In this chapter we introduce cost concepts that are used in day-to-day decision making by the business executive. In some cases these are crude when compared with the theoretical nicety of the concepts discussed in the preceding chapter. Real-world business situations, however, seldom provide the data necessary for direct application of the theoretical concepts. Nevertheless, an understanding of the theoretical concepts is important to ensure the proper application of the concepts that will be discussed in this chapter. Decision makers sometimes apply convenient rules of thumb to problems that confront them without first examining the applicability of those rules to the particular problem at hand. The danger of incorrectly applying these shortcuts is perhaps nowhere greater than in the area of costs, since poor decisions here operate directly to erode profitability.
In this chapter we shall first examine the differences between economic and accounting concepts of costs and profits. We shall see that some accounting costs, such as the depreciation of an asset purchased in an earlier period or the cost of an item taken from inventory purchased at an earlier, lower price, must be evaluated in terms of the current or future cost for economic decision-making purposes. This subject leads to a discussion of the relevant costs for decision making—some costs are relevant and others are irrelevant to the decision problem at hand. The relevant costs are all “incremental” costs. The three main types of incremental costs are introduced and discussed. “Contribution analysis” is based on the incremental costs of a decision, and the last section before the summary uses contribution analysis in the context of several types of decision problems. The appendix to this chapter considers “breakeven analysis,” with an examination of its applications and its limitations in the decision-making process.
The data for decision making with respect to costs typically come not from economists but from accountants. In most cases these data are adequate and appropriate, but in some cases, since they were derived for different purposes, they are less suitable for direct insertion into economic decision-making procedures. We shall examine several different economic and accounting cost concepts and the relationships between them.
In the business firm some costs are incurred that can be directly attributed to the production of a particular unit of a given product. The use of raw materials, labor inputs, and machine time involved in the production of each unit can usually be determined. On the other hand, the cost of fuel for heating, electricity, office and administrative expenses, depreciation of plant and buildings, and other items cannot easily and accurately be separated and attributed to individual units of production (except on an arbitrary basis). Accountants speak of the direct, or prime, costs per unit when referring to the separable costs of the first category and of indirect, or overhead, costs when referring to the joint costs of the second category. 1
Direct and indirect costs are not likely to coincide exactly with the economist’s variable cost and fixed cost categories. The criterion used by the economist to divide cost into either fixecT or variable is whether or not the cost varies with the level of output, but the criterion used by the accountant is whether or not the cost is separable with respect to the production of individual output units. To bring the accounting costs into line with the economic concepts we must find that part of the indirect or overhead costs that varies with the output level. Accounting statements often divide overhead expense into “variable overhead” and “fixed overhead” categories, in which case we would add the variable overhead expense per unit to the direct cost per unit to find what economists call average variable cost.
Example: Suppose that a company reports that during the past month it manufactured 1,480 units of output, and the accountant provides you with figures for the total expenditures on direct labor, direct materials, variable overhead, and fixed overhead, as shown in the left-hand side of Table 7-1. 1 he sum of the first three expenditures constitutes the total variable cost (TVC), and adding to it the fixed overhead, which we call total fixed cost (TFC), we arrive at total costs (TC). Per-unit costs, shown on the
See, for example, C. 1. Horngren, Introduction to Management Accounting , 5th ed. (Englewood Cliffs, N.J.: Prentice-Hall, Inc., 1981), chap. 3.
Table captionTABLE 7-1. The Interpretation of Accounting Reports in Economic Terms
Costs of Production | Total Costs | Average Cost |
Direct labor | $ 77,700 \ | If <So^Cj f $52.50 ^ |
Direct materials | 36,260 | 24.50 |
Variable overhead | 4,930 | 3.33 |
TVC = $118,890 | AVC = $ 80.33 ) | |
Fixed overhead | TFC = $ 36,800 | AFC = $ 24.86 |
Total costs | TC = $155,690 | AC = $105.19 |
c
right-hand side of the table, are found by dividing the total cost figures by the output level. 2
The accounting process is predominantly concerned with explicit costs. These are costs that actually involve a transfer of funds from the firm to another party that had previously supplied some materials or services. These are “out-of-pocket” expenses in the current time period, since they are an actual cash outflow in payment for resources. Other cost items, however, are implicit costs, in the sense that they do not involve an actual cash outflow in the current time period.
Example: One such cost in the accounting framework is depreciation, which is a charge against each year’s revenue of some portion of the cost of acquiring the capital equipment necessary to generate that revenue. The accounting procedures involve taking the initial cost of the asset, subtracting from this the asset’s estimated scrap or salvage value at the end of its useful life, and apportioning this net cost against revenues over the life of the asset. Straight-line depreciation procedures allocate the net cost evenly over the life of the assetTwhUeother methods, such as the sum-of-the-digits methods and double-declining-balance method, allocate proportionately more of the net cost against revenues early in the asset’s life. 3 Thus the accountant charges an implicit cost against revenues each year in order to spread the explicit cost of the asset over the period during which the asset is being used in the production process.
Accountants are constrained by the tax laws and by the laws governing financial reporting to shareholders to express many costs in terms of the actual or historic costs paid for the resources used in the production process. For decision-making purposes, howeve^ - , both accountants and economists agree that the appropriate cost concept is not the pa^t cost at which the resource was purchased, but the current or future cost at the time in which it is involved in the decision to be made.
