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1. 1. Define capital budgeting, in your own words.

2. 2. Define and explain the rationale for the NPV approach. Why is it used and what are its advantages?

3. 3. Give a short example of an IRR approach to determine the desirability of a project.

The Basics of Capital Budgeting:
Evaluating Cash Flows

CHAPTER 10

© 2020 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use.

Topics
Overview and “vocabulary”
Methods
NPV
IRR, MIRR
Profitability Index
Payback, discounted payback
Unequal lives
Economic life
Optimal capital budget

The Big Picture:
The Net Present Value of a Project

What is capital budgeting?
Analysis of potential projects.
Long-term decisions; involve large expenditures.
Very important to firm’s future.

Steps in Capital Budgeting
Estimate cash flows (inflows & outflows).
Assess risk of cash flows.
Determine r = WACC for project.
Evaluate cash flows.

Capital Budgeting Project Categories
Replacement to continue profitable operations
Replacement to reduce costs
Expansion of existing products or markets
Expansion into new products/markets
Contraction decisions
Safety and/or environmental projects
Mergers
Other

Independent versus Mutually Exclusive Projects
Projects are:
independent, if the cash flows of one are unaffected by the acceptance of the other.
mutually exclusive, if the cash flows of one can be adversely impacted by the acceptance of the other.

Cash Flows for Franchises L and S

NPV: Sum of the PVs of All Cash Flows

What’s Franchise L’s NPV?

Calculator Solution: Enter Values in CFLO Register for L

Rationale for the NPV Method
NPV = PV inflows – Cost
This is net gain in wealth, so accept project if NPV > 0.
Choose between mutually exclusive projects on basis of higher positive NPV. Adds most value.

Using the NPV measure, which franchise(s) should be accepted?
If Franchises S and L are mutually exclusive, accept S because NPVs > NPVL.
If S & L are independent, accept both; NPV > 0.
NPV is dependent on cost of capital.

Internal Rate of Return: IRR
IRR is the discount rate that forces
PV inflows = cost. This is the same
as forcing NPV = 0.

NPV: Enter r, solve for NPV.

IRR: Enter NPV = 0, Solve for IRR

IRR is an estimate of the project’s rate of return, so it is comparable to the YTM on a bond.

What’s Franchise L’s IRR?

How is the IRR on a project related to the yield to maturity (YTM) on a bond?
IRR: The discount rate that forces the present value of a project’s expected future cash flows to equal the initial cash flow.
YTM: The discount rate that forces the present value of a bondscash flows (i.e., coupons and maturity value) to equal the price of the bond.

Finding IRR if CFs are Constant (Use the Excel RATE function as though the project were a bond.)
IRR = RATE(3,40,100) = 9.7%
Alternatively:

Rationale for the IRR Method
If IRR > r, then the project’s rate of return is greater than its cost– some return is left over to boost stockholders’ returns.
Example:
r= 10%, IRR = 15%.
So this project adds extra return to shareholders.

Decisions on Franchises S and L per IRR
If S and L are independent, accept both: IRRS > r and IRRL > r.
If S and L are mutually exclusive, accept S because IRRS > IRRL.
IRR is not dependent on the cost of capital used.

Construct NPV Profiles
Enter CFs in CFLO and find NPVL and NPVS at different discount rates:
r NPVL NPVS
0 50 40
5 33 29
10 19 20
15 7 12
20 (4) 5

NPV Profile

NPV and IRR: No conflict for independent projects.

Mutually Exclusive Projects

To Find the Crossover Rate
Find cash flow differences between the projects. See data at beginning of the case.
Enter these differences in CFLO register, then press IRR. Crossover rate = 8.68%, rounded to 8.7%.
Can subtract S from L or vice versa and consistently, but easier to have first CF negative.
If profiles don’t cross, one project dominates the other.

Two Reasons NPV Profiles Cross
Size (scale) differences. Smaller project frees up funds at t = 0 for investment. The higher the opportunity cost, the more valuable these funds, so high r favors small projects.
Timing differences. Project with faster payback provides more CF in early years for reinvestment. If r is high, early CF especially good, NPVS > NPVL.

Modified Internal Rate of Return (MIRR)
MIRR is the discount rate that causes the PV of a project’s terminal value (TV) to equal the PV of costs.
TV is found by compounding inflows at WACC.
Thus, MIRR assumes cash inflows are reinvested at WACC.

MIRR for Franchise L (r = 10%) using the Excel RATE function.
A B C D
1 r = 10%
2 Year Year Year Year
3 0 1 2 3
4 (100) 10 60 80
5
6 MIRR = MIRR(A4:D4,B4,B4)
7 MIRR = 16.50%

Alternative Method to Find MIRR for Franchise L: First, find PV and TV (r = 10%).

Second, find discount rate that equates PV and TV.

To find MIRR with financial calculator:
(1 of 2)
Step 1, Find PV of inflows
First, enter cash inflows in CFLO register:
CF0 = 0, CF1 = 10, CF2 = 60, CF3 = 80
Second, enter I/YR = 10.
Third, find PV of inflows: Press NPV = 118.78
Step 2, Find TV of PV of inflows from Step 1.
Enter PV = -118.78, N = 3, I/YR = 10, PMT = 0.
Press FV = 158.10 = FV of inflows.

