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26
Short-Run Alternative
Choice Decisions
This chapter begins a discussion of the third use of management accounting information—for making alternative choice decisions. In such problems, the manager seeks to
choose the best one of several alternative courses of action. The quantitative analysis
of these alternatives focuses on the differences in their costs (and sometimes also differences in their revenues and assets employed). This chapter introduces the construct
of differential costs and contrasts it with the full cost construct that was discussed in
Chapters 17–19. This chapter also describes the use of differential costs (and differential revenues) in the analysis of several types of problems, each having a relatively
short time horizon. Alternative choice problems involving longer time horizons and
differential assets are discussed in Chapter 27.
The Differential Concept
Cost
Constructions
for Various
Purposes
Chapters 17–19 discussed the measurement of full costs, one type of cost construction.
In this chapter, we introduce a second main type of cost construction, called differential costs. Some people have difficulty accepting the idea that there is more than one
type of cost construction. They say, “When I pay a company $280 for a suit, the suit
surely cost me $280. How could the cost be anything else?” It is appropriate, therefore,
that we establish three points: (1) Cost has more than one meaning; (2) differences in
cost constructions relate to the purpose for which the cost information is to be used;
and (3) unless these differences are understood, serious mistakes can be made. To explain these points, consider the following example:
Example
A company manufactures and sells desks. According to its cost accounting records, the full
cost of making and marketing a certain desk is $500. Suppose that a customer offered to
buy such a desk for $450. If the company considered that the only relevant cost for this desk
was the $500 full cost, it would, of course, refuse the order. Its revenue would be only $450,
and its costs would be $500; therefore, the management would conclude that the company would incur a loss of $50 on the order.
But it might well be that the additional out-of-pocket costs of making and selling this one
desk—the lumber and other material, the earnings of the cabinetmaker who worked on the
desk, and the commission to the salesperson—would be only $350. The other items making up the $500 full cost were items of cost that would not be affected by this one order.
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The management might therefore decide to accept this order at $450. If it did, the company’s costs would increase by $350, its revenue would increase by $450, and its income
would increase by the difference, $100. Thus, the company would be $100 better off by accepting this order than by refusing it. Evidently, the company in this example could make
the wrong decision if the management relied on the full cost information.
In this example, we used both $500 and $350 as measures of the cost of the desk.
These numbers represent two types of cost constructions, each of which is used for a
different purpose. The $500 measures the full cost of the desk, which is the cost used
for the purposes described in Chapter 17. The $350 is another type of cost construction
and it is used for other purposes, one of which is to decide, under certain circumstances, whether to sell an item at a price below the item’s full cost. This latter type of
cost construction is differential cost.
Differential
Costs and
Revenues
More formally, differential costs are costs that are different under one set of conditions than they would be under another.1 Differential costs always relate to a specific
situation. In the previous example, the differential cost of the desk was $350. Under another set of circumstances—for example, if a similar problem arose several days
later—the differential costs might be something other than $350. The differential cost
to the buyer of the desk was $450; the buyer incurred a cost of $450 that would not
have been incurred if the desk had not been purchased.
The differential concept also applies to revenues. Differential revenues are those
that are different under one set of conditions than they would be under another. In the
desk example, the differential revenue of the desk manufacturer was $450; if it accepted the order for the desk, its revenue would differ by $450 from what revenue
would have been if it did not accept the order.
Contrasts with
Full Costs
There are three important differences between full costs and differential costs:
1. Nature of the Cost. The full cost of a product or other cost object is the sum of its
direct costs plus a fair share of applicable indirect costs. Differential costs include only
those elements of cost that are different under a certain set of conditions. This is the
most important distinction between full costs and differential costs.
In the example of the desk given above, the volume, or output, of the desk manufacturer would be higher by one desk if it accepted the order compared with what volume would have been if it did not accept the order. The proposal under consideration
therefore had an effect on volume as well as on costs. This is the case with a great many
problems involving differential costs. A thorough understanding of the cost behavior
concepts discussed in Chapter 16 is therefore a prerequisite for the analysis of many
differential accounting problems.
2. Source of Data. Information on full costs is taken directly from a company’s cost
accounting system. That system is designed to measure and report full costs on a regular basis. There is no comparable system for collecting differential costs. The appropriate items that constitute differential costs are assembled to meet the analytical
requirements of a specific problem.
Since the cost items that are differential in a given problem depend on the nature of
that specific problem, it is not possible to identify items of differential cost in the accounting system and to collect these costs on a regular basis. Instead, the accounting
1
Differential costs are also called relevant costs. This term is not descriptive, because all types of
cost constructions are relevant for certain purposes.
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system may be designed so that it can furnish the raw data that are useful in estimating the differential costs for a specific problem. Ideally, an accounting system should
be designed so that it separately identifies items of variable cost, step-function cost,
and fixed costs, making it clear to what measure of volume or “cost driver” each of the
variable and step-function costs relates. For example, raw materials cost relates to production volume, whereas selling commissions relate to sales volume.
In practice, though, relatively few companies’ routine accounting systems meet this
ideal. It is an unusual system that explicitly identifies step-function costs as a separate category, and many systems do not even make a distinction between fixed and
variable costs. Rather than elaborating their cost systems, some companies build
activity-based cost models to aid in making the cost estimates that are needed in alternative choice decisions.2
Whatever the source of cost data, recall from Chapter 16 that any cost behavior classification depends on the relevant time period that is assumed. The previous statements
about the desk assume a time period of one month; that is, an item of cost is variable if
the month’s total amount of that cost changes proportionately with the month’s volume
change. This is a common assumption in classifying costs as being variable.
3. Historical Cost. The full cost accounting system collects historical costs; that is, it
measures what the costs were. For some purposes, such as setting prices, these historical costs are adjusted to reflect the estimated impact of future conditions. But for other
purposes, such as financial reporting, the historical costs are used without change. Differential costs always relate to the future. They are intended to show what the costs will
be if a certain course of action is adopted in the future, rather than show what costs
were in the past.
Contribution Analysis
In calculating break-even volume (Chapter 16), the notion of unit contribution was introduced. This section extends this notion to a technique called contribution analysis.
We do so both because contribution analysis is an important tool in analyzing differential costs and because, in explaining the technique, we can clarify the relationships
among, and differences between, variable costs, fixed costs, direct costs, indirect costs,
full costs, and differential costs.
Contribution analysis focuses on what is called the contribution margin. The contribution margin for a company (or for a product line, division, or other segment of
a company) is the difference between its total revenues and its total variable costs.3
Illustration 26–1 contrasts the conventional income statement for a laundry and drycleaning company with the same data rearranged to measure the contribution margin
for each of its two services. Analysis of the underlying records shows that of the
$42,000 total revenues in June, $32,400 was earned on dry-cleaning work and
2
Although these activity-based cost models are sometimes referred to as activity-based cost systems,
most are not, in fact, cost systems. The models are usually limited in scope (e.g., one plant), reside
only on a local personal computer, and are not capable of recording sales and production transactions on a routine basis. Rather, the models are updated periodically, usually only once or twice a
year, which is adequate for their use in cost estimating.
3
We use the term contribution margin for the difference between total revenues and total variable
costs, and we use unit contribution or marginal income for the difference per unit. The more
complete term, unit contribution margin, is also used in practice instead of unit contribution.
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ILLUSTRATION
26–1
A. Income Statement—Conventional Basis
Month of June
Contrast between
Conventional and
Contribution
Margin Income
Statements
Revenues
Expenses:
Salaries and wages
Supplies
Heat, light, and power
Advertising
Rent
Depreciation on equipment
$42,000
$19,800
10,800
2,400
1,200
4,200
4,800
Other (telephone, insurance, etc.)
Total expense
Income (loss)
1,800
_______
45,000
________
$________
(3,000)
B. Income Statement—Contribution Margin Basis
Month of June
Dry Cleaning
Revenues
Variable expenses:
Wages
Supplies
Power
Total variable expenses
$32,400
$7,800
9,000
1,500
______
$9,600
$ 4,200
1,800
300
_______
18,300
________
14,100
6,300
______
3,300
3,600
________
10,500
1,200
______
2,100
再
Contribution margin
Direct fixed expenses:
Depreciation on equipment
Contribution to indirect expenses
Laundry
Total contribution
Indirect fixed expenses:
Salaries
Heat and light
Advertising
Rent
Other
Total indirect fixed expenses
Income (loss)
$12,600
$ 7,800
600
1,200
4,200
1,800
________
15,600
_______
$(3,000)
_______
$9,600 on laundry. The expense items4 on the income statement were analyzed to
determine which amounts were variable and, of these, how much was attributable to
dry cleaning and how much to laundry. Of the total amount of $19,800 for salaries
and wages, $7,800 of wages was a variable expense of dry cleaning and $4,200 was
a variable expense of laundry. The remaining $7,800 of salaries was a fixed expense
applicable to the business as a whole. The other variable expenses were found to be
4
Since this is an income statement, amounts deducted from revenues are called expenses. As pointed
out in Chapter 3, expenses are one type of cost (i.e., the costs that are applicable to the current accounting period). Thus, although the description in this chapter uses the broader term costs, it applies equally well to that type of cost labeled expense.
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supplies and power. The total amount of variable expense was $18,300 for dry cleaning and $6,300 for laundry.
The contribution margin, which is the difference between revenues and total variable expenses, was therefore $14,100 for dry cleaning and $3,300 for laundry.
In addition to variable expenses, dry cleaning had $3,600 of direct fixed expense; this
was the depreciation on the dry-cleaning equipment. Laundry had $1,200 of direct fixed
expenses. Subtracting these direct but fixed expenses from the contribution margin
shows how much each service contributed to the indirect fixed costs of the business.
These amounts were $10,500 for dry cleaning and $2,100 for laundry, a total of $12,600.
Since the total of the indirect fixed costs was $15,600, this contribution was not large
enough to produce income for the month. The difference was the loss of $3,000.
Types of Cost
We shall use the numbers in Illustration 26–1 to review the types of costs previously
discussed:
• Variable costs (here expenses) were $18,300 for dry cleaning and $6,300 for laundry. They were variable because they varied proportionately with the volume of dry
cleaning and laundry done.
• Fixed costs were the $4,800 of depreciation on equipment plus the $15,600 of indirect fixed expenses, a total of $20,400.
• Direct costs of the dry-cleaning service (cost object) included its variable costs
($18,300) and also its direct fixed costs (the $3,600 depreciation on dry-cleaning
equipment). The total direct cost of the dry-cleaning service was therefore $21,900.
It was direct because it included all costs that were traced directly to the drycleaning cost object. It was higher than the dry-cleaning variable costs because it
also included the direct fixed costs.
