
3.00 N 3.00 N
PMT 10,686.19 CPT PMT 10,686.19
1.00 INPUT {AMORT} = !3,840.00 <== Interest 2ND {AMORT} 2ND {CLR Work}
= 6,846.19 <== Principal
= !!!!− 17,153.81 <== Balance 1.00 ENTER ↓
2.00 INPUT {AMORT} = 2,744.61 <== Interest 1.00 ENTER ↓ − 17,153.81 <== Balance
= 7,941.58 <== Principal ↓ 6,846.19 <== Principal
= − 9,212.23 <== Balance ↓ 3,840.00 <== Interest
3.00 INPUT {AMORT} = !!!!!!!!!!!!!!!!!!!1,473.96 <== Interest ↓
= !!!!!!!!!!!! 9,212.23 <== Principal 2.00 ENTER ↓
= 0.00 <== Balance 2.00 ENTER ↓ − 9,212.23 <== Balance
↓ 7,941.58 <== Principal
↓ 2,744.61 <== Interest
↓
3.00 ENTER ↓
3.00 ENTER ↓ !!0.00 <== Balance
↓ 9,212.23 <== Principal
↓ 1,473.96 <== Interest
↓
Interest of $1,473.96 is paid in the third year.
Enter both a beginning and an ending period to compute the total amount of interest or principal paid over a particular period of time.
HP-10B BA II PLUS
–24,000.00 PV –24,000.00 PV
16.00 I/YR 16.00 I/Y
3.00 N 3.00 N
PMT 10,686.19 CPT PMT 10,686.19
1.00 INPUT 2ND {AMORT} 2ND {CLR Work}
3.00 {AMORT} = 8,058.57 <== Interest 1.00 ENTER ↓
= 24,000.00 <== Principal
= 0.00 <== Balance 3.00 ENTER ↓ 0.00 <== Balance
24,000.00 <== Principal
8,058.57 <== Interest
Total interest of $8,058.57 is paid over the life of the loan.
9. Interest Rate Conversions
Find the effective annual rate, EAR, corresponding to a 7 percent an-
nual percentage rate, APR, compounded quarterly.
HP-10B BA II PLUS
4.00 {P/YR} 2ND {IConv}
7.00 {NOM%} 7.00 ENTER
{EFF%} 7.19 ↓ ↓
4.00 ENTER
↓ CPT 7.19
The effective annual rate equals 7.19 percent.
↓
↓
ros13952_appd_631-633.indd 633 12/21/18 12:40 PM
634
Glossary
absolute priority rule (APR) The rule establishing
priority of claims in liquidation.
Accelerated Cost Recovery System (ACRS) De-
preciation method under U.S. tax law allowing for
the accelerated write-off of property under various
classifications.
accounts payable period The time between receipt
of inventory and payment for it.
accounts receivable financing A secured short-
term loan that involves either the assignment or
factoring of receivables.
accounts receivable period The time between sale
of inventory and collection of the receivable.
agency problem The possibility of conflict of
interest between the owners and management of a firm.
aging schedule A compilation of accounts receiv-
able by the age of each account.
alpha The excess return an asset earns based on the
level of risk taken.
American Depositary Receipt (ADR) A security
issued in the United States representing shares of a
foreign stock and allowing that stock to be traded in the
United States.
annual percentage rate (APR) The interest rate
charged per period multiplied by the number of periods
per year.
annuity A level stream of cash flows for a fixed
period of time.
annuity due An annuity for which the cash flows
occur at the beginning of the period.
arithmetic average return The return earned in an
average year over a particular period.
asked price The price a dealer is willing to take for
a security.
average accounting return (AAR) An investment’s
average net income divided by its average book value.
average tax rate Total taxes paid divided by total
taxable income.
balance sheet Financial statement showing a firm’s
accounting value on a particular date.
bankruptcy A legal proceeding for liquidating or
reorganizing a business. Also, the transfer of some or
all of a firm’s assets to its creditors.
bearer form A bond issued without record of the owner’s
name; payment is made to whomever holds the bond.
best efforts underwriting The underwriter sells as
much of the issue as possible but can return any unsold
shares to the issuer without financial responsibility.
beta coefficient Amount of systematic risk present
in a particular risky asset relative to that in an average
risky asset.
bid price The price a dealer is willing to pay for a
security.
bid-ask spread The difference between the bid price
and the asked price.
broker An agent who arranges security transactions
among investors.
business risk The equity risk that comes from the
nature of the firm’s operating activities.
call premium The amount by which the call price
exceeds the par value of the bond.
call protected bond Bond during period in which it
cannot be redeemed by the issuer.
call provision Agreement giving the issuer the option
to repurchase a bond at a specific price prior to maturity.
capital asset pricing model (CAPM) Equation
of the security market line showing the relationship
between expected return and beta.
capital budgeting The process of planning and
managing a firm’s long-term investments.
capital gains yield The dividend growth rate, or the
rate at which the value of an investment grows.
capital rationing The situation that exists if a firm
has positive net present value projects but cannot obtain
the necessary financing.
capital structure The mixture of debt and equity
maintained by a firm.
captive finance company A partially or wholly
owned subsidiary that handles the credit function for
the parent company.
ros13952_glos_634-640.indd 634 12/21/18 12:41 PM
G L O S S A R Y 635
carrying costs Costs that rise with increases in the
level of investment in current assets.
cash budget A forecast of cash receipts and
disbursements for the next planning period.
cash concentration The practice of and procedures
for moving cash from multiple banks into the firm’s
main accounts.
cash cycle The time between cash disbursement and
cash collection.
cash discount A discount given to induce prompt
payment. Also sales discount.
cash flow from assets The total of cash flow to
creditors and cash flow to stockholders, consisting of
the following: operating cash flow, capital spending,
and change in net working capital.
cash flow time line Graphical representation of the
operating cycle and the cash cycle.
cash flow to creditors A firm’s interest payments to
creditors less net new borrowing.
cash flow to stockholders Dividends paid out by a
firm less net new equity raised.
clean price The price of a bond net of accrued
interest; this is the price that is typically quoted.
clientele effect Argument that stocks attract
particular groups based on dividend yield and the
resulting tax effects.
collection policy Procedures followed by a firm in
collecting accounts receivable.
common stock Equity without priority for dividends
or in bankruptcy.
common-size statement A standardized financial
statement presenting all items in percentage terms.
Balance sheet items are shown as a percentage of assets
and income statement items as a percentage of sales.
compound interest Interest earned on both the
initial principal and the interest reinvested from prior
periods.
compounding The process of accumulating interest
in an investment over time to earn more interest.
consol A type of perpetuity.
contingency planning Taking into account the
managerial options implicit in a project.
controlled disbursement account A disbursement
practice under which the firm transfers an amount to a
disbursing account that is sufficient to cover demands
for payment.
corporation A business created as a distinct legal
entity owned by one or more individuals or entities.
cost of capital The minimum required return on a
new investment.
cost of debt The return that lenders require on the
firm’s debt.
cost of equity The return that equity investors
require on their investment in the firm.
coupon The stated interest payment made on a bond.
coupon rate The annual coupon divided by the face
value of a bond.
credit analysis The process of determining the
probability that customers will or will not pay.
credit cost curve Graphical representation of the
sum of the carrying costs and the opportunity costs of
a credit policy.
credit instrument The evidence of indebtedness.
credit period The length of time for which credit is
granted.
credit scoring The process of quantifying the pro ba-
bility of default when granting consumer credit.
cross-rate The implicit exchange rate between two
currencies (usually non-U.S.) quoted in some third
currency (usually the U.S. dollar).
cumulative voting A procedure in which a share-
holder may cast all votes for one member of the board
of directors.
current yield A bond’s coupon payment divided by
its closing price.
date of payment Date that the dividend checks are
mailed.
date of record Date by which holders must be on
record to receive a dividend.
dealer An agent who buys and sells securities from
inventory.
debenture Unsecured debt, usually with a maturity
of 10 years or more.
declaration date Date on which the board of
directors passes a resolution to pay a dividend.
default risk premium The portion of a nominal
interest rate or bond yield that represents compensation
for the possibility of default.
ros13952_glos_634-640.indd 635 12/21/18 12:41 PM
636 G L O S S A R Y
deferred call provision Bond call provision pro-
hibiting the company from redeeming the bond prior
to a certain date.
depreciation tax shield The tax saving that results
from the depreciation deduction, calculated as depre-
ciation multiplied by the corporate tax rate.
designated market makers (DMMs) NYSE mem-
bers who act as dealers in particular stocks. Formerly
known as “specialists.”
direct bankruptcy costs The costs that are di-
rec tly associated with bankruptcy, such as legal and
administrative expenses.
direct listing A security offering in which the com-
pany offers securities directly to investors, bypassing
underwriters.
dirty price The price of a bond including accrued
interest, also known as the full or invoice price. This is
the price the buyer actually pays.
discount Calculation of the present value of some
future amount.
discount rate The rate used to calculate the present
value of future cash flows.
discounted cash flow (DCF) valuation (a) Cal-
cu lating the present value of a future cash flow to
determine its value today. (b) The process of valuing an
investment by discounting its future cash flows.
distribution Payment made by a firm to its owners
from sources other than current or accumulated
retained earnings.
dividend Payment made out of a firm’s earnings to
its owners, in the form of either cash or stock.
dividend Payments by a corporation to shareholders,
made in either cash or stock.
dividend growth model A model that determines
the current price of a stock as its dividend next period
divided by the discount rate less the dividend growth rate.
dividend yield A stock’s expected cash dividend
divided by its current price.
DMM’s post A fixed place on the exchange floor
where the DMM operates.
DuPont identity Popular expression breaking
ROE into three parts: operating efficiency, asset use
efficiency, and financial leverage.
Dutch auction underwriting The type of under-
writing in which the offer price is set based on com-
petitive bidding by investors. Also known as a uniform
price auction.
economic order quantity (EOQ) The restocking
quantity that minimizes the total inventory costs.
effective annual rate (EAR) The interest rate
expressed as if it were compounded once per year.
efficient capital market Market in which security
prices reflect available information.
efficient markets hypothesis (EMH) The hypoth-
esis that actual capital markets, such as the New York
Stock Exchange, are efficient.
electronic communications networks (ECNs) Web -
sites that allow investors to trade directly with one
another.
erosion The cash flows of a new project that come at
the expense of a firm’s existing projects.
Eurobonds International bonds issued in multiple
countries but denominated in a single currency (usually
the issuer’s currency).
Eurocurrency Money deposited in a financial center
outside the country whose currency is involved.
exchange rate The price of one country’s currency
expressed in terms of another country’s currency.
exchange rate risk The risk related to having
international operations in a world where relative
currency values vary.
ex-dividend date Date two business days before the
date of record, establishing those individuals entitled to
a dividend.
expected return Return on a risky asset expected in
the future.
face value The principal amount of a bond that is
repaid at the end of the term. Also par value.
financial distress costs The direct and indirect
costs associated with going bankrupt or experiencing
financial distress.
financial ratios Relationships determined from a
firm’s financial information and used for comparison
purposes.
financial risk The equity risk that comes from the
financial policy (i.e., capital structure) of the firm.
firm commitment underwriting The underwriter
buys the entire issue, assuming full financial respon-
sibility for any unsold shares.
Fisher effect The relationship among nominal
returns, real returns, and inflation.
five Cs of credit The five basic credit factors to be
evaluated: character, capacity, capital, collateral, and
conditions.
ros13952_glos_634-640.indd 636 12/21/18 12:41 PM
G L O S S A R Y 637
float The difference between book cash and bank
cash, representing the net effect of checks in the process
of clearing.
floor brokers NYSE members who execute customer
buy and sell orders.
forecasting risk The possibility that errors in
projected cash flows will lead to incorrect decisions.
Also estimation risk.
foreign bonds International bonds issued in a single
country, usually denominated in that country’s currency.
foreign exchange market The market in which
one country’s currency is traded for another’s.
forward exchange rate The agreed-upon exchange
rate to be used in a forward trade.
forward trade Agreement to exchange currency at
some time in the future.
free cash flow Another name for cash flow from
assets.
future value (FV) The amount an investment is
worth after one or more periods. Also compound value.
general cash offer An issue of securities offered for
sale to the general public on a cash basis.
Generally Accepted Accounting Principles
(GAAP) The common set of standards and procedures
by which audited financial statements are prepared.
geometric average return The average compound
return earned per year over a multiyear period.
gilts British and Irish government securities.
