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CHAPTER 3
COST–VOLUME–PROFIT ANALYSIS
NOTATION USED IN CHAPTER 3 SOLUTIONS
SP: Selling price
VCU: Variable cost per unit
CMU: Contribution margin per unit
FC: Fixed costs
TOI: Target operating income
3-1 Cost-volume-profit (CVP) analysis examines the behavior of total revenues, total costs,
and operating income as changes occur in the units sold, selling price, variable cost per unit, or
fixed costs of a product.
3-2 The assumptions underlying the CVP analysis outlined in Chapter 3 are
1. Changes in the level of revenues and costs arise only because of changes in the number of
product (or service) units sold.
2. Total costs can be separated into a fixed component that does not vary with the units sold
and a variable component that changes with respect to the units sold.
3. When represented graphically, the behaviors of total revenues and total costs are linear
(represented as a straight line) in relation to units sold within a relevant range and time
period.
4. The selling price, variable cost per unit, and fixed costs are known and constant.
3-3 Operating income is total revenues from operations for the accounting period minus cost
of goods sold and operating costs (excluding income taxes):
Operating income = Total revenues from operations – Costs of goods sold and operating
costs (excluding income taxes)
Net income is operating income plus nonoperating revenues (such as interest revenue) minus
nonoperating costs (such as interest cost) minus income taxes. Chapter 3 assumes nonoperating
revenues and nonoperating costs are zero. Thus, Chapter 3 computes net income as:
Net income = Operating income – Income taxes
3-4 Contribution margin is the difference between total revenues and total variable costs.
Contribution margin per unit is the difference between selling price and variable cost per
unit. Contribution-margin percentage is the contribution margin per unit divided by selling
price.
3-5 Three methods to express CVP relationships are the equation method, the contribution
margin method, and the graph method. The first two methods are most useful for analyzing
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operating income at a few specific levels of sales. The graph method is useful for
visualizing the effect of sales on operating income over a wide range of quantities sold.
3-6 Breakeven analysis denotes the study of the breakeven point, which is often only an
incidental part of the relationship between cost, volume, and profit. Cost-volume-profit
relationship is a more comprehensive term than breakeven analysis.
3-7 CVP certainly is simple, with its assumption of output as the only revenue and cost driver,
and linear revenue and cost relationships. Whether these assumptions make it simplistic
depends on the decision context. In some cases, these assumptions may be sufficiently
accurate for CVP to provide useful insights. The examples in Chapter 3 (the software
package context in the text and the travel agency example in the Problem for Self-Study)
illustrate how CVP can provide such insights. In more complex cases, the basic ideas of
simple CVP analysis can be expanded.
3-8 An increase in the income tax rate does not affect the breakeven point. Operating income
at the breakeven point is zero, and no income taxes are paid at this point.
3-9 Sensitivity analysis is a “what–if” technique that managers use to examine how an outcome
will change if the original predicted data are not achieved or if an underlying assumption
changes. The advent of the electronic spreadsheet has greatly increased the ability to
explore the effect of alternative assumptions at minimal cost. CVP is one of the most
widely used software applications in the management accounting area.
3-10 Examples include:
Manufacturing––substituting a robotic machine for hourly wage workers
Marketing––changing a sales force compensation plan from a percent of sales dollars to
a fixed salary
Customer service––hiring a subcontractor to do customer repair visits on an annual
retainer basis rather than a per-visit basis
3-11 Examples include:
Manufacturing––subcontracting a component to a supplier on a per-unit basis to avoid
purchasing a machine with a high fixed depreciation cost
Marketing––changing a sales compensation plan from a fixed salary to percent of sales
dollars basis
Customer service––hiring a subcontractor to do customer service on a per-visit basis rather
than an annual retainer basis
3-12 Operating leverage describes the effects that fixed costs have on changes in operating
income as changes occur in units sold, and hence, in contribution margin. Knowing the degree of
operating leverage at a given level of sales helps managers calculate the effect of fluctuations in
sales on operating incomes.
3-13 CVP analysis is always conducted for a specified time horizon. One extreme is a very short-
time horizon. For example, some vacation cruises offer deep price discounts for people who offer
to take any cruise on a day’s notice. One day prior to a cruise, most costs are fixed. The other
extreme is several years. Here, a much higher percentage of total costs typically is variable.
