1. Introduction
The use of Cost Volume Profit (CVP) Analysis depends upon a number of clear assumptions, for its application in resolving problems, simplifying complexities and aiding decision-making in business issues. Areas of application, inter alia, include pricing, calculating contribution, computing costs, deciding sales mixes, estimating breakeven points, assessing profitability, and achieving profits. As a financial tool in the hands of accountants, (professionals who are generally more at home in dealing with simple and linear arithmetic than with the intricacies of statistics and calculus), it is invaluable, brilliant in its simplicity and in its ability for using straightforward calculations to make sense out of complicated business situations.

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CVP analyses work on certain basic assumptions in areas of sales, in unit price and volume, and costs, fixed and variable, for their simplest and most straightforward applications. However, the irregularities of actual business situations, their proneness to pick up complex variables, and their stubborn refusal to abide by the norms of arithmetical linearity, introduce a number of issues that sometimes make it difficult to apply simple arithmetical concepts like CVP towards their resolution.
The simplicity of an analytical tool such as CVP can cut both ways. It can be both its greatest virtue and its major shortcoming. The real world is complicated, no less so in the world of managerial affairs; and a typical analytical model will remove many of those complications in order to preserve a sharp focus. That sharpening is usually achieved in two basic ways: simplifying assumptions are made about the basic nature of the model and restrictions are imposed on the scope of the model. (Guidry, Horrigan & Craycraft, 1998)
Businesses that do not have a single product sales portfolio, and who, in the normal course of their activities, sell a number of products, sometimes quite dissimilar from each other, face even more difficult and complex challenges in the application of CVP concepts. It is the purpose of this assignment to examine the appropriateness of applying CPV techniques in business environments, wherein companies produce and sell a number of dissimilar products, with particular reference to the specific assumptions needed for such exercises.
2. Commentary
In base terms, a CVP analysis deals with sales, costs, contribution and ultimate profitability. Arithmetical manipulation of the relation between unit sale price, total sales, variable costs, contribution, fixed costs and profitability, results in information about breakeven volumes, the implications of both variable and fixed costs on margins and final profitability, thus helping decision making in such issues.
a. Sales
The first set of assumptions, in this methodology, concerns financial data regarding sales. CVP techniques work on the assumption that product sale prices will remain constant and total sales will necessarily be a linear multiple of the number of units sold. As such, if ‘x’ is the sales price in GBP and ‘a’ the volume in units, total sales will equal ax GBP. In most business situations, factors like volume and cash discounts, as well as introductory offers to new customers, often cause changes in sales prices. It is general practice for accountants, in such situations, to arrive at an average sales price depending upon the business environment, and the needs of the market, and apply it for CVP exercises. This situation could become complicated, if sales prices differ in different geographical areas, and infinitely more complex for analysis, if a company deals with a number of products, each of which may have a range of items, and different pricing policies. Furthermore, the use of average prices becomes patently unsuitable, if not downright silly, in environments where a number of diverse products make up the sales basket.
b. Variable Costs
Costs, for CVP analyses, consist of two broad categories, variable costs and fixed costs. Variable costs are costs that change directly in proportion to changes in volume. They include the wages of production workers or salespeople, raw materials, electric power to run machines, and the cost of maintaining inventory. While most variable costs are of a direct nature, their movement, in actuality, is never strictly linear and they tend to change somewhat, decreasing with initial volume increases, remaining stable for a substantial period and then inching upwards, after volumes exceed a certain limit. While accountants are aware that costs are never fully variable or fully fixed, this differentiation helps in some exercises, notably CVP applications. Costing and production departments thus try to segregate variable costs to the best of their knowledge and ability.
“Splitting out fixed and variable costs can be a long, time consuming process; and techniques such as the inspection of accounts method really are not suitable if the analysis is to be realistic. At the very least, some kind of statistical or mathematical analysis will have to be undertaken.”(Williamson, 2000)
The impact of different sales prices, and variable costs, of different items, for a company that deals in many diverse products, introduces a host of complexities in the use of CVP techniques, which primarily work on the assumptions of single product lines, constant sales prices, variable costs, and linear movements of both, in accordance with volumes. Fixed Costs, another important factor for CVPA exercises, comprise of expenses that do not change in proportion to the level of activity of a business. They can include both overheads, like rent and utilities, as well as direct costs like salaries. It also needs understanding that fixed costs remain steady only within a certain range of activity, and for a definite period. They are quite liable to change with time and with level of activity.
c. Multi product Situations
CVP exercises make use of all these components, namely sales prices, sales volume, variable costs and fixed costs to arrive at conclusions regarding contribution margins, breakeven points, pricing decisions, minimum volumes that need selling, and similar other financial issues. While CVP analyses progress on the assumption that primary factors will behave predictably, at least for single product companies, the situation in real life business environments is very different and sales prices, variable costs and fixed costs get impacted by developments like changes in pricing policies, needs for special discounts, inflation, and mid term salary increases. All organizations are subject to uncertainties, leading to risks of failing to meet expectations. Even though each organization is subject to distinctive business risks, all of them face uncertainties related to the economic environment.
These uncertainties increase manifold in the case of organisations that deal in various diverse products, with differing sales prices and variable costs. Even the treatment of fixed costs becomes complex because some fixed costs would be applicable to specific product lines, (e.g. departmental salaries or rent) while others would be applicable to all product groups like the MD’s remuneration or legal retainer fees. Such business settings lead to violation of basic assumptions needed for CVP exercises. Moreover, this sort of nonlinear behaviour, of both revenues and costs, and the increasing number of uncertainties could affect the assumptions required for CVP analyses and lead to invalid conclusions. In addition, it could be difficult to determine the point of operating activity where operations move into a new relevant range. Any simple and straightforward attempt at resolving CVP issues, even for a company with just ten product lines, each with different revenue and cost characteristics could thus fail without the use of mathematical modelling, which at times could become quite unwieldy.
Multi product situations, which automatically lead to the emergence of numerous variables and to the violation of the tenets of CVP methods, are inevitable in real life business situations, and it would thus be quite impossible to find problems that satisfy all CVP assumptions. Does this imply that the CVP method is just a simplistic arithmetical tool that is adequate for use in costing textbooks, as well as for simplifying basic cost issues for beginners, but actually of no use in real life situations where (a) the sales baskets of companies always have many products, and (b) costs are not amenable to straitjacketed behaviour?
Notwithstanding the meagre probability of the assumptions required for CVP exercises occurring in real life situations, CVP analyses still maintain their relevance in operational and financial decision making, even in multi product situations, albeit with some provisos and modifications. The most widespread application of CVO, in multi product situations happens in the formulation and determination of sales mix. In such situations where there are, for example, five products with differing unit sales prices and variable costs, it is possible to find the contribution of each product per piece, by subtracting the variable cost from the sales price. An analysis of comparative contributions thus provides information about the potential profitability of the different products, and determination of the product mix that will contribute most towards the profitability of the company. The use of a practical example will be of use in illustrating these statements
Data relating to hypothetical Company ABC