Green Shoe provision A contract provision giving
the underwriter the option to purchase additional shares
from the issuer at the offering price. Also overallotment
option.
hard rationing The situation that occurs when a
business cannot raise financing for a project under any
circumstances.
homemade leverage The use of personal borrowing
to change the overall amount of financial leverage to
which an individual is exposed.
income statement Financial statement summarizing
a firm’s performance over a period of time.
incremental cash flows The difference between a
firm’s future cash flows with a project and those without
the project.
indenture The written agreement between the corpo-
ration and the lender detailing the terms of the debt issue.
indirect bankruptcy costs The costs of avoiding a
bankruptcy filing incurred by a financially distressed firm.
inflation premium The portion of a nominal interest
rate that represents compensation for expected future
inflation.
initial public offering (IPO) A company’s first equity
issue made available to the public. Also unseasoned new
issue.
inside quotes The highest bid quotes and the lowest
ask quotes for a security.
interest on interest Interest earned on the
reinvestment of previous interest payments.
interest rate parity (IRP) The condition stating that
the interest rate differential between two countries is
equal to the percentage difference between the forward
exchange rate and the spot exchange rate.
interest rate risk premium The compensation
investors demand for bearing interest rate risk.
interest tax shield The tax saving attained by a firm
from the tax deductibility of interest expense.
internal growth rate The maximum possible growth
rate a firm can achieve without external financing of any
kind.
internal rate of return (IRR) The discount rate that
makes the net present value of an investment zero.
inventory loan A secured short-term loan to pur-
chase inventory.
inventory period The time it takes to acquire and
sell inventory.
invoice Bill for goods or services provided by the
seller to the purchaser.
just-in-time (JIT) inventory A system for managing
demand-dependent inventories that minimizes inven-
tory holdings.
line of credit A formal (committed) or informal
(noncommitted) prearranged, short-term bank loan.
liquidation Termination of the firm as a going
concern.
liquidity premium The portion of a nominal interest
rate or bond yield that represents compensation for lack
of liquidity.
lockboxes Special post office boxes set up to
intercept and speed up accounts receivable collections.
lockup agreement The part of the underwriting
contract that specifies how long insiders must wait after
an IPO before they can sell stock.
London Interbank Offered Rate (LIBOR) The
rate most international banks charge one another for
overnight Eurodollar loans.
ros13952_glos_634-640.indd 637 12/21/18 12:41 PM
638 G L O S S A R Y
M&M Proposition I The value of a firm is indepen-
dent of its capital structure.
M&M Proposition II A firm’s cost of equity capital is
a positive linear function of its capital structure.
managerial options Opportunities that managers
can exploit if certain things happen in the future. Also
known as “real” options.
marginal tax rate Amount of tax payable on the
next dollar earned.
market risk premium Slope of the security market
line; the difference between the expected return on a
market portfolio and the risk-free rate.
materials requirements planning (MRP) A set
of procedures used to determine inventory levels for
demand-dependent inventory types, such as work-in-
progress and raw materials.
maturity Specified date on which the principal
am ount of a bond is paid.
member As of 2006, a member is the owner of a
trading license on the NYSE.
multiple rates of return The possibility that more
than one discount rate will make the net present value
of an investment zero.
mutually exclusive investment decisions A
situation where taking one investment prevents the
taking of another.
net present value (NPV) The difference between
an investment’s market value and its cost.
net present value profile A graphical represen-
tation of the relationship between an investment’s net
present value and various discount rates.
net working capital Current assets less current
liabilities.
nominal rates Interest rates or rates of return that
have not been adjusted for inflation.
noncash items Expenses charged against revenues
that do not directly affect cash flow, such as depreciation.
normal distribution A symmetric, bell-shaped
frequency distribution that is completely defined by its
average and standard deviation.
note Unsecured debt, usually with a maturity of
under 10 years.
operating cash flow Cash generated from a firm’s
normal business activities.
operating cycle The time period between the
acquisition of inventory and the collection of cash from
receivables.
opportunity cost The most valuable alternative that
is given up if a particular investment is undertaken.
order flow The flow of customer orders to buy and
sell securities.
par value The principal amount of a bond that is
repaid at the end of the term. Also face value.
partnership A business formed by two or more
individuals or entities.
payback period The amount of time required for an
investment to generate cash flows sufficient to recover
its initial cost.
perpetuity An annuity in which the cash flows
continue forever.
political risk Risk related to changes in value that
arise because of political actions.
portfolio Group of assets such as stocks and bonds
held by an investor.
portfolio weight Percentage of a portfolio’s total
value in a particular asset.
precautionary motive The need to hold cash as a
safety margin to act as a financial reserve.
preferred stock Stock with dividend priority over
common stock, normally with a fixed dividend rate,
sometimes without voting rights.
present value (PV) The current value of future cash
flows discounted at the appropriate discount rate.
primary market The market in which new securities
are originally sold to investors.
principle of diversification Spreading an invest-
ment across a number of assets will eliminate some, but
not all, of the risk.
private placements Loans, usually long-term in
nature, provided directly by a limited number of
investors.
pro forma financial statements Financial state-
ments projecting future years’ operations.
profitability index (PI) The present value of an
investment’s future cash flows divided by its initial cost.
Also benefit-cost ratio.
prospectus A legal document describing details of
the issuing corporation and the proposed offering to
potential investors.
protective covenant A part of the indenture
limiting certain actions that might be taken during the
term of the loan, usually to protect the lender’s interest.
proxy A grant of authority by a shareholder allowing
another individual to vote his or her shares.
ros13952_glos_634-640.indd 638 12/21/18 12:41 PM
G L O S S A R Y 639
purchasing power parity (PPP) The idea that
the exchange rate adjusts to keep purchasing power
constant among currencies.
pure play approach Use of a weighted average cost
of capital that is unique to a particular project, based on
companies in similar lines of business.
quoted interest rate The interest rate expressed
in terms of the interest payment made each period.
Also stated interest rate.
real rates Interest rates or rates of return that have
been adjusted for inflation.
red herring A preliminary prospectus distributed to
prospective investors in a new issue of securities.
registered form The registrar of a company records
who owns each bond, and bond payments are made
directly to the owner of record.
registration statement A statement filed with the
SEC that discloses all material information concerning
the corporation making a public offering.
regular cash dividend Cash payment made by
a firm to its owners in the normal course of business,
usually quarterly.
reorganization Financial restructuring of a failing
firm to attempt to continue operations as a going
concern.
repurchase Refers to a firm’s purchase of its own
stock; an alternative to a cash dividend. Also called stock
repurchase.
reverse split Stock split under which a firm’s number
of shares outstanding is reduced.
rights offer A public issue of securities in which
securities are first offered to existing shareholders. Also
known as rights offering.
risk premium The excess return required from an
investment in a risky asset over that required from a
risk-free investment.
scenario analysis The determination of what
happens to net present value estimates when we ask
what-if questions.
seasoned equity offering (SEO) A new equity
issue of securities by a company that has previously
issued securities to the public.
secondary market The market in which previously
issued securities are traded among investors.
security market line (SML) Positively sloped
straight line displaying the relationship between
expected return and beta.
sensitivity analysis Investigation of what happens
to net present value when only one variable is changed.
shelf registration Registration permitted by SEC
Rule 415, which allows a company to register all issues
it expects to sell within two years at one time, with
subsequent sales at any time within those two years.
shortage costs Costs that fall with increases in the
level of investment in current assets.
simple interest Interest earned only on the original
principal amount invested.
sinking fund An account managed by the bond
trustee for early bond redemption.
soft rationing The situation that occurs when units
in a business are allocated a certain amount of financing
for capital budgeting.
sole proprietorship A business owned by a single
individual.
speculative motive The need to hold cash to take
advantage of additional investment opportunities, such
as bargain purchases.
spot exchange rate The exchange rate on a spot
trade.
spot trade An agreement to trade currencies based
on the exchange rate today for settlement within two
business days.
spread Compensation to the underwriter, determined
by the difference between the underwriter’s buying price
and offering price.
stakeholder Someone other than a stockholder or
creditor who potentially has a claim on the cash flows
of the firm.
stand-alone principle The assumption that evalu-
a tion of a project may be based on the project’s
incremental cash flows.
standard deviation The positive square root of the
variance.
Standard Industrial Classification (SIC) code
U.S. government code used to classify a firm by its type
of business operations.
stated interest rate The interest rate expressed
in terms of the interest payment made each period.
Also quoted interest rate.
static theory of capital structure Theory that
a firm borrows up to the point where the tax benefit
from an extra dollar in debt is exactly equal to the cost
that comes from the increased probability of financial
distress.
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640 G L O S S A R Y
stock dividend Payment made by a firm to its
owners in the form of stock, diluting the value of each
share outstanding.
stock split An increase in a firm’s shares outstanding
without any change in owners’ equity.
straight voting A procedure in which a shareholder
may cast all votes for each member of the board of directors.
strategic options Options for future, related business
products or strategies.
sunk cost A cost that has already been incurred
and cannot be recouped and therefore should not be
considered in an investment decision.
supplemental liquidity providers (SLPs) Invest-
ment firms that are active participants in stocks assigned
to them. Their job is to make a one-sided market (i.e.,
offering to either buy or sell). They trade purely for their
own accounts.
sustainable growth rate The maximum possible
growth rate a firm can achieve without external equity
financing while maintaining a constant debt-equity ratio.
swaps Agreements to exchange two securities or
currencies.
syndicate A group of underwriters formed to share
the risk and to help sell an issue.
systematic risk A risk that influences a large number
of assets. Also market risk.
systematic risk principle The expected return on a
risky asset depends only on that asset’s systematic risk.
taxability premium The portion of a nominal
interest rate or bond yield that represents compensation
for unfavorable tax status.
term loans Direct business loans of, typically, one
to five years.
term structure of interest rates The relationship
between nominal interest rates on default-free, pure
discount securities and time to maturity; that is, the
pure time value of money.
terms of sale Conditions under which a firm sells its
goods and services for cash or credit.
tombstone An advertisement announcing a public
offering.
trading range Price range between highest and
lowest prices at which a stock is typically traded.
transaction motive The need to hold cash to
satisfy normal disbursement and collection activities
associated with a firm’s ongoing operations.
Treasury yield curve A plot of the yields on
Treasury notes and bonds relative to maturity.
underwriters Investment firms that act as inter-
mediaries between a company selling securities and
the investing public.
unsystematic risk A risk that affects at most a small
number of assets. Also unique or asset-specific risk.
variance The average squared difference between
the actual return and the average return.
venture capital (VC) Financing for new, often high-
risk, ventures.
weighted average cost of capital (WACC) The
WACC is the overall return the firm must earn on its
existing assets to maintain the value of its stock.
working capital A firm’s short-term assets and
liabilities.
yield to maturity (YTM) The rate required in the
market on a bond.
zero coupon bond A bond that makes no coupon
payments, and thus is initially priced at a deep discount.
zero-balance account A disbursement account in
which the firm maintains a zero balance, transferring
funds in from a master account only as needed to cover
checks presented for payment.