• Indirect costs were those amounts (totaling $15,600) that were not traced directly
either to the dry-cleaning cost object or to the laundry cost object.
• Full costs are not shown in the analysis. In order to obtain the full costs of each of
the two cost objects, it would be necessary to allocate the $15,600 of indirect costs
to dry cleaning and to laundry on some equitable basis.
This list does not include differential costs, because they cannot be identified in general. Rather, they must always be related to a specific alternative choice problem.
Example
Suppose that the management is considering certain actions intended to increase the volume
of dry-cleaning work and it asks how increased volume will affect income. In this situation, the
differential costs are the variable costs (and the revenue is, of course, differential revenue).
Each additional dollar of dry-cleaning business is expected to add 44 cents to profit, the percentage of contribution margin to sales revenues ($14,100 $32,400 44 percent).
The message conveyed by the contribution analysis statement differs from the message conveyed by the conventional income statement. The income statement indicates
that the business operated at a loss. If the indirect expenses were allocated to the two
services in proportion, say, to their variable expenses, each of the two services also
would show a loss:
Contribution to indirect expenses
Allocated indirect expenses
Income (loss)
Total
Dry Cleaning
Laundry
$12,600
15,600
_______
$_________
(3,000)
_______
$10,500
11,605
_______
$
(1,105)
_________
_______
$ 2,100
3,995
_______
$(1,895)
______
____
______
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From these numbers, someone might conclude that one or the other of these services
should be discontinued in order to reduce losses. By contrast, the contribution analysis
shows that each of the services made a contribution to indirect fixed costs and that the
total loss of the business would therefore not be reduced by discontinuing either of
them. Later in this chapter, we discuss this type of analysis.
Alternative Choice Problems
In an alternative choice problem, two or more alternative courses of action are specified, and the manager chooses the one that he or she believes to be the best.5 In many
alternative choice problems, the choice is made on a strictly judgmental basis. That is,
there is no systematic attempt to define, measure, and assess the advantages and disadvantages of each alternative. Persons who make judgmental decisions may do so simply because they are not aware of any other way of making up their minds, or they may
do so because the problem is one in which a systematic attempt to assess alternatives
is too difficult, too expensive, or simply not possible. No mathematical formula will
help solve a problem in which the attitudes of the individuals involved or organizational politics are dominant factors. Nor is there any point in trying to make calculations if the available information is so sketchy or inaccurate that the results would be
completely unreliable.
In many other situations, however, it is useful to reduce at least some of the potential consequences of each alternative to a quantitative basis and to weigh these consequences in a systematic manner. In this and the next chapter, we discuss techniques for
making such an analysis.
In an alternative choice problem, the manager seeks the alternative most likely to
accomplish the objectives of the organization. When investors furnish equity capital to
a profit-oriented business, they do so in the expectation of earning a return—a profit—
on their investments. This return is received in the form of some combination of dividend revenue and capital gains. This idea leads to the statement that the objective of a
company is to maximize the value of the shareholders’ investment (or, as it is sometimes stated, to maximize shareholder wealth).
There are practical problems with using this concept in decision making, however.
For one, in the case of publicly traded shares, the market value of the shareholders’ investment may change literally by the minute. Second, in most instances it is not possible to estimate how much a specific decision will affect the price of the company’s
shares. Finally, the decision maker seldom knows which one out of many alternative
courses of action will produce a maximum outcome, and some actions that could increase value are ethically unacceptable. As a result of these problems, in practice an internal (not market) performance measure is used—return on investment (ROI)—and
the business objective is stated as earning a satisfactory (as opposed to maximum)
return on investment.
Satisfactory ROI is important, but it is by no means the only objective of a business.
In many practical problems, personal satisfaction, friendship, community responsibilities, or other considerations may be much more important than ROI. The company
also may have other measurable objectives, such as maintenance of its market position,
stabilization of employment, or increasing reported earnings per share. When these
5
In a broad sense, all management decisions involve a choice among alternatives. The problems discussed here are those in which the alternatives are clearly specified.
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considerations are dominant, the solution to the problem cannot be reached by the
techniques discussed here. The most these techniques can do is show the effect on ROI
of seeking some other objective.
Thus, the decision maker seeks a course of action that will produce a satisfactory
ROI. Of two alternative solutions to a problem, the manager will choose the one likely
to yield the greater ROI, provided this is consistent with other objectives. If the amount
of investment is unaffected by the decision, then the preferred alternative is the one resulting in the higher profit. If neither investment nor revenues are affected by the
choices, then the preferred alternative is the one with the lower cost.
The return-on-investment criterion is not ordinarily used in nonprofit organizations.
In these organizations, the objective is to provide services of acceptable quality at the
lowest possible cost. Nevertheless, the techniques for analyzing alternative choice
problems in nonprofit organizations are essentially the same as those applicable to
profit-oriented organizations. The preferred alternative is the one expected to provide
the desired amount of services at the lower cost.
Steps in the
Analysis
The analysis of most alternative choice problems involves the following steps:
1. Define the problem.
2. Select possible alternative solutions.
3. For each selected alternative, measure and evaluate those consequences that can be
expressed in quantitative terms.
4. Identify those consequences that cannot be expressed in quantitative terms and evaluate them against each other and against the measured consequences.
5. Reach a decision.
We shall focus primarily on information that can be expressed in quantitative terms.
Thus, we are interested primarily in step 3 of the above list. We will briefly mention the
other steps.
Steps 1 and 2: Define the Problem and Alternative Solutions
Unless the problem is clearly and precisely defined, quantitative amounts that are relevant to its solution cannot be determined. In many situations, the definition of the problem may be the most difficult part of the whole process. Moreover, even after the
problem has been identified, the possible alternative solutions to it may not be obvious.
Example
A manager is considering a proposal to buy a certain machine to produce an item that is
now being produced manually. At first glance, there appear to be two alternatives:
(1) Continue to make the item by manual methods or (2) buy the new machine. Actually,
however, several additional alternatives should be considered: (3) buy a machine other
than the one proposed, (4) improve the present manual method, or even (5) eliminate the
production operation altogether and buy the item from an outside source. Some thought
should be given to these other possibilities before attention is focused too closely on the
original proposal.
The more alternatives that are considered, the more complex the analysis becomes.
For this reason, having identified all the possible alternatives, the analyst should eliminate on a judgmental basis those that are clearly unattractive, leaving only a few for
detailed analysis.
In most problems, one alternative is to continue what is now being done—that is, to
reject a proposed change. This status quo alternative, called the base case, is used as a
benchmark against which other alternatives are measured.
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Step 3: Measure the Quantitative Factors
Usually, many advantages and disadvantages are associated with each alternative. The
decision maker’s task is to evaluate each relevant factor and to decide, on balance,
which alternative has the largest net advantage. If the factors, or variables, are expressed solely in words, such an evaluation is an exceedingly difficult task.
Example
Consider the statement: “A proposed production process will save labor, but it will result in
increased power consumption and require additional insurance protection.” Such a statement provides no way of weighing the relative importance of the saving in labor against the
increased power and insurance costs. If, by contrast, the statement is “The proposed
process will save $1,000 in labor, but power costs will increase by $200 and insurance costs
will increase by $100,” the net effect of these three factors can easily be determined; that is,
$1,000 ($200 $100) indicates a net advantage of $700 for the proposed process.
The above example demonstrates the reason for expressing as many factors as possible in quantitative terms: Once this is done, one can find the net effect of these factors simply by addition and subtraction.
Step 4: Evaluate the Unmeasured Factors
Most problems involve important factors that are not measurable. Final decisions must
take into account both measurable and unmeasurable differences between the alternatives. The process of weighing the relative importance of these unmeasured factors,
both as compared with one another and as compared with the net advantage or disadvantage of the measured factors, is a judgmental process.
It is easy to overlook the importance of these unmeasured factors. The numerical calculations for the measured factors often require hard work and result in a number that appears to be definite and precise. Yet all the factors that influence the final number may be
collectively less important than a simple factor that cannot be measured. For example,
many persons could meet their transportation needs less expensively by using taxis and
buses rather than by operating an automobile; but they nevertheless own a car for reasons of prestige, convenience, or other factors that cannot be measured quantitatively.
To the extent that calculations can be made, it is possible to express as a single number the net effect of many factors that bear on the decision. The calculations therefore
reduce the number of factors that must be considered separately in the final judgment
process that leads to the decision. That is, they narrow the area within which judgment
must be exercised. Rarely, if ever, do they eliminate the necessity for this crucial
judgment process.
Step 5: Reach a Decision
After the first attempt to identify, evaluate, and weigh the factors, the decision maker
has two choices: (1) Seek additional information or (2) make a decision and act on it.
Many decisions could be improved by obtaining additional information, and that is usually possible. However, obtaining the additional information always involves effort
(which means cost); more important, it involves delay. There comes a point, therefore,
when the manager concludes that it is better to act than to defer a decision until more
data have been collected.
Differential Costs
Earlier in this chapter, we introduced the type of cost construction called differential
costs. Since differential costs are normally used in analyzing alternative choice problems, we now discuss them in more depth.
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If some alternative to the base case, or status quo, is proposed, differential costs are
those that will be different under the proposed alternative than they are in the base
case. Items of cost that will be unaffected by the proposal are not differential and can
be disregarded. The terms out-of-pocket costs and avoidable costs are used generally
to mean the same thing as differential cost. No general category of costs can be labeled differential; differential costs always relate to the specific alternatives being
analyzed.
Example
A company is considering buying Part No. 101 from an outside supplier instead of manufacturing the part. The base case (case 1) is to continue manufacturing Part No. 101, and
the alternative (or case 2) is to purchase it from the outside supplier. All revenue items, selling and administrative expenses, and production costs other than those directly associated
with the manufacture of Part No. 101 will probably be unaffected by the decision. If so,
there is no need to consider them. Items of differential cost could be as follows:
If Part No. 101
Is Manufactured
(base case)
If Part No. 101
Is Purchased
(case 2)
$ 570
0
600
70
150
______
$1,390
$
0
1,700
0
0
0
______
$1,700
Direct material
Purchased parts
Direct labor
Power
Other costs
Total
Net differential cost
Difference
$ 570
$1,700
600
70
150
______
$1,390
|
_______
$ 1,700
1,390
_______
$ 310
Since costs would be increased by $310 if Part No. 101 were purchased, the indication
is that the proposal to purchase Part No. 101 should be rejected.
Mechanics of
the Calculation
There is no prescribed format for comparing the differential costs of several alternatives. The arrangement should be that which is most convenient and which most clearly
sets forth the facts to the decision maker.
