Accounting- Chapter 22 “Short-Term Decision Making: Differential Analysis”

| January 30, 2017

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Chapter 22 “Short-Term Decision Making: Differential Analysis” from Accounting Principles: Managerial
Accounting by Hermanson, Edwards, and Ivancevich is available under Creative Commons AttributionNoncommercial-Share Alike 3.0 license. © Textbook Equity (2011)

22 Short-term decision making:
Differential analysis
22.1 Learning objectives
After studying this chapter, you should be able to:
• Compare and contrast contribution margin income statements to traditional income

statements.
• Explain differential analysis and describe its components.
• Make pricing decisions using differential analysis.
• Use differential analysis to decide whether to accept or reject special orders.
• Decide whether to eliminate or add product lines or segments of the business using differential

analysis.
• Use differential analysis to decide whether to sell joint products at the split-off point or process

them further.
• Decide whether to make or buy products using differential analysis.
• Use differential analysis to decide whether to improve product quality.

In this chapter, we will discuss how companies use financial information in making decisions. The
framework for our discussion is differential analysis. We begin by presenting an alternative to the
traditional income statement format. This alternative, the contribution margin income statement,
generally is more useful for the managerial decisions we discuss in this chapter. Then we discuss
differential analysis as a method of choosing the best solution to decision problems. We also present
several applications of differential analysis to managerial problems that you will likely encounter.

22.2 Contribution margin income statements
Both this and the previous chapter discuss the use of accounting for managerial decision making.
We have introduced the concepts of fixed and variable costs, and shown how you can use these
concepts in making decisions. However, income statements published for external use do not break
costs down into fixed and variable components. We now present another income statement that not
only breaks down costs into their fixed and variable components but also presents the total
contribution margin. The contribution margin income statement subtracts variable costs from
revenues to show the contribution margin, and then subtracts fixed costs to derive net income.
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You can see the differences between the traditional and contribution margin income statements
by contrasting two income statements based on the same data. Assume Bart Company had the
following data relating to manufacturing and sales activities for May 2011:
Bart Company
May 2011
Variable manufacturing costs (per unit):
Direct materials
$1
Direct labor
1
Overhead
1
Total
3
Variable selling expenses (per unit)
$0.50
Fixed costs:
Manufacturing overhead ($1.00 per unit for $ 9,000
9,000 units)
Selling expenses
15,000
Administrative expenses
18,000
Selling price (per unit)
$9

Look at Exhibit 26, where we compare the traditional and contribution margin methods.
A. Traditional method
Bart company
Income statement
For the month ending 2011 May 31
Revenue (9,000 units at $9 per unit)
Less: Cost of goods sold (9,000 units at $4 manufacturing cost
per unit:
Less: $3 variable + $1 fixed)
Gross margin
Less: Selling and administrative expenses (9,000 units at $0.50
variable selling cost
per unit, plus fixed costs of $15,000 for selling and $18,000 for
administrative)
Net income tax
B. Contribution margin method
Bart company
Income statement
For the month ending 2011 May 31
Revenue (9,000 units at $9 per unit)
Less: Variable cost of goods sold (9,000 $27,000
units at $3 variable manufacturing cost
per unit)
Variable selling expenses (9,000 units at 4,500
$0.50 per unit)
Total contribution margin
Less: Fixed manufacturing costs
$ 9,000
Less: Fixed selling expenses
15,000
Less: Fixed administrative expenses
18,000
Net income before tax

$81,000
36,000
$45,000
37,500
$7,500

$81,000

31,500
$ 49,500
42,000
$ 7,500

Exhibit 26: Comparative income statements
The contribution margin method shows managers the amount of variable costs, the amount of
fixed costs, and the contribution the company is making toward covering fixed costs and earning net
income. For example, suppose the managers of Bart Company asked, “What would be the impact on
net income if we increase sales units by 10 per cent without changing unit price or variable cost per

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unit or total fixed costs?” Looking at the contribution margin statement, we predict the following
increases:
Revenue increase (10% of $81,000)
Variable cost of goods sold increase (10% of $2,700
$27,000)
Increase in total variable selling expense (10% 450
of $4,500)
Increase in total contribution margin

$8,100
3,150
$4,950

If we assume no increase in fixed costs, we expect Bart’s net income to increase by USD 4,950.
The traditional statement does not break down costs into fixed and variable components, so we
cannot easily answer the question posed by Bart’s management. Most companies use the traditional
approach for external financial statements, but they use the contribution margin format for internal
purposes because it is more informative. Management often needs information on the contribution
margin rather than the gross margin to calculate break-even points and make decisions regarding
special-order pricing.

