chapter
19(4)
Cost Behavior and Cost–
Volume-Profit Analysis
______________________________________________
OPENING COMMENTS
In Chapter 19(4), students learn how to conduct cost-volume-profit analysis. In preparation for this
activity, the chapter discusses variable, fixed, and mixed costs.
Cost-volume-profit analysis is conducted using both a formula-based mathematical approach and a
graphic approach. It is applied to single-product and multiple-product companies. The chapter concludes
with an appendix that discusses variable costing.
After studying the chapter, your students should be able to:
2. Compute the contribution margin, the contribution margin ratio, and the unit contribution margin.
4. Using a cost-volume-profit chart and a profit-volume chart, determine the break-even point and sales
necessary to achieve a target profit.
5. Compute the break-even point for a company selling more than one product, the operating leverage,
and the margin of safety.
KEY TERMS
absorption costing
activity bases (drivers)
break-even point
contribution margin
contribution margin ratio
356 Chapter 19(4) Cost Behavior and Cost-Volume-Profit Analysis
cost behavior
cost-volume-profit analysis
cost-volume-profit chart
fixed costs
high-low method
margin of safety
mixed costs
STUDENT FAQS
• Why does variable cost per unit stay the same but total cost varies with the number of units you
produce?
• How do you choose what activity base to use?
• Why does fixed cost remain the same in total dollar amount but increase or decrease per unit as the
level of activity changes?
• What do increases in fixed cost do to break-even analysis?
• What do increases in variable cost do to break-even analysis?
OBJECTIVE 1
Classify costs as variable costs, fixed costs, or mixed costs.
SYNOPSIS
Cost behavior is the manner in which a cost changes as activity changes. Managers find this relationship
useful as it allows managers to predict profits as sales and production volume change. Activity bases are
the things that cause cost to change, and the range over which the changes are of interest is called the
relevant range. Costs are classified as variable, fixed, or mixed costs. Variable costs are those that change
directly in proportion to changes in production volume. Direct materials and direct labor are usually
variable costs. Variable costs have certain characteristics, such as the cost per unit remains the same and
Chapter 19(4) Cost Behavior and Cost-Volume-Profit Analysis 357
historical data, including units produced and total costs. Subtract the lowest levels of production from the
highest levels of production computed as: variable cost per unit = difference in total cost/difference in
units produced. The fixed cost is then estimated by subtracting the total variable costs from the total fixed
costs, as follows: fixed cost = total costs – (variable cost per unit × units produced). Mixed costs contain a
fixed component even if nothing is produced.
Key Terms and Definitions
• Activity Base (Driver) – A measure of activity that is related to changes in cost. Used in
analyzing and classifying cost behavior. Activity bases are also used in the denominator in
calculating the predetermined factory overhead rate to assign overhead costs to cost objects.
• Cost Behavior – The manner in which a cost changes in relation to its activity base (driver).
• Fixed Costs – Costs that tend to remain the same in amount, regardless of variations in the level
of activity.
Relevant Example Exercises and Exhibits
• Example Exercise 19(4)-1 High-Low Method
• Exhibit 1 – Variable Cost Graphs
• Exhibit 2 – Variable Costs and Their Activity Bases
• Exhibit 3 – Fixed Cost Graphs
• Exhibit 4 – Fixed Costs and Their Activity Bases
• Exhibit 5 – Mixed Costs
• Exhibit 6 – Variable and Fixed Cost Behavior
• Exhibit 7 – Variable, Fixed, and Mixed Cost
SUGGESTED APPROACH
Knowing how costs behave enables management to estimate costs when evaluating alternative operating
proposals. Begin your coverage of this objective by reviewing the definitions of variable, fixed, and
358 Chapter 19(4) Cost Behavior and Cost-Volume-Profit Analysis
Mixed costs have both a fixed and a variable component. An example of a mixed cost is the price paid to
rent a moving van if that price includes a fixed fee plus a charge per mile (i.e., $50 plus $0.30 per mile).
