CHAPTER 5
Cost-Volume-Profit Analysis
Learning Objectives
After studying this chapter, you will be able to:
1. Understand the Cost-Volume-Profit (CVP) relation.
2. Use the CVP relation to plan profit.
3. Make short-term decisions using CVP analysis.
4. Measure risk using the CVP relation.
5. Perform CVP analysis with multiple products.
6. List the assumptions underlying CVP analysis.
Overview
How many tickets do the Chicago Cubs need to sell for a game to break even? How much will
profit increase if Starbucks sells another 1 million cups of coffee a year? When facing lower than
expected demand, would reducing the selling price be more profitable for Nike than increasing
advertising? Cost-Volume-Profit analysis, the focus of this chapter, is the tool we use to answer
such questions. We begin this chapter by examining the Cost-Volume- Profit (CVP) relation. We
then show you how to use the CVP relation for profit planning and for evaluating the profit
impact of short-term decisions. Following this, we extend the CVP relation to include multiple
products. Finally, we discuss the limitations of CVP analysis.
Learning Objective 1
Understand the Cost-Volume-Profit (CVP) relation.
The Cost-Volume-Profit (CVP) Relation
1. The Cost-Volume-Profit (CVP) relation follows directly from the contribution margin
statement that we studied in Chapter 4.
2. In this statement, we calculated profit by subtracting variable costs and fixed costs from
revenue.
3. Both revenues and variable costs are proportional to sales volume.
4. Revenues equal the number of units sold multiplied by the price per unit. Likewise,
variable costs equal the number of units sold multiplied by the unit variable cost.
5. Combining these observations, we can rearrange this profit equation to highlight the
Cost- Volume- Profit relation:
Profit before taxes = [(Price - Unit variable cost) x Sales volume in units] - Fixed costs
6. This expression captures the essence of the CVP relation because it relates sales volume
with profit and costs.
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7. Next, we define Unit contribution margin = Price - Unit variable cost. Using this
definition, we have:
Profit before taxes = (Unit contribution margin x Sales volume in units) - Fixed costs
= Contribution margin - Fixed costs
8. This final expression emphasizes that contribution margin is the appropriate measure for
evaluating short-term decisions.
9. Because fixed costs generally do not change in the short term, increasing contribution
margin increases profit by an identical amount.
10. For every unit sold, profit increases by an amount equal to the unit contribution margin.
How Firms Use the CVP Relation
Exhibit 5.3 shows that a relatively modest increase in sales volume leads to a substantial increase
in profit.
Learning Objective 2
Use the CVP relation to plan profit.
The CVP Relation and Profit Planning
Breakeven Volume
1. Breakeven volume is the sales volume at which profit equals zero.
2. As sales volume increases, total costs increase proportionally due to the variable costs
associated with making and selling products.
3. If the total costs line is steeper than the revenues line, the two lines will never meet—
profit will always be negative.
4. Thus, to have any chance of making a profit, a firm must have a positive unit contribution
margin; that is, price must exceed the unit variable cost.
5. The greater the unit contribution margin, the steeper the profit line and the more the
firm’s profit increases for a given increase in sales volume.
6. A positive unit contribution margin by itself does not guarantee profit, however.
7. The firm must sell enough units so that the contribution margin at least covers fixed
costs.
Breakeven Revenues
1. Organizations frequently prefer to express the breakeven point in terms of revenues rather
than in terms of units.
2. Ultimately, managers focus on dollars and the bottom line rather than on physical units.
3. Breakeven revenues are the sales dollars needed to break even:
Breakeven revenues = Breakeven volume x Price
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4. The contribution margin ratio is the portion of every sales dollar that remains after
covering variable costs—it is the portion that contributes toward covering fixed costs
and, ultimately, to profit.
5. We can calculate the contribution margin ratio either using unit-level data or using total
revenues and variable costs.
Target Profit
1. Organizations frequently specify annual, quarterly, and monthly profit goals for their
product and divisional managers.
