Relevant Costs and Revenues

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Constance Manning
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1 Harvard Business School Rev. 08/05/94 Relevant Costs and Revenues Companies often use the information in their accounting and control systems for multiple purposes. These purposes can range from tax reporting and shareholder reporting to the monitoring of management performance and the tracking of product performance. Each of these examples may require a different measure. For instance, the earnings before taxes reported to the government often differs from the earnings before taxes reported to the shareholders. When we want to analyze the economic consequences of decisions, we are interested in the effects of decision choices on cash. Using the simple assumption that more cash is better than less, 1 we shall look at the cash consequences of decisions. Suppose we are considering a decision with two choices: whether or not to introduce a new product. We could look at the company's (after-tax) cash flow resulting from a decision not to introduce, and compare it with the cash flow resulting from a decision to introduce. Introducing the new product might result in cash-flow consequences that differ over an extended period of time from the cash flow that would have resulted if the new product had not been introduced. If that were the case, the two streams of cash flows over time would be compared, possibly using net present value to reduce them to equivalent lump-sum values. The only cash available to a company is the cash that remains after taxes are paid. Accordingly, we ought to be computing the tax consequences of decisions. To do so would require discussion of depreciation, depletion, capital gains, and a host of issues that would obscure the issue of relevant cash flows. In order not to add unnecessary complications, therefore, we shall ignore taxes or, more precisely, assume that the tax rate on all transactions is 0. Furthermore, we shall consider decisions that have only short-run consequences on cash flow, or else consequences that generate differential cash flows that remain the same year after year. For example, if the corporate cash flow that results after choosing A is always $100 thousand per year higher than that from choosing B, then A is the better decision. 2 This note was prepared as a basis for class discussion. Copyright 1991 by the President and Fellows of Harvard College. To order copies, call (617) or write the Publishing Division, Harvard Business School, Boston, MA No part of this publication may be reproduced, stored in a retrieval system, used in a spreadsheet, or transmitted in any form or by any means electronic, mechanical, photocopying, recording, or otherwise without the permission of Harvard Business School. 1. Companies do not always make decisions in order to maximize cash. They may choose to sacrifice cash, for example, to reduce the volatility of earnings. In this note we shall not be concerned with tradeoffs of this kind. 2. If A resulted in cash flows that were better than B in some years and worse in others, net present value would provide a way of deciding whether the cash-flow streams favored A or B. 1

2 Relevant Costs and Revenues With these simplifications, the problem of choice in the new-product decision is very simple, in principle. Just look at two sets of cash flows: (1) Cash flows if the company introduces the new product, (2) Cash flows if the company does not introduce the new product. If (1) is greater than (2), the product should be introduced, but not otherwise. In practice, of course, calculation (1) would involve revenues and costs associated with other products, costs that were incurred regardless of product mix, and possibly revenues and costs associated with entirely unrelated divisions of the company, and these costs and revenues would be involved in calculation (2) as well. If they are the same for both (1) and (2), they are irrelevant to the decision, since it is only the difference between (1) and (2) that determines which choice is better. In deciding among alternatives, irrelevant revenues and costs need not be considered. Relevant Revenues and Costs From the above discussion, it should be clear that the relevance or irrelevance of revenues and costs depends on the decision under consideration; it is not a characteristic of the revenues and costs themselves. It is meaningless to discuss whether a cost or revenue is relevant or irrelevant unless a decision has been specified. Furthermore, in order to perform a correct economic analysis of a decision problem, you must identify and include all relevant revenues and costs. The inclusion of irrelevant revenues and costs will not harm the analysis, provided they are included correctly. For example, if you will incur the same overhead cost, regardless of whether you make decision A or decision B, then overhead cost is irrelevant to the choice, but if an analysis excluding overhead cost showed that A was better than B, the same conclusion will be reached if overhead is included as a cost attributable to both decisions. What, then, do we gain by restricting our attention just to relevant costs and revenues? First, we simplify and focus the analysis. Second, we avoid the errors in analysis that often occur when one mistakenly attributes irrelevant costs or revenues to one choice and not to the other, an error that may lead to decisions that do not maximize cash flow. A Tale of Three Products Once upon a time there was a company one of whose divisions manufactured three products, A, B, and C. Per-unit revenue and variable cost for each product, monthly unit sales, and "contribution" (the difference between per-unit revenue and variable cost, multiplied by unit sales) are shown for each product in the table below. 2

3 Relevant Costs and Revenues Product A B C Per-unit revenue $10 $15 $5 Per-unit variable cost $ 5 $ 5 $3 Monthly unit sales 10,000 2,000 2,500 Contribution $50,000 $20,000 $5,000 Corporate overhead of $60,000 per month was allocated to each product in equal parts. Product C, which was now losing money ($5,000 - $20,000) was dropped. Since the amount of the corporate overhead was fixed, it now had to be allocated over the remaining two products. The $30,000 overhead allocated to B exceeded the $20,000 contribution, so it, too, was dropped. This left A to support the entire overhead cost of $60,000. As it could not, the division was no more. The moral of this story is not that the overhead should have been allocated in some different way, but that for the specific decisions of which products should be dropped and which should continue to exist, the corporate overhead would remain the same so long as at least one product was manufactured, and hence is irrelevant to any decision involving dropping one or two of the three products. 3 (Notice that the overhead is relevant to the decision to drop all three products; had it been $80,000 per month, then all three should have been dropped.) Sequential Decisions Making an intelligent decision now may entail thinking through what you will do on future decisions. The idea of basing a decision to drop a product on whether or not its contribution covers allocated overhead is an attempt to reduce a two-stage problem to a one-stage problem by incorrectly converting a fixed cost into a variable cost. The correct way to view the problem is that first the company should decide whether to drop any products given that it wishes the division to remain in business (in which case the $60,000/month overhead is an irrelevant cost). It should then decide whether the division should continue in business. Given that the division is in business, it is clear that each product has positive contribution. Thus, given that the division is in business, all three products should be produced. The contribution from all three products is then $75,000 per month. Moving to the second decision, is a contribution of $75,000 per month sufficient to warrant expenditures of $60,000 per month on overhead? Answer, yes: the division should stay in business. But not if the fixed overhead had been $80,000 per month. Contribution "Contribution" is often defined as the difference between total revenue and total variable costs. (Per-unit contribution is then the difference between per-unit revenue and per-unit variable cost.) It is also often asserted that maximizing contribution maximizes cash flow. But this is not 3. Whether the allocation of corporate overhead should remain unchanged as products were dropped is a salient point, but this question is beyond the scope of this note. 3