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641
Name Index
A
Altman, Edward L., 448
Avila, Alex, 122
B
Beckman, Theodor N., 566
Benioff, Marc, 498
Bernanke, Ben, 150
Block, S. B., 259
Brav, A., 473, 476
Briloff, Abraham, 79
Brin, Sergey, 498
Buffett, Warren, 33, 339
C
Camp, Garrett, 1
Chetty, R., 472
D
Darvish, Yu, 122, 130
DeAngelo, H., 471, 474
DeAngelo, L., 471, 474
Dimson, Elroy, 333
E
Elton, E. J., 362
F
Farre-Mensa, J., 472
Ford, Henry, 311
Franklin, Benjamin, 110
G
Garoppolo, Jimmy, 122
Graham, J. R., 259, 473
Gruber, M. J., 362
H
Hadden, M. Shane, 488
Harvey, C. R., 259, 473, 476
I
Ibbotson, Roger, 316, 499, 500, 501
J
Jaffe, J. F., 394
Jordan, B. D., 394
K
Kalanick, Travis, 1
Keynes, John Maynard, 554
L
Lee, I., 509, 510, 511
Lochhead, S., 509, 510, 511
M
Mankiw, Gregory N., 33
Marsh, Paul, 333
Mayer, Marissa, 14
Mayweather, Floyd, 13
Mehra, Rajnish, 333
Michaely, R., 472, 473, 476
Miller, Merton, 431
Modigliani, Franco, 431
Moore, J. S., 259
O
Obama, Barack, 33
P
Pacquiao, Manny, 13
Page, Larry, 498
Partners, Trian, 13
R
Rasulo, Jay, 299
Reichert, A. K., 259
Ritter, Jay R., 488, 499, 500, 501, 502, 509, 510,
511
Roberts, Brian, 218
Romney, Mitt, 33
Ross, S. A., 394
S
Saez, E., 472
Santayana, George, 311
Schmalz, M. C., 472
Seides, Ted, 339
Sindelar, J. L., 499, 500, 501
Sinquefield, Rex, 316
Skinner, D., 471
Stanley, M. T., 259
Statman, Meir, 362
Staunton, Michael, 333
Stewart, Bennett, 399
T
Tan, Hock, 13
Travolta, John, 275
Truman, Harry, 458
Twain, Mark, 311
W
Westerfield, R. W., 394
Z
Zhao, Q., 509, 510, 511
ros13952_nndx_641.indd 641 12/21/18 12:42 PM
642
Subject Index
A
AAR. See Average accounting return
Abandonment, options, 298
ABC approach, 574–575
ABN AMRO, 171
Abnormal returns, 507
Absolute priority rule (APR), defining, 445
Absolute purchasing power parity, 596–597
Accelerated Cost Recovery System (ACRS)
defining, 284
depreciation allowances, 285
modified property classes, 285
Accounting. See also Average accounting return;
Generally accepted accounting principles
finance and, 3–4
insolvency, 444
Accounts payable period, 537
defining, 525
Accounts receivable financing, 539–540
Accounts receivable period, 535
defining, 524
ACRS. See Accelerated Cost Recovery System
Adobe, 367
ADR. See American Depository Receipt
Aflac, 478
Aftermarkets, 497
Aftertax cash flow, 279
Agency cost, 12
Agency problem, 12–15
Agency relationships, 12
Aggregate growth, 393
Aging schedule, 572
AIM. See Alternative Investment Market
Airlines, capital structure of, 442
Alibaba, 66, 498
Alma, 274
Alpha, defining, 375
Alphabet, 496, 589
Alternative Investment Market (AIM), 11
Alternative issue methods, 493–494
Alvarez & Marsal, 446
Amazon, 66
beta coefficient for, 367
America Online (AOL), 292
American Bankruptcy Institute, 445
American Century Giftrust, 339
American Depository Receipt (ADR),
defining, 590
American Electric Power, 443
American Stock Exchange, 221
AmeriServe, 182
Amortization
defining, 146
loans, 145–149, 632
schedule, 146, 148
spreadsheets for, 149
tables, 148
AMR Corp., 448
Announcements, 359–360
Annual depreciation, 288
Annual percentage rate (APR)
EARs and, 142–144
financial calculators for, 144
reporting, 143
spreadsheets for, 144
Annuities
defining, 132
financial calculators for, 137
interest rates of, 136
ordinary, 631–632
Annuities due, 631
defining, 137
Annuity cash flows, present value for,
132–137
Annuity future values, financial calculators
for, 137
Annuity payments
financial calculator for, 134–135
finding, 134–135
Annuity present values, 133
spreadsheets for, 134
Annuity tables, 133
AOL. See America Online
Apple, 589
beta coefficient for, 367
Appreciation, currency, 600
Appropriate discount rate, 391
APR. See Absolute priority rule; Annual
percentage rate
Arithmetic average returns, geometric average
returns and, 335–336
Arithmetic averages, defining, 334
Articles of incorporation, 8
Asked prices, defining, 188
Aspirant groups, 74
Assets
on balance sheet, 23
cash flow from, 38
cash flows from, 34–36
current, 522, 530, 535
defining, 23
management, 58–60
requirements over time, 533
return on, 61, 69–72, 78
total asset turnover, 60, 70
utilization, 63
Asset-specific risks, 361
Auction markets, 17
Average accounting return (AAR)
advantages of, 247
defining, 246
disadvantages of, 247
problems with, 247
rule, 247
summary of, 247
yearly revenues and costs, 246
Average collection period, 527
Average returns
arithmetic, 334
calculating, 321
capital market history, 321–322
geometric, 334
record of, 321
Average tax rates, 31
B
Balance sheet, 555
assets on, 23
common-size, 52
of corporations, 24
debt on, 25–26
defining, 23
equity on, 25–26
liabilities on, 23–24
liquidity on, 25
net working capital on, 24–25
Banker’s acceptance, 569
Bankruptcy
avoiding, 448
composition, 448
defining, 444
extensions, 448
financial management and, 446–448
legal, 444
liquidation, 444–445
prepackaged, 446
processes, 444–448
reorganization, 445
strategic, 448
Bankruptcy Abuse Prevention and Consumer
Protection Act (BAPCPA), 446
Bankruptcy costs
direct, 437
indirect, 437–438
Banks, 571
BAPCPA. See Bankruptcy Abuse Prevention and
Consumer Protection Act
Barclays, 605
BASF, 389
Basic present value equation, 109
BATS Exchange, 225
BATS Global Markets, 499
Bearer form, defining, 178
Bell curve, 327
BellSouth, 171
Benchmarks, 73–78
Best Buy, 78
Best case, 295
Best efforts cash offers, 494
Best efforts underwriting, defining, 496
Beta
expected returns, 371
portfolios, 368–369, 371
rates, 394
Beta coefficient
for Amazon, 367
for Apple, 367
for Costco, 367
defining, 365
estimation of, 394
for Facebook, 367
for Ford, 367
for Home Depot, 367
for Macy’s, 367
for Pfizer, 367
portfolio expected returns and, 371
for Prudential, 367
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S U B J E C T I N D E X 643
corporate taxes and, 434–437
cost of equity and, 431–434
defining, 6
of department stores, 442
of drugs, 442
of electric utilities, 442
of fabric apparel, 442
financial distress costs and, 441
financial structure and, 425
of motor vehicles, 442
observed, 442–444
optimal, 438–441
of paper production, 442
of petroleum refining, 442
Pie model, 431
proposals, 430
questions, 425–426, 440
of restaurants, 442
static theory of, 438–439
of steel works, 442
taxes and, 441
of television, 442
Capital structure weights
formulas, 397–398
WACC and, 397–398
CAPM. See Capital asset pricing model
Captive finance company, 570
Carrying costs, 532, 570, 574
defining, 531
inventory management and, 576–577
Cases
Beta for FLIR Systems, 388, 423
Bullock Gold Mining, 274
Cash Flows and Financial Statements at Sunset
Boards, Inc., 49
Cost of Capital for Layton Motors, 423
Electronic Timing, Inc., 486
Financing S&S Air’s Expansion Plans with a
Bond Issue, 204
Jobs at S&S Air, 348
McGee Cake Company, 21
Piepkorn Manufacturing Working Capital
Management, 552, 588
Ratios and Financial Planning at S&S Air, Inc., 95
S&S Air, Inc. Goes International, 615
S&S Air, Inc. Goes Public, 520
S&S Air’s Mortgage, 164
Stephenson Real Estate Recapitalization, 456
Stock Valuation at Ragan, Inc., 236
Cash balance, 537–538
Cash budget, 537–538
defining, 536
Cash collections, 284, 536–537
components of, 558–559
Cash concentration, 559–560
Cash costs, 284
Cash coverage, 58
Cash cycle
calculation of, 526–528
comparison, 529
defining, 525
interpretation of, 528–530
Cash disbursements, 537
management of, 560–562
Cash discounts, 567–569
Cash dividends
extra, 459
regular, 458–459
standard method, 459
stock repurchase or, 468–469
depreciation and, 286
market value and, 26–27, 286
Borrowers, defining, 176
BP, 295
Break-even measures, 245
Brexit, 605
Broadcom, 13
Brokers
defining, 220
floor, 221
in stock markets, 220–221
Buffet Challenge, 339
Bullock Gold Mining case, 274
Business ethics, 10
Business failure, 444
Business finance, defining, 4–5
Business organization
forms of, 7–9
partnerships, 7–8
sole proprietorship, 7
Business risk, defining, 433
C
Caesars Entertainment, 367
Calculatoredge, 139
Call premium, defining, 178
Call protected bonds, defining, 179
Call provisions, defining, 178
Cannibalism, 278
Canon, 581
Capital asset pricing model (CAPM), 376
defining, 374
SML and, 374–375
Capital budgeting
CFO use of, 259
considerations in, 297–300
contingency planning in, 297–299
defining, 6
managerial options and, 297–300
NPV and, 258–259
practice of, 258–260
primary uses of, 259
strategic options and, 299
Capital budgeting decision, 238
Capital expenditures, 537
Capital gains
calculating, 312
taxes, 464
Capital gains yield, defining, 213
Capital intensity ratio, 60
Capital loss, calculating, 312
Capital market history, 311
average returns, 321–322
diversification and, 362–363
efficiency, 337–341
record of, 315–322
using, 330–332
Capital rationing
defining, 299
hard, 300
soft, 299–300
Capital requirements, projected, 280
Capital spending, 289
cash flow and, 35
net working capital and, 283
project, 281
Capital structure
of airlines, 442
of computer equipment, 442
risk premium and, 369–373
systematic risk and, 365–368
total risk and, 368
Bid prices, defining, 188
Bid-ask spread, 223
defining, 188
Big Mac index, 598
Bi-Lo, 47
Black Panther (film), 275
Blanket inventory lien, 540
Blockchain, 493
Blue Bird, 447
BMW, 603
Boeing, 50
Bond prices, 166
clean, 189
dirty, 189
financial calculator for, 173
finding, 632
quotes, 188–189
reporting, 188–189
spreadsheet for, 174
Bond ratings, 180–182
investment-quality, 181
junk, 181
Moody’s, 181
Standard & Poor’s, 181
Bond valuation, 166–175
Bond yields, 173
determinants of, 192–195
yield curve and, 193–195
Bondholders, defining, 23
Bonds
buying, 186–187
calculators, 169
call protected, 179
CAT, 186
convertible, 185
corporate, 316, 322
coupon rate of, 166
death, 186
defining, 23
discount, 168
Eurobonds, 590
exotic, 186
face value, 166
features of, 166, 175–180
floating-rate, 184–185
foreign, 590
funds, 348
government, 182–183, 316, 322
long-term corporate, 316
long-term government, 316
markets, 186–189
maturity of, 166
municipal, 182
par value, 166
premium, 168
put, 185
ratings, 396
registered form of, 178
returns on, 318
selling, 186–187
sprint, 177
terms of, 178
Treasury, 188
zero coupon, 183
Bonus depreciation, 286
Book building, 496
Book value
ros13952_sndx_642-652.indd 643 12/21/18 12:43 PM
644 S U B J E C T I N D E X
Corporate taxes, 31
capital structure and, 434–437
Corporations
balance sheets of, 24
business organization, 8–9
financial markets and, 15–17
international, 9, 589
smooth dividends, 474
Cost of capital
calculations, 401
defining, 377
divisional, 407–411
financial policy and, 391
funds in, 391
optimal capital structure and, 439–441
project, 407–411
required returns and, 390–391
weighted average, 389
Cost of debt
calculating, 401
defining, 396
Eastman Chemical, 404–405
Cost of equity
calculating, 401
dividend growth model approach for,
392–394
Eastman Chemical, 403–404
financial leverage and, 431–432
WACC and, 432
Cost of factoring, 539–540
Cost of money, 390
Cost of preferred stock, 396–397
Costco, beta coefficient for, 367
Costs
cash, 284
on income statement, 29
opportunity, 277–278
sunk, 277
Coupon rate
of bonds, 166
defining, 166
Coupons
defining, 166
interest rates and, 170–171
semiannual, 169
Covered interest arbitrage, 600–601
CPI. See Consumer price index
Credit analysis, 570–571
defining, 565
Credit cards, 162
Credit cost curve, defining, 569
Credit evaluation, 571
Credit function, organizing, 569–570
Credit information, 570–571
Credit instruments, 568–569
Credit manager, 525
Credit period
defining, 566
length of, 566–567
Credit policy, components of, 565
Credit ratings, 182
Credit reports, 571
Credit risk, 567
Creditors
cash flow to, 36, 38–39
defining, 176
Cross-rate, defining, 590
Crowdfunding
defining, 491
equity, 491
Collection float, 555–556
Collection policy
defining, 565
monitoring receivables, 571–572
Collections, cash, 284
College savings, 112
Combination approach, for MIRR, 256–257
Comic books, 111
Commercial draft, 569