2. These goals guide managers’ actions during the period.
3. Managers can use the CVP relation to answer important questions about profit.
4. The unit contribution margin or ratio is used to answer those questions.
CVP Analysis and Taxes
1. Taxes are an unavoidable part of doing business. As a result, firms usually are interested
in earning a target profit after taxes.
2. We can readily modify the CVP relation to include taxes:
Profit after taxes =
Profit before taxes - (Profit before taxes x Tax rate) = Profit before taxes x (1 - Tax rate)
3. Taxes reduce profit by a certain percentage beyond the breakeven point.
4. In Exhibit 5.7, we see that, above the breakeven point, the slope of the profit line
decreases by the taxes paid.
Learning Objective 3
Make short-term decisions using CVP analysis.
Using the CVP Relation to Make Short-Term Decisions
In addition to planning profits, the CVP relation helps organizations make short-term decisions.
Using the CVP Relation to Evaluate Price Changes
1. In most markets, increases in price reduce sales volume.
2. Conversely, retail companies such as J.C. Penney, Mattress Firm, and Sears reduce prices
in an effort to stimulate sales.
3. Thus far, we have not taken this “inverse” relation between price and sales volume into
account.
4. At low prices, increasing prices to raise contribution overcomes the effect of lost demand.
5. As prices increase even more, the demand loss overcomes the effect of gaining more
contribution from each unit sold.
6. It should be noted that reducing the price too much could hurt profit.
7. CVP analysis allows firms to evaluate the trade-off between price and quantity, and their
effect on profit.
8. Price reductions may pay off in the short term, but they often are not beneficial in the
long term.
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Learning Objective 4
Measure risk using the CVP relation.
Using the CVP Relation to Evaluate Operating Risk
1. A key question that can be answered is whether acquiring the new technology will
increase profit.
2. Adding more equipment (technology) can increase profits.
3. However, this option also changes the cost structure and can add to fixed costs.
4. Firms are usually reluctant to add to fixed costs because they represent a sure outflow.
5. In contrast, actual revenues and variable costs are uncertain because their amounts
depend on the actual demand.
6. Thus, the new technology could subject a firm to greater risk.
7. How should we evaluate the risk arising from a firm’s choice of cost structure? In this
section, we discuss two common measures of operating risk. These two measures—
margin of safety and operating leverage—originate from the CVP relation.
8. Two measures originating from the CVP relation, margin of safety and operating
leverage can be used to evaluate the risks arising from a firm’s choice of cost structure.
Margin of Safety
1. The CVP relation allows firms to evaluate risk by considering the amount by which
expected sales exceeds breakeven sales.
2. We refer to this cushion, expressed in percentage terms, as the firm’s margin of safety.
3. The formula is shown below:
Margin of safety

Sales in units - Breakeven volume
Sales in units

Revenues - Breakeven revenue s
Revenues
4. By reducing the breakeven point, and thereby increasing the margin of safety, the new
technology lowers Sierra’s operating risk at the expected level of operations.
5. In general, the higher the margin of safety, the lower the risk of a loss should actual sales
fall short of expectations.
6. There is no hard and fast rule on what is an appropriate margin of safety. It varies from
industry to industry and from firm to firm.
7. In industries with stable demand conditions, a small margin of safety might be enough to
reduce the risk of losses to acceptable levels.
8. Conversely, firms that face highly variable demand conditions might require high
margins of safety.
Margin of Safety and Profit Sensitivity
1. As we saw in Exhibit 5.3, a small change in sales can have a large impact on profit.
2. The effect is particularly large for sales volumes near the breakeven point, where margins
of safety are very low.
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Operating Leverage
1. By their choice of technology, firms can influence the proportion of fixed and variable
costs they incur.
2. Typically, firms with higher fixed costs have lower variable costs and, hence, higher
contribution margins.
3. However, at lower volumes, higher fixed costs impose higher risk because they result in
greater total costs.