Example
For the problem described in the preceding example, the same result can be obtained with
somewhat less effort by finding the net differences between the alternatives:
Purchase price of Part No. 101
Costs saved by not manufacturing Part No. 101:
Direct material
Direct labor
Power
Other costs
Total costs saved
Net disadvantage in purchasing
$ 1,700
$570
600
70
150
_____
1,390
_______
$ 310
Unaffected Costs
Cost items unaffected by the decision are not differential and may be disregarded. Nevertheless, a listing of some or all of these unaffected costs may be useful, especially if
more than two alternatives are being compared. If this is done, the unaffected costs
must be treated in exactly the same way under each of the alternatives. The net
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ILLUSTRATION
26–2
Profit on Product A
Calculation of
Differential Profit
Revenue
Costs:
Direct material
Purchased parts
Direct labor
Power
Other costs
Occupancy costs
General and administrative
Total costs
Profit
Differential profit of base case
Base Case
___________________
$10,000
Purchase of
Part
No. 101
___________________
$10,000
$1,570
0
3,000
200
1,450
800
2,000
_______
$1,000
1,700
2,400
130
1,300
800
__2,000
_____
9,020
_______
980
_______
670
$ 310
9,330
_______
670
|
difference between the costs of any two alternatives, which is the result sought, is not
changed by adding equal amounts to the cost of each alternative.
Example
Part No. 101 is a component of Product A. It may be convenient to list each of the items of
cost and the revenue of Product A for each of the alternatives, as in Illustration 26–2. The
difference in profit is the same $310 arrived at in the earlier examples, because the proposal
to purchase Part No. 101 affected neither Product A’s revenue nor Product A’s costs beyond
the effects already listed.
The calculation in Illustration 26–2 requires somewhat more effort than those in the
preceding examples, but it may be easier to understand. Also, the practice of listing
each item of cost and revenue may help to ensure that no items of differential cost are
overlooked.
Danger of Using Full Cost
The full costs that are measured in a full cost accounting system may be misleading in
alternative choice problems. In particular, when estimating differential costs, items of
cost that are allocated to products should be viewed with skepticism. For example, a
company may allocate production overhead costs to products as 150 percent of direct
labor costs. But this does not mean that if direct labor costs are decreased by $600,
there will be a corresponding decrease of $900 in overhead costs. Overhead costs may
not decrease at all, they may decrease but by an amount less than $900, or they may
even increase due to an increased procurement and inspection workload resulting from
the purchase of Part No. 101. In order to estimate what will actually happen to overhead costs, one must go behind the overhead rate and analyze what will happen to the
various elements of overhead cost.
Example
The full costs of Product A shown in Illustration 26–2 included $800 for occupancy costs and
$2,000 for general and administrative costs. Occupancy cost is the cost of the building in
which Product A is manufactured, and the $800 represents the share of total occupancy cost
allocated to Product A. If Part No. 101 (one part in Product A) is purchased, the floor space
in which Part No. 101 is now manufactured no longer would be required. It does not necessarily follow, however, that occupancy costs would thereby be reduced. The costs of rent,
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heat, light, and other items of occupancy cost might not be changed at all by the decision
to purchase Part No. 101. Unless the actual amount of occupancy cost were changed—that
is, unless some occupancy costs would be avoided—this item of cost is not differential.
Similarly, general and administrative costs of the whole company probably would
be unaffected by a decision to purchase Part No. 101. Unless the actual amount of these
costs would be affected, they are not differential.
Fringe Benefits
Labor costs are an important item of cost in many decisions. The real cost of labor is
significantly higher than the actual amount of wages earned. It includes such items as
the employer’s share of Social Security taxes; insurance, medical, and pension plans;
vacation and holiday pay; and other fringe benefits. It is typical in the United States for
these benefits to amount to 30 or 40 percent of wages earned. In estimating differential
labor costs, fringe benefits usually should be taken into account.
Opportunity Costs
Opportunity cost is a measure of the value that is lost or sacrificed when the choice of
one course of action requires giving up an alternative course of action. Opportunity
costs are not costs in the usual sense of the word; that is, they are not associated with
cash outlays. Rather, an opportunity cost is income (profit) forgone, or given up, which
has the same downward impact on net income as a cost incurred.
Example
If the floor space required to make Part No. 101 can be used for some other profitproducing purpose, then the sacrifice involved in using this space for Part No. 101 is an
opportunity cost of making that part. This cost is measured by the income that would be
sacrificed if the floor space is instead used for Part No. 101; this income is not the same as
the allocated occupancy cost. If the floor space used for Part No. 101 could be used to manufacture another item that could be sold for a profit of $400, the $400 then becomes a cost
of continuing to manufacture Part No. 101.
Example
An attorney has more work available to her than she can accept; that is, she is working “at
capacity.” She bills clients $125 an hour for her services. She also does four hours a week
volunteer legal work for a local nonprofit organization. The opportunity cost to her of this
volunteer work is $500 a week (4 hours * $125), the amount of the billings (income) she
forgoes in order to do the volunteer work.
Opportunity costs are not measured in accounting records, and they are not relevant in
many alternative choice problems. They are significant, however, in situations where resources are constrained (i.e., limited), as in the above case of the attorney. In such situations, a decision to undertake a certain activity precludes performing some other activity.
In general, if accepting an alternative requires devoting to that alternative any facilities
or other resources that otherwise could be used for some other income-producing purpose, then there is an opportunity cost. This cost is measured by the income that would
have been earned had the resources been devoted to the other purpose.
By their very nature, opportunity costs are “iffy.” In most situations, it is extremely
difficult to estimate what, if any, additional profit could be earned if the resources in
question were devoted to some other use.
Other
Terminology
The term differential costs does not necessarily have the same meaning as the term variable costs. Variable costs are those that vary proportionately with changes in the volume
of output. By contrast, differential costs are always related to specific alternatives that
are being analyzed. If, in a specific problem, the alternatives involve operating at
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different volumes within the relevant range of a cost–volume diagram, then differential
costs may well be the same as variable costs. Depending on the problem, however, the
differential costs may include nonvariable items. A proposal to change the number of
security guards and their duties, for example, involves no elements of variable cost. A
proposal to discontinue a product usually involves some differential fixed costs and
step-function costs as well as the differential variable costs.
Marginal cost is a term used in economics for what accountants call variable costs.
The marginal cost of a product is the cost of producing one additional unit of that product. Thus, marginal costs may be the same as differential costs in those problems in
which an alternative under consideration involves changing the volume of output.
Incremental cost and relevant cost are terms that usually mean the same thing as differential cost, as are the above-mentioned terms out-of-pocket cost and avoidable cost.
Estimates of
Future Costs
Because the alternatives under consideration always relate to the future, differential
costs are always estimates of future costs. Nevertheless, in many instances, the best information about future costs is derived from an analysis of historical costs. One can
easily lose sight of the fact that historical costs, as such, are irrelevant. Historical costs
may be a useful guide as to what costs are likely to be in the future, but using them as
a guide is basically different from using them as if they were factual statements of what
the future costs are going to be.
Except where future costs are determined by long-term contractual arrangements,
differential costs necessarily are estimates. Usually, they cannot be close estimates. An
estimated labor saving of $50,000 a year for five years, for example, implies assumptions as to future wage rates, future fringe benefits, future labor productivity, future activity levels (volumes), and other factors that cannot be known with certainty. Consequently, carrying computations of cost estimates to several decimal places ordinarily
serves no purpose. In fact, there is a danger of being misled by the illusion of precision
that such calculations give.
Sunk Costs
A sunk cost is a cost that has already been incurred and therefore cannot be changed by
any decision currently being considered. All historical costs (for example, the book
value of depreciable assets) are sunk costs. Since it exists because of actions taken in the
past, a sunk cost is not a differential cost. No decision made today can change what has
already happened. Decisions made now can affect only what will happen in the future.
The book value of plant and equipment and the related depreciation expense can
cause difficulty in the analysis of alternative choice problems. It is sometimes argued
that when a proposed alternative involves disposal of an existing machine, the depreciation on that machine will no longer be a cost and this saving in depreciation expense
should therefore be taken into account as an advantage of the proposed alternative.
This is not true. The argument overlooks the fact that the book value of the machine
will sooner or later be recorded as an expense, regardless of whether the proposed alternative is adopted. If the alternative is not adopted, depreciation on the machine will
continue. If the alternative is adopted, the remaining book value will be written off
when the machine is disposed of. In either case, the total amount of cost is the same, so
the book value is not a differential cost.
Example
Assume that Part No. 101 from the previous examples is now manufactured on a certain
machine and that depreciation of $1,000 on this machine is one of the items of “other
costs” in Illustration 26–2. The machine was purchased six years ago for $10,000; since depreciation has been recorded at $1,000 a year, a total of $6,000 has been recorded to date.
The machine therefore has a net book value of $4,000. The machine has zero scrap value.
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It is sometimes argued that the calculation in Illustration 26–2 neglects the $1,000 annual saving in depreciation costs that will occur if the machine is disposed of and that purchasing Part No. 101 is therefore the preferable alternative. (If the cost of purchasing Part
No. 101 is reduced by $1,000, then the profit of this alternative becomes $1,670, which is
$690 greater than the $980 profit for the base case.) This is a fallacious argument. If the machine is scrapped, its book value must be written off, and this amount exactly equals the
total depreciation charge over the machine’s remaining life. Thus, there is no differential
cost associated with the book value of the existing machine.
The irrelevance of sunk costs is demonstrated in Illustration 26–3 by comparison of two
income statements for the complete time periods of the remaining life of the machine. One
shows the results of operations if Part No. 101 is purchased and the machine is scrapped.
The other shows the results if Part No. 101 continues to be made on the machine. Illustration 26–3 shows that over the four-year period, the differential profit favoring the base case
is $1,240. This is $310 per year, the same amount shown in Illustration 26–2.
The cost of a depreciable asset is supposed to be written off over its useful life. If a
machine is scrapped, its useful life obviously has come to an end. If its total cost has
not been written off by that time, one knows by hindsight that an estimating error has
been made: If the machine’s useful life and residual value had been correctly estimated
when it was acquired, then the net book value of the machine would be zero when it is
scrapped. Because this error was made in the past, no current decision can change it.
If the machine had a disposal value, this fact would be relevant because the machine’s
sale would then bring in additional cash. If the income tax effect of writing off the loss
on disposal were different from the tax effect of writing off depreciation over the fouryear period, the effect of taxes would be relevant. (The method of allowing for this tax
effect will be discussed in Chapter 27.) The book value of the machine itself, however,
is not relevant.