In addition to understanding how costs behave, managers need to know what activities create costs. These
activities are called activity bases (or activity drivers). Ask your students to identify the activity base that
drives their textbook expenditures. (Answer: the number of courses taken)
GROUP LEARNING ACTIVITY—Variable, Fixed, and Mixed Costs
Divide your class into small groups. Ask them to list examples of fixed, variable, and mixed costs
incurred by a McDonald’s restaurant. Encourage them to list as many examples as they can. Also instruct
DEMONSTRATION PROBLEM—High-Low Method
For most business analysis, mixed costs must be separated into their fixed and variable components. Use
the following problem to demonstrate the high-low method.
Once the high and low points have been identified, the variable portion of the cost is determined using the
following equation:
Difference in Total Cost
Variable Cost/Unit Difference in Machine Hours
=
Chapter 19(4) Cost Behavior and Cost-Volume-Profit Analysis 359
Using data from July:
$1,900 = ($0.05/unit 14,000) + Fixed Costs
$1,900 – $700 = Fixed Costs
$1,200 = Fixed Costs
OBJECTIVE 2
Compute the contribution margin, the contribution margin ratio, and the unit contribution
margin.
SYNOPSIS
Cost-volume-profit analysis is useful for managerial decision making. The analysis may be used to
analyze the following: the effects of changes in selling price on profits, the effects of changes in costs of
profits, the effects of changes in volume on profits, how to set prices, how to select the mix of products to
sell, and how to choose marketing strategy. The contribution margin provides insights in to the profit
Key Terms and Definitions
• Contribution Margin – Sales less variable costs and variable selling and administrative
expenses.
• Contribution Margin Ratio – The percentage of each sales dollar that is available to cover the
fixed costs and provide an operating income.
Relevant Example Exercises and Exhibits
• Example Exercise 19(4)-2 Contribution Margin
• Exhibit 8 – Contribution Margin Income Statement Format
SUGGESTED APPROACH
Give students the following formulas related to contribution margin (CM):
CM = Sales – Variable Costs
CM Ratio = CM/Sales
360 Chapter 19(4) Cost Behavior and Cost-Volume-Profit Analysis
Stress that contribution margin is the amount of funds left from a sale after the variable costs have been
paid. Contribution margin is used to pay the fixed costs of the business. Once all fixed costs have been
covered, any contribution margin left represents profit.
GROUP LEARNING ACTIVITY—Contribution Margin
Give your students the following sales and cost data for Van Buren Company. The total sales and cost
information is based on the sale of 20,000 units.
Total Per Unit
Sales $570,000 $28.50
Variable costs $387,600 $19.38
Fixed costs $140,000
Divide the class into small groups. Ask students to compute the total contribution margin, contribution
margin ratio, and unit contribution margin for this company. Also instruct them to compute the increase
in net income that will result from a $50,000 increase in sales and a 1,000-unit increase in sales.
The answers to this exercise are as follows:
2. Contribution margin ratio: 32 percent
4. Increase in net income from $50,000 increase in sales: $50,000 32% = $16,000
5. Increase in net income from 1,000-unit increase in sales: 1,000 $9.12 = $9,120
OBJECTIVE 3
Determine the break-even point and sales necessary to achieve a target profit.
SYNOPSIS
The cost-volume-profit analysis allows a business to determine the break-even point in sales and to
determine the sales needed to make a desired profit. The break-even point is the level of sales at which a
company’s revenues and expenses are equal. It is computed as follows: break-even sales units = fixed
costs/unit contribution margin. This number can also be computed using sales dollars as follows: break-
even sales (dollars) = fixed costs/contribution margin ratio. The break-even point is affected by changes
Chapter 19(4) Cost Behavior and Cost-Volume-Profit Analysis 361
opposite direction. If the sales price increases, the break-even point decreases, and if the sales price
decreases, the break-even point increases. A summary of the effects is shown in Exhibit 13. By modifying
the break-even equation, a business can determine what sales are necessary to achieve a target profit. The
equation is: sales (units) = (fixed costs + target profit)/unit contribution margin.
Key Terms and Definitions
• Break-Even Point – The level of business operations at which revenues and expired costs are
equal.
Relevant Example Exercises and Exhibits
• Example Exercise 19(4)-3 Break-Even Point
• Example Exercise 19(4)-4 Target Profit
• Exhibit 9 – Break-Even Point
SUGGESTED APPROACH
Under this objective, the text presents formulas to calculate the break-even point in units and the unit
sales necessary to achieve a target profit. Use the following lecture notes to explain these formulas.