4. Moreover, the greater the fixed cost, the more sensitive is profit to changes in volume.
5. Exhibit 5.13 is useful for understanding this trade-off between fixed and variable costs.
6. Firms use operating leverage as a measure of risk arising from having more fixed costs.
7. We calculate operating leverage as follows:
Operating leverage

Fixed costs
Fixed costs  Variable costs

Fixed costs
Total costs
8. In general, we prefer the technology with a smaller operating leverage at lower sales
volumes and technology with a larger operating leverage at higher volumes.
Learning Objective 5
Perform CVP analysis with multiple products.
Multiproduct CVP Analysis
1. CVP analysis can be extended to settings in which a firm makes multiple products or
many versions of the same product.
2. Because products share resources such as the plant, equipment, and supervisors, and such
costs are fixed in the short term, it does not make sense to allocate or assign these fixed
costs to any particular product.
3. CVP analysis is performed by taking into consideration all products at once as a group.
4. CVP analysis with many products is essentially the same as for a single product.
5. Like the single-product CVP relation, the multiproduct CVP relation also stems from the
contribution margin statement.
6. However, each of a firm’s many products usually has a different unit contribution margin
(There is a need for a segment contribution margin statement).
Profit Planning with Multiple Products
There are two equivalent methods for performing multiproduct CVP analysis: the weighted unit
contribution margin method and the weighted contribution margin ratio method.
Weighted Unit Contribution Margin Method
1. In a multiproduct CVP analysis, the weighted unit contribution margin is simply the
contribution margin per average unit.
2. We can also calculate the weighted unit contribution margin using unit-level data.
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Weighted Contribution Margin Ratio Method
1. Comparing contribution margin ratios across products often makes more sense than
comparing unit contribution margins.
2. Firms often use different units for their products.
3. We can always compare contribution margin ratios because they represent the fraction of
each sales dollar that goes toward covering fixed costs and profit.
Making Decisions Using CVP Analysis
1. Decisions may not reinforce each other’s profit impact.
2. Expanding the analysis to include every possible combination of stand-alone options
usually is not advisable.
3. Combining each choice with every other choice rapidly expands the opportunity set.
4. Good managers excel in narrowing their choices to those that complement each other and
are most promising.
Learning Objective 6
List the assumptions underlying CVP analysis.
CVP Analysis—A Critical Evaluation
1. The CVP relation crisply captures how revenues, costs, and profit vary as the volume of
business varies.
2. It enables decision makers to assess how much volume they need to avoid a loss (break
even) or to maintain a certain margin of safety.
3. Moreover, CVP analysis is useful for numerous short-term decisions related to pricing,
advertising, cost structure, and more. However, any decision tool is only as good as the
assumptions needed to make it work.
4. Consequently, we need to understand the assumptions underlying CVP analysis and the
extent to which they are likely to be valid.
5. The assumptions are as follows:
a. Revenues increase proportionally with sales volume.
b. Variable costs increase proportionally with sales volume.
c. Selling prices, unit variable costs, and fixed costs are known with certainty.
d. Single-period analysis.
e. Product-mix assumptions.
f. CVP analysis does not always provide the “best” solutions to short-term
decisions.
g. Availability of capacity.
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CHAPTER 5 REVIEW QUESTIONS
TRUE/FALSE
1. The CVP relation follows directly from the contribution margin statement.
2. Unit contribution margin equals unit selling price less unit variable cost less fixed cost.
3. The contribution margin is the appropriate measure for evaluating long-term decisions.
4. At the breakeven volume, the firm makes zero profit, which means that revenues equal total
costs.
5. If the Sun's contribution margin equals $1,000,000 and its revenues are $1,500,000, then its
contribution margin ratio is .5667 or 56.67%
6. Two common measures of operating risk are margin of safety and operating leverage.
7. The weighted unit contribution margin method is not one of the equivalent methods for
performing multiproduct CVP analysis.