■ Definition: Opportunity costs , or alternative costs as they are often called, refer to the value of a resource in its best alternative employment. For resources that are purchased outright or hired, such as raw materials and labor inputs, there is usually little difference between historic costs and opportunity costs. The market price at which they are purchased or hired should reflect their opportunity cost, since producers must bid for these goods in their respective markets. If not willing to pay at least what the resources are worth in their best alternative usage, the firm will not be able to purchase the services of these resources.
A difference will almost certainly arise between historic cost and opportunity cost if the resources are purchased and held in inventory for some time before they are used in the production process. If the market value of those resources changes, the opportunity cost diverges from the historic cost. Given the continuing problem of inflation, input prices tend to move upwards on a more or less continuous basis, although in some cases rapid technological advances can cause the market value of resources held in inventory to decline. For decision-making purposes, the current market value of the resource is its implicit cost to the firm, and this cost should be incorporated into any decision process rather than the (either higher or lower) historic cost. Note that if the firm wanted to replenish its inventories it must pay the current market price for the resource, or alternatively, if it wanted to sell the resource to another firm, it could do so at the current market value, rather than at the historic cost of the resource.
Now let us reconsider depreciation, which is intended to represent the implicit cost of assets such as land, buildings, and equipment purchased in the past. The accountant depreciates the cost of these assets by allocating a portion of the net cost of the asset against the current period’s revenues. The economist determines the opportunity cost of these services on the basis of what the land and buildings might have earned in alternative employment or on the basis of the interest which the funds tied up in those assets could have earned in alternative investment, whichever is greater. The opportunity costs of the capital tied up in land, buildings, and equipment may be quite different from the depreciation charge made against revenues, since the latter is determined on an entirely different basis. For decision-making purposes, depreciation of assets involved in the production process must be treated as the opportunity cost of those assets.
Example: The owner of a small farm might forgo $10,000 per annum in camping fees by continuing to use the land for farming rather than to take in campers. This is the opportunity cost of the land, unless the market value of the land is so high that the interest earned on the proceeds of the farm’s sale would earn more. Suppose the farm could be sold for $100,000, which the farmer (supposing he owns the farm free and clear) could deposit for 15 percent interest. Thus the opportunity cost of continuing to farm the land is $15,000, this being the best alternative use of the resource.
The farmer’s own labor must similarly be valued at its opportunity cost. If he could alternatively work for another farmer or take a job demonstrating and selling farm machinery, at say $20,000 per annum, this figure is his opportunity cost and should be included in the analysis for decision-making purposes.
The economist’s concept of profit differs from that of the accountant. Both consider profit as the excess of revenues over costs, but they regard costs differently. The accountant subtracts from revenues only the costs that are actually incurred plus an allowance for depreciation of some of the previously incurred one-time expenditures, such as the cost of plant and machinery. Profits thus represent the net income to the owners of the firm; profits are their reward for having invested time and capital in the venture. The economist, on the other hand, is concerned with the wider notion of efficient allocation of resources and is thus concerned that all resources are employed where they will earn the maximum for their owners. A means of ensuring this is to consider the opportunity cost of each resource.
Example: Let us illustrate with reference to the example of a small-store owner who has $50,000 invested as equity in the store and inventory. As shown in Table 7-2, the annual sales revenues were $160,000, from which must be deducted the cost of goods sold, salaries of hired labor, and depreciation of equipment and buildings. The accounting profit to the store is thus $15,000.
In Table 7-3 we show the economic statement of profit of the same store. Note that the sales revenues, cost of goods sold, salaries, and depreciation are the same as in the preceding table. (We suppose that we have checked and foun d that the market values of the equipment and buildings have in fact declined by $5,000 over the current
TABLE 7-2. Accounting Income Statement for the Small-Store Owner
Sales
Cost of goods sold Salaries
Depreciation expense
Accounting profit
$160,000
$ 120,000
20,000
5,000
145,000 $ 15,000
TABLE 7-3. Economic Statement of Profit to Smail-Store Owner
Sales
$160,000
Cost of goods sold Salaries
Depreciation expense Imputed salary to owner-manager Imputed interest cost on equity
$ 120,000
20,000
5,000
15,000
4,000
164,000
$-4,000
Economic profit
year and that the depreciation charge, therefore, fairly reflects the opportunity costs of these resources.)
The economist, however, would add two other items relating to the implicit cost of resources that are owned by the manager. Suppose that the owner-manager could earn $15,000 as a departmental manager in a large store and that this is his best opportunity for salary. Then we would add a cost to the business of $15,000, the imputed salary of the owner-manager. 4 Similarly, the owner-manager has $50,000 equity in the store and inventory, a sum of money that could easily be employed elsewhere for financial gain. Suppose it could be banked or invested elsewhere at comparable risk and would receive 8 percent interest on the principal, or $4,000 per annum. By choosing to invest the $50,000 in the store rather than elsewhere, the owner-manager is therefore forgoing an income of $4,000 per annum, and the economist adds this as an implicit cost on the income statement. Thus the total economic costs, or the opportunity costs of all resources used in the production process, are $164,000, and in economic terms the store owner has incurred a loss of $4,000. That is, the store owner could have earned $4,000 more with the resources at his disposal if he had sold the building and inventory, invested the money at 8 percent per annum, and worked in a similar job elsewhere for a salary of $15,000 per annum. 5
■ Definition: Normal profits are earned when total revenues equal total costs, if total costs are calculated to reflect the opportunity costs of all services provided. If revenues just equal these costs, then all factors are earning the same in that particular employ-
Of the owner-manager were to make drawings from the business of cash or goods, these must be accounted for. Suppose he had drawn $10,000 from the business in cash and goods over the year. This plus another $5,000 should be charged against sales revenues, in order that his opportunity cost is properly valued at $15,000.