4 Relevant Costs and Revenues necessarily true. In the three-products case just discussed, "contribution" is maximized when all three products are manufactured, but if divisional overhead is $80,000 per month, cash flow is maximized by closing down the division, despite the fact that total revenue exceeds total variable cost. To preserve the idea that maximization of contribution maximizes cash flow, we need a more flexible definition of contribution. In the three-products case, let us define the difference between total revenue and total variable cost as the product line contribution. Then Product A contributes $50,000 per month, and all three products jointly contribute $75,000. Now let us define the difference between this $75,000 per month of product line contribution and the $60,000 per month divisional overhead as the divisional contribution. It is this contribution that we seek to maximize by deciding whether to drop some or all of the three products. In general, for any problem that involves a sequence of decisions, there is a relevant contribution corresponding to each level of decision. That contribution may involve some overhead or fixed costs as well as variable costs and revenues. To make clear what contribution we are talking about, it is important to specify what entity provides the contribution. Joint Costs Linked Decisions Relevant costs permit us to narrow the scope of an analysis. In the three-products example, we could restrict our analysis to the division alone, without considering any cash flows generated by the rest of the company. But focusing too narrowly, on the individual-product level, for example, could result in incorrect decisions. The reason why the decision problem could not be decomposed into three separate problems was that all three products involved a joint cost divisional overhead that was incurred if any or all of the products were made. Decisions about products or activities become linked when joint costs are involved. There are many other situations that give rise to linkages. Two that occur frequently in practice may involve substitution or complementarity, and products or activities competing for scarce resources. Substitution and Complementarity Many decisions that seem to involve only one product directly may also involve other products indirectly, and these indirect effects give rise to costs and revenues that are relevant to the product under consideration. If sales of Product A will cannibalize sales of Products B and C, this substitution effect is relevant: dropping Product A may, as a consequence, increase sales of B and C. If this should occur, then the decrease in contribution resulting from dropping A must be offset by the increased contribution generated by the increased substitute sales of B and C. In the extreme case, if all customers who would have purchased A would instead purchase B when A was dropped, the decision to drop A would be a good one: each unit demanded would now generate per-unit contribution of $10 instead of $5. 4

5 Relevant Costs and Revenues If, on the other hand, sales of A tend to increase sales of B (think of A as a flashlight and B as a set of batteries), this complementary effect is also relevant: dropping A will not only directly reduce Product A's contribution, but will also have an indirect effect of further reducing contribution as a result of the reduction in sales of B. Even if the three products had not been linked by sharing divisional overhead as a joint cost, they might have been linked via substitutability or complementarity. Competition for Scarce Resources: Opportunity Costs Suppose that a distributor needing warehouse space offers to lease for $7,000 per month the floor space currently devoted to the production of Product C. We can see at once that the $7,000 lease exceeds the $5,000 per month product line contribution that Product C generates, and that the distributor's proposal should, therefore, be accepted, provided that demand for A or B neither substitutes for nor is complementary to demand for C. Comparing the economic consequences of the two decisions implicitly under consideration continue to manufacture Product C vs lease the floor space to the distributor it is apparent that the first decision produces $2,000 per month less contribution than the second. The two decisions are linked because they both compete for the same scarce resource: the floor space. Throughout this note, the choices in a decision have been evaluated by explicitly considering the cash flows associated with each choice. In this example, we compared the cash flow from producing Product C with the cash flow from leasing Product C's floor space. As an alternative approach, we can make this comparison implicit by assessing Product C with the cost of using the floor space. Because using the floor space to manufacture Product C denies the division the opportunity to earn $7,000 per month from the distributor, the $7,000 is a monthly opportunity cost of using the space for manufacturing. It affects the product line contribution as follows: Revenue: 2,500 $5 = $ 12,500 Variable Cost: 2,500 $3 = 7,500 Opportunity cost of using the floor space for manufacturing instead of warehousing 7,000 Contribution - $ 2,000 Although the opportunity cost is not a cash flow directly attributable to the Product-C decision, it is a relevant cost: it correctly tells us that producing C is $2,000 per month worse than the alternative (leasing the space to the distributor), and that therefore Product C should be dropped in favor of this alternative. Even if an explicit alternative like leasing the space to a distributor is not under consideration, the floor space may be useable for something else to make another product, to make into company offices, to close down the area and save the associated heating and lighting costs, etc. Each of these alternatives, and others not explicitly considered, has a "value". The value of the best implicit or explicit alternative to the current use of the space is the opportunity cost of the space. It is a cost relevant to the evaluation of continuing to use the space to make Product C. This opportunity cost will only by a rare coincidence be equal to the (irrelevant) cost of floor space allocated to Product C by the cost-accounting system. 5

Note on Marketing Arithmetic and Related Marketing Terms

Harvard Business School 574-082 Rev. April 29, 1983 Note on Marketing Arithmetic and Related Marketing Terms This note is about several terms and basic calculations used in the analysis of marketing problems.