Importance of
the Time Span
The question of what costs are differential depends to a great extent on the time span
of the problem. If the proposal is to make literally only one additional unit of an item,
only the direct material costs may be differential. The work could conceivably be done
ILLUSTRATION
26–3
Profit on Product A
(total for four years)
Irrelevance of Sunk
Costs
Revenue
Costs, other than machine
Depreciation
Loss on disposal of machine
Total costs
Profit
Differential profit of base
case, four years
Annual differential profit
($1,240 4)
* ($9,020 $1,000) * 4 years.
†
($9,330 $1,000) * 4 years.
‡
Same amount as in Illustration 26–2.
Base Case
_____________________
$40,000
$32,080*
4,000
0
_______
36,080
_______
3,920
2,680
_______
$ 1,240
$
310‡
Purchase of
Part
No. 101
___________________
$40,000
$33,320†
0
4,000
_______
37,320
_______
$ 2,680
|
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without any differential labor costs if workers were paid on a daily basis and had some
idle time. At the other extreme, if the proposal involves a commitment to produce an item
over the foreseeable future, almost all items of production costs would be differential.
In general, the longer the time span of the proposal, the more items of cost that are
differential. In the very long run, all costs are differential. Thus, in very long-run problems, differential costs include the same elements as full costs because one must consider even the replacement of buildings and equipment, which are sunk costs in the
short run. By contrast, in many short-run problems, relatively few cost items are subject to change by a management decision.
Example:
Operating an
Automobile
To illustrate that the cost elements that are differential in an alternative choice problem
vary with the nature of the problem, consider the relevant costs for various decisions
that may be made about owning and operating an automobile. In 2009, the American
Automobile Association estimated the five-year cost of owning a 2009 Ford Taurus SE
driven 75,000 miles in stop-and-go conditions as follows:
Average
per Mile (¢)
Variable costs:
Gasoline
Maintenance and repairs
Total variable costs
15.3
3.1
____
18.4¢
Amount
per Year ($)
Fixed costs:
Insurance
License, registration, taxes
Depreciation
Finance charges6
Total fixed costs
1,259
70
3,067
770
______
5,166
Assuming that these costs are valid estimates of future costs (which actually is not
the case because of inflation), what are the differential costs in each of the circumstances cited below?
1. You own a typical domestic sedan and have it registered. You are thinking about
making a trip of 1,000 miles. What are the differential costs?
Answer: An estimate of the differential cost is 18.4 cents a mile times the estimated mileage of the trip. A trip of 1,000 miles therefore has a differential cost of
$184. Whether this estimate is accurate depends, to a large extent, on whether repairs are needed on this trip. If they are, the estimate could easily be low. If they are
not, the estimate would be high. But the average cost of many such trips should be
close to $184. The fixed costs are not relevant since they will continue whether or
not the trip is made.
2. You own a car but have not registered it. You are considering whether to register it
for next year or to use alternative forms of transportation that you estimate will cost
$4,000. If you register the car, you expect to drive it 10,000 miles during the year.
Should you register it?
6
Assumes a 60-month loan at 8.75 percent interest with a 20 percent down payment.
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Answer: The differential costs are the insurance ($1,259) and license,
registration, and taxes of $70 plus 18.4 cents a mile times the 10,000 miles you
expect to travel by car, a total of $3,169. If alternative transportation will cost
$4,000, you are well advised to register the car.
3. You do not own a car but are considering the purchase of the car described above. If
your estimate is that you will drive 10,000 miles per year for five years and that alternative transportation will cost $4,000 per year, should you do so?
Answer: The differential costs are $5,166 a year plus 18.4 cents a mile times the
10,000 miles you expect to travel per year: $5,166 $1,840 $7,006. If alternative transportation will cost $4,000 a year, you are well advised to use alternative
transportation (disregarding noneconomic considerations).7
Each of the above answers is, of course, an oversimplification because it omits nonquantitative factors and relies on averages. In an actual problem, decision makers need
data that more closely approximate the costs of owning the automobile of their choice
in their locale with their driving habits.
Types of Alternative Choice Problems
As noted earlier, a dominant objective of a business is to earn a satisfactory return on
investment (ROI). Three basic elements—costs, revenue, and investment—are involved in a company’s ROI:
Revenues Costs
ROI Investment
Although the general approach to all alternative choice problems is similar, it is useful
to discuss three subcategories separately: problems that involve only the cost element
(discussed below), problems including both revenue and cost elements (also discussed
below), and problems that involve investment as well as revenues and costs (discussed
in Chapter 27).
Problems
Involving Costs
Alternative choice problems involving only costs have several general characteristics:
The base case is the status quo, and an alternative to the base case is proposed. If the
alternative is estimated to have lower differential costs than the base case, it is accepted
(assuming nonquantitative factors do not offset this cost advantage). If there are several alternatives, the one with the lowest differential cost is accepted. Problems of this
type are often called trade-off problems because one type of cost is traded off for
another. Some examples are mentioned here.
Methods Change
The alternative being proposed is the adoption of some new method of performing an
activity. If the differential costs of the proposed method are significantly lower than
those of the present method, the method should be adopted (unless offsetting nonquantitative considerations are present).
7
Since this question has a multiyear time horizon, the present value analytical approach described in
Chapter 27 should be used in answering it. Although the conclusion stated here is correct, the
analysis would differ if such present value techniques were used.
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Operations Planning
In a manufacturing plant that has a variety of machines, or in a chemical processing
plant, several routes for scheduling products through the plant are possible. The route
with the lowest differential costs is preferred. Similar planning problems exist in nonmanufacturing settings: for example, deciding which of several warehouses should
ship appliances to each of the retailers selling these appliances, or deciding which
group of architects should be assigned to work on a new project.
Other production decisions can be analyzed in terms of differential costs. One example is deciding whether to use one shift plus overtime or to add a second shift. Another is deciding, when demand is low, whether to operate temporarily at a low volume
or to shut down until operations at normal volume are again economical.
Make or Buy
Among the most common types of alternative choice problems are outsourcing choices
(also called make-or-buy choices). At any given time, an organization performs certain
activities with its own resources, and it pays outside firms to perform certain other activities. It constantly seeks to improve the balance between these two types of activities
by asking: Should we contract with some outside party to perform some function that
we are now performing ourselves, or should we ourselves perform some activity that we
now pay an outside party to do? An outsourcing analysis can be made for practically any
activity that the organization performs or might perform. At one extreme is the analysis
of producing individual parts, illustrated above. At the other extreme, a company may
consider whether to contract with an outside manufacturer to produce the whole product.
For example, some companies that sell computers buy the completed product from other
manufacturers and simply attach their own brand name; other companies, even the
largest ones, manufacture some of their component parts, buy others, and assemble
the finished computer.
As the example given in Illustration 26–2 shows, the cost of the outside service (the
“buy” alternative) usually is easy to estimate. The more difficult problem is to find the
differential costs of the “make” alternative because of the short-run nondifferential nature of many of the cost items.
Order Quantity
When replenishing inventory of an item involves setup costs that are incurred only once
for each batch produced (or ordering costs for each batch ordered from a supplier), the
question arises of how many units should be made (ordered) in one batch. If the demand
is predictable and if sales are reasonably steady throughout the year, the optimum quantity to produce (order) at one time—the economic order quantity (EOQ)—is arrived at
by considering the trade-off between two offsetting costs: setup (ordering) costs, whose
total decreases with increasing batch size, and inventory carrying costs, which increase
as batch size increases. The relevant costs are differential costs.
Problems
Involving Both
Revenues and
Costs
In the second class of alternative choice problems, the proposal being studied affects
both costs and revenues. Insofar as the quantitative factors are concerned, the best alternative is the one with the largest difference between differential revenue and differential cost, that is, the alternative with the most differential income or differential
profit. Some problems of this type are described briefly here.
Supply-Demand-Price Analysis
In general, the lower the selling price of a product, the greater the quantity that will be
sold. This relationship between a product’s selling price and the quantity sold is called
its demand schedule, or demand curve. As the quantity sold increases by one unit,
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the total cost of making the product increases by the variable cost of that one additional
unit. Since fixed costs do not change, total costs increase less than proportionately with
increases in demand. This semivariable relationship between total production costs
and volume is called the product’s supply schedule, or supply curve; it looks like the
C-V diagram in Illustration 16–4 on page 460, which assumes that step-function costs
remain constant within the relevant range.
The supply schedule usually can be estimated with a reasonable degree of accuracy.
If the demand schedule also can be estimated, then the optimum selling price can be
determined. This optimum price is found by estimating the total revenues and total
variable costs for various quantities sold and selecting the selling price that yields the
greatest total contribution.
Example
Assume that fixed costs for a product are $20,000 per month and that variable costs are
$100 per unit. The supply–demand analysis is given in the following table:
Unit
Selling
Price
Unit
Variable
Cost
Unit
Contribution
Estimated
Quantity
Sold
Total
Contribution
Fixed
Costs
Profit
$300
250
200*
150
125
$100
100
100
100
100
$200
150
100
50
25
125
200
310
450
550
$25,000
30,000
31,000
22,500
13,750
$20,000
20,000
20,000
20,000
20,000
$ 5,000
10,000
11,000
2,500
(6,250)
* Preferred alternative.
Clearly, $200 is the best selling price: At that price, the profit of $11,000 is more than
the profit at either a higher or lower price. Since the fixed costs are a constant, they
could be eliminated from the calculation; that is, the same decision can be reached by
choosing the price that yields the greatest total contribution.
Such an analysis is feasible only if the demand schedule can be estimated. In most
situations, there is no reliable way of estimating how many units will be sold at various selling prices; this type of analysis cannot be used in such circumstances. Instead,
the selling price is arrived at by adding a profit margin to the full cost of the product (as
described in Chapter 17), or it is set by competitive market forces. Also, the analysis is
more complicated if some step-function costs will change between the lowest and highest sales volumes being considered.
Contribution Pricing
Although full cost is the normal basis for setting selling prices and a company must recover its full costs or eventually go out of business, differential costs and revenues
are appropriately used in some pricing situations. In normal times, a company may
refuse to take orders at prices that are not high enough to yield a satisfactory profit. But
if times are bad, such orders may be accepted if the differential revenue obtained
from them exceeds the differential costs of filling the order. The company is better off
to receive some revenue above its differential costs than to receive nothing at all. These
off-price orders make some contribution to fixed costs and profit. Such a selling price
is therefore called a contribution price to distinguish it from a normal price.
The practice of selling surplus quantities of a product in a selected marketing area
at a price below full costs, called dumping, is another version of the contribution idea.
However, dumping may violate the Robinson-Patman Amendment in domestic markets and generally is prohibited by trade agreements in foreign markets.