Psychic income, or the utility derived from being one’s own boss in this case, should always be considered. This storekeeper should continue in his own store if the monetary value of being his own boss exceeds $4,000 per annum. Similarly, many business school professors continue to teach in business schools, rather than accept positions with substantially higher salaries in business and government, because of the psychic income associated with the academic life. (Occasional consulting work represents a nice compromise).
ment as they could earn elsewhere. If revenues exceed these costs, we say that the firm is earning a pure , or economic, profit. Remembering that the owners of the firm are the effective suppliers of the services of the land and buildings mentioned, you will see that an economic profit means that the owners of the firm are earning more profit than they could by investing their capital elsewhere. The accounting profit must be adjusted for the opportunity cost of the owned resources—that is, for what the firm would pay for the services of those resources if they were purchased or hired—before the alternative investment possibilities can be assessed. Accounting profit will exceed economic profit if some implicit opportunity costs are not subtracted from revenues.
This is not to say that either the accountant’s or economist’s view of profit is incorrect; each is designed for a different purpose. The accountant’s purpose is to find, once the capital has been invested in a particular pursuit, the return to the owners of that capital. The economist’s purpose is to ensure that all resources are employed in their most efficient uses. The existence of economic profit confirms this.
Note: A normal profit (when TR = TC) does not mean no profit. Since total costs in the economic sense include the opportunity cost of all resources used, the return on capital invested is included as a cost, rather than counted as a residual in the accounting sense. Normal profit means a sufficient return on the owner’s investment in the firm, sufficient to prevent him or her from liquidating this investment and investing it in the next best alternative investment, since the return on the next best alternative investment opportunity is included as an economic cost of production. Normal profit, therefore, means as much profit as the owners could get elsewhere.
Considering that investments are not equally risky, we need to qualify our concept of normal profits to take into account the different degrees of risk in investment opportunities. Investing money in government bonds is relatively risk free, for example, since there is virtually no risk of default in mature economies. Dividends are paid on schedule, and bonds are redeemed on the due date as long as the government exists. Investing money in the development of a new product, on the other hand, is relatively risky. Investors may not receive dividends on their investments, and in many cases they may lose all the capital they put in. Accordingly, government bonds pay a relatively low rate of interest (5 percent to 10 percent), whereas companies prospecting for oil and minerals, introducing new products, and engaging in other high-risk businesses must offer relatively high rates of interest (15 percent to 20 percent) in order to attract the required investment funds. Although investors are generally averse to risk, they are willing to take risks, but only if there is a promise of sufficiently higher returns to compensate for the risks they are taking. The extra return on high-risk investments necessary to compensate investors is known as the risk premium. The higher the risk involved, the larger the risk premium demanded by investors.
SThccTai ternative investment opportunities could earn more or less, depending on the degree of risk, we must confine our considerations to alternative investments of
the same or similar degree of risk, for the sake of comparability. In effect, this is the familiar ceteris paribus requirement: the comparison of one investment with other investments of equal risk. The highest return on these alternative investments of equal risk is the opportunity cost of investing in the chosen area. It follows that the opportunity cost of investing in a low-risk business is lower than the opportunity cost of investing in a relatively high-risk business. In turn, the normal profit of a low-risk business is lower than the normal profit of a high-risk business. In accounting terms, a firm in a low-risk business may be content to earn an 8 percent return on investment after taxes, whereas a firm in a high-risk industry might require a 15 percent return on investment after taxes in order to keep them in that particular business.
We turn now to incremental costs, the most important cost concept for decision making.
■ Definition: Incremental costs are those costs that will be incurred as the result of a decision. Incremental costs are measured by the change in total costs that results from a particular decision’s being made. Incremental costs may therefore be either fixed or variable, since a new decision may require purchase of additional capital facilities plus extra labor and materials. When we compare incremental costs with incremental revenues, that is, with the change in total revenues that occurs as a result of the decision, we can see whether a proposed decision is likely to be profitable or not. Clearly, if incremental revenues exceed incremental costs, the proposed decision will add to total profits (or will reduce losses if the total revenues generated do not cover the total costs incurred).
Note : Incremental costs are not identical with marginal costs. As defined in the preceding chapter, marginal costs are the change in total cost for a one-unit change in the output level. Incremental costs, on the other hand, are the aggregate change in costs that results from a decision. This decision may involve a change in the output level of 20 or of 2,000 units, or it may not involve a change in the output level at all. For example, the decision may be whether or not to introduce a new technology of producing the same output level. Knowledge of marginal costs, however, may be very important for the calculation of the incremental costs.
The incremental costs must be accurately identified. Only those costs that actually change as a result of the decision may be included, but all costs that change as a result of the decision must be included. Factors that have been lying idle, with no alternative use, do not have an incremental cost and therefore may be regarded as being costless for the particular decision at hand. Similarly, costs that have been expended in the past for machinery or plant and buildings must be regarded as sunk costs and should not enter the decision-making procedure unless their opportunity cost is positive. That is, unless there is a competing and profitable use for an owned resource, the incremental cost of involving that resource in the present decision will be zero.