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CVP itself is not made any less relevant when the time horizon lengthens. What happens
is that many items classified as fixed in the short run may become variable costs with a longer time
horizon.
3-14 A company with multiple products can compute a breakeven point by assuming there is a
constant sales mix of products at different levels of total revenue.
3-15 Yes, gross margin calculations emphasize the distinction between manufacturing and
nonmanufacturing costs (gross margins are calculated after subtracting variable and fixed
manufacturing costs). Contribution margin calculations emphasize the distinction between fixed
and variable costs. Hence, contribution margin is a more useful concept than gross margin in CVP
analysis.
3-16 (10 min.) CVP computations.
Fill in the blanks for each of the following independent cases.
Case
Revenues
Variable
Costs
Fixed Costs
Total Costs
Operating
Income
a.
$800
$1,200
$1,000
b.
$2,400
$400
$ 700
c.
$ 900
$500
$ 900
d.
$1,800
$400
SOLUTION
Variable
Fixed
Total
Operating
Contribution
Contribution
Revenues
Costs
Costs
Costs
Income
Margin
Margin %
a.
$2,200
$ 800
$400
$1,200
$1,000
$1,400
63.64%
b.
2,400
1,300
400
1,700
700
1,100
45.83%
c.
900
500
400
900
0
400
44.44%
d.
1,800
900
400
1,300
500
900
50.00%
3-17 (10–15 min.) CVP computations.
Garrett Manufacturing sold 410,000 units of its product for $68 per unit in 2014. Variable cost per
unit is $60, and total fixed costs are $1,640,000.
Required:
1. Calculate (a) contribution margin and (b) operating income.
2. Garrett’s current manufacturing process is labor intensive. Kate Schoenen, Garrett’s
production manager, has proposed investing in state-of-the-art manufacturing equipment,
which will increase the annual fixed costs to $5,330,000. The variable costs are expected to
decrease to $54 per unit. Garrett expects to maintain the same sales volume and selling price
next year. How would acceptance of Schoenen’s proposal affect your answers to (a) and (b) in
requirement 1?
3. Should Garrett accept Schoenen’s proposal? Explain.
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SOLUTION
1a. Sales ($68 per unit × 410,000 units) $27,880,000
Variable costs ($60 per unit × 410,000 units) 24,600,000
Contribution margin $ 3,280,000
1b. Contribution margin (from above) $3,280,000
Fixed costs 1,640,000
Operating income $1,640,000
2a. Sales (from above) $27,880,000
Variable costs ($54 per unit × 410,000 units) 22,140,000
Contribution margin $ 5,740,000
2b. Contribution margin $5,740,000
Fixed costs 5,330,000
Operating income $ 410,000
3. Operating income is expected to decrease by $1,230,000 ($1,640,000 − $410,000) if Ms.
Schoenen’s proposal is accepted.
The management would consider other factors before making the final decision. It is likely
that product quality would improve as a result of using state of the art equipment. Due to increased
automation, probably many workers will have to be laid off. Garrett’s management will have to
consider the impact of such an action on employee morale. In addition, the proposal increases the
company’s fixed costs dramatically. This will increase the company’s operating leverage and risk.
3-18 (35–40 min.) CVP analysis, changing revenues and costs.
Brilliant Travel Agency specializes in flights between Toronto and Jamaica. It books passengers
on Ontario Air. Brilliant’s fixed costs are $36,000 per month. Ontario Air charges passengers
$1,300 per round-trip ticket.
Calculate the number of tickets Brilliant must sell each month to (a) break even and (b) make a
target operating income of $12,000 per month in each of the following independent cases.
Required:
1. Brilliant’s variable costs are $34 per ticket. Ontario Air pays Brilliant 10% commission on
ticket price.
2. Brilliant’s variable costs are $30 per ticket. Ontario Air pays Brilliant 10% commission on
ticket price.
3. Brilliant’s variable costs are $30 per ticket. Ontario Air pays $46 fixed commission per ticket
to Brilliant. Comment on the results.
4. Brilliant’s variable costs are $30 per ticket. It receives $46 commission per ticket from Ontario
Air. It charges its customers a delivery fee of $8 per ticket. Comment on the results.
