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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 Define cost–volume–profit analysis.
Cost-volume-profit (CVP) analysis examines the behavior of total revenues, total costs, and
3-2 Describe the assumptions underlying CVP analysis.
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.
3-3 Distinguish between operating income and net income.
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 –
3-4 Define contribution margin, contribution margin per unit, and contribution margin
percentage.
3-5 Describe three methods that managers can use to express CVP relationships.
Three methods to express CVP relationships are the equation method, the contribution margin
3-6 Why is it more accurate to describe the subject matter of this chapter as CVP analysis
rather than as breakeven analysis?
Breakeven analysis denotes the study of the breakeven point, which is often only an incidental
3-7 “CVP analysis is both simple and simplistic. If you want realistic analysis to underpin
your decisions, look beyond CVP analysis.” Do you agree? Explain.
CVP certainly is simple, with its assumption of output as the only revenue and cost driver, and
3-8 How does an increase in the income tax rate affect the breakeven point?
An increase in the income tax rate does not affect the breakeven point. Operating income at the
3-9 Describe sensitivity analysis. How has the advent of the electronic spreadsheet affected
the use of sensitivity analysis?
Sensitivity analysis is a “what-if” technique that managers use to examine how an outcome will
3-10 Give an example of how a manager can decrease variable costs while increasing fixed
costs.
Examples of decreasing variable costs and increasing fixed costs include:
3-11 Give an example of how a manager can increase variable costs while decreasing fixed
costs.
Examples of decreasing fixed costs and increasing variable costs include:
3-12 What is operating leverage? How is knowing the degree of operating leverage helpful to
managers?
Operating leverage describes the effects that fixed costs have on changes in operating income as
3-13 “There is no such thing as a fixed cost. All costs can be ‘unfixed’ given sufficient time.”
Do you agree? What is the implication of your answer for CVP analysis?
CVP analysis is always conducted for a specified time horizon. One extreme is a very short-time
3-14 How can a company with multiple products compute its breakeven point?
A company with multiple products can compute a breakeven point by assuming there is a
3-15 “In CVP analysis, gross margin is a less-useful concept than contribution margin.” Do
you agree? Explain briefly.
3-16 Jack’s Jax has total fixed costs of $25,000. If the company’s contribution margin is 60%,
the income tax rate is 25% and the selling price of a box of Jax is $20, how many boxes of Jax
would the company need to sell to produce a net income of $15,000?
a. 5,625 b. 4,445
c. 3,750 d. 3,333
SOLUTION
Choice "c" is correct. The number of boxes needed to be sold is calculated as follows:
Selling Price per box: $20 per box
Total fixed costs $25,000 + target operating income, $20,000 = $45,000
Boxes necessary to produce target operating income: $45,000 / $12 per box = 3,750 boxes
Choice "a" is incorrect. The contribution margin of 60% means that variable costs are 40% of the
sale price, not 60% of the sales price.
3-17 During the current year, XYZ Company increased its variable SG&A expenses while
keeping fixed SG&A expenses the same. As a result, XYZ’s:
a. Contribution margin and gross margin will be lower.
b. Contribution margin will be higher, while its gross margin will remain the same.
c. Operating income will be the same under both the financial accounting income statement and
contribution income statement.
d. Inventory amounts booked under the financial accounting income statement will be lower than
under the contribution income statement.
SOLUTION
Choice "c" is correct. Operating income is the bottom line figure under both the financial
Choice "a" is incorrect. The contribution margin will be lower due to an increase in variable
Choice "b" is incorrect. The gross margin will remain the same, as SG&A expenses do not factor
3-18 Under the contribution income statement, a company’s contribution margin will be:
a. Higher if fixed SG&A costs decrease.
b. Higher if variable SG&A costs increase.
c. Lower if fixed manufacturing overhead costs decrease.
d. Lower if variable manufacturing overhead costs increase.
SOLUTION
Choice "d" is correct. An increase in any variable costs will cause the contribution margin to be
Choice "a" is incorrect. Fixed SG&A costs do not factor into the contribution margin calculation.
3-19 A company needs to sell 10,000 units of its only product in order to break even. Fixed
costs are $110,000, and the per unit selling price and variable costs are $20 and $9, respectively.
If total sales are $220,000, the company’s margin of safety will be equal to:
a. $0 b. $20,000
c. $110,000 d. $200,000
SOLUTION
Choice "b" is correct. The margin of safety is equal to total actual sales − breakeven sales dollars.