■ Definition: The relevant costs for decision-making purposes are those costs that will be incurred as a result of the decision being considered. The relevant costs are, therefore, the incremental costs. Costs that have been incurred already and costs that will be incurred in the future regardless of the present decision, are irrelevant costs as far as the current decision problem is concerned.
Example: The manager of a gift store thinks that he has found a miracle product that will sell rapidly and give him large profits. It is an “antenna hat” comprised of two brightly colored balls on the end of flexible springs affixed to a headband. When worn by a person, the balls swing around like the antennae of some giant insect. The manager is convinced these “hats” will sell and has purchased 5,000 of them. His cost was $1.00 each, payable $0.50 immediately and $0.50 within thirty days. He then spent $2,500 promoting these gimmicks, in newspaper advertisements and by hiring students to wear them around campus and at public events. He set the price at $4.95 and waited for his fortune to come rolling in. Three weeks have passed and he still has 4,975 of these antenna hats. His assistant manager suggested that he cut the price to $1.25 in order to get rid of what was obviously an ill-considered venture. The manager is adamant that he will never let the price fall that low since “his cost” was $1.50 per unit and he doesn’t want to take a loss on this item.
But is $1.50 the relevant cost? The manager is about to make a pricing decision, and, as a result of that decision, costs may or may not be incurred and revenues may or may not be earned. The relevant costs are those that will be incurred as a result of the decision. The initial outlays of $2,500 on the antenna hats and $2,500 on promotion are irrelevant costs since they have already been incurred and cannot be retrieved. These are sunk costs. The second payment of $2,500 for the hats is also an irrelevant cost since it must be paid whether or not the price is changed and whether or not any more of the hats are sold. The relevant costs are those, if any, that will be incurred following the pricing decision. Suppose that storage costs must be incurred if the hats are not sold within another week. These costs will be incremental to a decision to maintain price at $4.95 but not incremental to a decision to cut price to $1.25, presuming that the assistant manager’s judgment is correct and all units would sell at the lower price. Note that the marketability of the item is declining; it is a novelty item and must be sold before the public tires of its novelty value. Thus price should be set not with an eye on the irrelevant costs (sunk costs and committed costs) but with an eye on the incremental costs. To include the irrelevant costs in the present decision is to let an earlier bad decision cause another bad decision to be made. In business parlance, the gift-store manager should “cut his losses” and “avoid sending good money after bad.”
There are three main categories of relevant, or incremental, costs. These are the present-period explicit costs, the opportunity costs implicitly involved in the decision, and the future cost implications that flow from the decision. Let us examine these in turn.
Present-Period Explicit Costs. Direct labor and materials costs and changes in the variable overhead costs, such as electricity, are fairly easy to anticipate as a consequence of a decision, for example, to increase the output level. If this increase also requires the purchase of additional capital equipment, this capital cost is incremental to the decision and should be included in full rather than apportioned in any way, notwithstanding that the equipment may have a useful life remaining after the present decision has been carried out. 6
Thus the incremental costs of a decision will include all present-period explicit costs that will be incurred as a consequence of that decision. It will exclude any present-period explicit costs that will be incurred regardless of the present decision.
Opportunity Costs. Items taken from inventory may not have an explicit present- period cost if the firm does not choose to replace them in inventory by current purchases. Nevertheless, the relevant cost is the opportunity cost of that item—it could presumably be sold to another firm for its market value. If an item in inventory is worthless, having no market value (because it is outmoded by a new item, for example), its opportunity cost is zero, regardless of its historic cost. The historic cost of purchasing the item is an irrelevant, sunk, cost for the purposes of the present decision.
The most common application of the opportunity cost doctrine in decision making concerns the situation in which a particular resource has one or more uses at the same point of time. In this case, if the resource is used in the production of a particular output, it precludes the production of one or more other outputs.
Example: Telarah Lite-Fab Industries produces steel gates, fences, balcony and porch railings, and similar items cut and welded from wrought iron. This firm does custom orders but also produces standard gates and railings, which are sold to retail hardware stores. The firm finds it can sell as much as it can produce of the standard gates and railings but prefers to do custom orders since the latter are invariably more profitable. At the present time the firm has no custom orders outstanding, and its labor force is producing standard items at the rate of $10,000 per week sales value. Materials cost is $2,000 per week. Suppose now that a large custom order arrives that would take a week to manufacture and would cost $4,000 in materials. What is the opportunity cost of the firm’s resources presently employed in the manufacture of the standard gates and railings? Note that with the standard items the firm is making $8,000 per week over and above materials cost. It must forgo this $8,000 contribution to its other costs and profits if it takes the custom order. Thus the firm must make at least $8,000 over and above materials cost on the custom order before it should even consider accepting the order. That is, the materials cost and the opportunity cost of
' If future revenues may be expected from an item of equipment or from other capital investment, these will be incorporated into the analysis on the revenue side of contribution analysis, as we shall see in the next section.
the custom order add up to $12,000, and the firm must set its price at least that high or it would be better off sticking to the standard items.
Future Costs. Many decisions will have implications for future costs, both explicit and implicit. If the firm can form an expectation of a future cost that will be incurred or is likely to be incurred as a consequence of the present decision, that cost must be included in the present analysis. Of course, it will be incorporated in present-value terms if known for certain or in expected-present-value terms if there is a probability distribution of the future cost’s occurring.