SOLUTION
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1a. SP = 10% × $1,300 = $130 per ticket
VCU = $34 per ticket
CMU = $130 – $34 = $96 per ticket
FC = $36,000 a month
Q =
CMU
FC
=
$36,000
$96 per ticket
= 375 tickets
1b. Q =
CMU
TOI FC +
=
$36,000 $12,000
$96 per ticket
+
=
$48,000
$96 per ticket
= 500 tickets
2a. SP = $130 per ticket
VCU = $30 per ticket
CMU = $130 – $30 = $100 per ticket
FC = $36,000 a month
Q =
CMU
FC
=
$36,000
$100 per ticket
= 360 tickets
2b. Q =
CMU
TOI FC +
=
$36,000 $12,000
$100 per ticket
+
=
$48,000
$100 per ticket
= 480 tickets
3a. SP = $46 per ticket
VCU = $30 per ticket
CMU = $46 – $30 = $16 per ticket
FC = $36,000 a month
Q =
CMU
FC
=
$36,000
$16 per ticket
= 2,250 tickets
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3b. Q =
CMU
TOI FC +
=
$36,000 $12,000
$16 per ticket
+
=
$48,000
$16 per ticket
= 3,000 tickets
The reduced commission sizably increases the breakeven point and the number of tickets required
to yield a target operating income of $12,000:
10%
Commission Fixed
(Requirement 2) Commission of $60
Breakeven point 360 2,250
Attain OI of $12,000 480 3,000
4a. The $8 delivery fee can be treated as either an extra source of revenue (as done below) or
as a cost offset. Either approach increases CMU $8:
SP = $54 ($46 + $8) per ticket
VCU = $30 per ticket
CMU = $54 – $30 = $24 per ticket
FC = $36,000 a month
Q =
CMU
FC
=
$36,000
$24 per ticket
= 1,500 tickets
4b. Q =
CMU
TOI FC +
=
$36,000 $12,000
$24 per ticket
+
=
$48,000
$24 per ticket
= 2,000 tickets
The $8 delivery fee results in a higher contribution margin, which reduces both the breakeven
point and the tickets sold to attain operating income of $12,000.
3-19 (20 min.) CVP exercises.
The Incredible Donut owns and operates six doughnut outlets in and around Kansas City. You are
given the following corporate budget data for next year:
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Revenues
$10,400,000
Fixed costs
$ 2,100,000
Variable costs
$ 7,900,000
Variable costs change based on the number of doughnuts sold.
Compute the budgeted operating income for each of the following deviations from the original
budget data. (Consider each case independently.)
Required:
1. An 11% increase in contribution margin, holding revenues constant
2. An 11% decrease in contribution margin, holding revenues constant
3. A 4% increase in fixed costs
4. A 4% decrease in fixed costs
5. A 7% increase in units sold
6. A 7% decrease in units sold
7. An 11% increase in fixed costs and a 11% increase in units sold
8. A 4% increase in fixed costs and a 4% decrease in variable costs
9. Which of these alternatives yields the highest budgeted operating income? Explain why this is
the case.
SOLUTION
Revenues
Variable
Costs
Contribution
Margin
Fixed
Costs
Budgeted
Operating
Income
Orig.
$10,400,000G
$7,900,000G
$2,500,000
$2,100,000G
$400,000
1.
10,400,000
7,625,000
2,775,000a
2,100,000
675,000
2.
10,400,000
8,175,000
2,225,000b
2,100,000
125,000
3.
10,400,000
7,900,000
2,500,000
2,184,000c
316,000
4.
10,400,000
7,900,000
2,500,000
2,016,000d
484,000
5.
11,128,000e
8,453,000f
2,675,000
2,100,000
575,000
6.
9,672,000g
7,347,000h
2,325,000
2,100,000
225,000
7.
11,544,000i
8,769,000j
2,775,000
2,331,000k
444,000
8.
10,400,000
7,584,000l
2,816,000
2,184,000m
632,000
Gstands for given.
a$2,500,000 × 1.11; b$2,500,000 × 0.89; c$2,100,000 × 1.04; d$2,100,000 × 0.96; e$10,400,000 × 1.07;
f$7,900,000 × 1.07; g$10,400,000 × 0.93; h$7,900,000 × 0.93; i$10,400,000 × 1.11; j$7,900,000 × 1.11;
k$2,100,000 × 1.11; l$7,900,000 × 0.96; m$2,100,000 × 1.04
9. Alternative 1, a 11% increase in contribution margin holding revenues constant, yields the
highest budgeted operating income because it has the highest increase in contribution margin
without increasing fixed costs.