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It is difficult to generalize about the circumstances that determine whether full costs
or differential costs are the appropriate approach to setting prices. Even in normal times,
an opportunity may be accepted to make some contribution to profit by using temporarily idle facilities. Conversely, even when current sales volume is low, the contribution
concept may be rejected on the grounds that the low price may “spoil the market”; that
is, other customers will demand the lower price, or competitors may drop their prices.
(With deregulation of fares in the airline industry, many air carriers painfully learned the
meaning of spoiling the market with contribution-based discount fares.) Also, perhaps
more sales in fact can be obtained at normal profit margins if the marketing organization works harder or is more creative.
Discontinuing a Product
If the selling price of a product is below its full cost, then conventional accounting
reports will indicate that the product is being sold at a loss. This fact may lead some
people to recommend that the product be discontinued, an action that may make the
company worse off rather than better off. If there is excess production capacity, retaining a product that makes some contribution to fixed overhead and profit is better than
not having the product at all. Only if the product’s total contribution is less than the differential fixed and step-function costs that could be saved by dropping the product will
the company be better off doing so. An analysis of differential revenues and differential costs is the proper approach to problems of this type.
Adding Services
A company can add to its income by finding additional ways of using idle capacity in
its assets, if the differential revenue from these uses exceeds the differential costs of
providing them. For this reason, a chain of fast-food restaurants may add breakfast
items to its menu and open four hours earlier each day; a grocery store may decide to
remain open on Sundays; and a hotel may offer special rates on weekends when volume is low. In all these situations, differential costs rather than full costs are relevant.
When analyzing such problems, one must take care to ensure that the differential
revenue is truly differential and does not represent a diversion from normal revenue. For
example, a grocery store will not earn additional income by staying open Sundays if the
revenue earned on Sunday comes from customers who would otherwise have shopped
at that store on some other day of the week. Similarly, care must be taken to ensure
that the so-called fixed costs are truly fixed, as opposed to being step-function costs that
could be reduced if the capacity-filling initiative were not undertaken. For example, it
might be better for an airline to drop a flight, or even a route, than to try to attract a few
more passengers with discounted fares. Thus, in addition to considering ways to use the
idle capacity, the company should consider the savings that would result if it eliminated
the excess capacity.
Sale versus Further Processing
Many companies, particularly those that manufacture a variety of finished products
from basic raw materials, must address the problem of whether to sell a product that has
reached a certain stage in the production process or do additional work on it. Meat packers, for example, can sell an entire carcass of beef, they can continue to process the carcass into various cuts, or they can go even further and make frozen dinners out of some
of the cuts. The decision requires an analysis of the differential revenues and costs.
Let us designate the alternative of selling the product at a certain stage as case 1 and
that of processing it further as case 2. The case 2 product, having received more processing than the case 1 product, presumably can be sold at a higher price. But the case
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2 product also involves processing costs (and possibly marketing costs) not incurred in
case 1. If the differential revenue in case 2 (i.e., the difference between the case 2 revenue and the case 1 revenue) exceeds the additional processing and marketing costs,
then case 2 is preferred. The important point to note is that the analysis may disregard
all costs up to the point in the production process where this decision is made. These
costs are incurred whether or not additional processing takes place and therefore are
not differential.
Other Marketing Tactics
The same analytical approach can be used for a number of other marketing problems.
Examples include deciding which customers are worth soliciting by sales personnel
and how often the salesperson should call on each customer; whether to open additional warehouses or, conversely, whether to consolidate existing warehouses; whether
to improve the reliability of a product in order to reduce the number of maintenance
calls; the minimum size of customer order that will be accepted; and whether to put
more meat in each hamburger and increase its price.
Differential
Investment
Chapter 27 discusses alternative choice decisions that affect the amount of funds committed to investments in noncurrent assets; the analytical approach to these problems is
more complicated than the one described in this chapter for short-run decisions. However, both short-run and long-term decisions may lead to changes in the entity’s
investment in current assets, particularly accounts receivable and inventories. For example, a decision to lower the price of a product below its full cost in order to increase
its unit sales volume may cause related increases in receivables and inventories.
When a decision does impact the level of current assets, the cost of holding these
differential assets should be built into the analysis. For receivables, the holding cost
rate used is typically equal to the sum of the short-term interest rate (since, if the customer had paid cash, the seller could invest the funds short term or reduce short-term
debt) plus the cost of bad debts. Sometimes a billing and collection cost also is included. For inventories, there tends to be great variation in the holding cost rate used,
ranging from a low of around 10 percent (representing primarily financing costs) to a
high of 30–35 percent (the higher rates also including such inventory-related costs as
ordering, handling, storage, pilferage, and insurance). To the extent that a portion of
the differential inventories is financed by differential, interest-free accounts payable,
there is a partial offset of the differential financing costs.
Example
One of Devin Company’s product-line managers has proposed increasing the line’s sales
volume and profit over the next 12 months by simultaneously liberalizing the credit terms
to certain major customers and reducing prices on several items in the line. The estimated
impact of the proposal on current assets is an accounts receivable increase of $450,000
and an inventory increase of $200,000 throughout the 12-month period. The company
estimates its accounts receivable and inventory holding cost rates to be 10 percent and 25
percent, respectively. The analysis of the proposal should therefore include differential costs
of $95,000 [($450,000 * .10) ($200,000 * .25)] for holding these differential current
assets.
Sensitivity
Analysis
All types of alternative choice problems involve making assumptions and estimates
about the future. When analyzing a particular problem, it is important to make note of
each of these assumptions. For example, “I assumed that selling and administrative
costs would not be differential between the two alternatives,” or “I assumed an inflation
rate of 5 percent for the next 10 years.” But it is equally important not to get bogged
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down in worrying about whether the assumption made was the best assumption that
could have been made. In particular, cost estimates often do not need to be refined,
because the initial analysis so overwhelmingly favors one alternative that such refinement could not possibly change the conclusion.
After doing an analysis with the first set of assumptions, it is often useful—particularly when it comes time to sell the results of the analysis to others—to redo the analysis several times using different assumptions. Because its purpose is to determine how
sensitive the initial conclusion was to the initial assumptions, this is called a sensitivity
analysis. If a small change in, say, the estimate of future labor costs changes the initial
conclusion, then we say that the problem is sensitive to labor costs. With spreadsheet
programs for personal computers, these what-if sensitivity analyses often can be performed in a few minutes.
The “Just One”
Fallacy
When one considers the impact on costs of a specific activity, it is possible to take a
perspective that is too narrowly or near-term focused and, as a result, to underestimate
the differential costs. For example, what is the differential cost for a large grocery
store to service one additional customer per hour (excluding the cost of the goods that
the customer purchases)? Looked at narrowly, the answer probably is that the differential cost is essentially zero—no more than the cost of a few additional inches of cash
register tape and power to run the checkout conveyor belt for a few additional seconds.
The store likely has enough capacity to handle one more customer per hour without
adding any personnel or other resources. However, the store would not be able to service 100 additional customers per hour without adding resources: additional checkout
clerks and baggers; other personnel such as another butcher, produce person, or shelf
stocker; and maybe even additional grocery carts or another checkout lane. Thus, there
definitely is a differential cost associated with 100 additional customers per hour. This
suggests a paradox: The differential cost of each additional customer per hour is zero,
yet the differential cost of 100 additional customers is not zero. How can this be? Is not
100 times zero equal to zero?
We call this paradox the “just one” fallacy. If one thinks about the underlying cause
of the paradox, it is the existence of step-function costs in the cost structure. As described in Chapter 16, many resources (such as checkout clerks) are added in discrete
“chunks,” each one resulting in an increment of capacity that can handle a certain additional volume of activity (customers, in this example). An increase in volume of just
one unit does not require the addition of capacity; but a series of increases of one unit
will cumulate to the point where another chunk of capacity—another step-up in
costs—will be required to service the collective additional volume.
How does one deal with this phenomenon in an analysis of differential costs? The
treatment of maintenance costs in the earlier automobile operating cost example illustrates the correct approach. Although no cash outlays may be made for maintenance on
a specific trip, these costs should nevertheless be treated as differential since each additional trip causes these costs to be incurred sooner than if the trip were not made.
The mileage-based step-function costs associated with having routine maintenance
performed are treated as though they were variable costs, as suggested by Illustration 26–4. It would not be reasonable that most trips be charged nothing for maintenance costs incurred, say, every 3,000 miles, nor would it be reasonable to charge only
the one specific trip that caused the odometer to exceed a multiple of 3,000 miles (e.g.,
21,000 miles) with all of these costs. In effect, then, each “chunk” of step-function cost
is averaged over the additional units of volume (here, miles; earlier, grocery store customers) that will be served by this additional increment of resources.
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Analytical
Treatment of StepFunction Costs
Cost
ILLUSTRATION
26–4
Actual cost behavior
Analytical treatment
Volume
As suggested in Chapter 16, some companies have not recognized how costs that
may appear not to be differential when a single decision is focused on are nevertheless
differential when a broader and longer-term perspective is taken. For example, some
companies with excess manufacturing capacity have accepted numerous small incremental orders at reduced prices on the rationale that “the fixed costs stay fixed, so any
contribution from an incremental order falls right to the bottom line as profit.” Yet, having accepted many such orders, these companies find that their overall profits have not
increased because their fixed costs have increased. What is happening is this: The collective additional orders have placed enough additional demands on various support
activities—order processing, production scheduling, setting up equipment, material
handling, and so on—that capacity has needed to be added to these activities, causing
a step-up in their costs (just as in the grocery store example). These step-function costs
were treated as fixed and nondifferential in the analysis of the profitability of each
incremental order, when in fact they should have been treated as though they were variable because collectively all of the additional orders have created differential stepfunction costs.
In sum, one must be cautious when analyzing the differential costs of a narrowly
specified alternative—attract just one more customer; sell just this one product on a
contribution pricing basis; and so on. Costs that are not differential with an increase of
literally just one do become differential when the incremental volume of activity is
larger, as it is when the “just one” rationale gets used repeatedly in a given time period.
This phenomenon is also symmetrical in the sense that it also holds for reductions
in levels of activity. For example, it is commonly argued that if a company drops a
product it is selling at a price below full cost, the company will be worse off because
the product’s contribution to fixed costs will be lost. While true for just one product,
this is not generally true if a number of marginal products are dropped. In fact, some
companies have discovered that they can increase their profits by decreasing the number of smaller orders they accept or by pruning small-volume products from their product lines, because these decisions result in step-function cost reductions that more than
offset the lost contribution margin.