Example: A firm decides to produce a special order which it knows will cause severe wear and tear on its equipment, to the point where an overhaul will be required within one year after the job is completed. Otherwise, the equipment would serve out its useful life without a major overhaul. This overhaul is expected to cost $2,000 and will be paid one year from now. Supposing an opportunity discount rate of 15 percent, the appropriate discount factor is 0.8696, and the present value of that cost is $2,000 X 0.8696 = $1,739.20. This figure should be included as an incremental cost of deciding to produce the special order.
Example: Consider now a future cost which has a probability distribution of outcomes. Suppose a firm is considering copying another firm’s design and knows that the other firm may sue for loss of business as a result. The possible legal costs and damages and the probabilities attached to each level of these costs are shown in Table 7-4. Given the congestion in the courts, it will take three years for the case to be resolved. We suppose that the firm’s opportunity discount rate is 15 percent. Thus the discount factor used to find the present value of the expected costs is 0.6575.
Thus the EPV of the future legal costs is $72,325, a figure that should be included in the incremental costs of the decision to copy the other firm’s design. Note that the firm should consider the possibility of such legal claims even when it does not willfully copy another firm’s design. It may feel that its design is sufficiently different but that a court may nevertheless rule against it in the event of a lawsuit. In such cases
Table captionTABLE 7-4. Expected Present Value of Future Incremental Costs
Costs | Expected | ||
Expected | Present | Value | |
($) | lYY Value | Probability | ($) |
0 | 0 | 0.10 | 0 |
50,000 \ | . 15^702,875 | 0.20 | 6,575.00 |
100,000 | 65,750 | 0.30 | 19,725.00 |
150,000 | 98,625 | 0.25 | 24,656.25 |
200,000 | 131,500 | 0.10 | 13,150.00 |
250,000 | 164,375 | 0.05 | 8,218.75 |
Expected Present Value | $72,325.00 |
290 Production and Cost Analysis
the firm should calculate the EPV of the possible lawsuit and include this in its calculations.
Other future costs include labor problems, loss of future business, deterioration of supplier relations leading to higher input prices, and cash-flow problems necessitating borrowing costs. Any future cost, whether explicit or implicit, which can reasonably be expected to follow as a consequence of the current decision should be quantified in EPV terms and included in the incremental costs of the decision.
The cost concepts that were mentioned previously are summarized in Table 7-5. Note that by “relevant” or “irrelevant” we mean with respect to the decision at hand. If a cost is expected to be a consequence of the decision to be made, it is a relevant, or incremental, cost. Some subsequent (future) costs are not consequent (relevant) costs, because the firm is committed to them and they will be incurred anyway. No prior expenditures (sunk costs) are incremental costs.
We proceed now to use the concept of incremental costs in the contribution analysis of decision problems.
■ Definition: The contribution of a decision is defined as the incremental revenues of that decision less the incremental costs of that decision. It should be interpreted as the
TABLE 7-5. Summary of Cost Concepts for Decision Making
RELEVANT COSTS IRRELEVANT COSTS
Incremental Costs" Committed Costs" Sunk Costs*
Present period explicit costs: Variable:
Direct labor Direct materials Variable overheads Fixed:
New equipment New personnel
Opportunity costs:
Contribution forgone on the best alternative use of the resources involved
Managers’ salaries
Payments on debt
Rental and lease costs
Wage contracts or wages of ongoing workers
All other payments that must be made regardless of the decision at hand
Previously paid-for purchases of assets, including land, buildings, plant and equipment, and depreciation expenses based on these assets
Prepaid and nonrecoverable expenses
Future period incremental costs: EPV of probable costs to follow in the future as a consequence of the decision
"Future costs. '’Past costs.
“contribution made to overhead costs and profits” by the decision. Clearly, only those decisions that have a positive contribution should be undertaken; and where decisions are mutually exclusive, the one with the larger expected contribution is to be preferred. We shall illustrate contribution analysis with three common types of decision problems, but first let us clarify the notion of incremental revenues.
Rz—iv <S-1_ ^
a A At/ I -r i v, ( — c s'
~~l X rT* c-i I ~T X
Definition: Incremental revenues are defined as the revenues which follow as a consequence of a particular decision. We should expect incremental revenues, like incremental costs, to have an explicit current-period component, a possible opportunity component, and a possible future component.
Example: A firm bidding on a contract to supply electric light fixtures to a government office building tenders a very low bid for $265,000 and expects to avoid layoff costs of $100,000 if it wins the contract. It also expects to win future government contracts if it is the successful bidder on this contract, since this contract provides the firm with the opportunity to prove that it can supply a quality product and meet its production schedule.
The explicit current-period incremental revenues if the firm wins the contract will be $265,000. But the contract is worth much more than $265,000 to the firm. If it doesn’t win the contract, it will have to lay off workers and incur subsequent severance pay and future start-up costs associated with recruiting and training totaling $100,000. If the firm does win the contract, this $100,000 is not spent and therefore stays in the bank. Avoidance of a cost as the result of a decision amounts to an opportunity revenue of the same amount.
■ Definition: An opportunity revenue is a cost avoided as the result of a decision. Although there is no actual inflow of revenues, the outflow of revenues is avoided so that money that would otherwise be spent is still sitting in the bank, and the net effect is the same. The future revenues associated with this pricing decision will be the expected present value of the contribution to overheads and profits associated with the future business generated as the result of winning the present contract.