MULTIPLE CHOICE
1. What is Savannah Market's profit before tax using the following information: price = $30,
unit variable cost = $15, sales volume in units = 50,000, and fixed costs = $250,000.
A. $1,250,000
B. $750,000
C. $500,000
D. ($200,000)
2. Which of the following is not an assumption underlying CVP analysis?
A. The typical CVP analysis assumes that all revenues and costs occur in a single period.
B. CVP analysis is a tool that helps managers improve profit by answering "what if"
questions.
C. With many products, CVP analysis assumes a known and constant product mix.
D. The CVP analysis assumes the unit variable cost is constant and does vary with sales
volume.
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3. Using the CVP Relation to evaluate operating risk, what are the two most common measures?
A. Margin of Safety and Weighted Unit Contribution Margin Method.
B. Margin of Safety and Operating Leverage
C. Operating Leverage and Product Mix.
D. Operating Leverage and Weighted Unit Contribution Margin Method.
4. Suppose Max's Shuttle Service wants to earn a profit before taxes of $375,000 in the coming
year. Max's selling price is $40, its variable cost per unit is $20, and its fixed costs are $150,000.
How many tickets must the company sell?
A. 26,520
B. 26,250
C. 18,750
D. 11,250
5. Which is a true statement when performing CVP analysis with multiple products?
A. CVP analysis is performed by taking into consideration all products at once as a group.
B. CVP analysis can be extended to settings in which a firm makes multiple products or
many versions of the same product.
C. Like the single-product CVP relation, the multiproduct CVP relation also stems from the
income statement.
D. A and B Only.
6. In a multiproduct CVP analysis, the weighted unit contribution margin is simply the:
A. contribution margin per average unit.
B. contribution margin per variable unit.
C. profit margin per average unit.
D. contribution margin per fixed unit.
7. A firm performs CVP analysis for three primary purposes:
A. calculating measures that help assess operating risk
B. evaluating the profit impact of short-term decision alternatives
C. profit planning
D. All of the Above
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8. Using the following information for Max's Mattresses, Inc.:
Description
Standard
Deluxe
Expected product mix (in units)
50
35
Proportion of each product mix
75%
25%
Unit Contribution Margin
$200
$550
The weighted unit contribution margin for Max's Mattresses, Inc. is:
A. $287.50
B. $278.50
C. $375.00
D. $462.50
9. If revenues are $450,000, breakeven revenues are $200,000, and fixed costs are $100,000, the
margin of safety is
A. 33.33%
B. 44.44%
C. 55.56%
D. 22.22%
10. A firm reported a contribution margin equal to 45% of revenues and profit before taxes
equal to 20% of revenues. If fixed costs were $100,000, what were the firm's revenues?
A. $400,000
B. $500,000
C. $222,222
D. $153,846
MATCHING
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1.
Match the items below by entering the appropriate code letter in the space provided.
A.
B.
C.
D.
E.
____ 1.
Unit Contribution Margin
Breakeven Revenues
Operating Leverage
Product Mix
Margin of Safety
F.
G.
H.
I.
J.
Breakeven Revenues
Contribution Margin Ratio
Weighted Unit Contribution Margin
Weighted Contribution Margin Ratio
Breakeven Volume
Selling price per unit less variable cost per unit.
____ 2. The sales volume in units at which profit equals zero.
____ 3.
The percentage by which current sales exceed break even sales.
____ 4. Fixed costs divided by total costs.
____ 5. The sales volume in units at which profit equals zero.
____ 6. Represents the portion of each sales dollar that, after covering variable costs, goes
toward covering fixed costs and, ultimately, profit.
____ 7.
The proportion, expressed in units, in which products are expected to be sold.
____ 8.
Unit contribution margin averaged across multiple products, with each product's unit
contribution margin being weighted by the product mix.
____ 9. Fixed costs divided by contribution margin ratio.
____ 10.
One of the equivalent methods for performing multiproduct CVP analysis.