Expected Values
All the numbers used in alternative choice problems are estimates of what will happen
in the future. In the text examples, we used single-value or point estimates. That is,
each estimate was a single number representing someone’s best estimate as to what differential costs or revenues would be. Some companies use estimates in the form of
probability distributions rather than single numbers. For example, instead of stating, “I
think sales of Item X will be $100,000 if the proposed alternative is adopted,” the
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estimator develops a range of possibilities for sales, together with an estimate of
the probability that each will occur. Then the separate possibilities are weighted by the
probabilities. The sum of these weighted amounts is called the expected value of
the probability distribution. Decision makers then will choose the alternative that
promises the highest expected value.
People in business do not find it easy to develop estimates in the form of probability distributions. But if they can do so, they will make better value-producing decisions
for their organization.
Decision Tree
Analysis
Another simplifying characteristic of the problems described in this chapter is that a
single decision had to be made, and estimated revenues would be earned and estimated
costs would be incurred as a consequence of that decision. In many cases, however, a
series of decisions must be made, at various time intervals, with each decision influenced by the information available at the time it is made.
An analytical tool that is useful for analyzing such sequential decision-making
problems is the decision tree. In its simplest form, a decision tree is a diagram that
shows several decisions, or acts, and the possible consequences of each act; these consequences are called events. In a more elaborate form, the probabilities and the revenues or costs of each event’s outcomes are estimated, and these are combined to give
an expected value for the event. Detailed descriptions and illustrations of decision tree
analyses are outside the scope of this textbook.
Some Practical Pointers
In attacking specific problems, the following points may be helpful:
1. Use imagination in choosing the alternatives to be considered, but don’t select so
many that you bog down before you begin. A fine but crucial line divides the alternative that is a stroke of genius and the alternative that is a hare-brained idea.
2. Don’t yield to the natural temptation to give too much weight to the factors that can
be reduced to numbers, even though the numbers have the appearance of being definite and precise.
3. On the other hand, don’t slight the numbers because they are “merely” approximations. A reasonable approximation is much better than nothing at all.
4. Often, it is easier to work with total costs rather than with unit costs. Unit cost is a
fraction:
Total cost
Unit cost Num ber of units
Changes in either the numerator or the denominator result in changes in unit
costs. Taking one of these changes into account and overlooking the other produces an error.
5. There is a tendency to underestimate the cost of doing something new, because all
the consequences may not be foreseen.
6. The number of arguments is irrelevant in an alternative choice problem. A dozen
reasons may be, and often are, advanced against trying out something new; but all
these reasons put together may not be so strong as a single argument in favor of the
proposal.
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7. Be realistic about the margin of error in any calculation involving the future. Precise conclusions cannot be drawn from rough estimates, nor is an answer necessarily valid just because you spent a long time calculating it.
8. Despite uncertainties, you should make a decision if you have as much information as you can obtain at a reasonable cost and within a reasonable time. Postponing action is the same as deciding to perpetuate the existing situation, which may
be the worst possible decision.
9. Show clearly the assumptions you made and the results of a sensitivity analysis, so
that others going over your work can substitute their own judgmental assumptions
if they wish.
10. Do not expect that everyone will agree with your conclusion simply because it is
supported with carefully worked-out numbers. Think about how you can sell your
conclusion to those who must act on it.8
Summary
Differential costs and revenues are those that are different under one set of conditions
than they would be under another set. Differential costs always relate to a specified set of
future conditions. Variable costs are an important category of differential costs in situations where changes in volume are involved. Fixed costs and step-function costs also are
differential in many alternative choice problems.
When an alternative choice problem involves changes in costs but not in revenue or
investment, the best solution is the one with the lowest differential costs, insofar as cost
information bears on the solution. Although historical costs may provide a useful guide
to what costs will be in the future, we are always interested in future costs, never in
historical costs for their own sake. In particular, sunk costs are irrelevant. Also, allocated costs must be analyzed with care to see if they are differential. The longer the
time span involved, the more costs are differential.
When the problem involves both cost and revenue considerations, differential revenues as well as differential costs must be estimated. The best alternative is the one
having the largest differential profit.
Differential costs and revenues rarely provide the answer to any business problem,
but they facilitate comparisons and narrow the area within which judgment must be
applied in order to reach a sound decision.
8
For an advanced discussion of this topic, see John S. Hammong, Ralph L. Keeney, and Howard Raiffa,
Smart Choices: A Practical Guide to Making Better Decisions (Boston: Harvard Business School Press, 1998).
Problems
Problem 26–1.
Dover Rubber Company had been offered a contract to supply 500,000 premium automobile
tires to a large automobile manufacturer at a price of $41.65 per tire. Dover’s full cost of producing the tire is $51.80. The normal sales price for the tire is $73.50 to both distributors and
some selected retailers. Variable costs per tire amount to $34.30; however, in order to meet the
needs of the auto manufacturer, Dover will have to cut its sales to regular customers by 100,000
tires annually. The automaker has clearly indicated that it will enter into the agreement only if
Dover will agree to supply all 500,000 of the tires requested.
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Required:
Should Dover accept the offer?
Problem 26–2.
Vulcan Swimsuit Company is considering dropping its line of women’s beach robes. A
recent product income statement for the robe line follows:
Revenue
Cost of goods sold
$950,760
861,840
_________
Gross margin
Selling and administrative expenses
88,920
136,800
_________
$
(47,880)
_________
_________
Net loss
Factory overhead accounts for 35 percent of the cost of the goods sold and is one-third
fixed. These data are believed to reflect conditions in the immediate future.
Required:
Should the line be dropped?
Problem 26–3.
George Jack operates a small machine shop. He manufactures one standard product available from other similar businesses, and he also manufactures products to customer order.
His accountant prepared the annual income statement shown below:
Sales
Material
Labor
Depreciation
Power
Rent
Heat and light
Other
Custom
Sales
Standard
Sales
Total
$100,000
_________
20,000
40,000
12,600
1,400
12,000
1,200
800
_________
$50,000
________
16,000
18,000
7,200
800
2,000
200
1,800
________
$150,000
_________
36,000
58,000
19,800
2,200
14,000
1,400
2,600
_________
88,000
_________
$__________
12,000
________
46,000
__
______
$
4,000
__
________
______
134,000
___
______
$
___
______
___16,000
______
The depreciation charges are for machines. The power charge is apportioned based on estimated power consumed. The rent is for the building space that has been leased for 10 years
at $14,000 per year. The rent and heat and light are apportioned to the product lines based
on amount of floor space occupied. All other costs are current expenses identified with the
product line causing them.
A valued custom parts customer has asked Mr. Jack if he would manufacture 5,000 special units for him. Mr. Jack is working at capacity and would have to give up some other
business in order to take this business. He can’t renege on customer orders already agreed
to, but he could reduce the output of his standard product by about one-half for one year
while producing the specially requested custom part. The customer is willing to pay $16.00
for each part. The material cost will be about $4.50 per unit and the labor will be $8.00 per
unit. Mr. Jack will have to spend $4,500 for a special device that will be discarded when the
job is done.
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Required:
a. Calculate the following costs related to the 5,000-unit custom order.
(1) The differential cost of the order.
(2) The full cost of the order.
(3) The opportunity cost of taking the order.
(4) The sunk costs related to the order.
b. Should Mr. Jack take the order? Explain your answer.
(CMA adapted)
Problem 26–4.
Taylor Electronics, Inc. (TEI), has been approached by a new customer who wants to place
a one-time order for a component similar to one that TEI makes for another customer. Existing sales will not be affected by acceptance of this order. TEI has a policy of setting its
targeted selling price at 60 percent over full manufacturing cost. The manufacturing costs
and the targeted selling price for the component currently being made are as follows:
Direct materials
Direct labor
Variable manufacturing overhead
(75% of direct labor cost)
Fixed manufacturing overhead
(150% of direct labor cost)
Total manufacturing cost
Markup (60% of full manufacturing cost)
Targeted selling price
$ 2.30
3.60
2.70
5.40
______
$14.00
8.40
______
$22.40
______
______
TEI has excess capacity to produce the quantity of the component desired by the new customer. The direct materials used in the component for the new customer would cost the
manufacturer $.25 less than those in the component currently being made. The variable
selling expenses (packaging and shipping) would be the same as for the component currently being made, or $.90 per unit.
Required:
What is the minimum unit price at which TEI would be willing to accept the special order?
Problem 26–5.
Tran Company makes two radio models, Y and Z. They are both manufactured totally in
two departments: A, which has a total capacity of 240 labor-hours per week; and B, which
has a capacity of 480 labor-hours per week. The labor requirements (hours per unit) for
each model are
Department A
Department B
Model Y
Model Z
1.0
0.5
0.8
2.0
The unit contribution of ModelY is $4.00 and for Model Z it is $5.00. The total production of
Y can be sold, but only a weekly maximum of 200 units of Model Z can be sold.
Required:
How many of each radio should be manufactured? (Construct the basic equations and solve
graphically.)
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Cases
Case 26–1
Import Distributors, Inc.*
Import Distributors, Inc. (IDI), imported appliances
and distributed them to retail appliance stores in the
Rocky Mountain states. IDI carried three broad lines
of merchandise: audio equipment (tuners, tape decks,
CD players, etc.), television equipment (including
videotape recorders), and kitchen appliances (refrigerators, freezers, and stoves that were more compact than
U.S. models). Each line accounted for about one-third
of total IDI sales revenues. Although each line was re-
ferred to by IDI managers as a “department,” until
1994 the company did not prepare departmental income statements.
In late 1993, departmental accounts were set up in
anticipation of preparing quarterly income statements
by department starting in 1994. In early April of 1994,
the first such statements were distributed to the management group. Although in the first quarter of 1994
IDI had earned net income amounting to 4.3 percent of
sales, the television department had shown a gross margin that was much too small to cover the department’s
operating expenses (see Exhibit 1).
* Copyright © James S. Reece.
EXHIBIT 1
TELEVISION DEPARTMENT
Income Statement
For the First 3 Months of 1994
Percent
Net sales revenues
Cost of sales
$1,612,403
1,422,473
__________
100.0
88.2
_____
Gross margin
189,930
__________
__________
11.8
_____
_____
Operating expenses:
Personnel expenses (Note 1)
Department manager’s office
Rent (Note 2)
Inventory, taxes, and insurance
Utilities (Note 3)
Delivery costs (Note 4)
Sales commissions (Note 5)
Administrative costs (Note 6)
Inventory financing charge (Note 7)
10,140
12,393
50,107
37,274
3,006
32,248
80,621
40,310
23,708
__________
Total operating expenses
Income taxes (credit)
Net income (loss)
289,807
__________
(34,957)
__________
$__________
(64,920)
__________
_____
18.0
_____
(2.2)
_____
(4.0)
_____
_____
Notes:
1. These were warehouse personnel. Although merchandise in the warehouse was arranged by department, these personnel performed tasks for all three departments on any given day.