Commercial paper, 540, 564
Committed lines of credit, 539
Common stock
classes of, 217–218
dividends, 218–219
features of, 216–219
frequency distribution of, 323
proxy voting and, 217
shareholder rights in, 216–217
Common stock valuation
cash flow and, 206–207
comparables for, 214–215
constant growth in, 208–209
nonconstant growth and, 211–212
required returns in, 213–214
special cases, 207–213
summary of, 215
supernormal growth and, 212
zero growth in, 208
Common-size balance sheets, 52
Common-size income statements, 53–54
Common-size statements, 52
Company stock, 348
Company valuation, with WACC, 411
Comparables, for common stock valuation,
214–215
Competition, 567
Components of return
systematic, 361–362
unsystematic, 361–362
Compound interest, 102
defining, 99
Compounding, 98–104
defining, 99
effective annual rates and, 140–141
frequency, 631
Computer equipment, capital structure of, 442
Concentration banks, 560
Conch Republic Electronics, 309
Consols, defining, 138
Constant growth, in common stock valuation,
208–209
Consumer demand, 567
Consumer price index (CPI), 316
Continental Airlines, 447
Contingency planning
in capital budgeting, 297–299
defining, 297
Controlled-disbursement accounts, 562
Controllers, 525
Conventional factoring, 539
Convertible bonds, 185
Corporate bonds, long-term, 316, 322
Corporate borrowing, homemade leverage and,
429–430
Corporate ethics, 11
Corporate finance
basic areas of, 2–3
defining, 2
Corporate investors, 465
Corporate securities, 17
Cash flow
aftertax, 279
analysis, 632
annuity, 132–137
from assets, 34–36, 38, 412
capital spending and, 35
common stock valuation and, 206–207
to creditors, 36, 38–39
defining, 33
discounted, 106, 239, 249, 260, 291–293
dividend policy and, 462
expected, 243
firm and, 15
free, 36
future value with multiple, 123–126
incremental, 276
investment examples, 315
multiple, 123–131
net working capital and, 35
nonconventional, 251–252
operating, 34–35, 282, 288
project, 240
projected total, 281–282, 290
relevant, 276
to stockholders, 36, 38–39
time line, 525
timing, 130–131
total, 289
Cash holding, 554–555
Cash inflow, 281
Cash management, 553–558
Cash manager, 525
Cash offers
best efforts, 494
Dutch auction, 494
firm commitment, 494
general, 494
nontraditional, 494
traditional negotiated, 494
Cash outflows, 537
Cash ratio, 56
Cash reserves, 534
Cash revenues, net working capital and, 283
Cash sources, 523
Cash uses, 523
CAT bonds, 186
CBOE, 225
Certificates of deposit (CDs), 564
CFO. See Chief financial officer
Charter Communications, 292, 448
Check Into Cash, 143
Chevron, 258
Chief financial officer (CFO), 5
capital budgeting techniques of, 259
surveys of, 260
China, 330
Chrysler, 448
Cisco, 367, 535
CIT Group, 448
Clean price, defining, 189
Cleanup period, 539
Clearing, 555
Clientele effect, 466
CNN Money, 367
Coca-Cola, 171
Collateral
defining, 178
value, 567
Collectibles, as investments, 111
Collection effort, 572
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S U B J E C T I N D E X 645
aggregate real, 467
calculating, 312
cash, 458–459
common stock, 218–219
corporations smooth, 474
cumulative, 219
defining, 218, 458
ex-dividend date, 460
income, 313
knowledge about, 471–473
liquidating, 459
noncumulative, 219
payout, 459
per share, 459
special, 459
stock, 477–479
survey evidence on, 476–477
yield, 459
Divisional cost of capital, 407–411
DJIA. See Dow Jones Industrial Average
DMMs. See Designated market makers
DOJ. See Department of Justice
Dollar returns, 311–312
total, 313
Domo, Inc., 509
Dot-com crash, 473
Dow Corning, 448
Dow Jones Industrial Average (DJIA), 328
DowDuPont, 67
Dropbox, 487, 504
Drugs, capital structure of, 442
Dun & Bradstreet, 571
DuPont analysis, 66–68
charts, 67
DuPont identity, 64–68
defining, 65
Dutch auction cash offer, 494
Dutch auction underwriting, 496
E
E. F. Hutton, 557
EAR. See Effective annual rates
Earnings before interest, taxes, depreciation, and
amortization (EBITDA), 58
Earnings before interest and taxes (EBIT), 411
EPS and, 427–429
Earnings management, 30–31
Earnings per share (EPS), 28, 214
EBIT and, 427–429
financial leverage and, 426–427
share repurchase and, 470
Eastman Chemical
cost of debt, 404–405
cost of equity, 403–404
WACC for, 401–407
EBIT. See Earnings before interest and taxes
EBITDA. See Earnings before interest, taxes,
depreciation, and amortization
ECNs. See Electronic communications networks
Economic order quantity (EOQ), 575–578
extensions to, 579
Economic value added (EVA), 399
EDGAR, 25
EDI. See Electronic data interchange
Effective annual rates (EAR)
APRs and, 142–144
calculation of, 141–142
comparing, 141–142
equity and, 509
spread for, 511
Direct expenses, 508
Direct listing, 498
Direct placement, 494
Direct rights offer, 494
Dirty price, defining, 189
Disbursement float, 555
controlling, 561
increasing, 560–561
Discount, 359
cash, 567–569
sales, 567
Discount bonds, 168
Discount rate
appropriate, 391
defining, 106
determining, 109–112
Discounted cash flow (DCF), 249
criteria, 260
defining, 106
forecasting risk and, 292–293
NPV and, 239
rate of return, 291
valuation, 106, 239
Discounting
defining, 105
present value and, 104–108, 127
Discounting approach, for MIRR, 256
Disney, 171
Disneyland Paris, 298–299
Distribution, defining, 458
Diversification, 376
capital market history and, 362–363
effect of, 362–363
principle of, 363–364
systematic risk and, 364–365
unsystematic risk and, 364
Dividend growth model
advantages of, 393–394
for cost of equity, 392–394
defining, 209
disadvantages of, 393–394
estimation in, 392–393
implementation of, 392
Dividend payments
chronology, 459–460
date of payment, 460
date of record, 460
declaration date, 459
ex-dividend date, 459
knowledge about, 471–473
pros and cons of, 477
Dividend policy, 70, 457–458
alternative, 462
cash flow and, 462
current, 462
current income and, 464–465
flotation costs and, 464
high payout, 464–465
initial, 462
irrelevance of, 462–463
knowledge about, 471–477
low payout, 463–464
restrictions, 464
survey responses on, 476
taxes and, 463–464
tests of, 463
Dividend yield, defining, 213
Dividends
project, 491
Cumulative dividends, of preferred stock, 219
Cumulative voting, defining, 216
Currency appreciation, 600
Currency depreciation, 600
Currency symbols, 592
Current assets, 522
alternative policies for, 532–534
financing of, 530, 532–534
investment in, 530–532
in practice, 535
Current events, 172
Current income, dividend policy and, 464–465
Current liabilities, 522
in practice, 535
Current ratio, 55–56
Customer type, 567
D
Date of payment, 460
Date of record, 460
Days’ sales in inventory, 58–59
Days’ sales in receivables, 527
DCF. See Discounted cash flow
Dealer markets, 17
Dealers
defining, 220
in stock markets, 220–221
Death bonds, 186
Debentures, 176
Debt. See also Cost of debt
on balance sheet, 25–26
embedded debt cost, 396
equity and, 25–26, 176
long-term, 176, 512–513
preferred stock as, 219–220
securities, 176
short-term, 176
total debt ratio, 57
unfunded, 176
usage, 507
Debtors, defining, 176
Declaration date, 459
Deepwater Horizon, 295
Default risk
premium, defining, 194
short-term securities and, 564
Deflation, 190
Delta Airlines, 448
Dentists, 150
Department of Justice (DOJ), 11
Department stores, capital structure of, 442
Depreciation, 284–287
ACRS and, 285
annual, 288
bonus, 286
book value and, 286
currency, 600
MACRS, 285–287
market value and, 286
Depreciation tax shield, defining, 282
Derived-demand inventories, 579–581
Designated market makers (DMMs)
defining, 221
post, 222
Determinants of growth, 70–71
Direct bankruptcy costs, defining, 437
Direct costs, 510
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Financial policy, 70
cost of capital and, 391
Financial problems, short-term, 525
Financial ratios, common, 63
Financial risk, defining, 433
Financial statements, 75–77, 279–280, 570–571
analysis, 79–80
common-size, 52
DowDuPont, 67
evaluation of, 72–73
standardized, 51–54
Financial structure, capital structure and, 425
Financing
best policies, 534–535
of current assets, 530, 532–534
Financing costs, incremental cash flows and,
278–279
Financing life cycle
first-stage, 488
second-stage, 488
venture capital in, 488–489
Finished goods, 573
FINRA. See Financial Industry Regulatory
Authority
Firm, control of, 13
Firm commitment cash offers, 494
Firm commitment underwriting, 495–496
First-stage financing, 488
Fisher effect, 190–191
Five Cs of credit, 571
FLIR Systems, 388
Float, 553–558
collection, 555–556
defining, 555
disbursement, 555, 560–561
management, 556–557
net, 555–556
Floating-rate bonds, 184–185
Floor brokers, defining, 221
Floor planning, 540
Flotation costs, dividend policy and, 464
Ford, 51
beta coefficient for, 367
Forecasting risk
DCF and, 292–293
defining, 292
Foreign bonds, defining, 590
Foreign exchange market, 591
Forward exchange rate, defining, 595
Forward trade, defining, 595
401(k) plans, 348
Free cash flow, 36
FreeSeas, Inc., 479
Frequency distributions
of common stock, 323
historical average, 327
inflation, 327
Treasury bills, 327
of variability, 323
Future value, 98–104, 616–623
annuity, 137
defining, 98
on financial calculators, 103
with multiple cash flows, 123–126
of ordinary annuities, 631–632
present value and, 108–109
sample problems, 631–632
of single sum, 631
time lines and, 125
Future value interest factor, 99
unexpected returns and, 358–359
Expected risk premium, 352
Expenses
direct, 508
indirect, 508
Exploding Kittens, 491
ExxonMobil, 258, 470, 471
F
Fabric apparel, capital structure of, 442
Face value bonds, defining, 166
Facebook, 14, 71
beta coefficient for, 367
Factoring
conventional, 539
maturity, 539
FASB. See Financial Accounting Standards Board
Federal Reserve Bank, 162, 188
Fiat Chrysler, 581
Fidelity Magellan Fund, 325
Fiduciary responsibilities, 465
Field warehouse financing, 540
Finance. See also Business finance; Corporate
finance
accounting and, 3–4
international, 3
management and, 4
marketing and, 3
study of, 3–4
Financial Accounting Standards Board (FASB),
25, 604
Financial calculators
for annuities, 137
for annuity future values, 137
for annuity payments, 134–135
for APR, 144
for bond prices, 173
for EAR, 144
future value on, 103
for interest rates, 137
for multiple cash flows, 129
for present value, 129
settings, 631
wrong answers with, 103–104
Financial crisis of 2008, 329–330
Financial distress costs
capital structure and, 441
defining, 437
Financial Industry Regulatory Authority
(FINRA), 491
Financial institutions, defining, 3
Financial leverage, 26
cost of equity and, 431–432
EPS and, 426–427
impact of, 426–429
ratios, 57
ROE and, 426–427
Financial management
bankruptcy and, 446–448
in corporations, 10
general, 10
goals of, 9–12
profit maximization and, 9–10
Financial management decisions, 5–6
Financial manager, 573
defining, 5
Financial markets, corporation and, 15–17
Financial planning, short-term, 541
Effective annual rates (EAR)—Cont.
compounding and, 140–141
defining, 141, 142
financial calculators and, 144
spreadsheets for, 144
Efficient markets
defining, 337
forms of, 340
price behavior in, 337
stocks and, 338
Efficient markets hypothesis (EMH)
defining, 338
misconceptions about, 339–341
Electric utilities, capital structure of, 442
Electronic communications networks (ECNs)
defining, 224
NASDAQ, 224–225
Electronic data interchange (EDI), 557
Electronic Timing, Inc. (ETI), 486
Embedded debt cost, 396
EMH. See Efficient markets hypothesis
END mode, 631
Energen, 402
Energy Future Holdings Corp., 448
Enron, 446, 473
Enterprise value-EBITDA ratio, 62–63
EOQ. See Economic order quantity
EPS. See Earnings per share
Equations, basic present value, 109
Equity. See also Cost of equity
on balance sheet, 25–26
cost of, 395
crowdfunding, 491
debt and, 25–26, 176
defining, 23
direct costs and, 509
return on, 61, 69–72, 78, 426–427
sales, 507
securities, 176
Erosion, defining, 278
Estimation risk, 292
Ethereum, 493
Ethics
business, 10
corporate, 11
ETI. See Electronic Timing, Inc.