3-20 (20 min.) CVP exercises.
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The Doral Company manufactures and sells pens. Currently, 5,000,000 units are sold
per year at $0.50 per unit. Fixed costs are $900,000 per year. Variable costs are $0.30 per unit.
Consider each case separately:
Required:
1. a. What is the current annual operating income?
b. What is the present breakeven point in revenues?
Compute the new operating income for each of the following changes:
2. A $0.04 per unit increase in variable costs
3. A 10% increase in fixed costs and a 10% increase in units sold
4. A 20% decrease in fixed costs, a 20% decrease in selling price, a 10% decrease in variable cost
per unit, and a 40% increase in units sold
Compute the new breakeven point in units for each of the following changes:
5. A 10% increase in fixed costs
6. A 10% increase in selling price and a $20,000 increase in fixed costs
SOLUTION
1a. [Units sold (Selling price – Variable costs)] – Fixed costs = Operating income
[5,000,000 ($0.50 – $0.30)] – $900,000 = $100,000
1b. Fixed costs ÷ Contribution margin per unit = Breakeven units
$900,000 ÷ [($0.50 – $0.30)] = 4,500,000 units
Breakeven units × Selling price = Breakeven revenues
4,500,000 units × $0.50 per unit = $2,250,000
or,
Contribution margin ratio =
price Selling
costs Variable price Selling –
=
$0.50
$0.30 – $0.50
= 0.40
Fixed costs ÷ Contribution margin ratio = Breakeven revenues
$900,000 ÷ 0.40 = $2,250,000
2.
5,000,000 ($0.50 – $0.34) – $900,000
=
$ (100,000)
3.
[5,000,000 (1.1) ($0.50 – $0.30)] – [$900,000 (1.1)]
=
$ 110,000
4.
[5,000,000 (1.4) ($0.40 – $0.27)] – [$900,000 (0.8)]
=
$ 190,000
5.
$900,000 (1.1) ÷ ($0.50 – $0.30)
=
4,950,000 units
6.
($900,000 + $20,000) ÷ ($0.55 – $0.30)
=
3,680,000 units
3-21 (10 min.) CVP analysis, income taxes.
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Brooke Motors is a small car dealership. On average, it sells a car for $27,000, which it purchases
from the manufacturer for $23,000. Each month, Brooke Motors pays $48,200 in rent and utilities
and $68,000 for salespeople’s salaries. In addition to their salaries, salespeople are paid a
commission of $600 for each car they sell. Brooke Motors also spends $13,000 each month for
local advertisements. Its tax rate is 40%.
Required:
1. How many cars must Brooke Motors sell each month to break even?
2. Brooke Motors has a target monthly net income of $51,000. What is its target monthly
operating income? How many cars must be sold each month to reach the target monthly net
income of $51,000?
SOLUTION
1. Monthly fixed costs = $48,200 + $68,000 + $13,000 = $129,200
Contribution margin per unit = $27,000 – $23,000 – $600 = $ 3,400
Breakeven units per month =
Monthly fixed costs
Contribution margin per unit
=
$129,200
$3,400 per car
= 38 cars
2. Tax rate 40%
Target net income $51,000
Target operating income =
Target net income $51,000 $51,000
1 tax rate (1 0.40) 0.60
= = =
−−
$85,000
Quantity of output units
required to be sold
=
Fixed costs + Target operating income $129,200 $85,000
Contribution margin per unit $3,400
+
==
63 cars
3-22 (20–25 min.) CVP analysis, income taxes.
The Swift Meal has two restaurants that are open 24 hours a day. Fixed costs for the two restaurants
together total $456,000 per year. Service varies from a cup of coffee to full meals. The average
sales check per customer is $9.50. The average cost of food and other variable costs for each
customer is $3.80. The income tax rate is 30%. Target net income is $159,600.
Required:
1. Compute the revenues needed to earn the target net income.
2. How many customers are needed to break even? To earn net income of $159,600?
3. Compute net income if the number of customers is 145,000.