2. Allocated to departments on the basis of square footage utilized. IDI had a five-year noncancelable lease for the facilities.
3. Allocated to departments on the basis of square footage utilized.
4. Allocated on the basis of sales dollars. A delivery from IDI to a retail store typically included merchandise from all three
departments.
5. Salespersons were paid on a straight commission basis; each one sold all three lines.
6. Allocated on the basis of sales dollars.
7. An accounting entry that was not limited solely to the cost of financing inventory; assessed on average inventory in order to
motivate department managers not to carry excessive stocks. This charge tended to be about three times the company’s actual
out-of-pocket interest costs.
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The television department’s poor showing
prompted the company’s accountant to suggest that
perhaps the department should be discontinued. “This
is exactly why I proposed that we prepare departmental statements—to see if each department is carrying
its fair share of the load,” the accountant explained.
This suggestion led to much discussion among the
management group, particularly concerning two issues: First, was the first quarter of the year representative enough of longer-term results to consider discontinuing the television department? And second, would
Short-Run Alternative Choice Decisions
847
833
discontinuing television equipment cause a drop in
sales in the other two departments? One manager,
however, stated that “even if the quarter was typical
and other sales wouldn’t be hurt, I’m still not convinced we’d be better off dropping our television line.”
Question
What action should be taken with regard to the television department?
Case 26–2
Forner Carpet Company*
Forner Carpet Company produced high-grade carpeting materials for use in automobiles and recreational
vans. Forner’s products were sold to finishers, who cut
and bound the material so that it would fit perfectly in
the passenger compartment or cargo area (e.g., automobile trunk) of a specific model vehicle. These finishers also made carpet floor mats. Some of these
finishers were captive operations of major automobile
assembly divisions, particularly those that assembled
the “top of the line” cars that included high-grade carpeting; other finishers concentrated on the replacement and van customizing markets.
Late in 1993, the marketing manager and the chief
accountant of Forner met to decide on the list price for
carpet number L-42. It was industry practice to announce prices just prior to the January–June and
July–December “seasons.” Over the years, companies
in the industry had adhered to their announced prices
throughout a six-month season unless significant unexpected changes in costs occurred.
Forner was the largest company in its segment of
the automobile carpet industry; its 1993 sales had been
over $40 million. Forner’s salespersons were on a
salary basis, and each one sold the entire product line.
Most of Forner’s competitors were smaller than
Forner; accordingly, they usually awaited Forner’s
price announcement before setting their own selling
prices.
Carpet L-42 had an especially dense nap; as a result, making it required a special machine, and it was
* Copyright © James S. Reece.
produced in a department whose equipment could not
be used to produce Forner’s other carpets. Effective
January 1, 1993, Forner had raised its price on this carpet from $3.95 to $4.75 per square yard. This had been
done in order to bring L-42’s margin up to that of the
other carpets in the line. Although Forner was financially sound, it expected a large funds need in the next
few years for equipment replacement and possible diversification. The 1993 price increase was one of several decisions made in order to provide funds for these
plans.
Forner’s competitors, however, had held their 1993
prices at $3.95 on carpets competitive with L-42. As
shown in Exhibit 1, which includes estimates of industry volume on these carpets, Forner’s price increase had
apparently resulted in a loss of market share. The marketing manager, Kim Gurskis, estimated that the industry would sell about 630,000 square yards of these
carpets in the first half of 1994. Gurskis was sure
Forner could sell 150,000 yards if it dropped the price
of L-42 back to $3.95. But if Forner held its price at
$4.75, Gurskis feared a further erosion in Forner’s
share. However, because some customers felt that L-42
was superior to competitive products, Gurskis felt that
Forner could sell at least 75,000 yards at the $4.75
price.
During their discussion, Gurskis and the chief accountant, Brooks Coleman, identified two other aspects
of the pricing decision. Coleman wondered whether
competitors would announce a further price decrease if
Forner dropped back to $3.95. Gurskis felt it was unlikely that competitors would price below $3.95
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EXHIBIT 1 Carpet L-42: Prices and Production, 1991–1993
Production Volume
(square yards)
Price
(per square yard)
Selling
Season*
Industry
Total
Forner
Carpet
Most
Competitors
Forner
Carpet
1991–1
1991–2
1992–1
1992–2
1993–1
1993–2
549,000
517,500
387,000
427,500
450,000
562,500
192,000
181,000
135,500
149,500
135,000
112,500
$4.75
4.75
3.95
3.95
3.95
3.95
$4.75
4.75
3.95
3.95
4.75
4.75
*199x–1 means the first 6 months of 199x; 199x–2 means the second six months of 199x.
EXHIBIT 2 Estimated Cost per Square Yard of Carpet L-42 at Various Production Volumes
First Six Months of 1994
Volume (square yards)
Raw materials
Materials spoilage
Direct labor
Department overhead:
Direct*
Indirect†
General overhead‡
Factory cost
Selling and administrative§
Total cost
50,000
75,000
100,000
125,000
150,000
175,000
$0.520
0.052
1.026
$0.520
0.051
0.989
$0.520
0.049
0.979
$0.520
0.049
0.962
$0.520
0.051
0.975
$0.520
0.052
0.997
0.568
1.240
0.308
______
3.714
1.671
______
$5.385
______
______
0.544
0.827
0.297
______
3.228
1.453
______
$4.681
______
______
0.524
0.620
0.294
______
2.986
1.344
______
$4.330
______
______
0.520
0.496
0.289
______
2.836
1.276
______
$4.112
______
______
0.520
0.413
0.293
______
2.772
1.247
______
$4.019
______
______
0.520
0.354
0.299
______
2.742
1.234
______
$3.976
______
______
* Materials handlers, supplies, repairs, power, fringe benefits.
†
Supervision, equipment depreciation, heat, and light.
‡
30 percent of direct labor.
§
45 percent of factory cost.
because none of them was more efficient than Forner,
and there were rumors that several of them were in poor
financial condition. Coleman’s other concern was
whether a decision relating to carpet L-42 would have
any impact on the sales of Forner’s other carpets.
Gurskis was convinced that since L-42 was a specialized item, there was no interdependence between its
sales and those of other carpets in the line.
Exhibit 2 contains cost estimates that Coleman had
prepared for various volumes of L-42. These estimates
represented Coleman’s best guesses as to costs during
the first six months of 1994, based on past cost experience and anticipated inflation.
Questions
1. What was the relationship (if any) between the L-42
pricing decision and the company’s future need for
capital funds?
2. Assuming no other prices are to be considered,
should Forner price L-42 at $3.95 or $4.75?
3. If Forner’s competitors hold their prices at $3.95,
how many square yards of L-42 would Forner need
to sell at a price of $4.75 in order to earn the same
profit as selling 150,000 square yards at a price of
$3.95?
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4. What additional information would you wish to
have before making this pricing decision? (Despite the absence of this information, still answer
question 2)
Short-Run Alternative Choice Decisions
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5. With hindsight, was the decision to raise the price
in 1993 a good one?
Case 26–3
Precision Worldwide, Inc.*
In late May 2004, Hans Thorborg, the general manager
of the German plant of Precision Worldwide, Inc.
(PWI), scheduled an afternoon meeting with his sales
manager, accountant, and development engineer to discuss the introduction by the French firm Henri Poulenc
(a competitor) of a plastic ring substitute for the steel
retaining rings presently used in certain machines sold
by Precision Worldwide. The plastic ring, new to the
market, not only had a much longer life than the PWI
steel ring but also apparently had a much lower manufacturing cost. Thorborg’s problem stemmed from
PWI’s large quantity of steel rings on hand and the substantial inventory of special steel that had been purchased for their manufacture. After a thorough survey,
he had found that the special steel could not be sold,
even for scrap; the total book value of these inventories
exceeded $390,000.
For nearly 90 years PWI had manufactured industrial machines and equipment for sale in numerous countries. The particular machines involved in
Thorborg’s dilemma were made only at the company’s
plant in Frankfurt, Germany, which employed more
than one thousand people. The different models were
priced between $18,900 and $28,900 and were sold by
a separate sales organization. Repair and replacement
parts, which accounted for a substantial part of the
company’s business, were sold separately. As with the
steel rings, these parts could often also be used on similar machines manufactured by competitors. The company’s head office was in Toledo, Ohio, U.S.A. In
general, plants outside the United States were allowed
considerable leeway in administering their own affairs;
the corporate headquarters, however, was easily accessible by telephone, email, or during executive visits to
the individual plants.
In the late 1990s, competition had increased. Japanese manufacturers, with low-priced spare parts, had
* Copyright © by the President and Fellows of Harvard
College. Harvard Business School case 9-197-103.
successfully entered the field. Other companies had
appeared with lower-quality and lower-priced machines. There was little doubt that future competition
would be more intense.
The steel ring manufactured by PWI had a normal
life of about two months, depending upon the extent to
which the machine was used. A worn-out ring could be
replaced in a few seconds, and although different models of the machines required from two to six rings, the
rings were usually replaced individually as they wore
out.
The sales manager, Gerhard Henk, had learned of
the new plastic ring shortly after its appearance and had
immediately asked when PWI would be able to supply
them, particularly for sale to customers in France,
where Henri Poulenc was the strongest competition
faced by PWI. Bodo Eisenbach, the development engineer, estimated that the plastic rings could be produced
by mid-September. The necessary tools and equipment
could be obtained for about $7,500. Eisenbach had initially raised the issue of the steel-ring inventories that
would not be used up by September. Henk believed that
if the new ring could be produced at a substantially
lower cost than the steel ones, the inventory problem
was irrelevant; he suggested that the inventory be sold,
or if that was impossible, thrown away. The size of the
inventory, however, caused Thorborg to question this
suggestion. He recalled that the size of the inventory
resulted from having to order the highly specialized
steel in large amounts so that a mill would be willing to
handle the order.
Henk reported that Henri Poulenc was said to be
selling the plastic ring at about the same price as the
PWI steel ring; since the production cost of the plastic
ring would be much less than the steel, he emphasized
that PWI was ignoring a good profit margin if it did not
introduce a plastic ring. As the meeting concluded, it
was decided that the company should prepare to manufacture the new ring as soon as possible but that until
the inventories of the old model and the steel were
850
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TABLE A
100 Plastic Rings
100 Steel Rings
Material
Direct labor
Overheada
Departmental
Administrative
$ 17.65
65.50
$321.90
196.50
131.00
________
65.50
________
393.00
_________
196.50
_________
Total (cost)
$279.65
$1,107.90
a
Overhead was allocated on the basis of direct labor cost. It was estimated that the variable overhead costs included here were largely
fringe benefits related to direct labor and amounted to 80¢ per direct labor dollar or about 40 percent of the departmental amounts.
exhausted, the plastic ring would only be sold in those
markets where it was offered by competitors. It was
expected that the new rings would not be produced by
any company other than Henri Poulenc for some time,
and this meant that no more than 10 percent of Precision Woldwide’s markets would be affected.
