Cost-Volume-Profit Analysis
Chapter 18
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Wild, Shaw, and Chiappetta
Financial & Managerial Accounting
6th Edition
Copyright © 2016 McGraw-Hill Education. All rights reserved. No
reproduction or distribution without the prior written consent of
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18-C1: Fixed Costs
2
Identifying Cost Behavior
Cost-volume-profit analysis is used to answer questions
such as:
– How much does income increase if we install a
new machine to reduce labor costs?
– What is the change in income if selling prices
decline and sales volume increases?
– How will income change if we change the sales
mix of our products or services?
– What sales volume is needed to earn a target
income?
C1
3
Fixed Costs
C1
4
Variable Costs
C1
5
Mixed Costs
C1
6
Step-Wise Costs
Total cost increases to a new higher cost for the next higher range of
activity, but remains constant within a range of activity.
C1
7
Curvilinear Costs
C1
Costs that increase when activity
increases, but in a nonlinear manner.
8
NEED-TO-KNOW
Determine whether each of the following is best described as a fixed, variable, mixed, step-wise, or curvilinear
cost with respect to product units.
Rubber used to manufacture tennis balls
$0.50 per tennis ball
Depreciation (straight-line method)
Electricity cost
Supervisory salaries
A salesperson’s commission is 7% for sales of up to $100,000, and
10% of sales for sales above $100,000
Variable cost
$0.50 per tennis ball - Variable
$6,000
Total Cost
$5,000
$4,000
$3,000
$2,000
$1,000
$0
0
2,000
4,000
6,000
8,000
10,000
Units Produced
C1
9
NEED-TO-KNOW
Determine whether each of the following is best described as a fixed, variable, mixed, step-wise, or curvilinear
cost with respect to product units.
Rubber used to manufacture tennis balls
$0.50 per ball
Depreciation (straight-line method)
$2,000 per month
Electricity cost
Supervisory salaries
A salesperson’s commission is 7% for sales of up to $100,000, and
10% of sales for sales above $100,000
Variable cost
Fixed cost
$2,000 per month - Fixed
$2,500
Total Cost
$2,000
$1,500
$1,000
$500
$0
0
2,000
4,000
6,000
8,000
10,000
Units Produced
C1
10
NEED-TO-KNOW
Determine whether each of the following is best described as a fixed, variable, mixed, step-wise, or curvilinear
cost with respect to product units.
Rubber used to manufacture tennis balls
$0.50 per ball
Depreciation (straight-line method)
$2,000 per month
Electricity cost
$500 + $0.10 per ball
Supervisory salaries
A salesperson’s commission is 7% for sales of up to $100,000, and
10% of sales for sales above $100,000
Variable cost
Fixed cost
Mixed cost
$500 + $0.10 per unit- Mixed
$1,600
$1,400
Total Cost
$1,200
$1,000
$800
$600
$400
$200
$0
0
2,000
4,000
6,000
8,000
10,000
Units Produced
C1
11
NEED-TO-KNOW
Determine whether each of the following is best described as a fixed, variable, mixed, step-wise, or curvilinear
cost with respect to product units.
Rubber used to manufacture tennis balls
$0.50 per ball
Depreciation (straight-line method)
$2,000 per month
Electricity cost
$500 + $0.10 per ball
Supervisory salaries 4,000 units per shift
$5,000 per mo. per supervisor
A salesperson’s commission is 7% for sales of up to $100,000, and
10% of sales for sales above $100,000
Variable cost
Fixed cost
Mixed cost
Step-wise cost
$5,000 per supervisor per month - Step-wise
$16,000
$14,000
$12,000
Total Cost
$10,000
$8,000
$6,000
$4,000
$2,000
$0
0
2,000
4,000
6,000
8,000
10,000
Units Produced
C1
12
NEED-TO-KNOW
Determine whether each of the following is best described as a fixed, variable, mixed, step-wise, or curvilinear
cost with respect to product units.