SHORT PROBLEMS
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1. D&C Company manufacturing piping. At a volume of 20,000 units, per-unit price and cost
data for the year just ended follow:
Item
Selling Price
Variable manufacturing costs
Fixed manufacturing costs
Gross Margin
Variable selling costs
Fixed selling and administrative costs
Profit Margin
Value per Unit
$100
$40
$25
$35
$ 5
$10
$20
Required
What is D&C Company's breakeven point?
2. Mike's Cycle Shop sells a variety of bikes for all ages, as well as biking gear and accessories.
Although its products are considerably more expensive than those available at department stores,
Mike's Cycle Shop has a loyal clientele willing to pay a premium price for premium quality. In a
typical month, Mike Cycle Shop generates revenue of $25,000 and earns a profit of $4,750.
Mike's Cycle Shop's contribution margin is 35%.
Required
a. What is Mike's Cycle Shop's margin of safety at its current sales level?
b. What is Mike's Cycle Shop's operating leverage?
CHAPTER 5 REVIEW QUESTIONS ANSWER KEY
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TRUE/FALSE
1. L01 – True
2. L01 – False
3. L01 – False
4. L02 – True
5. L02 – False
6. L04 – True
7. L05 – False
MULTIPLE CHOICE
1. L01 – C; [(30-15) x 50,000] - 250,000 = $500,000
2. L06 – D
3. L04 – B
4. L02 – B; 375,000 = [($40-$20) x Sales Volume in units (tickets) - $150,000
5. L05 – D
6. L05 – A
7. L01 – D
8. L05 – A; (.75 x $200) + (.25 x $550) = $287.50
9. L04 – C; ($450,000 - $200,000) / $450,000 = 55.56%
10. L01 – A; Profit before taxes = .20 * Revenues (fact 1) = 45*Revenues – $100,000 (fact 2).
Setting these equations equal to each other… Revenues = $100,000/.25 = $400,000.
MATCHING
1.
2.
3.
4.
5.
A
J
E
C
B
6.
7.
8.
9.
10.
G
D
H
F
I
SHORT PROBLEMS
1. L01:
First, we need to calculate unit contribution and fixed costs. We have unit contribution =
(price – variable costs) = ($100 - $40 - $5) = $55. At a volume of 20,000 units, fixed
costs are $25 + $10 = $35 per unit, or $700,000 in total.
Then, from the profit equation:
0 = unit contribution × breakeven volume – fixed costs
0 = $55 per unit × breakeven volume - $700,000
Breakeven volume = $700,000 / $55 per unit = 12,727 units.
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SHORT PROBLEMS (CONT.)
2. L04:
We first need to determine Mike's Cycle Shop's breakeven sales. Using the contribution
margin ratio to write the profit equation, we have:
Profit before taxes = (Contribution margin ratio  Revenue) – Fixed costs.
Because we do not know Mike's Cycle Shop's fixed costs, we first have to use the model
to “back out” fixed costs and then derive breakeven sales. Accordingly,
$4,750 = (0.35  $25,000) – Fixed costs
Fixed costs = $4,000
Next, setting target profit equal to $0 will allow us to calculate breakeven revenue:
$0 = (0.35  Breakeven revenue) – $4,000
Breakeven revenue = $11,429 (rounded)
Mike's Cycle Shop's Margin of Safety =
( $25,000 - $11,429 ) = 54.28%.
$25,000
In dollars, the margin of safety equals $25,000 – $11,429 = $13,571.
a. Operating leverage = Fixed costs/Total costs.
We know that the contribution margin (in dollars) = Contribution margin ratio 
Revenue. Thus, we have:
Contribution margin = 0.35  25,000 = $8,750.
Because contribution margin = revenues – variable costs, variable costs can be calculated
as $16,250. Given that fixed costs are $4,000, the total costs are $20,250.
Consequently, Operating Leverage = fixed costs / total costs
= $4,000/$20,250 = 0.198 (rounded)
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