Euro Disney, 298
Eurobonds, defining, 590
Eurocurrency, defining, 590
Euronext, 221
EVA. See Economic value added
Excel, 121, 293
Excess return, 322
Exchange quotations, 593
Exchange rates
defining, 592
forward, 595
risk, 602–605
spot, 595
Ex-dividend date, 459
price behavior around, 460
Exit strategy, 490
Exotic bonds, 186
Expansion, options, 298
Expected returns, 351–353
betas, 371
calculation of, 352
defining, 352
portfolios, 355–356, 370, 372
systematic risk and, 373
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standard deviations, 327
Treasury bills, 327
Internal growth, 68–72, 71
rate, 69
Internal rate of return (IRR), 248–257
calculating, 250, 251
defining, 248
MIRR and, 257
modified, 256–257, 260
mutually exclusive investments and,
253–254
nonconventional cash flow and, 251–252
NPV and, 248
problems with, 251
redeeming qualities of, 255–256
rule, 248
spreadsheets for, 251
Internal Revenue Service (IRS), 8–9, 31
International corporations, 9, 589
International currency symbols, 592
International finance, defining, 3
Inventory costs, 574
Inventory depletion, 576
Inventory loan, 540
Inventory management
ABC approach, 574–575
carrying costs and, 576–577
shortage costs and, 577
total costs, 577–578
Inventory period, defining, 524
Inventory turnover, 58–59, 527
Inventory types, 573
Investments
cash flow and, 315
collectibles as, 111
in current assets, 530–532
defining, 2
evaluation of, 109
in growth stocks, 332
guides to, 331
of idle cash, 562–565
payback periods and, 242
in portfolios, 316
for single period, 98–104
Investors
corporate, 465
tax-exempt, 465
IPO. See Initial public offering
IRR. See Internal rate of return
IRS. See Internal Revenue Service
Issue costs, 507
J
Jackpots, 128
JOBS Act, 491
John Deere, 581
Johnson & Johnson, 443
Joint stock companies, 9
JPMorgan, 487
Just-in-time inventory, defining, 581
K
Kanban, 581
Keiretsu, 581
Key employee retention plans (KERPs), 446
Kickstarter, 491
Kiting, 557
Income statements, pro forma, 288
Incorporation, articles of, 8
Incremental cash flows
defining, 276
financing costs and, 278–279
opportunity costs and, 277–278
side effects, 277
sunk costs and, 277
Indenture, defining, 177
Independence, 251
India, 330
Indirect bankruptcy costs, 437–438
defining, 437
Indirect costs, 510
Indirect expenses, 508
Inefficient markets, stocks and, 338
Inflation, 190–192
average, 321
frequency distributions, 327
standard deviations, 327
year-to-year, 319
Inflation premium, defining, 193
Initial coin offerings (ICOs), 493
Initial public offering (IPO)
costs of, 512
defining, 494
file price range, 505
first-day returns, 505
global, 502
gross proceeds, 501
numbers of, 501
underpricing and, 498–507
Innovation, 359
Innovative Motors Company (IMC), 278
Inside quotes, 224
Insolvency
accounting, 444
technical, 444
Intercontinental Exchange (ICE), 221
Interest
compound, 99, 102
covered interest arbitrage, 600–601
future value interest factor, 99
on interest, 99
present value interest factor, 106
simple, 99
Interest rate risk premiums, defining, 193
Interest rates. See also Annual percentage rate;
Effective annual rates
of annuities, 136
comparing, 140–144
conversions, 633
coupons and, 170–171
effective annual, 140–141
financial calculators for, 137
finding, 136, 632
maturity and, 170
nominal, 190–192
parity, 601–602
pure, 192
quoted, 141
real, 190–191
relative, 534
risk, 169–171
stated, 141
term structure of, 192–193
Interest tax shield, 434
defining, 435
Interest-only loans, 145–146
Intermediate-term government bonds
G
GAAP. See Generally accepted accounting
principles
GameStop, stock, 314
GDP. See Gross domestic product
General cash offers, defining, 494
General Electric, 471
General Growth Properties, Inc., 448
General Motors, 51, 184, 186, 448, 581
General partners, 7
Generally accepted accounting principles
(GAAP), 26–27, 79
income statement and, 28
Geometric average returns
arithmetic average returns and, 335–336
calculation of, 334–335
defining, 334
Gifts, defining, 591
Gilead Sciences, 205
Globalization, 590
Goldman Sachs, 487
Google, 14, 496, 499
Government bonds, 182–183
long-term, 316, 322
Great Depression, 311
Green Shoe option, 508
Green Shoe provision, defining, 497
Gross domestic product (GDP), 358, 359
Growth stocks, 207
investment in, 332
Gulf of Mexico, 295
H
Hard rationing, defining, 300
Hedge funds, 339
Hedging, maturity, 534
Helios & Matheson, 514
Historical variance, 324
Hollywood, 298
Home Depot, 64
beta coefficient for, 367
Homemade leverage
corporate borrowing and, 429–430
defining, 429–430
Honda, 603
Hormel, 350
earnings, 360
Hurdle rate, 390
Hurricane Katrina, 186
Hybrid market, 221
I
IBM, 52
ICE. See Intercontinental Exchange
Iceland, 330
ICOs. See Initial coin offerings
Idle cash, investment of, 562–565
IMC. See Innovative Motors Company
Income statement
common-size, 53–54
costs on, 29
defining, 27
GAAP, 28
noncash items, 28–29
projected, 280
time on, 29
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discounting approach for, 256
IRR and, 257
reinvestment approach for, 256
Money market, 562
funds, 348
securities, 564–565
Monster Trucks (film), 275
Moody’s, 162
bond ratings, 181
Mortgage securities, 178
Mortgage-backed securities, 186
Motley Fool, 208
Motor vehicles, capital structure of, 442
MRP. See Materials requirements planning
Multinationals, 589
Multiple cash flows
financial calculator for, 129
future value with, 123–126
present value with, 126–130
spreadsheets for, 131
Multiple period present value, 105
Multiple rates of return, defining, 253
Municipal bonds, 182
Mutually exclusive investments
IRR and, 253–254
NPV for, 254
N
NAICS. See North American Industry
Classification System
Nanocaps, 226
NASD. See National Association of Securities
Dealers
NASDAQ, 12, 17, 473, 479, 510
ECNs, 224–225
operations, 223–224
NASDAQ Composite Index, 310
National Association of Securities Dealers
(NASD), 17
National Football League (NFL), 331
National Payday, 143
Negative covenants, 180
Negotiated offer basis, defining, 495
Neiman Marcus, 74
Net capital spending, 38
Net cash inflow, 537
Net float, 555–556
Net income, 28
Net present value (NPV), 260
basic idea behind, 238–239
basic problems in, 291–292
calculation of, 241
capital budgeting and, 258–259
DCF and, 239
defining, 239
estimation of, 239–242, 258, 291–293
internal rate of return and, 248
for mutually exclusive investments, 254
positive, 337
profile, 250, 254
rule, 240
sensitivity analysis, 296–297
sources of, 293
spreadsheets for, 241
underestimation of, 298
Net working capital, 34, 38, 288, 521
on balance sheet, 24–25
capital spending and, 283
cash flow and, 35
M
MACRS. See Modified Accelerated Cost Recovery
System
Macy’s, beta coefficient for, 367
Majestic Mulch and Compost Company (MMCC),
287–291
Management. See also Financial manager
finance and, 4
goals, 12–13
stockholder interests and, 13–15
Managerial compensation, 13
Managerial options
capital budgeting and, 297–300
defining, 297
Manville, 448
Marginal tax rates, 31
Marillion, 491
Market portfolios, 374
Market rates, 172
Market risk, 361
Market risk premium, 374
Market value
book value and, 26–27, 286
depreciation and, 286
ratios, 63
Marketability, of short-term securities, 564
Marketable securities, 535
Marketing, finance and, 3
Marketing manager, 525
Markets
auction, 17
dealer, 17
primary, 15–17
secondary, 15–17
Market-to-book ratio, 62–63
Marriott, 410
Materials requirements planning (MRP), 580
Maturity
of bonds, 166
factoring, 539
hedging, 534
interest rates and, 170
of short-term securities, 563–564
yield to, 166
McDonald’s, 410, 459
McGee Cake Company, 21
Members, defining, 221
Meridian Magnesium, 581
Mezzanine level, 489
MF Global Holdings Ltd., 448
MGM Resorts, 470
Microcaps, 226
Microsoft, 292, 350, 367, 589
earnings, 360
stock, 314
Milbank, Tweed Hadley, & McCloy, 446
MIRR. See Modified internal rate of return
M&M Proposition I, 431, 439
summary of, 436
taxes and, 435
M&M Proposition II, 431–432
summary of, 436
MMCC. See Majestic Mulch and Compost
Company
Modified Accelerated Cost Recovery System
(MACRS)
book values, 286
depreciation, 285–287
Modified internal rate of return (MIRR), 260
combination approach for, 256–257
L
Large-company stocks, 315, 348
returns on, 317, 322
risk premiums of, 322
standard deviations, 327
total return, 317
Layton Motors, 423
Ledger, 555
Legal bankruptcy, 444
Lehman Brothers, 445, 448
Lender, defining, 176
Letter of comment, 490
Liabilities
on balance sheet, 23–24
current, 522, 535
limited liability company, 8, 9
on owners’ equity, 23–24
LIBOR. See London Interbank Offered Rate
Lime Energy, 479
Limited liability company (LLC), 8, 9
Limited partners, 7
Line of credit, 539
Liquidating dividends, 459
Liquidation
bankruptcy, 444–445
defining, 444
Liquidity
on balance sheet, 25
defining, 25
premium, 193, 195
supplemental liquidity providers, 221
Listing, 17–18
LLC. See Limited liability company
Lloyds Banking Group, 605
Loans
agreements, 177
amortization, 145–149, 632
interest-only, 145–146
payday, 143
pure discount, 145
secured, 539–540
student, 150
term, 513
types, 145–149
unsecured, 539
Lockboxes
defining, 559
processing, 560
Lockup agreements, defining, 497
London Interbank Offered Rate (LIBOR), defining,
591
London Stock Exchange (LSE), 17
Long-run exposure, 603
Long-term corporate bonds, 316
returns on, 322
risk premiums of, 322
standard deviations, 327
Treasury bills, 327
Long-term debt, 176
issuing, 512–513
Long-term financing expenses, 537
Long-term government bonds, 316
returns on, 322
risk premiums of, 322
standard deviations, 327
Treasury bills, 327
Long-term solvency, 57–58, 63
Lotteries, 128
Lowe’s, 64
LSE. See London Stock Exchange
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inflation, 193
interest rate risk, 193
Prepackaged bankruptcy, 446, 447
Present value. See also Net present value
annuity, 133–134
for annuity cash flows, 132–137
basic equation, 109
calculation of, 127
defining, 105
discounting and, 104–108, 127
financial calculator for, 129
future value and, 108–109
with multiple cash flows, 126–130
multiple period, 105
of ordinary annuities, 631–632
of single sum, 631
single-period, 105
spreadsheets for, 131
Present value interest factor, 106
Price appreciation, 213
Price behavior, in efficient markets, 337
Price behavior around, ex-dividend date, 460
Price-earnings ratio (PE), 62
Price-sales ratio, 52
Primary markets
defining, 220
secondary markets and, 15–17
PrimeEnergy, 205
Principle of diversification, 364
defining, 363
Private placements, defining, 513
Privileged subscription, 494
Pro forma financial statements, defining, 279
Pro forma income statements, 288
Probabilities, unequal, 353, 354
Procter & Gamble, 13, 474
Production manager, 525
Profit margin, 61, 70
Profit maximization, financial management and,
9–10
Profitability, 567
measures, 60–61
ratios, 63
Profitability index (PI), 257, 260
advantages of, 258
disadvantages of, 258
Project cash flows, 240
net working capital and, 283–284
operating, 280–281
Project cost of capital, 407–411
Project net working capital, 281
Projected cash flows, 290
Projected revenues, 288
Projected risk premiums, 352
Promissory notes, 568–569
Proportionality, 218
Prospectus, defining, 490
Protective covenants, defining, 180
Protonex Technologies, 12
Proxy fight, 13
Proxy voting, common stock and, 217
Prudential, beta coefficient for, 367
Public information, 340
Purchasing power parity (PPP)
absolute, 596–597
defining, 596
relative, 598–600
results, 599
Pure discount loans, 145
Pure interest rates, 192
P
Palm, Inc., 504
Paper production, capital structure of, 442
Par value bonds, defining, 166
Paramount Pictures, 275
Parmalat, 448
Partial adjustment, 504–505
Partnerships
agreement, 7
business organization, 7–8
defining, 7–8
general, 7
limited, 7
Payables manager, 525
Payback criteria, 260
Payback periods, defining, 242
Payback rule
analyzing, 244
defining, 242–244
redeeming features of, 244–245
summary of, 245
Payday loans, 143
Payments, history, 571
PE. See Price-earnings ratio
Peer group analysis, 73
Penny stocks, 226
Pennzoil, 448
Percentage returns, 313–315
Perishability, 567
Perpetuities, defining, 138
Pessimism, 295
Petroleum refining, capital structure of, 442
Pfizer, beta coefficient for, 367
Philadelphia Eagles, 331
PI. See Profitability index
Piepkorn Manufacturing, 552, 588
Piracy, 278
Plowback ratio, 68
Political risk, 605
management of, 606–607
Portfolios
beta, 368–369, 371
defining, 355
expected returns, 355–356, 370, 372
investments in, 316
market, 374
returns, 362
standard deviation and, 357, 362
Treasury bills, 316
variance, 357–358
weights, 355
Positive covenants, 180
PPP. See Purchasing power parity
Precautionary motive, defining, 554
Preemptive right, 218
Preferred stock, 140
cost of, 396–397
cumulative dividends of, 219
as debt, 219–220
features, 219–220
noncumulative dividends of, 219
stated value of, 219
Premium
default risk, 194
liquidity, 193, 195
risk, 321–322, 351–352, 369–373
taxability, 195
Premium bonds, 168
Premiums
call, 178
cash revenues and, 283
changes in, 35, 283, 289
defining, 24
incremental cash flows and, 278
project, 281
tracing, 522–523
New York Stock Exchange (NYSE), 17
floor activity, 222–223
operations, 222
order flow at, 222
organization of, 221–223
News, 359–360
NFL. See National Football League
Nikkei, 459
Nokia, 292
Nominal interest rates, 192
Noncash items, income statement, 28–29
Noncommitted lines of credit, 539
Nonconstant growth, common stock valuation and,
211–212
Nonconventional cash flow, IRR and, 251–252
Noncumulative dividends, of preferred stock, 219
Nondiversifiable risk, 364
Normal distribution, defining, 327
North American Industry Classification System
(NAICS), 74
Notes, 176, 178
NPV. See Net present value
NYSE. See New York Stock Exchange
O
