978-1337119207 Chapter 19 Part 2

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Chapter 19(5) Cost-Volume-Profit Analysis 363

. . . 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)

X = (Fixed Costs + Income from Operations)/Unit Contribution Margin

Note: “Target profit” is a company’s desired income from operations.

In reality, students also can solve break-even and target profit problems using the equation:

Sales Price (X) – Variable Cost (X) – Fixed Costs = Income from Operations. Some of your students will

find this equation easiest to remember and use.

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(5)-2 presents several what-ifs for your students to answer in small groups. Solutions are

presented on TM 19(5)-3.

WRITING EXERCISE—Break-Even Point

Ask your students to write an answer to the following questions [TM 19(5)-4]:

Would an increase in variable costs per unit cause a company’s break-even point to

increase or decrease? Why?

Possible response: An increase in variable costs will cause the break-even point in unit

sales to increase. An increase in variable costs leaves less contribution margin to apply

toward fixed costs, requiring more units to be sold to cover the fixed costs.

Would an increase in per-unit selling price cause a company’s break-even point to

increase or decrease? Why?

Possible response: An increase in sales price will cause the break-even point in unit sales

to decrease. An increased sales price provides additional contribution margin to cover

fixed costs, requiring fewer sales to break even.

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(5) Cost-Volume-Profit Analysis 364

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

costs. Another useful chart is the profit-volume chart; it plots only the difference between total sales and

total costs. This chart allows managers to determine the operating profit (or loss) for various levels of

units sold. This graphic approach is made easier by computers. Managers can vary assumptions regarding

selling process, costs, and volume and observe the effects of each change on the break-even point and

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 Check Up Corner and Exhibits

 Exhibit 14—Cost-Volume-Profit Chart

 Exhibit 15—Revised Cost-Volume-Profit Chart

 Exhibit 16—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.

Exhibit 16 illustrates a profit-volume (PV) chart. A profit line is plotted on a PV chart. The break-even

point occurs where the profit line intersects the zero horizontal profit line. This represents the point where

profits equal zero.

volume (PV) charts.

Chapter 19(5) Cost-Volume-Profit Analysis 365

GROUP LEARNING ACTIVITY—CVP and PV Charts

Handout 19(5)-1 solutions:

Chart 1: Question—See Exhibit 14 in the text for sales and cost line identification; Question 2—40,000

units; Question 3—$40,000; Question 4—Variable cost $.50 per unit [VC = ($60,000 –

$40,000)/40,000)]; Question 5—profit at 80,000 units is $40,000 [CM × (Unit Sales – Break-Even Units)]

OR [($1 × (80,000 – 40,000)]

Break-Even Units)] OR [1.67 × (30,000 – 15,000)]

OBJECTIVE 5

Compute the break-even point for a company selling more than one product, the operating

leverage, and the margin of safety.

SYNOPSIS

contribution margin/income from operations. The difference between contribution margin and income

from operations is fixed costs. The impact of a change in sales on income from operations for companies

with high and low operating leverage is summarized in Exhibit 20. The margin of safety indicates the

possible decrease in sales that may occur before an operating loss results. It may be expressed as dollars

break-even point/sales.

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

Relevant Check Up Corner and Exhibits

 Exhibit 18—Multiple Product Sales Mix

Chapter 19(5) Cost-Volume-Profit Analysis 366

 Exhibit 19—Break-Even Sales: Multiple Products

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.

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.

as follows:

Unit Contribution Margin Sales Mix

Candy $1.50 50%

Nuts $2.00 30%

Cookies $1.00 20%

$1.50  50% = $0.75

$2.00  30% = 0.60

$1.00  20% = 0.20

$1.55

Candy: 18,000  50% = 9,000

Nuts: 18,000  30% = 5,400

Cookies: 18,000  20% = 3,600

18,000

Chapter 19(5) Cost-Volume-Profit Analysis 367

DEMONSTRATION PROBLEM—Operating Leverage

Operating leverage compares contribution margin to operating income. The formula is:

Contribution Margin

Operating Leverage Operating Income



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

Original Data + 5% in Sales

Sales $800,000 $840,000

Variable costs 200,000 210,000

Contribution margin $600,000 $630,000

Fixed costs 400,000 400,000

Operating income $200,000 $230,000

$30,000

15% increase

$200,000



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:

Sales Sales at Break-Even Point

Margin of Safety Sales





Chapter 19(5) Cost-Volume-Profit Analysis 368

ADM OBJECTIVE

service business.

SYNOPSIS

The break-even point is as relevant in a service company as it is in a manufacturing company. The cost–

volume-profit relationship in a service company is measured with respect to customers and activities,

rather than to units of product. The process of break-even analysis for a service company involves

are defined as fixed or variable.

Relevant Check Up Corner and Exhibits

 Make a Decision – Cost-Volume-Profit Analysis for Service Companies

Handout 19(5)-1

1. Identify the sales

and cost lines.

2. What is the break-

even point in units?

3. What is the

company’s total

fixed cost?

4. What is the

company’s variable

cost per unit?

5. What is the

company’s profit at

sales of 80,000

units?

1. What is this

company’s break–

even point in units?

2. What is the company’s

total fixed cost?