Shortly after this, Patrick Corrigan, from the parent
company in Ohio, visited Frankfurt. During a review
of company problems, the plastic-ring question was
discussed. Although the ring was only a small part of
the finished machines, Corrigan was interested in the
problem because the company wanted to establish
policies for the production and pricing of all such parts
that, in total, accounted for a substantial portion of
PWI’s revenues. Corrigan agreed that the company
should proceed with plans for its production and try to
find some other use for the steel; he then said, “If this
does not seem possible, I would, of course, expect you
to use this material and produce the steel rings.”
A few days after Corrigan’s visit, both Eisenbach
and Henk came in to see Thorborg. Eisenbach came
because he felt that since tests had indicated that the
plastic ring had at least four times the wearing properties of the steel ring, it would completely destroy demand for the steel ring. He understood, however, that
the price of the competitive ring was high, and he felt
that the decision to sell the plastic ring only in markets
where it was sold by competitors was a good one. He
observed, “In this way we will probably be able to continue supplying the steel ring until stocks, at least of
processed parts, are used up.”
Henk still strongly opposed sales of any steel rings
once the plastic ones became available. If steel rings
were sold in some areas, he argued, while plastic rings
were being sold elsewhere, customers who purchased
steel rings would eventually find out. This would harm
the sale of Precision Worldwide machines—the selling
price of which was many times that of the rings. He
produced figures to show that if the selling price of
both rings remained at $1,350.00 per hundred, the additional profit from the plastic rings (manufactured at a
cost of $279.65 per hundred versus the $1,107.90 per
hundred for steel rings) would more than recover the
value of the steel inventory, and do so within less than
a year at present volume levels. Thorborg refused to
change the decision of the previous meeting but agreed
to have another discussion within a week.
Anticipating this third meeting and also having
Corrigan’s concern in mind, Thorborg obtained the
data displayed in Table A from the cost accounting department on the cost of both plastic and steel rings.
Thorborg also learned that the inventory of special
steel had cost $110,900 and represented enough material to produce approximately 34,500 rings. Assuming
that sales continued at the current rate of 690 rings per
week, without any further production, some 15,100 finished rings would be left on hand by mid-September.
Thorborg then recalled that during the next two or three
months the plant would not be operating at capacity;
during slack periods, the company had a policy of employing excess labor (at about 70 percent of regular
wages) on various make-work projects rather than laying workers off. He wondered if it would be a good idea
to use some of this labor to convert the steel inventory
into rings during this period.
Question
What action should Hans Thorborg take? Why?
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Chapter 26
Short-Run Alternative Choice Decisions
837
Case 26–4
Baldwin Bicycle Company*
In May 1989 Suzanne Leister, marketing vice president
of Baldwin Bicycle Company, was mulling over the
discussion she had had the previous day with Karl
Knott, a buyer from Hi-Valu Stores, Inc. Hi-Valu operated a chain of discount department stores in the Northwest. Hi-Valu’s sales volume had grown to the extent
that it was beginning to add “house-brand” (also called
“private-label”) merchandise to the product lines of
several of its departments. Mr. Knott, Hi-Valu’s buyer
for sporting goods, had approached Ms. Leister about
the possibility of Baldwin’s producing bicycles for HiValu. The bicycles would bear the name “Challenger,”
which Hi-Valu planned to use for all of its house-brand
sporting goods.
Baldwin had been making bicycles for almost 40
years. In 1989 the company’s line included 10 models,
ranging from a small beginner’s model with training
* Copyright © Professor Robert N. Anthony.
wheels to a deluxe 12-speed adult’s model. Sales were
currently at an annual rate of about $10 million. (The
company’s 1988 financial statements appear in Exhibit 1.) Most of Baldwin’s sales were through independently owned toy stores and bicycle shops. Baldwin had never before distributed its products through
department store chains of any type. Ms. Leister felt
that Baldwin bicycles had the image of being above
average in quality and price, but not a “top of the line”
product.
Hi-Valu’s proposal to Baldwin had features that
made it quite different from Baldwin’s normal way of
doing business. First, it was very important to Hi-Valu
to have ready access to a large inventory of bicycles,
because Hi-Valu had had great difficulty in predicting
bicycle sales, both by store and by month. Hi-Valu
wanted to carry these inventories in its regional warehouses, but did not want title on a bicycle to pass from
Baldwin to Hi-Valu until the bicycle was shipped from
one of its regional warehouses to a specific Hi-Valu
EXHIBIT 1 Financial Statements (thousands of dollars)
BALDWIN BICYCLE COMPANY
Balance Sheet
As of December 31, 1988
Assets
Liabilities and Owners’ Equity
Cash
$
Accounts receivable
Inventories
Plant and equipment (net)
1,359
2,756
3,635
______
$8,092
______
______
342
Current liabilities
$3,478
Noncurrent liabilities
Total liabilities
Owners’ equity
1,512
______
4,990
3,102
______
$8,092
______
______
Income Statement
For the Year Ended December 31, 1988
Sales revenues
Cost of sales
Gross margin
Other expenses
Income before taxes
Income tax expense
Net income
$10,872
8,045
_______
2,827
2,354
_______
473
218
_______
$_______
255
_______
852
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EXHIBIT 2 Data Pertinent to Hi-Valu Proposal Notes Taken by Suzanne Leister
1. Estimated first-year costs of producing Challenger bicycles (average unit costs, assuming a constant mix
of models):
Materials
Direct labor
Overhead (@ 125% of direct labor)
$39.80*
19.60
24.50
_______
$83.90†
* Includes items specific to models for Hi-Valu, not used in our standard models.
†
Accountant says about 40 percent of total production overhead cost is variable; 125 percent
of DL$ rate is based on volume of 100,000 bicycles per year.
2. One-time added costs of preparing drawings and/or arranging sources for fenders, seats, handlebars, tires,
and shipping boxes that differ from those used in our standard models; approximately $5,000 (based on
estimated two person-months of effort at $2,500 per month).
3. Unit price and annual volume: Hi-Valu estimates it will need 25,000 bikes a year and proposes to pay us
(based on the assumed mix of models) an average of $92.29 per bike for the first year. Contract to contain
an inflation escalation clause such that price will increase in proportion to inflation-caused increases in
costs shown in item 1, above; thus, the $92.29 and $83.90 figures are, in effect, “constant-dollar”
amounts. Knott intimated that there was very little, if any, negotiating leeway in the $92.29 proposed initial price.
4. Asset-related costs (annual variable costs, as percent of dollar value of assets):
Pretax cost of funds (to finance receivables or inventories)
Recordkeeping costs (for receivables or inventories)
Inventory insurance
State property tax on inventory
Inventory-handling labor and equipment
Pilferage, obsolescence, damage, etc.
11.5
2.0
0.6
0.7
6.0
2.2
5. Assumptions for Challenger-related added inventories (average over the year):
Materials: two months’ supply.
Work in process: 1,000 bikes, half completed (but all materials for them issued).
Finished goods: 500 bikes (awaiting next carload-lot shipment to a Hi-Valu warehouse).
6. Impact on our regular sales: Some customers comparison shop for bikes, and many of them are likely to
recognize a Challenger bike as a good value when compared with a similar bike (either ours or a
competitor’s) at a higher price in a nonchain toy or bicycle store. In 1988, we sold 98,791 bikes. My best
guess is that our sales over the next three years will be about 100,000 bikes a year if we forgo the Hi-Valu
deal. If we accept it, I think we’ll lose about 3,000 units of our regular sales volume a year, since our retail
distribution is quite strong in Hi-Valu’s market regions. These estimates do not include the possibility that a
few of our current dealers might drop our line if they find out we’re making bikes for Hi-Valu.
store. At that point, Hi-Valu would regard the bicycle
as having been purchased from Baldwin, and would
pay for it within 30 days. However, Hi-Valu would
agree to take title to any bicycle that had been in one of
its warehouses for four months, again paying for it
within 30 days. Mr. Knott estimated that on average a
bike would remain in a Hi-Valu regional warehouse
for two months.
Second, Hi-Valu wanted to sell its Challenger bicycles at lower prices than the name-brand bicycles it
carried, and yet still earn approximately the same
dollar gross margin on each bicycle sold—the rationale being that Challenger bike sales would take away
from the sales of the name-brand bikes. Thus, Hi-Valu
wanted to purchase bikes from Baldwin at lower prices
than the wholesale prices of comparable bikes sold
through Baldwin’s usual channels.
Finally, Hi-Valu wanted the Challenger bike to be
somewhat different in appearance from Baldwin’s other
bikes. While the frame and mechanical components
could be the same as used on current Baldwin models,
the fenders, seats, and handlebars would need to be
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Chapter 26
somewhat different, and the tires would have to have the
name “Challenger” molded into their sidewalls. Also,
the bicycles would have to be packed in boxes printed
with the Hi-Valu and Challenger names. Ms. Leister
thought that possibly these requirements would increase Baldwin’s purchasing, inventorying, and production costs over and above the added costs that would
be incurred for a comparable increase in volume for
Baldwin’s regular products.
On the positive side, Ms. Leister was acutely aware
that the “bicycle boom” had flattened out, and this plus
a poor economy had caused Baldwin’s sales volume to
fall the past two years. As a result, Baldwin currently
was operating its plant at about 75 percent of one-shift
capacity. Thus, the added volume from Hi-Valu’s purchases could possibly be very attractive. If agreement
could be reached on prices, Hi-Valu would sign a contract guaranteeing to Baldwin that Hi-Valu would buy
its house-brand bicycles only from Baldwin for a
three-year period. The contract would then be automatically extended on year-to-year basis, unless one
party gave the other at least six-months’ notice that it
did not wish to extend the contract.
Short-Run Alternative Choice Decisions
853
839
Suzanne Leister realized she needed to do some
preliminary financial analysis of this proposal before having any further discussions with Karl Knott.
She had written on a pad the information she had gathered to use in her initial analysis; this information is
summarized in Exhibit 2.
Questions
1. What is the expected added profit from the Challenger line?
2. What is the expected impact of cannibalization of
existing sales?
3. What costs will be incurred on a one-time basis
only?
4. What are the additional assets and related carrying
costs?
5. What is the overall impact on the company in terms
of (a) profits, (b) return on sales, (c) return on assets, and (d) return on equity?
6. What are the strategic risks and rewards?
7. What should the company do? Why?