An accounting perspective:
Uses of technology
Generating multiple financial reports in different formats does not mean companies
must keep several sets of books. After data are entered into a database, it is relatively
simple for computer software to generate several sets of financial statements—a
contribution margin income statement for managers, a traditional income statement
for external financial reporting, and yet another report for tax purposes. Two
problems remain: First, the reports are only as good as the quality of the data in the
database. Second, people who read the financial statements must be sufficiently
informed to understand the differences in the way the information is presented.

22.3 Differential analysis
Differential analysis involves analyzing the different costs and benefits that would arise from
alternative solutions to a particular problem. Relevant revenues or costs in a given situation are
future revenues or costs that differ depending on the alternative course of action selected.
Differential revenue is the difference in revenues between two alternatives. Differential cost or
expense is the difference between the amounts of relevant costs for two alternatives.4
4 Some authors equate relevant cost and differential cost. This text uses the term relevant to
identify which costs should be considered in a situation and the term differential to identify the
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Future costs that do not differ between alternatives are irrelevant and may be ignored since they
affect both alternatives similarly. Past costs, also known as sunk costs, are not relevant in decision
making because they have already been incurred; therefore, these costs cannot be changed no matter
which alternative is selected.
For certain decisions, revenues do not differ between alternatives. Under those circumstances,
management should select the alternative with the least cost. In other situations, costs do not differ
between alternatives. Accordingly, management should select the alternative that results in the
largest revenue. Many times both future costs and revenues differ between alternatives. In these
situations, the management should select the alternative that results in the greatest positive
difference between future revenues and expenses (costs).
To illustrate relevant, differential, and sunk costs, assume that Joanna Bennett invested USD 400
in a tiller so she could till gardens to earn USD 1,500 during the summer. Not long afterward,
Bennett was offered a job at a horse stable feeding horses and cleaning stalls for USD 1,200 for the
summer. The costs that she would incur in tilling are USD 100 for transportation and USD 150 for
supplies. The costs she would incur at the horse stable are USD 100 for transportation and USD 50
for supplies. If Bennett works at the stable, she would still have the tiller, which she could loan to her
parents and friends at no charge.
The tiller cost of USD 400 is not relevant to the decision because it is a sunk cost. The
transportation cost of USD 100 is also not relevant because it is the same for both alternatives. These
costs and revenues are relevant:

Revenues
Costs
Net benefit in favor of tilling
service

Performing
tilling service
$1,500
150

Working at
horse stable
$1,200
50

Differential
$300
100
$200

Based on this differential analysis, Joanna Bennett should perform her tilling service rather than
work at the stable. Of course, this analysis considers only cash flows; nonmonetary considerations,
such as her love for horses, could sway the decision.
In many situations, total variable costs differ between alternatives while total fixed costs do not.
For example, suppose you are deciding between taking the bus to work or driving your car on a
particular day. The differential costs of driving a car to work or taking the bus would involve only the
variable costs of driving the car versus the variable costs of taking the bus.
Suppose the decision is whether to drive your car to work every day for a year versus taking the
bus for a year. If you bought a second car for commuting, certain costs such as insurance and an auto
license that are fixed costs of owning a car would be differential costs for this particular decision.
amount by which these costs differ.
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Before studying the applications of differential analysis, you must realize that (1) two types of
fixed costs exist and (2) opportunity costs are also relevant in choosing between alternatives. For this
reason, we discuss committed fixed costs, discretionary fixed costs, and opportunity costs before
concentrating on the applications of differential analysis.
Up to this point, we have treated fixed costs as if they were all alike. Now we describe two types of
fixed costs—committed fixed costs and discretionary fixed costs.
Committed fixed costs Committed fixed costs relate to the basic facilities and
organizational structure that a company must have to continue operations. These costs cannot be
changed in the short run without seriously disrupting operations. Examples of committed fixed costs
are leases on buildings and equipment and salaries of key executives. In the short run, these costs are
not subject to the discretion or control of management. These costs result from past decisions that
committed the company for several years. For instance, once a company constructs a building to
house production operations, it is committed to use the building for many years. Thus, unlike some
other types of fixed costs, the depreciation on that building is not as subject to management’s control.
Discretionary fixed costs In contrast to committed fixed costs, management controls
discretionary fixed costs from year to year. Each year management decides how much to spend
on advertising, research and development, and employee training or development programs. Because
it makes such decisions each year, these costs are under management’s discretion. Management is
not locked in or committed to a certain level of expense for longer than one budget period. In the next
period, management may change the level of expense or eliminate the expense completely.
To some extent, management’s philosophy can affect which fixed costs are committed and which
are discretionary. For instance, some companies terminate people in the upper levels of management
when they downsize, while other companies keep their management team intact. Thus, in some
companies the salaries of top-level managers are discretionary while in other companies they are
committed.
The discussion of committed fixed costs and discretionary fixed costs is relevant to CVP analysis.
When almost all of a company’s fixed costs are committed fixed costs, it has more difficulty reducing
its break-even point for the next budget period than if most of its fixed costs are discretionary. A
company with a large proportion of discretionary fixed costs may be able to reduce fixed costs
dramatically in recessionary periods. By running lean, the company may show some income even
when economic conditions are difficult. As a result, the company may enhance its chances of long-run
survival.
Another cost concept relevant to decision making is opportunity cost. An opportunity cost is
the potential benefit that is forgone by not following the next best alternative course of action. For

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example, assume that the two best uses of a plot of land are as a mobile home park (annual income of
USD 100,000) and as a golf driving range (annual income of USD 60,000). The opportunity cost of
using the land as a mobile home park is USD 60,000, while the opportunity cost of using the land as
a driving range is USD 100,000.
Companies do not record opportunity costs in the accounting records because they are the costs of
not following a certain alternative. Thus, opportunity costs are not transactions that occurred but
that did not occur. However, opportunity cost is a relevant cost in many decisions because it
represents a real sacrifice when one alternative is chosen instead of another.

22.4 Applications of differential analysis
To illustrate the application of differential analysis to specific decision problems, we consider five
decisions: (1) setting prices of products; (2) accepting or rejecting special orders; (3) adding or
eliminating products, segments, or customers; (4) processing or selling joint products; and (5)
deciding whether to make products or buy them. Although these five decisions are not the only
applications of differential analysis, they represent typical short-term business decisions using
differential analysis. Our discussion ignores income taxes.
When applying differential analysis to pricing decisions, each possible price for a given product
represents an alternative course of action. The sales revenues for each alternative and the costs that
differ between alternatives are the relevant amounts in these decisions. Total fixed costs often remain
the same between pricing alternatives and, if so, may be ignored. In selecting a price for a product,
the goal is to select the price at which total future revenues exceed total future costs by the greatest
amount, thus maximizing income.
A high price is not necessarily the price that maximizes income. The product may have many
substitutes. If a company sets a high price, the number of units sold may decline substantially as
customers switch to lower-priced competitive products. Thus, in the maximization of income, the
expected volume of sales at each price is as important as the contribution margin per unit of product
sold. In making any pricing decision, management should seek the combination of price and volume
that produces the largest total contribution margin. This combination is often difficult to identify in
an actual situation because management may have to estimate the number of units that can be sold at
each price.
For example, assume that a company selling fried chicken in the New York market estimates
product demand for its large bucket of chicken for a particular period to be:
Choice
1
2
3

Demand
15,000 units at $6 per unit
12,000 units at $7 per unit
10,000 units at $8 per unit

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4

7,000 units at $9 per unit

The company’s fixed costs of USD 20,000 per year are not affected by the different volume
alternatives. Variable costs are USD 5 per unit. What price should be set for the product? Based on
the calculations shown in the table below, the company should select a price of USD 8 per unit
because choice (3) results in the greatest total contribution margin. In the short run, maximizing total
contribution margin maximizes profits.
Choice
1
2
3
4
*Sales price
– Variable
cost.

