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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
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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