LECTURE NOTES—Break-Even Point and Target Profit
Although students generally like to use a “formula” in solving accounting problems, they dislike
memorizing them. Remind students that they can use the following formula to solve both break-even and
target profit problems as long as they remember that profit is zero at the break-even point.
Fixed Costs + Target Profit
Sales (units) Unit Contribution Margin
=
Many students benefit from seeing formulas derived from equations they already understand. The text’s
formula can be derived as follows:
362 Chapter 19(4) Cost Behavior and Cost-Volume-Profit Analysis
. . . or (solving for X)
Sales Price (X) – Variable Cost (X) = Fixed Costs + Income from Operations
X (Sales Price – Variable Cost) = Fixed Costs + Income from Operations
X = (Fixed Costs + Income from Operations)/(Sales Price – Variable Cost)
GROUP LEARNING ACTIVITY—Break-Even and Target Profit
One of the true benefits of cost-volume-profit analysis is that a business can analyze a variety of “what-if”
scenarios. TM 19(4)-2 presents several what-ifs for your students to answer in small groups. Solutions are
presented on TM 19(4)-3.
WRITING EXERCISE—Break-Even Point
Ask your students to write an answer to the following questions [TM 19(4)-4]:
Would an increase in variable costs per unit cause a company’s break-even point to
increase or decrease? Why?
OBJECTIVE 4
Using a cost-volume-profit chart and a profit-volume chart, determine the break-even point
and sales necessary to achieve a target profit.
SYNOPSIS
Managers often want to know a business’s profit at multiple sales, costs, and the related profits. To
achieve this, a cost-volume-profit chart is constructed over the relevant range. The horizontal axis of the
Chapter 19(4) Cost Behavior and Cost-Volume-Profit Analysis 363
chart is the sales volume expressed in units; the vertical axis displays the dollar amounts of total sales and
total costs. A total sales line is plotted by connecting the point at zero on the left corner of the graph to a
second point on the chart. A total cost line is plotted by beginning with total fixed costs on the vertical
axis. A second point is determined by multiplying the maximum number of units in the relevant range,
which is found on the far right of the horizontal axis by the unit variable costs and adding the total fixed
Key Terms and Definitions
• Cost-Volume-Profit Chart – A chart used to assist management in understanding the
relationships among costs, expenses, sales, and operating profit or loss.
• Profit-Volume Chart – A chart used to assist management in understanding the relationship
between profit and volume.
Relevant Example Exercises and Exhibits
• Exhibit 14 – Cost-Volume-Profit Chart
• Exhibit 15 – Revised Cost-Volume-Profit Chart
• Exhibit 16 – Profit-Volume Chart
• Exhibit 17 – Original Profit-Volume Chart and Revised Profit-Volume Chart
SUGGESTED APPROACH
The mathematical (formula-based) approach to calculating a break-even point is usually more accurate
than the graphic approach. Most students also find the mathematical approach to be a quicker and easier
way to solve problems. However, because it is important that students learn how to read business graphs,
the graphic approach to break-even analysis deserves attention.
364 Chapter 19(4) Cost Behavior and Cost-Volume-Profit Analysis
GROUP LEARNING ACTIVITY—CVP and PV Charts
Handout 19(4)-1 presents a CVP chart and a PV chart. It also poses several questions to test your
students’ ability to read and interpret these graphs. Distribute copies of the handout to your students and
ask them to work in small groups to answer the questions.
Handout 19(4)-1 solutions:
OBJECTIVE 5
Compute the break-even point for a company selling more than one product, the operating
leverage, and the margin of safety.
SYNOPSIS
The sales mix is the relative distribution of sales among the products sold by a company. For break-even
analysis, it is useful to think of the unit selling price as a constant. The constant is the sum of the unit
selling prices of each product multiplied by the sale mix percentage. The equation using E as the constant
is: break-even sales (units) for E = fixed costs/unit contribution margin. If the sales mix changes, the
Key Terms and Definitions
• Margin of Safety – Indicates the possible decrease in sales that may occur before an operating
loss results.