Product

A

B

C

D

E

Sales Price

GBP

5

6

8

11

12

Sales Volumes

Nos.

100

250

325

25

200

Product Mix

%

11

28

36

3

22

Variable Costs

GBP

3

2

4

5

7

Contribution

GBP

2

4

4

6

5

Total Contribution

GBP

200

1000

1300

150

1000

The use of simple CVP analyses makes it possible to come to the following conclusions.

Product E, even though it has the highest Sales Price does not give the highest contribution, either per piece or in totality.
Product D, even if it has the highest contribution per piece gives the lowest total contribution
Product C, which has a medium contribution of 4 GBP provides the highest total contribution to the company
Profit optimising activities should primarily focus on (a) increasing the contribution of Product A and (b) increasing the sales of Product E and D.

Apart from these conclusions, CVP techniques will be useful in calculating the breakeven point of the company’s current operations, after ascertainment of fixed costs, and by using the weighted average of contributions of the total products, based on the current product mix. In this particular case the weighted average of the contribution of the company’s products, obtained by dividing the total contribution of 3650 GBP by total sales of 900 units works, out to 4.05 GBP per piece.
Thus, if the fixed costs of the company are 4500 GBP per year, the company will have to sell (4500/4.05) 1112 units to break even, considering maintenance of the current product mix. Income tax does not come into play until achievement of break-even levels. However, once breakeven levels are crossed, the profit after tax at various levels of sales is easily obtainable by multiplying the sales numbers, in excess of the BEP, with the weighted contribution per unit and obtaining the product of this figure and the post tax percentage. If, for example the company plans to sell 2000 products during a year, and the level of tax is 30 %, the total after tax profits can be worked out by multiplying 882 (2000 – 1112) with 4.05 and then again with 70% (being the post tax income). As such, 882 * 4.05 * 70 %, which equals to 2500 GBP will be the post tax profits at a sale level of 2000 units with the same product mix, sales prices, variable and fixed costs.
The use of Excel sheets becomes very useful for such exercises and enables accountants to work upon a number of options with varying products mixes, changes in sales prices and the impact of different factors on variable and fixed costs. It thus becomes possible to forecast a number of situations and engage in a number of sensitivity exercises.
3. Conclusion
The use of CVP analysis depends upon a number of assumptions in areas of sales and costs for its proper application. Many of these assumptions get violated in actual business situations, more so when a company deals in a number of products with different price and cost structures. While these factors do lead to difficulties in using CVP techniques, the availability of spreadsheets, particularly the options available with Microsoft Excel make it possible for accountants to use these techniques in different business scenarios with changes in assumptions without great difficulty or tedious and repetitive calculations. In case of situations where the number of variables becomes extensive, the use of probabilistic models helps in CVP analysis. However, the use of probabilistic techniques in normal business situations is quite rare, and the careful and knowledgeable use of CVP techniques, with the aid of spreadsheets, proves adequate in handling many multi product requirements. CPV analysis also faces criticism because conclusions and recommended decisions, arising out of its use, disregards wealth and risk implications. Nevertheless, its continuous use and adaptability reinforces the robustness of the model and its adaptability to changing business needs.
Word Count: 2128 words
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