Oasis Films, 275
Okta, 350
Open market purchases, 467
Operating cash flow, 37–39, 288
defining, 34–35, 282
tax shield and, 282
Operating cycle
calculation of, 526–528
defining, 524–525
organizational chart and, 525–526
Oppenheimer Enterprise Fund, 339
Opportunity costs, 570
defining, 277
incremental cash flows and, 277–278
Optimal capital structure, 438
cost of capital and, 439–441
Optimism, 295
Options
to abandon, 298
to expand, 298
Green Shoe, 508
managerial, 297–300
strategic, 299
to wait, 298
Order costs, 531
Order flow
defining, 222
at NYSE, 222
Ordinary annuities
future value of, 631–632
present value of, 631–632
Organizational charts, simplified, 5
OTC. See Over-the-counter
OTCBB. See Over-the-Counter Bulletin Board
Over-the-counter (OTC), 17
Over-the-Counter Bulletin Board (OTCBB), 226
Overvaluing, 373
Owners’ equity, liabilities on, 23–24
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Secondary markets
defining, 220
primary markets and, 15–17
Second-stage financing, 488
Secured loans, 539–540
Securities
debt, 176
equity, 176
money market, 564–565
mortgage, 178
mortgage-backed, 186
selling, 490–493
short-term, 563–564
Securities Act of 1933, 490
Securities and Exchange Commission (SEC), 16
Securities Exchange Act of 1934, 490, 514
Security market line (SML), 351, 376
advantages of, 395
approach, 394–395
CAPM and, 374–375
defining, 374
disadvantages of, 395
implementation of, 394–395
subjective approach and, 411
WACC and, 408–409
Seed money, 488
Semiannual coupons, 169
Semistrong form efficient, 340
Seniority, 179
Sensitivity analysis
defining, 296
NPV, 296–297
for unit sales, 296
what-if, 296–297
SEO. See Seasoned equity offering
Share repurchase, EPS and, 470
Shareholder rights, in common stock,
216–217
Shelf registration, 514
defining, 513
Shortage costs, 574
defining, 531
inventory management and, 577
Short-run exposure, 602–603
Short-term borrowing, 535, 539–540
Short-term debt, 176
Short-term financial planning, 541
Short-term financial policy, aspects of, 530–535
Short-term financial problems, 525
Short-term securities
default risk and, 564
marketability of, 564
maturity of, 563–564
taxes and, 564
Short-term solvency, 55–56, 63
Short-term tax-exempts, 564
SIC codes. See Standard Industrial Classification
codes
Sight draft, 569
Sign changes, 631
Simple interest, defining, 99
Single period investments, 98–104, 109
Single-period present value, 105
Sinking funds, defining, 179
Sirius XM, 14
SLPs. See Supplemental liquidity providers
Small-cap funds, 348
Small-company stocks, 316
returns on, 322
risk premiums on, 322
total, 317, 318, 376
on Treasury bills, 318, 322
unexpected, 358–359
year-to-year, 320
Revenues, projected, 288
Reverse splits, 478–479
Revolving credit arrangement, 539
Reward-to-risk ratio, 370–371, 376
fundamental results, 372–373
Rights offer
defining, 494
direct, 494
standby, 494
Risk
adjustment for, 394
asset-specific, 361
business, 433
credit, 567
default, 194, 564
estimation, 292
exchange rates, 602–605
expected returns and, 373
financial, 433
interest rates, 169–171
market, 361
nondiversifiable, 364
political, 605–607
returns and, 375
reward-to-risk ratio, 370–371, 376
systematic, 360, 364–365, 373, 376
total, 368, 376
unique, 361
unsystematic, 360, 364, 376
Risk premiums, 321, 351
beta coefficient, 369–373
defining, 322
expected, 352
interest rate, 193
of large-company stocks, 322
of long-term corporate bonds, 322
of long-term government bonds, 322
market, 374
projected, 352
on small-company stocks, 322
stock market, 332–333
of Treasury bills, 322
Risk-free returns, 322
ROA. See Return on assets
Road shows, 496
ROE. See Return on equity
Rule 415, 514
Rule of 72, 110, 321
Russia, 330
S
Safety reserves, 531
Safety stocks, 579
Sales discount, 567
Sangamo Therapeutics, 310
Sarbanes-Oxley Act (Sarbox), 11–12
Savings, 106, 124
college, 112
Scenario analysis
defining, 294
what-if, 294–295
Sears, 310, 366
Seasonal cash demands, 563
Seasoned equity offering (SEO), defining, 494
SEC. See Securities and Exchange Commission
Pure play approach
defining, 410
for WACC, 409–410
Pure time value of money, 374
Put bonds, 185
Q
Quick ratio, 56
Quiet period, 498
Quoted interest rate, defining, 141
R
Ragan, Inc., 236
Ratio analysis, 54–64
Rationing
capital, 299–300
hard, 300
soft, 299–300
Raw material, 573
Reasonableness, 293
Red herring, defining, 490
Registered form
of bonds, 178
defining, 178
Registers, clearing, 631
Registration statement, defining, 490
Regulation CF, 491
Reinvestment approach, for MIRR, 256
Relative interest rates, 534
Relative purchasing power parity, 598–600
Relevant cash flow, 276
Reorder points, 579
Reorganization
bankruptcy, 445
defining, 444
Repayment, defining, 179
Required returns
in common stock valuation, 213–214
cost of capital and, 390–391
Restaurants, capital structure of, 442
Restocking costs, 578
Retention ratio, 68
Retirement, 112
Return on assets (ROA), 61, 69–72, 78
Return on equity (ROE), 61, 69–72, 78
financial leverage and, 426–427
Returns. See also Expected returns; Internal rate
of return
abnormal, 507
annual, 321
average, 321–322, 334–335
on bonds, 318
calculating, 314
components of, 361–362
dollar, 311–313
excess, 322
first-day, 505
historical average, 327
on large-company stocks, 317, 322
on long-term corporate bonds, 322
on long-term government bonds, 322
percentage, 313–315
portfolios, 362
rate of, 110
risk and, 375
risk-free, 322
on small-company stocks, 322
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S U B J E C T I N D E X 651
SVA. See Stockholder value added
Swaps, defining, 591
Sweepstakes, 128
SWIFT. See Society for Worldwide Interbank
Financial Telecommunications
Syndicate, defining, 495
Systematic components of return, 361–362
Systematic risk, 376
amount of, 374
bearing, 374
beta coefficient and, 365–368
defining, 360
diversification and, 364–365
expected returns and, 373
measurement of, 365–368
principle, 365
T
TANSTAAFL, 277
Targeted repurchase, 468
Tax Cuts and Jobs Act, 22, 286, 424, 589, 606
Tax Reform Act, 284
Tax shield
depreciation, 282
interest, 434–435
operating cash flow and, 282
Taxability premium, defining, 195
Taxes, 537
average, 31
capital gains, 464
capital structure and, 441
corporate, 31
dividend policy and, 463–464
marginal, 31
M&M Proposition I and, 435
short-term securities and, 564
WACC and, 398–400
Tax-exempt investors, 465
Technical insolvency, 444
Television, capital structure of, 442
Temporary cash surpluses, 563
Tender offers, 467
Term loans, defining, 513
Term structure
determination of, 193
of interest rates, 192–193
Terms of sale, 566
defining, 565
Tesla Motors, 423
Teva Pharmaceuticals, 182, 292
Texaco, 448
Texas, 402
Thornburg Mortgage, Inc., 448
3Com, 504
TIE. See Times interest earned
Time, on income statement, 29
Time draft, 569
Time lines, 123
drawing, 124
future value and, 125
Time value of money, 98
importance of, 114
pure, 374
spreadsheets for, 114
Time Warner, 292
Times interest earned (TIE), 57–58
Time-trend analysis, 73
Token sales, 493
Tokyo Stock Exchange (TSE), 17
Stephenson Real Estate Company, 456
Stern Stewart, 399
Stock
buybacks, 470
common, 216–219, 323
company, 348
GameStop, 314
growth, 207, 332
large-company, 315, 317, 348
Microsoft, 314
penny, 226
preferred, 140
returns, 352
safety, 579
small-company, 316, 318
states of economy and, 352
unlevering, 430
Stock dividends
defining, 477
large, 477
small, 477
trading range of, 478
value of, 478
Stock markets
brokers in, 220–221
dealers in, 220–221
reporting, 227
Stock repurchase
aggregate real, 467
cash dividends or, 468–469
defining, 466
real-world considerations in, 469–470
Stock split
defining, 477
reverse, 478–479
trading range of, 478
value of, 478
Stockholder value added (SVA), 399
Stockholders
cash flow to, 36, 38–39
management and interests of, 13–15
Stocks
efficient markets and, 338
inefficient markets and, 338
Straight voting, defining, 216
Straight-line, 29
Strategic bankruptcies, 448
Strategic options
capital budgeting and, 299
defining, 299
Strong form efficient, 340
Structured notes, 185
Student loans, 150
Subjective approach
SML and, 411
for WACC, 410–411
Sunk costs
defining, 277
incremental cash flows and, 277
Sunnylife, 367
Sunset Boards, Inc., 49
Super Bowl, 331
Supernormal growth, common stock valuation
and, 212
Supplemental liquidity providers (SLPs), defining,
221
Supply chain management, 581
Surprise, 359
Sustainable growth, 68, 71
rate, 69–70
standard deviations, 327
total return on, 318
SML. See Security market line
Society for Worldwide Interbank Financial
Telecommunications (SWIFT), 591
Soft rationing, 300
defining, 299
Sole proprietorship
business organization, 7
defining, 7
Southeastern Grocers, 47
Southern Company, 367
Special cases, common stock valuation, 207–213
Special dividends, 459
Speculative motive, defining, 554
SPO Global, 367
Spot exchange rate, 595
Spot trade, defining, 595
Spread, 508
defining, 495
for direct costs, 511
Spreadsheets
for amortization, 149
for annuity present values, 134
for APR, 144
for bond prices, 174
for EAR, 144
for internal rate of return, 251
for multiple cash flows, 131
for NPV, 241
for present value, 131
for time value of money calculations, 114
Sprint bonds, 177
S&S Air, Inc., 95, 164, 204, 348, 520, 615, 625
Staggered boards, 217
Stakeholders, defining, 15
Stamps, 111
Stand-alone principle, 277
defining, 276
Standard deviations
calculation of, 326
defining, 323
equations for, 353
historical average, 327
intermediate-term government bonds, 327
large-company stocks, 327
long-term corporate bonds, 327
long-term government bonds, 327
portfolios and, 357, 362
small-company stocks, 327
Treasury bills, 327
variance and, 357
Standard Industrial Classification (SIC) codes,
73–74
Standard & Poor’s, 329
bond ratings, 181
Standard & Poor’s 500 Index, 339
Dividend Aristocrat list, 474
returns, 310
Standardization, 567
Standby rights offers, 494
Stanley Works, 474
Staple Supply Co., 287
Stated interest rate, defining, 141
Stated value, of preferred stock, 219
States of economy, 351
stock and, 352
Static theory of capital structure, defining, 438–439
Statistics, 332
Steel works, capital structure of, 442
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652 S U B J E C T I N D E X
Walmart, 71, 74, 223, 424, 535
Walt Disney Studios, 298
Warehouse problem, WACC and, 400–401
Warrants, 495
Warrior Met Coal, 461
Weak form efficient, 340
Weighted average cost of capital (WACC), 389,
390, 425
calculation of, 400–407, 432
capital structure weights, 397–398
company valuation with, 411–413
cost of equity and, 432
defining, 398
formula for, 399
pure play approach for, 409–410
SML and, 408–409
subjective approach for, 410–411
taxes and, 398–400
warehouse problem and, 400–401
Weil, Gotshal & Manges, 446
What-if analyses
scenario, 294–295
sensitivity, 296–297
starting, 293–294
Winn-Dixie, 47
Working capital management, 521
defining, 6
Piepkorn Manufacturing, 552, 588
Work-in-progress, 573
World Wrestling Federation (WWF), 491,
492, 503
WorldCom, 473
Worst case, 295
WWF. See World Wrestling Federation
Y
Yahoo!, 14
Yahoo! Finance, 367
Yield curve
bond yields and, 193–195
Treasury, 194
Yield to maturity (YTM), 166
finding, 171–175
Z
Zero coupon bonds, 183–184
Zero growth, in common stock valuation, 208
Zero-balance accounts, 562
existence of, 505–506
IPO and, 498–507
in 1999-2000, 499–500
Underwriters
best efforts, 496
choosing, 495
defining, 495
Dutch auction, 496
firm commitment, 495–496
types of, 495–496
Unequal probabilities, 353, 354
Unexpected returns, expected returns and,
358–359
Unfunded debt, 176
Uniform price auction, 496
Unique risks, 361
Unit sales, sensitivity analysis for, 296
Unsecured loans, 539
Unsystematic components of return,
361–362
Unsystematic risk, 376
defining, 360
diversification and, 364
V
Value, sources of, 293
Value Line, 367
ValuePro, 406
Variability, frequency distributions of, 323
Variance
calculation of, 326, 353–355
defining, 323
equations for, 353
historical, 324
portfolios, 357–358
standard deviation and, 357
Venture capital (VC)
choosing, 489
defining, 488
in financing life cycle, 488–489
Verizon, 14
Voluntary restraint agreements
(VRAs), 597
W
WACC. See Weighted average cost of capital
Wages, 537
Waiting, options, 298
Tombstones, 492
defining, 491
Total asset turnover, 60, 70
Total cash flow, 289
Total costs, inventory management, 577–578
Total debt ratio, 57
Total dollar returns, 313
Total return, 376
formula for, 359
on large-company stocks, 317
on small-company stocks, 318
Total risk, 376
beta coefficient and, 368
Total value, 289
Toyota, 51, 581, 603
TRACE, 187, 188
Trade acceptance, 569
Trade credit, 540
Trading costs, 531
Trading range
of stock dividends, 478
of stock split, 478
Transaction motive, defining, 554–555
Transactions, types of, 595–596
Translation, 604–605
Transparency, 187
Treasury bills, 145, 564
frequency distributions, 327
intermediate-term government bonds, 327
long-term corporate bonds, 327
long-term government bonds, 327
portfolios, 316
rates, 394
returns on, 318, 322
risk premiums of, 322
standard deviations, 327
Treasury bonds, 188
Treasury yield curve, defining, 194
Trex Company, 478
Treynor index, 370
Trian Partners, 13
Triangle arbitrage, 593
Trust
deed of, 177
receipt, 540
TSE. See Tokyo Stock Exchange
U
Underpricing, 508
evidence on, 499–500
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Cover
Title
Copyright
About the Authors
From the Authors
Organization of the Text
Learning Solutions
Comprehensive Teaching and Learning Package
Acknowledgments
Brief Contents
Contents
List of Boxes
PART ONE: OVERVIEW OF FINANCIAL MANAGEMENT
1 Introduction to Financial Management
1.1 Finance: A Quick Look
The Four Basic Areas
Corporate Finance
Investments
Financial Institutions
International Finance
Why Study Finance?