• Operating Leverage – A measure of the relative mix of a business’s variable costs and fixed
costs, computed as contribution margin divided by operating income.
• Sales Mix – The relative distribution of sales among the various products available for sale.
Relevant Example Exercises and Exhibits
• Example Exercise 19(4)-5 Sales Mix and Break-Even Analysis
Chapter 19(4) Cost Behavior and Cost-Volume-Profit Analysis 365
SUGGESTED APPROACH
Cost-volume-profit analysis can be applied to companies that sell more than one product, as long as their
sales mix is constant. Use the Demonstration Problem to illustrate this modification to basic break-even
analysis.
Ask your students to identify examples of sales mixes for various real-life businesses. An example would
be car dealerships that sell different makes of cars, such as Cadillacs and Buicks.
DEMONSTRATION PROBLEM—Sales Mix
To calculate the break-even point for a company that sells more than one product, a weighted average
contribution margin must be determined. The text illustrates this calculation by multiplying the sales price
and then the unit variable cost by the sales mix percentage and adding these two amounts. The calculation
can also be performed directly on the unit contribution margin.
A weighted average unit contribution margin would be as follows:
$1.50 50% = $0.75
To break even, the company would need to sell 18,000 gift boxes ($27,900/$1.55). Using the sales mix,
the number of each type of gift box can be calculated.
Candy: 18,000 50% = 9,000
Nuts: 18,000 30% = 5,400
366 Chapter 19(4) Cost Behavior and Cost-Volume-Profit Analysis
DEMONSTRATION PROBLEM—Operating Leverage
Operating leverage compares contribution margin to operating income. The formula is:
Ask your students to calculate the operating leverage of a company with $800,000 in sales, $200,000 in
variable costs, and $400,000 in fixed costs.
Operating Leverage = $600,000/$200,000 = 3
An operating leverage of 3 indicates that operating income will increase three times any percentage
increase in sales. For example, if sales increase 5 percent, operating income will increase 15 percent. You
may want to prove this by presenting the follow example.
Original Data + 5% in Sales
Sales $800,000 $840,000
GROUP LEARNING ACTIVITY—Margin of Safety
Explain that margin of safety measures the amount by which current sales exceed sales at the break-even
point. It may be expressed in dollars, in units, or as a percentage. When expressed as a percentage, margin
of safety shows the percentage that sales can drop without resulting in an operating loss. The formula to
calculate margin of safety as a percentage of current sales is as follows:
Chapter 19(4) Cost Behavior and Cost-Volume-Profit Analysis 367
INTERNET ACTIVITY—Review of Chapter Concepts
CCH Business Owner’s Toolkit is an excellent Web site for reviewing cost-volume-profit analysis and
related topics from the chapter. Direct your students to the following Web site:
http://www.toolkit.cch.com/text/P06_7500.asp
APPENDIX—VARIABLE COSTING
SYNOPSIS
GAAP accounting requires absorption costing for financial statements. The previous chapters have shown
absorption costing. Alternative reports may be prepared using variable or direct costing. These are for use
in internal decision making. In variable costing, fixed factory overhead costs do not become a part of the
Key Terms and Definitions
• Absorption Costing – The reporting of the costs of manufactured products, normally direct
materials, direct labor, and factory overhead, as product costs.
Relevant Example Exercises and Exhibits
• Exhibit 21 – Absorption Versus Variable Cost of Goods Manufactured
• Exhibit 22 – Variable Costing Income Statement
• Exhibit 23 – Absorption Costing Income Statement
• Exhibit 24 – Relationship Between Variable and Absorption Costing Income
• Exhibit 25 – Units Manufactured Exceed Units Sold
SUGGESTED APPROACH
368 Chapter 19(4) Cost Behavior and Cost-Volume-Profit Analysis
GROUP LEARNING ACTIVITY—Absorption and Variable Costing
To review absorption costing, ask your students to prepare an income statement for Laurens Incorporated,
using the data on TM 19(4)-7.
TM 19(4)-8 displays Laurens’ income statement under absorption costing. It also shows the company’s
income statement under variable costing. Point out the $30,000 difference in the two income statements.