Example: Suppose the firm mentioned in the preceding example feels that if it wins the present job, it has a 50 percent chance of winning a similar contract next year. Suppose further that the next contract would be for $300,000 and would have an incremental cost of $250,000. The contribution from the next contract is, thus, $50,000 (if won). Given an opportunity discount rate of 15 percent, the present value of this contribution is $50,000 X 0.8696 = $43,480. The expected present value is the present value times the probability of receiving it, or $43,480 X 0.50 = $21,740. Thus the EPV of the future revenue is $21,740, and this figure should be included in the incremental revenue calculation.
The firm’s incremental revenue is the sum of the present-period explicit revenues, the opportunity revenues, and the EPV of future (consequential) revenues. Thus the contract has total incremental revenues of $265,000 + $100,000 + $21,740, or $386,740 in total. This contract would, therefore, offer a positive EPV of contribution as long as incremental costs were less than $386,740.
Note: The EPV of the contribution to be received from future business resulting from the present decision can be regarded as the goodwitt associated with the present decision. Goodwill is the EPV of contribution from future business, and if a decision involves an increment to goodwill, the amount of that contribution in EPV terms should be included as an incremental revenue. Conversely, the present decision may cause the loss of future business. The EPV of the future contribution lost as the result of the present decision can be regarded as the ill will Associated with this decision.
Example: Consider a construction firm that is considering bidding for a contract to move city garbage while the garbage workers are on strike. If this contract involves the possibility that the firm will lose future construction contracts because of the buyer’s fear of retaliatory disruption by unionized construction workers, the EPV of the contribution expected to be lost on future jobs must be included as an incremental cost of taking the present contract to move the city’s garbage.
Let us now demonstrate the application of contribution analysis in the context of three common types of decision problems.
Example: Suppose a firm is considering adopting either project A or project B but cannot adopt both, since they use the same set of machinery and labor. Project A, as shown in Table 7-6, promises sales of 10,000 units at $2 each, with materials, labor, variable overhead, and allocated overhead costs as shown, such that there is an apparent profit of $2,000. Project B promises sales revenues of $18,000, with materials, direct labor, and variable and allocated overhead as shown. The apparent profit from
Table captionTABLE 7-6. Income Statements for Projects A and B
Project A | Project B | ||||
Revenues (10,000 @ $2) | $20,000 | Revenues (6,000 @ $3) | $18,000 | ||
Costs | Costs | ||||
Materials | $2,000 | Materials | $5,000 | ||
Direct labor | 6,000 | Direct labor | 3,000 | ||
Variable overhead | 4,000 | Variable overhead | 3,000 | ||
Fixed overhead | 6,000 | 18,000 | Fixed overhead | 3,000 | 14,000 |
Profit | $ 2,000 | Profit | $ 4,000 |
project B is $4,000, and it would seem that project B is preferable to project A by virtue of its higher profitability.
When contribution analysis is applied to the above decision problem, however, the answer may be surprising. Consider Table 7-7, in which the incremental costs are subtracted from the incremental revenues to find the contribution of each project. Since the fixed overhead was not a cost incurred as a result of this particular decision, it is excluded from the contribution analysis, and it can be seen that project A contributes more to overheads and profits than does project B. The danger of including arbitrary allocations of fixed overhead is exemplified here. The fixed overhead was allocated on the basis of a particular criterion, in this case as 100 percent of direct labor, but if it had been included in the decision process it would have caused an inferior decision to be made. Whatever method of fixed overhead allocation is used, the danger is likely to persist. Hence we use contribution analysis, which allows an incisive look at the actual changes in costs and revenues that follow a particular decision.
Note that in this example we implicitly assumed the absence of all opportunity costs and revenues and that we proceeded as if there were neither future costs nor future revenues associated with either project. In practice, decision makers should not proceed so blithely but instead should assure themselves that all incremental costs and incremental revenues are included in the decision analysis. In the above example the difference between projects A and B was only $1,000. Hence, our decision to choose project A was very sensitive to the assumption of zero opportunity and future costs and revenues. Our decision would have been reversed if A had opportunity and future costs (in EPV terms) exceeding $1,000, for example. More generally, if the net opportunity and future revenues of project B had exceeded those of A by more than $1,000, the decision would have been reversed. 7
Table captionTABLE 7-7. Contribution Analysis for Projects A and B
Project A | Project B | ||||
Incremental revenues Incremental costs Materials Direct labor | $2,000 6,000 | $20,000 | Incremental revenues Incremental costs Materials Direct labor | $5,000 3,000 | $18,000 |
Variable overhead Contribution | 4,000 | 12,000 $ 8,000 | Variable overhead Contribution | 3,000 | 11,000 $ 7,000 |
Example: The Wilson Tool Company manufactures high-quality power tools such as drills, jigsaws, and sanders. All these tools require the same roller-bearing unit, which the company manufactures in its own bearing department. Pertinent cost data for the past year of operations in that department are shown in Table 7-8.
Demand estimates indicate that the company should expand its production of some of the power tools and that an additional 7,500 bearing units will be required. The company could produce these in its bearing department but is considering having the additional units supplied by a firm that specializes in bearings. Wilson anticipates that it will require an increase of 15 percent in total direct labor costs and 12 percent in total materials costs to produce these additional units in house. No additional capital expenditure will be necessary, since some machines currently have idle capacity. A specialist bearing producer who has been approached has studied the specifications and has offered to supply the 7,500 bearing units at a total cost of $30,000, or $4 per unit. Should Wilson make or buy the additional units?