Marketing and Finance
Accounting and Finance
Management and Finance
You and Finance
1.2 Business Finance and the Financial Manager
What Is Business Finance?
The Financial Manager
Financial Management Decisions
Capital Budgeting
Capital Structure
Working Capital Management
Conclusion
1.3 Forms of Business Organization
Sole Proprietorship
Partnership
Corporation
A Corporation by Another Name…
1.4 The Goal of Financial Management
Profit Maximization
The Goal of Financial Management in a Corporation
A More General Financial Management Goal
Sarbanes-Oxley Act
1.5 The Agency Problem and Control of the Corporation
Agency Relationships
Management Goals
Do Managers Act in the Stockholders' Interests?
Managerial Compensation
Control of the Firm
Conclusion
Stakeholders
1.6 Financial Markets and the Corporation
Cash Flows to and from the Firm
Primary versus Secondary Markets
Primary Markets
Secondary Markets
Summary and Conclusions
Critical Thinking and Concepts Review
What's on the Web?
CHAPTER CASE: The McGee Cake Company
PART TWO: UNDERSTANDING FINANCIAL STATEMENTS AND CASH FLOW
2 Financial Statements, Taxes, and Cash Flow
2.1 The Balance Sheet
Assets: The Left-Hand Side
Liabilities and Owners' Equity: The Right-Hand Side
Net Working Capital
Liquidity
Debt versus Equity
Market Value versus Book Value
2.2 The Income Statement
GAAP and the Income Statement
Noncash Items
Time and Costs
Earnings Management
2.3 Taxes
Corporate Tax Rates
Average versus Marginal Tax Rates
2.4 Cash Flow
Cash Flow from Assets
Operating Cash Flow
Capital Spending
Change in Net Working Capital
Conclusion
A Note on "Free" Cash Flow
Cash Flow to Creditors and Stockholders
Cash Flow to Creditors
Cash Flow to Stockholders
Conclusion
An Example: Cash Flows for Dole Cola
Operating Cash Flow
Net Capital Spending
Change in NWC and Cash Flow from Assets
Cash Flow to Creditors and Stockholders
Summary and Conclusions
Chapter Review and Self-Test Problem
Answer to Chapter Review and Self-Test Problem
Critical Thinking and Concepts Review
Questions and Problems
What's on the Web?
Excel Master It! Problem
CHAPTER CASE: Cash Flows and Financial Statements at Sunset Boards, Inc.
3 Working with Financial Statements
3.1 Standardized Financial Statements
Common-Size Balance Sheets
Common-Size Income Statements
3.2 Ratio Analysis
Short-Term Solvency, or Liquidity, Measures
Current Ratio
Quick (or Acid-Test) Ratio
Cash Ratio
Long-Term Solvency Measures
Total Debt Ratio
Times Interest Earned
Cash Coverage
Asset Management, or Turnover, Measures
Inventory Turnover and Days' Sales in Inventory
Receivables Turnover and Days' Sales in Receivables
Total Asset Turnover
Profitability Measures
Profit Margin
Return on Assets
Return on Equity
Market Value Measures
Price-Earnings Ratio
Price-Sales Ratio
Market-to-Book Ratio
Enterprise Value-EBITDA Ratio
3.3 The DUPont Identity
An Expanded DuPont Analysis
3.4 Internal and Sustainable Growth
Dividend Payout and Earnings Retention
ROA, ROE, and Growth
The Internal Growth Rate
The Sustainable Growth Rate
Determinants of Growth
A Note on Sustainable Growth Rate Calculations
3.5 Using Financial Statement Information
Why Evaluate Financial Statements?
Internal Uses
External Uses
Choosing a Benchmark
Time-Trend Analysis
Peer Group Analysis
Problems with Financial Statement Analysis
Summary and Conclusions
Chapter Review and Self-Test Problems
Answers to Chapter Review and Self-Test Problems
Critical Thinking and Concepts Review
Questions and Problems
What's on the Web?
Excel Master It! Problem
CHAPTER CASE: Ratios and Financial Planning at S&S Air, Inc.
PART THREE: VALUATION OF FUTURE CASH FLOWS
4 Introduction to Valuation: The Time Value of Money
4.1 Future Value and Compounding
Investing for a Single Period
Investing for More Than One Period
4.2 Present Value and Discounting
The Single-Period Case
Present Values for Multiple Periods
4.3 More on Present and Future Values
Present versus Future Value
Determining the Discount Rate
Finding the Number of Periods
Summary and Conclusions
Chapter Review and Self-Test Problems
Answers to Chapter Review and Self-Test Problems
Critical Thinking and Concepts Review
Questions and Problems
What's on the Web?
Excel Master It! Problem
5 Discounted Cash Flow Valuation
5.1 Future and Present Values of Multiple Cash Flows
Future Value with Multiple Cash Flows
Present Value with Multiple Cash Flows
A Note on Cash Flow Timing
5.2 Valuing Level Cash Flows: Annuities and Perpetuities
Present Value for Annuity Cash Flows
Annuity Tables
Finding the Payment
Finding the Rate
Future Value for Annuities
A Note on Annuities Due
Perpetuities
5.3 Comparing Rates: The Effect of Compounding Periods
Effective Annual Rates and Compounding
Calculating and Comparing Effective Annual Rates
EARs and APRs
EARs, APRs, Financial Calculators, and Spreadsheets
5.4 Loan Types and Loan Amortization
Pure Discount Loans
Interest-Only Loans
Amortized Loans
Summary and Conclusions
Chapter Review and Self-Test Problems
Answers to Chapter Review and Self-Test Problems
Critical Thinking and Concepts Review
Questions and Problems
What's on the Web?
Excel Master It! Problem
CHAPTER CASE: S&S Air's Mortgage
PART FOUR: VALUING STOCKS AND BONDS
6 Interest Rates and Bond Valuation
6.1 Bonds and Bond Valuation
Bond Features and Prices
Bond Values and Yields
Interest Rate Risk
Finding the Yield to Maturity: More Trial and Error
6.2 More on Bond Features
Is It Debt or Equity?
Long-Term Debt: The Basics
The Indenture
Terms of a Bond
Security
Seniority
Repayment
The Call Provision
Protective Covenants
6.3 Bond Ratings
6.4 Some Different Types of Bonds
Government Bonds
Zero Coupon Bonds
Floating-Rate Bonds
Other Types of Bonds
6.5 Bond Markets
How Bonds Are Bought and Sold
Bond Price Reporting
A Note on Bond Price Quotes
6.6 Inflation and Interest Rates
Real versus Nominal Rates
The Fisher Effect
6.7 Determinants of Bond Yields
The Term Structure of Interest Rates
Bond Yields and the Yield Curve: Putting It All Together
Conclusion
Summary and Conclusions
Chapter Review and Self-Test Problems
Answers to Chapter Review and Self-Test Problems
Critical Thinking and Concepts Review
Questions and Problems
What's on the Web?
Excel Master It! Problem
CHAPTER CASE: Financing S&S Air's Expansion Plans with a Bond Issue
7 Equity Markets and Stock Valuation
7.1 Common Stock Valuation
Cash Flows
Some Special Cases
Zero Growth
Constant Growth
Nonconstant Growth
Components of the Required Return
Stock Valuation Using Comparables, or Comps
7.2 Some Features of Common and Preferred Stock
Common Stock Features
Shareholder Rights
Proxy Voting
Classes of Stock
Other Rights
Dividends
Preferred Stock Features
Stated Value
Cumulative and Noncumulative Dividends
Is Preferred Stock Really Debt?
7.3 The Stock Markets
Dealers and Brokers
Organization of the NYSE
Members
Operations
Floor Activity
NASDAQ Operations
ECNs
Stock Market Reporting
Summary and Conclusions
Chapter Review and Self-Test Problems
Answers to Chapter Review and Self-Test Problems
Critical Thinking and Concepts Review
Questions and Problems
What's on the Web?
Excel Master It! Problem
CHAPTER CASE: Stock Valuation at Ragan, Inc.
PART FIVE: CAPITAL BUDGETING
8 Net Present Value and Other Investment Criteria
8.1 Net Present Value
The Basic Idea
Estimating Net Present Value
8.2 The Payback Rule
Defining the Rule
Analyzing the Rule
Redeeming Qualities of the Rule
Summary of the Rule
8.3 The Average Accounting Return
8.4 The Internal Rate of Return
Problems with the IRR
Nonconventional Cash Flows
Mutually Exclusive Investments
Redeeming Qualities of the IRR
The Modified Internal Rate of Return (MIRR)
Method 1: The Discounting Approach
Method 2: The Reinvestment Approach
Method 3: The Combination Approach
MIRR or IRR: Which Is Better?
8.5 The Profitability Index
8.6 The Practice of Capital Budgeting
Summary and Conclusions
Chapter Review and Self-Test Problems
Answers to Chapter Review and Self-Test Problems
Critical Thinking and Concepts Review
Questions and Problems
What's on the Web?