Ask students to examine the income statements, silently on their own, and look for the reason the
LECTURE AID—Variable Costing
Although variable costing is not permitted for financial reporting, many managers find it useful for
management reporting. Variable costing tends to show costs in the same manner as they are incurred:
variable costs on a per-unit basis and fixed costs in total.
Another benefit of variable costing is the ability to isolate the impact of changes in sales or costs. TM
Handout 19(4)-1
2. What is the company’s
Type Item Description LO(s) Difficulty Time Est BUSPROG AICPA ACBSP – APC Bloom’s EE Excel GL SMH FAI Service Real World Writing Ethics Internet Group
DQ 1 1 Easy 5 min. Analytic Measurement Variable and Fixed Costs Knowledge
DQ 2 1 Easy 5 min. Analytic Measurement Variable and Fixed Costs Knowledge
DQ 3 1 Easy 5 min. Analytic Measurement Variable and Fixed Costs Knowledge
DQ 4 1 Easy 5 min. Analytic Measurement Variable and Fixed Costs Knowledge
DQ 5 2 Easy 5 min. Analytic Measurement Variable and Fixed Costs Knowledge
DQ 6 2 Easy 5 min. Analytic Measurement Contribution Margin Knowledge
DQ 7 3 Easy 5 min. Analytic Measurement Break-even point Knowledge
DQ 8 3 Easy 5 min. Analytic Measurement Break-even point Knowledge
DQ 9 5 Easy 5 min. Analytic Measurement Break-even point Knowledge
DQ 10 5 Easy 5 min. Analytic Measurement Break-even point Knowledge
PE 1A High-low method 1 Easy 10 min. Analytic Measurement Variable and Fixed Costs Application x
PE 1B High-low method 1 Easy 10 min. Analytic Measurement Variable and Fixed Costs Application x
PE 2A Contribution margin 2 Easy 10 min. Analytic Measurement Contribution Margin Application x
PE 2B Contribution margin 2 Easy 10 min. Analytic Measurement Contribution Margin Application x
PE 3A Break-even point 3 Easy 10 min. Analytic Measurement Break-even point Application x
PE 3B Break-even point 3 Easy 10 min. Analytic Measurement Break-even point Application x
PE 4A Target profit 3 Easy 10 min. Analytic Measurement Margin of safety/sales target Application x
PE 4B Target profit 3 Easy 10 min. Analytic Measurement Margin of safety/sales target Application x
PE 5A Sales mix and break-even analysis 5 Easy 10 min. Analytic Measurement Margin of safety/sales target Application x
PE 5B Sales mix and break-even analysis 5 Easy 10 min. Analytic Measurement Margin of safety/sales target Application x
PE 6A Operating leverage 5 Easy 5 min. Analytic Measurement CVP Analysis Application x
PE 6B Operating leverage 5 Easy 5 min. Analytic Measurement CVP Analysis Application x
PE 7A Margin of safety 5 Easy 5 min. Analytic Measurement Margin of safety/sales target Application x
PE 7B Margin of safety 5 Easy 5 min. Analytic Measurement Margin of safety/sales target Application x
EX 1 Classify costs 1 Easy 15 min. Analytic Measurement Variable and Fixed Costs Knowledge
EX 2 Identify cost graphs 1 Easy 15 min. Analytic Measurement CVP Analysis Application
EX 3 Identify activity bases 1 Easy 15 min. Analytic Measurement Managerial Accounting Features/Costs Knowledge
EX 4 Identify activity bases 1 Easy 15 min. Analytic Measurement Managerial Accounting Features/Costs Knowledge
EX 5 Identify fixed and variable costs 1 Easy 15 min. Analytic Measurement Variable and Fixed Costs Knowledge
EX 6 Relevant range and fixed and variable costs 1 Moderate 20 min. Analytic Measurement Variable and Fixed Costs Application x
EX 7 High-low method 1 Easy 15 min. Analytic Measurement Variable and Fixed Costs Application x x
EX 8 High-low method for a service company 1 Moderate 20 min. Analytic Measurement Variable and Fixed Costs Application x x
EX 9 Contribution margin ratio 2 Easy 10 min. Analytic Measurement Contribution Margin Application x
EX 10 Contribution margin and contribution margin ratio 2 Moderate 15 min. Analytic Measurement Break-even point Application x x