We begin by comparing the incremental costs of the two alternatives facing Wilson. The incremental costs of buying them from the specialist come to $30,000, since this is the dollar amount that Wilson must spend to obtain the additional units. To calculate the incremental costs of making the units in house, we begin by calculating the increases in materials and direct labor costs that would be occasioned by the manufacture of those units. The 12 percent increase in the total material cost would imply an incremental material cost of $4,637, and a 15 percent increase in total direct labor costs would imply a $18,959 increase in that cost category. As shown in Table 7-9, the total of these two figures is $23,596, which is less than the incremental cost of buying the units from outside. The decision to make, rather than buy, the additional units would thus appear to save the Wilson Tool Company a total of $6,404. 8
Table captionTABLE 7-8. Wilson Tool Company: Bearing Department Costs
Total | Per Unit | |
Direct materials | $ 38,640 | $ 0.56 % |
Direct labor | 126,390 | 1.81 |
Allocated overhead | 252,780 | 3763 |
Total bearing units produced: | $417,810 | $ 6.00 69,635 |
"Since the incremental revenue is the same whether Wilson makes or buys the parts, we can do the contribution analysis on the basis of the incremental costs alone. Presuming that the incremental revenues exceed the incremental costs, the make alternative would seem to contribute more to overheads and profits than does the “buy” alternative.
Table captionTABLE 7-9. Incremental Costs of Making the Bearing Units
Table captionTotal Per Unit
Direct materials Direct labor Allocated overhead | 17 -°/* | $ 4,637 18,959 (?) | $0.62 2.53 (?) | |
$23,596 | $3.15 | 2 - | ||
c^t_ —j *7 y |
Variability of Overheads. The above analysis, however, does not consider the possibility that some part of overhead expenses may vary with the level of production of the bearing units. It is conceivable that some overhead cost components, such as electricity, office and administration expense, and cafeteria expense, might vary to some degree as a result of producing these units in house. Rather than make arbitrary assumptions about the proportion of overheads that will vary, and since we do not have the information necessary to make a reasoned judgment, let us perform a sensitivity analysis on the decision that has been made. That is, we wish to know by how much the overhead expenses may vary before the decision to make the product would be the wrong decision. The answer is obviously that if overheads vary more than $6,404 as a result of this decision, the best decision would be to buy the product from the outside supplier. A $6,404 variation in overhead represents slightly more than a 2.5 percent variation in the allocated overhead. It is up to the decision maker to judge whether a variation of this percentage or dollar magnitude is likely to follow the decision to produce the product in house.
Longer-Term Incremental Costs. A number of other considerations should also enter into this decision. First, there is the issue of long-term supplier relations. Since Wilson may need a specialist producer some time in the future when it may be unable to produce the bearings in house because of capacity limitations, it can perhaps establish itself as a customer of the supplier by giving this contract out at the present time, so that in future situations supply could be assured.
Second, there is the issue of the quality of the bearing units supplied by the outside firm as compared with those produced by Wilson. The decision maker would have to be assured that the units supplied from outside would be at least equal in quality to the standards desired. On the other hand, the specialist producer may be able to produce consistently higher quality bearing units, with subsequent impact upon the quality of Wilson Tools and on long-term buyer goodwill.
Third, the issue of labor relations must be considered. The decision to make the units involves an increase in the labor force, which may lead to crowded working conditions and overtaxed washroom and cafeteria facilities. The data indicate that labor efficiency is decreasing, since the incremental cost per unit to make the additional 7,500 units is $3.15 as compared with the total of $2.37 for direct materials and labor per unit shown in Table 7-8. It is conceivable that the hiring of additional labor units and the resultant increased congestion and reduced efficiency could cause a lowering
of employee morale, with subsequent longer-term disadvantages to the profitability of the Wilson Tool Company.
In total, the decision maker must decide whether or not the expected present value of these eventualities, plus the possible variable components in overhead costs, is likely to exceed $6,404. If so, the decision should be to buy the product from outside.
Other Considerations. There are several additional issues that should be considered. First, the decision maker would need to be assured of the accuracy of the estimations that are involved in this decision. If, for example, demand for the tools does not increase as predicted and Wilson purchased the roller-bearing units from outside, this would be an irreversible commitment involving considerable expense, whereas the decision to make the units in house could soon be suspended. The cost estimates are likewise subject to some doubt. These are presumably extrapolations on the estimated marginal costs of producing the units in house. The decision maker would need to be assured that these extrapolations were based on the most reasonable assumptions concerning the efficiency of direct labor and material usage and that they are, consequently, the best estimates. To the extent that there is a distribution of both demand and cost estimates, a decision based on the most likely point estimate alone may result in an outcome that is quite different from the expected value.
Another question that arises in the problem is whether or not the price quotation received is in fact the lowest-cost source of supply of these bearing units. We might assume that bids were solicited and that the lowest bid was being considered, but if this were not the case the decision maker should consult alternative sources of supply to confirm that the $30,000 price was in fact the best price at which the units may be bought from outside.
With these qualifications in mind, we turn now to the third category of decision problems in which contribution analysis is an appropriate solution procedure.