Contribution
margin per unit*
x
$1
2
3
4

Number
of units =

Total
Fixed
margin costs

Net
income (loss)

15,000
12,000
10,000
7,000

$15,000
24,000
30,000
28,000

$(5,000)
4,000
10,000
8,000

$20,000
20,000
20,000
20,000

Sometimes management has an opportunity to sell its product in two or more markets at two or
more different prices. Movie theaters, for example, sell tickets at discount prices to particular groups
of people—children, students, and senior citizens. Differential analysis can determine whether
companies should sell their products at prices below regular levels.
Good business management requires keeping the cost of idleness at a minimum. When operating
at less than full capacity, management should seek additional business. Management may decide to
accept such additional business at prices lower than average unit costs if the differential revenues
from the additional business exceed the differential costs. By accepting special orders at a discount,
businesses can keep people employed that they would otherwise lay off.
To illustrate, assume Rios Company produces and sells a single product with a variable cost of
USD 8 per unit. (See Exhibit 27 for details.) Annual capacity is 10,000 units, and annual fixed costs
total USD 48,000. The selling price is USD 20 per unit and production and sales are budgeted at
5,000 units. Thus, budgeted income before income taxes is USD 12,000, as shown in Exhibit 27.

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Rios company
Income statement
For the period ending 2011
May 31
Revenue (5,000 units at $20)
Variable costs:
Direct materials cost
Labor
Overhead
Marketing and administrative
costs
Total variable costs ($8 per
unit)
Fixed costs:
Overhead
Marketing and administrative
costs
Total fixed costs
Total costs ($17.60 per unit)
Net income

$100,000
$20,000
5,000
10,000
5,000
$40,000
$28,000
20,000
48,000
88,000
$12,000

Exhibit 27: Rios company before special order
Assume the company receives an order from a foreign distributor for 3,000 units at USD 10 per
unit. This USD 10 price is not only half of the regular selling price per unit, but also less than the USD
17.60 average cost per unit (USD 88,000/5,000 units). However, the USD 10 price offered exceeds
the variable cost per unit by USD 2. If the company accepts the order, net income increases to USD
18,000.
As shown in the income statement in Exhibit 28, revenue increases to USD 130,000 with the
special order. Each of the variable costs increases in total by 60 per cent because total volume
increases by 60 per cent (3,000 units in the special order/5,000 units regularly produced).
Rios company
Income statement
For the period ending 2011 May
31
Revenue (5,000 units at $20, 3,000
units at $10)
Variable costs:
Direct materials cost
Labor
Overhead
Marketing and administrative costs
Total variable costs ($8 per unit)
Fixed costs:
Manufacturing overhead
Marketing and administrative costs
Total fixed costs
Total costs ($14 per unit)
Net income

$130,000
$32,000
8,000
16,000
8,000
$64,000
$28,000
20,000
48,000
112,000
$18,000

Exhibit 28: Rios company if special order is accepted
Note that the fixed costs do not increase with the special order. Because the special order does not
increase the fixed costs, the special order’s revenues need only cover its variable costs.
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If Rios Company continues to operate at 50 per cent capacity (producing 5,000 units) it would
generate income of only USD 12,000. By accepting the special order, net income increases by USD
6,000.
Differential analysis would provide the following calculations:

Revenues
Costs
Net benefit of accepting order

Accept
order
$130,000
112,000

Reject
order
$100,000
88,000

Differential
$30,000
24,000
$6,000

Variable costs set a floor for the selling price in special-order situations. Even if the price exceeds
variable costs only slightly, the additional business increases net income, assuming fixed costs do not
change. However, pricing just above variable costs of special-order business often brings only shortterm increases in net income. In the long run, companies must cover all of their costs, not just the
variable costs.
Periodically, management has to decide whether to add or eliminate certain products, segments,
or customers. If you have watched a store or a plant open or close in your area, you have seen the
results of these decisions. Differential analysis is useful in this decision making because a company’s
income statement does not automatically associate costs with certain products, segments, or
customers. Thus, companies must reclassify costs as those that the action would change and those
that it would not change.
If companies add or eliminate products, they usually increase or decrease variable costs. The fixed
costs may change, but not in many cases. Management bases decisions to add or eliminate products
only on the differential items; that is, the costs and revenues that change.
To illustrate, assume that the Campus Bookstore is considering eliminating its art supplies
department. If the bookstore dropped the art supplies department, it would lose revenues of USD
100,000 annually. The bookstore’s management assigns costs of USD 110,000 (USD 80,000 variable
and USD 30,000 fixed) to the art supplies department. Therefore, art supplies has an apparent
annual loss of USD 10,000 (USD 100,000 revenue minus USD 110,000 costs). But careful cost
analysis reveals that if the art supplies department were dropped, the reduction in costs would be
only USD 80,000. The USD 30,000 fixed costs were general bookstore fixed costs allocated to the art
supplies department. These fixed costs would continue to be incurred and would not be saved by
closing the art supplies department. Look at the differential analysis in Exhibit 29. Note that the art
supplies department has been contributing USD 20,000 (USD 100,000 revenues – USD 80,000
variable costs) annually toward covering the fixed costs of the business. Consequently, its elimination
could be a costly mistake unless there is a more profitable use for the vacated facilities.

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Revenues
Variable costs
Fixed costs
Net benefit of keeping art supplies
department

Art Supplies
Keep
$100,000
80,000
30,000

Department
Close
$-0-030,000

Differential
$100,000
80,000
-0$ 20,000

Exhibit 29: Differential analysis: Decision whether to close a department
If the company has a profitable alternative use for the vacated facilities, the potential income from
that alternative represents an opportunity cost of retaining the product, segment, or customer.
Assume, for example, that the bookstore could use the facilities currently occupied by the art supplies
department to open a new department to display and sell personal computers, printers, and software.
This new department would contribute USD 35,000 to the bookstore’s income.
The relevant costs in the decision to retain the art supplies department are USD 115,000 (USD
80,000 of variable manufacturing costs and USD 35,000 of opportunity cost), while the relevant
revenues are still USD 100,000. Therefore, the bookstore has a net disadvantage in keeping the art
supplies department because it loses USD 15,000 compared to the computer department.
Sometimes two or more products result from a common raw material or production process; these
products are called joint products. Companies can process these products further or sell them in
their current condition. For instance, when Chevron refines crude oil, it produces a wide variety of
fuels, solvents, lubricants, and residual petrochemicals.
Management can use differential analysis to decide whether to process a joint product further or
to sell it in its present condition. Joint costs are those costs incurred up to the point where the joint
products split off from each other. These costs are sunk costs and are not considered when deciding
whether to process a joint product further before selling it or to sell it in its condition at the split-off
point.
The following example illustrates the issue of whether to process or sell joint products. Assume
that Pacific Paper, Inc., produces two paper products, A and B, from a common manufacturing
process. Each of the products could either be sold in its present form or processed further and sold at
a higher price. Data for both products follow:
Product
A
B

Selling price per
unit at split-off
point
$10
12

Cost per unit
of further
processing
$6
7

Selling price per unit
after further
processing
$21
18

The differential revenues and costs of further processing of the two products are as follows:
Product

A

Different
revenue of
further
processing
$11

Differential cost Net advantage
of further
(disadvantage)
processing
of further
processing
$6
$5

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B

6

7

(1)

Based on this analysis, Pacific Paper should process product A further to increase income by USD
5 per unit sold. The company should not process product B further because that would decrease
income by USD 1 per unit sold.
Companies use this same fo…

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