EX 11 Break-even sales and sales to realize income from operations 3 Easy 10 min. Analytic Measurement Break-even point Application x
EX 12 Break-even sales 3 Moderate 15 min. Analytic Measurement Break-even point Application x
EX 13 Break-even sales 3 Easy 10 min. Analytic Measurement Break-even point Application x
EX 14 Break-even analysis 3 Easy 10 min. Analytic Measurement Break-even point Application
EX 15 Break-even analysis 3 Moderate 15 min. Analytic Measurement Break-even point Application x
EX 16 Break-even analysis for a service company 3 Moderate 15 min. Analytic Measurement Break-even point Application x x x
EX 17 Cost-volume-profit chart 4 Moderate 20 min. Analytic Measurement CVP Analysis Application x
EX 18 Profit-volume chart 4 Moderate 20 min. Analytic Measurement CVP Analysis Application
EX 19 Break-even chart 4 Moderate 15 min. Analytic Measurement Break-even point Application
EX 20 Break-even chart 4 Moderate 15 min. Analytic Measurement Break-even point Application
EX 21 Sales mix and break-even sales 5 Moderate 15 min. Analytic Measurement Break-even point Application x
EX 22 Break-even sales and sales mix for a service company 5 Moderate 20 min. Analytic Measurement Break-even point Application x
EX 23 Margin of safety 5 Moderate 15 min. Analytic Measurement Margin of safety/sales target Application x
EX 24 Break-even and margin of safety relationships 5 Moderate 10 min. Analytic Measurement Margin of safety/sales target Application x
EX 25 Operating leverage 5 Moderate 15 min. Analytic Measurement CVP Analysis Application x
EX 26 Items on variable costing income statement Appendix Easy 5 min. Analytic Measurement CVP Analysis Application
EX 27 Variable costing income statement Appendix Moderate 15 min. Analytic Measurement CVP Analysis Application x
EX 28 Absorption costing income statement Appendix Moderate 20 min. Analytic Measurement CVP Analysis Application x
PR 1A Classify costs 1 Moderate 45 min. Analytic Measurement Variable and Fixed Costs Application
PR 2A Break-even sales under present and proposed conditions 2,3 Challenging 2 hours Analytic Measurement Break-even point Application x x
PR 3A Break-even sales and cost-volume-profit chart 3,4 Moderate 1 hour Analytic Measurement Break-even point Application
PR 5A Sales mix and break-even sales 5 Easy 1.5 hours Analytic Measurement Break-even point Application x
PR 6A Contribution margin, break-even sales, cost-volume-profit chart, margin of safety, and operating leverage 2,3,4,5 Challenging 1.5 hours Analytic Measurement Contribution Margin Application x
PR 1B Classify costs 1 Moderate 45 min. Analytic Measurement Variable and Fixed Costs Application
PR 2B Break-even sales under present and proposed conditions 2,3 Challenging 2 hours Analytic Measurement Break-even point Application x x
PR 4B Break-even sales and cost-volume-profit chart 3,4 Challenging 1.5 hours Analytic Measurement Break-even point Application
PR 5B Sales mix and break-even sales 5 Easy 1.5 hours Analytic Measurement Break-even point Application x
PR 6B Contribution margin, break-even sales, cost-volume-profit chart, margin of safety, and operating leverage 2,3,4,5 Challenging 1.5 hours Analytic Measurement Contribution Margin Application x
CP 1 Ethics and professional conduct in business 3 Moderate 15 min. Ethics Measurement Break-even point Analysis x x
CP 2 Break-even sales, contribution margin 2,3 Moderate 15 min. Analytic Measurement Break-even point Comprehension x x
CP 3 Break-even analysis 3 Moderate 15 min. Analytic Measurement Break-even point Analysis x
CP 4 Variable costs and activity bases in decision making 3,4 Moderate 30 min. Analytic Measurement Variable and Fixed Costs Analysis x
CP 5 Variable costs and activity bases in decision making 3,4 Challenging 30 min. Analytic Measurement Variable and Fixed Costs Analysis x
CP 6 Break-even analysis 3 Moderate 1 hour Analytic Measurement Break-even point Application x
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