To find MIRR with financial calculator:
(2 of 2)
Step 3, Find PV of outflows.
For this problem, there is only one outflow:
CF0 = -100, so the PV of outflows is -100.
For other problems there may be negative cash flows for several years, and you must find the present value for all negative cash flows.
Step 4, Find “IRR” of TV of inflows and PV of outflows.
Enter FV = 158.10, PV = -100, PMT = 0, N = 3.
Press I/YR = 16.50% = MIRR.

Profitability Index
The profitability index (PI) is the present value of future cash flows divided by the initial cost.
It measures the “bang for the buck.”

Franchise L’s PV of Future Cash Flows

Franchise L’s Profitability Index

What is the payback period?
The number of years required to recover a project’s cost,
or how long does it take to get the business’s money back?

Payback for Franchise L

Payback for Franchise S

Strengths and Weaknesses of Payback
Strengths:
Provides an indication of a project’s risk and liquidity.
Easy to calculate and understand.
Weaknesses:
Ignores the TVM.
Ignores CFs occurring after the payback period.
No specification of acceptable payback.

Discounted Payback: Uses Discounted CFs

Normal vs. Nonnormal Cash Flows
Normal Cash Flow Project:
Cost (negative CF) followed by a series of positive cash inflows.
One change of signs.
Nonnormal Cash Flow Project:
Two or more changes of signs.
Most common: Cost (negative CF), then string of positive CFs, then cost to close project.
For example, nuclear power plant or strip mine.

Inflow (+) or Outflow (-) in Year
0 1 2 3 4 5 N NN
– + + + + + N
– + + + + – NN
– – – + + + N
+ + + – – – N
– + + – + – NN

Pavilion Project: NPV and IRR?
Enter CFs in CFLO, enter I/YR = 10.
NPV = -386,777
IRR = ERROR. Why?

Nonnormal CFs—Two Sign Changes, Two IRRs

Logic of Multiple IRRs
At very low discount rates, the PV of CF2 is large & negative, so NPV < 0. At very high discount rates, the PV of both CF1 and CF2 are low, so CF0 dominates and again NPV < 0. In between, the discount rate hits CF2 harder than CF1, so NPV > 0.
Result: 2 IRRs.

Finding Multiple IRRs with Calculator
1. Enter CFs as before.
2. Enter a “guess” as to IRR by storing the guess. Try 10%:
10 STO
IRR = 25% = lower IRR
(See next slide for upper IRR)

Finding Upper IRR with Calculator
Now guess large IRR, say, 200:
200 STO
IRR = 400% = upper IRR

When there are nonnormal CFs and more than one IRR, use MIRR.

Accept Project P?
NO. Reject because
MIRR = 5.6% < r = 10%. Also, if MIRR < r, NPV will be negative: NPV = -$386,777. © 2020 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. Projects T (for two years) and F (for four years) are mutually exclusive and will be repeated; r = 10%. 0 1 2 3 4 T: -100 F: -100 60 33.5 60 33.5 33.5 33.5 Note: CFs shown in $ Thousands © 2020 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license distributed with a certain product or service or otherwise on a password-protected website for classroom use. NPVF > NPVT, but which is better? T can be repeated!
T F
CF0 -100 -100
CF1 60 33.5
NJ 2 4
I/YR 10 10
NPV 4.132 6.190

Equivalent Annual Annuity Approach (EAA)
Convert the PV into a stream of annuity payments with the same PV.
T: N=2, I/YR=10, PV=-4.132, FV = 0. Solve for PMT = EAAT = $2.38.
F: N=4, I/YR=10, PV=-6.190, FV = 0. Solve for PMT = EAAF = $1.95.
T has higher EAA, so it is a better project.

Replacement Chain
Note that Project T could be repeated after 2 years to generate additional profits.
Use replacement chain to put on common life.

Replacement Chain Approach: F with Replication ($ thousands)

Or, Use NPVs

Suppose the cost to repeat T in two years rises to $105,000?

Economic Life versus Physical Life (1 of 2)
Consider another project with a 3-year life.
If terminated prior to Year 3, the machinery will have positive salvage value.
Should you always operate for the full physical life?
See next slide for cash flows.

Economic Life versus Physical Life (2 of 2)
Year CF Salvage Value
0 -$5,000 $5,000
1 2,100 3,100
2 2,000 2,000
3 1,750 0

CFs Under Each Alternative (000s)
Years: 0 1 2 3
1. No termination -5 2.1 2 1.75
2. Terminate 2 years -5 2.1 4
3. Terminate 1 year -5 5.2

NPVs under Alternative Lives
(Cost of Capital = 10%)
NPV(3 years) = -$123.
NPV(2 years) = $215.
NPV(1 year) = -$273.

Conclusions
The project is acceptable only if operated for 2 years.
A project’s engineering life does not always equal its economic life.

(
)
N
t
t
t0
CF
NPV
1r
=
=
+
å
(
)
N
t
t
t0
CF
0
1IRR
=
=
+
å
L
L
S
PV future CF$118.79
PI
Initial cost$100
PI 1.1879
PI 1.1998
==
=
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