Example: The Idaho Instruments Company produces a variety of pocket calculators and sells them through a distributing company. The purchasing agent for a large chain of department stores has recently approached Idaho Instruments with an offer to buy 20,000 units of its model XI at the unit price of $8. Idaho’s present production level of that model is 160,000 units annually, and it could supply the additional 20,000 units by forgoing production (and sale) of 5,000 of its more sophisticated X2 model. Pertinent data relating to these two models are shown in Table 7-10. Because of the highly mechanized production process, the per-unit variable costs of each model are believed to be constant over a wide range of outputs. The sales manager for Idaho Instruments is reluctant to sell the XI model for $8 when she normally receives $12 from the distributing company, and she has attempted to negotiate with the purchasing agent. The latter, however, insists that $8 is his only offer. Should Idaho Instruments take it or leave it?
Cost Concepts for Decision Making 297
Table captionTABLE 7-10.
Table captionIdaho Instruments Company: Per-Unit Data on Calculators
Model XI | Model X2 | |
Materials | < $ 1.65 | / $ 1.87 |
Direct labor | > 2.32 | 3.02 |
Variable overhead | 1.03 | 1.11 |
Fixed overhead allocation | 5.00 | 6.00 |
Profits | 2.00 | 2.40 |
Price to distributor | $12.00 | $14.40 |
Since the average variable cost for both models is expected to be constant over a wide range, we can calculate the incremental cost of this decision on the basis of the average variable cost. The average variable cost is the sum of the first thiee components in the table, and hence 20,000 additional units of model XI (with AVC = $5.00) will add $100,000 to the cost levels. This figure is not the total incremental cost, however, since there is an opportunity cost involved. The production of the additional 20,000 units will come partly from the idle capacity that is to be utilized and partly at the expense of 5,000 units of model X2. The opportunity cost of using the resources that previously produced the X2 are the value of those resources in that alternate use. The net value to Idaho Instruments of employing the resources in the production of 5,000 units of the X2 is the contribution made by those 5,000 units. From Table 7-10 it can be found that the contribution per unit to overheads and profits is $8.40. Hence the opportunity costs are the total forgone contribution, or 5,000 units X $8.40 = $42,000. In Table 7-11 we show the contribution analysis of this problem. The incremental revenues are $160,000, and the incremental costs add up to $142,000. Hence the contribution to overheads and profits that would follow from the decision to take the department store’s offer is $18,000. Thus profits would be $18,000 greater than they would be otherwise, or losses would be $18,000 less.
An alternate method of arriving at the same contribution would be to subtract from the incremental revenues the revenues forgone when the 5,000 units of X2 were not sold at $14.40 (that is, $72,000) and subtract from the incremental cost of producing the extra units of the model XI the decremental costs of not producing 5,000 units
TABLE 7-11. Contribution Analysis of Calculator Decision Problem
Incremental revenues
20,000 units of XI @ $8.00
Incremental costs
Variable costs ,
20,000 units of XI @ $5.00 V ) Opportunity costs (contribution forgone) 5,000 units of X2 @ $8.40 Contribution
$100,000
42,000
$160,000
142,000 $ 18,000
298 Production and Cost Analysis
of the model X2 (that is, $30,000). The net adjustment as the result of these manipulations is $72,000 — $30,000, or $42,000, which is exactly the opportunity cost figure we have entered in Table 7-11. The opportunity cost method achieves the same results with some economy of effort, but more importantly, perhaps, it draws the decision maker’s attention to the possible alternate uses of resources.
The preceding decision is sensitive to some of the underlying assumptions, however. The first issue is that of substitutability between the units sold to the department store and those sold to the distributing company. The analysis has proceeded upon the implicit assumption that the sale of 20,000 units to the department store will be in addition to, and nonsubstitutable with, the 160,000 units sold through the distributing company. To the extent that some customers now buy this product through the department store rather than through the distributing company, Idaho Instruments will be forgoing an amount of $4 per unit, or the difference in the price charged to the two wholesale buyers. If the department stores will tap a totally new market for the calculators, we can presume that total sales will increase by the entire 20,000 units and that there would indeed be a contribution of $18,000 following this decision. On the other hand, if the sale to the department store reduces normal sales, to what degree could this happen before the decision to take the offer becomes the wrong one? Since the difference in contribution per unit is $4, the number of units that it would take to erode that $18,000 total contribution down to zero is $18,000 -r- 4 = 4,500. Thus, if in the judgment of the decision maker there are likely to be at least 4,500 units purchased from the department stores that would otherwise have been purchased from the normal distribution channels, the decision should be reversed.
An additional consideration here is that of retailer relations. Doubtless the firms in the normal distributing channels will become aware that the department stores were given a better deal, and these firms may in turn look elsewhere for their supplies. Thus any short-term gain by selling to the department store may be outweighed by longer-term losses from a deterioration of the relationship currently enjoyed with the distributing company and with other firms. 9
A third area of concern relates to the image of Idaho Instruments’ calculators. Presumably the department stores, having purchased at a relatively low cost per unit, will price below the current market price for the model XI. This reduced price may have a detrimental impact upon the quality image currently held by that model. Since many consumers judge quality on the basis of price when they have no alternate means of discovering quality or durability, the lowering of the price of the XI may reduce the consumer’s perception of its quality. Alternatively, this contract with the department store may be the beginning of a long and successful relationship with that particular buyer and may add to rather than detract from the image of the calculators and the total sales.
‘’In fact, if Idaho Instruments continues to favor the department store with a lower price, it may run afoul of legislation concerning price discrimination. Legal constraints on pricing are discussed in Appendix 10A.
In summary, then, the decision maker must consider all possible future ramifications of the decision and must calculate the expected present value or loss of each eventuality. The net expected present value or loss must be added to or subtracted from the immediate contribution before the final decision is made.