3. What is the company’s

profit at sales of

30,000 units?

Type Item Description Video Excel CLGL LO(s) Difficulty Time Est BUSPROG AICPA

ACBSP – Primary Bloom’s ADM Service Real World

Writing

Ethics

MC 1 1 Easy 5 min. Analytic FN – Measurement Variable and Fixed Costs Remembering

MC 2 2 Easy 5 min. Analytic FN – Measurement Contribution Margin Applying

MC 3 3 Easy 5 min. Analytic FN – Measurement Break-even point Applying

MC 4 4 Easy 5 min. Analytic FN – Measurement Break-even point Applying

MC 5 5 Easy 5 min. Analytic FN – Measurement CVP Analysis Applying

LREX 1 High-low method x 1 Easy 10 min. Analytic FN – Measurement Variable and Fixed Costs Applying

LREX 2 Contribution margin x 2 Easy 10 min. Analytic FN – Measurement Contribution Margin Applying

LREX 3 Break-even point x 3 Easy 10 min. Analytic FN – Measurement Break-even point Applying

LREX 4 Target profit x 3 Easy 10 min. Analytic FN – Measurement Margin of safety/sales target Applying

LREX 5 Sales mix and break-even analysis x 5 Easy 10 min. Analytic FN – Measurement Margin of safety/sales target Applying

LREX 6 Operating leverage x 5 Easy 5 min. Analytic FN – Measurement CVP Analysis Applying

LREX 7 Margin of safety x 5 Easy 5 min. Analytic FN – Measurement Margin of safety/sales target Applying

PP Problem n/a Challenging 1 hour Analytic FN – Measurement CVP Analysis Applying

DQ 1 n/a Easy 5 min. Analytic FN – Measurement Variable and Fixed Costs Remembering

DQ 2 n/a Easy 5 min. Analytic FN – Measurement Variable and Fixed Costs Remembering

DQ 3 n/a Easy 5 min. Analytic FN – Measurement Variable and Fixed Costs Remembering

DQ 4 n/a Easy 5 min. Analytic FN – Measurement Variable and Fixed Costs Remembering

DQ 5 n/a Easy 5 min. Analytic FN – Measurement Variable and Fixed Costs Remembering

DQ 6 n/a Easy 5 min. Analytic FN – Measurement Contribution Margin Remembering

DQ 7 n/a Easy 5 min. Analytic FN – Measurement Break-even point Remembering

DQ 8 n/a Easy 5 min. Analytic FN – Measurement Break-even point Remembering

BE 5 Sales mix and break-even analysis x 5 Easy 10 min. Analytic FN – Measurement Margin of safety/sales target Applying

BE 6 Operating leverage x 5 Easy 5 min. Analytic FN – Measurement CVP Analysis Applying

BE 7 Margin of safety x 5 Easy 5 min. Analytic FN – Measurement Margin of safety/sales target Applying

EX 1 Classify costs 1 Easy 15 min. Analytic FN – Measurement Variable and Fixed Costs Remembering

EX 8 High-low method for a service company x 1 Moderate 20 min. Analytic FN – Measurement Variable and Fixed Costs Applying x

EX 9 Contribution margin ratio x 2 Easy 10 min. Analytic FN – Measurement Contribution Margin Applying

EX 10 Contribution margin and contribution margin ratio x 2 Moderate 15 min. Analytic FN – Measurement Break-even point Applying x

EX 11 Break-even sales and sales to realize income from operations x 3 Easy 10 min. Analytic FN – Measurement Break-even point Applying

EX 18 Profit-volume chart 4 Moderate 20 min. Analytic FN – Measurement CVP Analysis Applying

EX 19 Break-even chart 4 Moderate 15 min. Analytic FN – Measurement Break-even point Applying

EX 20 Break-even chart 4 Moderate 15 min. Analytic FN – Measurement Break-even point Applying

EX 21 Sales mix and break-even sales x 5 Moderate 15 min. Analytic FN – Measurement Break-even point Applying

PR 3A Break-even sales and cost-volume-profit chart 3,4 Moderate 1 hour Analytic FN – Measurement Break-even point Applying

PR 4A Break-even sales and cost-volume-profit chart 3,4 Challenging 1.5 hours Analytic FN – Measurement Break-even point Applying

PR 5A Sales mix and break-even sales 5 Easy 1.5 hours Analytic FN – Measurement Break-even point Applying x

PR 6A

Contribution margin, break-even sales, cost-volume-profit chart, margin o

x 2,3,4,5 Challenging 1.5 hours Analytic FN – Measurement Contribution Margin Applying

Contribution margin, break-even sales, cost-volume-profit chart, margin o

ADM 1 Break-even number of passengers for a cruise ADM Moderate 30 min. Analytic FN – Measurement CVP Analysis Analyzing x x

ADM 2 Break-even subscribers for a video service ADM Moderate 20 min. Analytic FN – Measurement CVP Analysis Analyzing x

ADM 3 Break-even number of guests for a theme park ADM Moderate 30 min. Analytic FN – Measurement CVP Analysis Analyzing x

TIF 1 Ethics in action n/a Easy 15 min. Ethics FN – Reporting CVP Analysis Analyzing x x

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