Excel Master It! Problem
CHAPTER CASE: Bullock Gold Mining
9 Making Capital Investment Decisions
9.1 Project Cash Flows: A First Look
Relevant Cash Flows
The Stand-Alone Principle
9.2 Incremental Cash Flows
Sunk Costs
Opportunity Costs
Side Effects
Net Working Capital
Financing Costs
Other Issues
9.3 Pro Forma Financial Statements and Project Cash Flows
Getting Started: Pro Forma Financial Statements
Project Cash Flows
Project Operating Cash Flow
Project Net Working Capital and Capital Spending
Projected Total Cash Flow and Value
The Tax Shield Approach
9.4 More on Project Cash Flow
A Closer Look at Net Working Capital
Depreciation
Modified ACRS (MACRS) Depreciation
Bonus Depreciation
Book Value versus Market Value
An Example: The Majestic Mulch and Compost Company (MMCC)
Operating Cash Flows
Changes in NWC
Capital Spending
Total Cash Flow and Value
Conclusion
9.5 Evaluating NPV Estimates
The Basic Problem
Forecasting Risk
Sources of Value
9.6 Scenario and Other What-If Analyses
Getting Started
Scenario Analysis
Sensitivity Analysis
9.7 Additional Considerations in Capital Budgeting
Managerial Options and Capital Budgeting
Contingency Planning
Strategic Options
Conclusion
Capital Rationing
Soft Rationing
Hard Rationing
Summary and Conclusions
Chapter Review and Self-Test Problems
Answers to Chapter Review and Self-Test Problems
Critical Thinking and Concepts Review
Questions and Problems
Excel Master It! Problem
CHAPTER CASE: Conch Republic Electronics
PART SIX: RISK AND RETURN
10 Some Lessons from Capital Market History
10.1 Returns
Dollar Returns
Percentage Returns
10.2 The Historical Record
A First Look
A Closer Look
10.3 Average Returns: The First Lesson
Calculating Average Returns
Average Returns: The Historical Record
Risk Premiums
The First Lesson
10.4 The Variability of Returns: The Second Lesson
Frequency Distributions and Variability
The Historical Variance and Standard Deviation
The Historical Record
Normal Distribution
The Second Lesson
2008: The Bear Growled and Investors Howled
Using Capital Market History
More on the Stock Market Risk Premium
10.5 More on Average Returns
Arithmetic versus Geometric Averages
Calculating Geometric Average Returns
Arithmetic Average Return or Geometric Average Return?
10.6 Capital Market Efficiency
Price Behavior in an Efficient Market
The Efficient Markets Hypothesis
Some Common Misconceptions about the EMH
The Forms of Market Efficiency
Summary and Conclusions
Chapter Review and Self-Test Problems
Answers to Chapter Review and Self-Test Problems
Critical Thinking and Concepts Review
Questions and Problems
What's on the Web?
Excel Master It! Problem
CHAPTER CASE: A Job at S&S Air
11 Risk and Return
11.1 Expected Returns and Variances
Expected Return
Calculating the Variance
11.2 Portfolios
Portfolio Weights
Portfolio Expected Returns
Portfolio Variance
11.3 Announcements, Surprises, and Expected Returns
Expected and Unexpected Returns
Announcements and News
11.4 Risk: Systematic and Unsystematic
Systematic and Unsystematic Risk
Systematic and Unsystematic Components of Return
11.5 Diversification and Portfolio Risk
The Effect of Diversification: Another Lesson from Market History
The Principle of Diversification
Diversification and Unsystematic Risk
Diversification and Systematic Risk
11.6 Systematic Risk and Beta
The Systematic Risk Principle
Measuring Systematic Risk
Portfolio Betas
11.7 The Security Market Line
Beta and the Risk Premium
The Reward-to-Risk Ratio
The Basic Argument
The Fundamental Result
The Security Market Line
Market Portfolios
The Capital Asset Pricing Model
11.8 The SML and the Cost of Capital: A Preview
The Basic Idea
The Cost of Capital
Summary and Conclusions
Chapter Review and Self-Test Problems
Answers to Chapter Review and Self-Test Problems
Critical Thinking and Concepts Review
Questions and Problems
What's on the Web?
Excel Master It! Problem
CHAPTER CASE: The Beta for FLIR Systems
PART SEVEN: LONG-TERM FINANCING
12 Cost of Capital
12.1 The Cost of Capital: Some Preliminaries
Required Return versus Cost of Capital
Financial Policy and Cost of Capital
12.2 The Cost of Equity
The Dividend Growth Model Approach
Implementing the Approach
Estimating g
Advantages and Disadvantages of the Approach
The SML Approach
Implementing the Approach
Advantages and Disadvantages of the Approach
12.3 The Costs of Debt and Preferred Stock
The Cost of Debt
The Cost of Preferred Stock
12.4 The Weighted Average Cost of Capital
The Capital Structure Weights
Taxes and the Weighted Average Cost of Capital
Solving the Warehouse Problem and Similar Capital Budgeting Problems
Calculating the WACC for Eastman Chemical
Eastman's Cost of Equity
Eastman's Cost of Debt
Eastman's WACC
12.5 Divisional and Project Costs of Capital
The SML and the WACC
Divisional Cost of Capital
The Pure Play Approach
The Subjective Approach
12.6 Company Valuation with the WACC
Summary and Conclusions
Chapter Review and Self-Test Problems
Answers to Chapter Review and Self-Test Problems
Critical Thinking and Concepts Review
Questions and Problems
What's on the Web?
Excel Master It! Problem
CHAPTER CASE: Cost of Capital for Layton Motors
13 Leverage and Capital Structure
13.1 The Capital Structure Question
13.2 The Effect of Financial Leverage
The Impact of Financial Leverage
Financial Leverage, EPS, and ROE: An Example
EPS versus EBIT
Corporate Borrowing and Homemade Leverage
13.3 Capital Structure and the Cost of Equity Capital
M&M Proposition I: The Pie Model
The Cost of Equity and Financial Leverage: M&M Proposition II
Business and Financial Risk
13.4 Corporate Taxes and Capital Structure
The Interest Tax Shield
Taxes and M&M Proposition I
Conclusion
13.5 Bankruptcy Costs
Direct Bankruptcy Costs
Indirect Bankruptcy Costs
13.6 Optimal Capital Structure
The Static Theory of Capital Structure
Optimal Capital Structure and the Cost of Capital
Capital Structure: Some Managerial Recommendations
Taxes
Financial Distress
13.7 Observed Capital Structures
13.8 A Quick Look at the Bankruptcy Process
Liquidation and Reorganization
Bankruptcy Liquidation
Bankruptcy Reorganization
Financial Management and the Bankruptcy Process
Agreements to Avoid Bankruptcy
Summary and Conclusions
Chapter Review and Self-Test Problems
Answers to Chapter Review and Self-Test Problems
Critical Thinking and Concepts Review
Questions and Problems
What's on the Web?
Excel Master It! Problem
CHAPTER CASE: Stephenson Real Estate Recapitalization
14 Dividends and Dividend Policy
14.1 Cash Dividends and Dividend Payment
Cash Dividends
Standard Method of Cash Dividend Payment
Dividend Payment: A Chronology
More on the Ex-Dividend Date
14.2 Does Dividend Policy Matter?
An Illustration of the Irrelevance of Dividend Policy
Current Policy: Dividends Set Equal to Cash Flow
Alternative Policy: Initial Dividend Greater Than Cash Flow
A Test
Some Real-World Factors Favoring a Low Payout
Taxes
Flotation Costs
Dividend Restrictions
Some Real-World Factors Favoring a High Payout
Desire for Current Income
Tax and Legal Benefits from High Dividends
Clientele Effects: A Resolution of Real-World Factors?
14.3 Stock Repurchases: An Alternative to Cash Dividends
Cash Dividends versus Repurchase
Real-World Considerations in a Repurchase
Share Repurchase and EPS
14.4 What We Know and Do Not Know about Dividend and Payout Policies
Dividends and Dividend Payers
Corporations Smooth Dividends
Putting It All Together
Some Survey Evidence on Dividends
14.5 Stock Dividends and Stock Splits
Value of Stock Splits and Stock Dividends
The Benchmark Case
Popular Trading Range
Reverse Splits
Summary and Conclusions
Chapter Review and Self-Test Problem
Answer to Chapter Review and Self-Test Problem
Critical Thinking and Concepts Review
Questions and Problems
What's on the Web?
CHAPTER CASE: Electronic Timing, Inc.
15 Raising Capital
15.1 The Financing Life Cycle of a Firm: Early-Stage Financing and Venture Capital
Venture Capital
Some Venture Capital Realities
Choosing a Venture Capitalist
Conclusion
15.2 Selling Securities to the Public: The Basic Procedure
Crowdfunding
Initial Coin Offerings
15.3 Alternative Issue Methods
15.4 Underwriters
Choosing an Underwriter
Types of Underwriting
Firm Commitment Underwriting
Best Efforts Underwriting
Dutch Auction Underwriting
The Green Shoe Provision
The Aftermarket
Lockup Agreements
The Quiet Period
Direct Listing
15.5 IPOs and Underpricing
Evidence on Underpricing
IPO Underpricing: The 1999–2000 Experience
The Partial Adjustment Phenomenon
Why Does Underpricing Exist?
15.6 New Equity Sales and the Value of the Firm
15.8 Issuing Long-Term Debt
15.9 Shelf Registration
Summary and Conclusions
Chapter Review and Self-Test Problem
Answer to Chapter Review and Self-Test Problem
Critical Thinking and Concepts Review
Questions and Problems
What's on the Web?
CHAPTER CASE: S&S Air Goes Public
PART EIGHT: SHORT-TERM FINANCIAL MANAGEMENT
16 Short-Term Financial Planning
16.1 Tracing Cash and Net Working Capital
16.2 The Operating Cycle and the Cash Cycle
Defining the Operating and Cash Cycles
The Operating Cycle
The Cash Cycle
The Operating Cycle and the Firm's Organizational Chart
Calculating the Operating and Cash Cycles
The Operating Cycle
The Cash Cycle
Interpreting the Cash Cycle
16.3 Some Aspects of Short-Term Financial Policy
The Size of the Firm's Investment in Current Assets
Alternative Financing Policies for Current Assets
Which Financing Policy Is Best?
Current Assets and Liabilities in Practice
16.4 The Cash Budget
Sales and Cash Collections
Cash Outflows
The Cash Balance
16.5 Short-Term Borrowing
Unsecured Loans
Secured Loans
Accounts Receivable Financing
Inventory Loans
Other Sources
16.6 A Short-Term Financial Plan
Summary and Conclusions
Chapter Review and Self-Test Problems
Answers to Chapter Review and Self-Test Problems
Critical Thinking and Concepts Review
Questions and Problems
What's on the Web?
Excel Master It! Problem
Chapter Case: Piepkorn Manufacturing Working Capital Management, Part 1
17 Working Capital Management
17.1 Float and Cash Management
Reasons for Holding Cash
The Speculative and Precautionary Motives
The Transaction Motive
Benefits of Holding Cash
Understanding Float
Disbursement Float
Collection Float and Net Float
Float Management
Ethical and Legal Questions
Electronic Data Interchange and Check 21: The End of Float?
17.2 Cash Management: Collection, Disbursement, and Investment
Cash Collection and Concentration
Components of Collection Time
Cash Collection
Lockboxes
Cash Concentration
Managing Cash Disbursements
Increasing Disbursement Float
Controlling Disbursements
Investing Idle Cash
Temporary Cash Surpluses
Characteristics of Short-Term Securities
Some Different Types of Money Market Securities
17.3 Credit and Receivables
Components of Credit Policy
Terms of Sale
The Basic Form
The Credit Period
Cash Discounts
Credit Instruments
Optimal Credit Policy
The Total Credit Cost Curve
Organizing the Credit Function
Credit Analysis
Credit Information
Credit Evaluation and Scoring
Collection Policy
Monitoring Receivables
Collection Effort
17.4 Inventory Management
The Financial Manager and Inventory Policy
Inventory Types
Inventory Costs
17.5 Inventory Management Techniques
The ABC Approach
The Economic Order Quantity Model
Inventory Depletion
Carrying Costs
Shortage Costs
Total Costs
Extensions to the EOQ Model
Safety Stocks
Reorder Points
Managing Derived-Demand Inventories
Materials Requirements Planning
Just-in-Time Inventory
Summary and Conclusions
Chapter Review and Self-Test Problems
Answers to Chapter Review and Self-Test Problems
Critical Thinking and Concepts Review
Questions and Problems
What's on the Web?
Chapter Case: Piepkorn Manufacturing Working Capital Management, Part 2
PART NINE: TOPICS IN BUSINESS FINANCE
18 International Aspects of Financial Management
18.1 Terminology
18.2 Foreign Exchange Markets and Exchange Rates
Exchange Rates
Exchange Rate Quotations
Cross-Rates and Triangle Arbitrage
Types of Transactions
18.3 Purchasing Power Parity
Absolute Purchasing Power Parity
Relative Purchasing Power Parity
The Basic Idea
The Result
Currency Appreciation and Depreciation
18.4 Exchange Rates and Interest Rates
Covered Interest Arbitrage
Interest Rate Parity
18.5 Exchange Rate Risk
Short-Run Exposure
Long-Run Exposure
Translation Exposure
Managing Exchange Rate Risk
18.6 Political Risk
The Tax Cuts and Jobs Act
Managing Political Risk
Summary and Conclusions
Chapter Review and Self-Test Problems
Answers to Chapter Review and Self-Test Problems
Critical Thinking and Concepts Review
Questions and Problems
What's on the Web?
Excel Master It! Problem
Chapter Case: S&S Air Goes International
Appendix A: Mathematical Tables
Appendix B: Key Equations
Appendix C: Answers to Selected End- of-Chapter Problems
Appendix D: Using the HP-10B and TI BA II Plus Financial Calculators
Glossary
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Name Index
Subject Index
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