Choice "a" is incorrect. There is no margin of safety when total sales are equal to breakeven
Choice "c" is incorrect. The margin of safety is incorrectly calculated here as total sales − fixed
3-20 Once a company exceeds its breakeven level, operating income can be calculated by
multiplying:
a. The sales price by unit sales in excess of breakeven units.
b. Unit sales by the difference between the sales price and fixed cost per unit.
c. The contribution margin ratio by the difference between unit sales and breakeven sales.
d. The contribution margin per unit by the difference between unit sales and breakeven sales.
SOLUTION
Choice "d" is correct. The contribution margin per unit represents the difference between sales
Choice "a" is incorrect. This equation does not take into account the variable costs per unit that
3-21 CVP computations. Fill in the blanks for each of the following independent cases.
SOLUTION
(10 min.) CVP computations.
Variable Fixed Total Operating Contribution Contribution
Revenues Costs Costs Costs Income Margin Margin %
a. $2,400 $ 600 $200 $ 800 $1,600 $1,800 75%
b. 2,500 1,400 200 1,600 900 1,100 44%
c. 500 300 200 500 0 200 40%
d. 1,200 900 200 1,100 100 300 25%
3-22 CVP computations. Garrett Manufacturing sold 410,000 units of its product for $68 per
unit in 2017. 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.
SOLUTION
(10–15 min.) CVP computations.
1a. Sales ($68 per unit × 410,000 units) $27,880,000
1b. Contribution margin (from above) $3,280,000
2a. Sales (from above) $27,880,000
2b. Contribution margin $5,740,000
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
3-23 CVP analysis, changing revenues and costs. Sunset Travel Agency specializes in flights
between Toronto and Jamaica. It books passengers on Hamilton Air. Sunset’s fixed costs are
$23,500 per month. Hamilton Air charges passengers $1,500 per round-trip ticket.
Calculate the number of tickets Sunset must sell each month to (a) break even and (b) make a
target operating income of $10,000 per month in each of the following independent cases.
Required:
1. Sunset’s variable costs are $43 per ticket. Hamilton Air pays Sunset 6% commission on ticket
price.
2. Sunset’s variable costs are $40 per ticket. Hamilton Air pays Sunset 6% commission on ticket
price.
3. Sunset’s variable costs are $40 per ticket. Hamilton Air pays $60 fixed commission per ticket
to Sunset. Comment on the results.
4. Sunset’s variable costs are $40 per ticket. It receives $60 commission per ticket from
Hamilton Air. It charges its customers a delivery fee of $5 per ticket. Comment on the results.
SOLUTION
(35–40 min.) CVP analysis, changing revenues and costs.
1a. SP = 6% × $1,500 = $90 per ticket
2b. Q =
CMU
TOI FC
=
$23,500 $10,000
$50 per ticket
+
=
$33,500
$50 per ticket
= 670 tickets
3a. SP = $60 per ticket
VCU = $40 per ticket
CMU = $60 – $40 = $20 per ticket
FC = $23,500 a month
Q =
CMU
FC
=
$23,500
$20 per ticket
= 1,175 tickets
3b. Q =
CMU
TOI FC
=
$23,500 $10,000
$20 per ticket
+
=
$33,500
$20 per ticket
= 1,675 tickets
The reduced commission sizably increases the breakeven point and the number of tickets
required to yield a target operating income of $10,000:
6%
Commission Fixed
(Requirement 2) Commission of $60
Breakeven point 470 1,175
4a. The $5 delivery fee can be treated as either an extra source of revenue (as done below) or
as a cost offset. Either approach increases CMU $5:
SP = $65 ($60 + $5) per ticket
Q =
CMU
FC
=
$23,500
$25 per ticket
= 940 tickets
4b. Q =
CMU
TOI FC
=
$23,500 $10,000
$25 per ticket
+
=
$33,500
$25 per ticket
= 1.340 tickets
The $5 delivery fee results in a higher contribution margin, which reduces both the breakeven
point and the tickets sold to attain operating income of $10,000.
3-24 CVP exercises. The Deli-Sub Shop owns and operates six stores in and around
Minneapolis. You are given the following corporate budget data for next year:
Revenues $11,000,000
Fixed costs $ 3,000,000
Variable costs $ 7,500,000
Variable costs change based on the number of subs sold.
Compute the budgeted operating income for each of the following deviations from the original
budget data. (Consider each case independently.)
Required:
1. A 10% increase in contribution margin, holding revenues constant
2. A 10% decrease in contribution margin, holding revenues constant
3. A 5% increase in fixed costs
4. A 5% decrease in fixed costs
5. A 5% increase in units sold
6. A 5% decrease in units sold
7. A 10% increase in fixed costs and a 10% increase in units sold
8. A 5% increase in fixed costs and a 5% decrease in variable costs
9. Which of these alternatives yields the highest budgeted operating income? Explain why this
is the case.