Rubber used to manufacture tennis balls
$0.50 per ball
Depreciation (straight-line method)
$2,000 per month
Electricity cost
$500 + $0.10 per ball
Supervisory salaries 4,000 units per shift
$5,000 per mo. per supervisor
A salesperson’s commission is 7% for sales of up to $100,000, and
10% of sales for sales above $100,000
Variable cost
Fixed cost
Mixed cost
Step-wise cost
Curvilinear cost
Sales Commissions - Curvilinear
$30,000
$25,000
Total Cost
$20,000
$15,000
$10,000
$5,000
$0
$0
$50,000
$100,000
$150,000
$200,000
$250,000
$300,000
Sales $
C1
13
18-P1: Measuring Cost Behavior
14
Measuring Cost Behavior
The objective is to classify all costs as either fixed
or variable. We will look at three methods:
1. Scatter diagrams.
2. The high-low method.
3. Least–squares regression.
A scatter diagram is a plot of cost data points on a
graph. It is almost always helpful to plot cost data to
be able to observe a visual picture of the relationship
between cost and activity.
P1
15
Scatter Diagrams
P1
16
The High-Low Method
The following relationships between units
produced and total cost are observed:
P1
Using these two levels of activity, compute:
 the variable cost per unit.
 the total fixed cost.
17
The High-Low Method
High activity level - October
Low activity level - February
Change in activity
P1
Units
67,500
17,500
50,000
Cost
$ 29,000
20,500
$ 8,500
Total cost = $17,525 + $0.17 per unit produced
18
Least-Squares Regression
Least-squares regression is usually covered
in advanced cost accounting courses. It is
commonly used with spreadsheet programs
or calculators.
The objective of the cost
analysis remains the
same: determination of
total fixed cost and the
variable unit cost.
P1
19
Comparison of Cost Estimation
Methods
P1
20
NEED-TO-KNOW
Using the information below, use the high-low method to determine the cost equation
(total fixed costs plus variable costs per unit).
Activity
Level
Lowest
Highest
Units
Total Cost
Produced
1,600
$9,800
4,000
17,000
Variable Cost = Cost at high point - Cost at low point
Units at high point - Units at low point
($17,000 - $9,800)
(4,000 - 1,600)
$7,200
2,400
$3 per unit produced
Fixed Costs (at high point)
Total cost = Fixed costs + $3 per unit
$17,000 = Fixed costs + ($3 x 4,000)
$5,000 = Fixed costs
Fixed Costs (at low point)
Total cost = Fixed costs + $3 per unit
$9,800 = Fixed costs + ($3 x 1,600)
$5,000 = Fixed costs
Total costs = $5,000 + $3 per unit
P1
21
NEED-TO-KNOW
Slope = Variable Cost $3 per unit
y-intercept = Fixed Costs $5,000
Total Cost = $5,000 + $3 per unit
$18,000
(4,000 units, $17,000)
$16,000
Total Cost
$14,000
$12,000
$10,000
(1,600 units, $9,800)
$8,000
$6,000
(0 units, $5,000)
$4,000
$2,000
$0
0
500
1,000
1,500
2,000
2,500
3,000
3,500
4,000
4,500
Units Produced
P1
22
18-A1: Contribution Margin and
Its Measures
23
Contribution Margin and Its
Measures
A1
24
18-P2: Computing the BreakEven Point
25
Using Break-Even Analysis
The break-even point (expressed in
units of product or dollars of sales) is the
unique sales level at which a company
earns neither a profit nor incurs a loss.
P2
26
Computing the Break-Even Point
P2
27
Computing the Margin of Safety
P2
28
NEED-TO-KNOW
A manufacturer predicts fixed costs of $400,000 for the next year. Its one product sells for $170 per unit,
and it incurs variable costs of $150 per unit. The company predicts total sales of 25,000 units for the next
year.
1. Compute the contribution margin per unit.
$20 per unit
2. Compute the break-even point (in units).
3. Compute the margin of safety (in dollars).
Contribution margin per unit, or unit contribution margin, is the amount by which a
product’s unit selling price exceeds its total variable cost per unit.
Sales
Variable costs
Contribution margin
P2
$170 per unit
150 per unit
$ 20 per unit
29
NEED-TO-KNOW
A manufacturer predicts fixed costs of $400,000 for the next year. Its one product sells for $170 per unit,
and it incurs variable costs of $150 per unit. The company predicts total sales of 25,000 units for the next
year.
1. Compute the contribution margin per unit.
$20 per unit
2. Compute the break-even point (in units).
20,000 units
3. Compute the margin of safety (in dollars).
Break-even point in units =
Fixed costs
Contribution margin per unit
$400,000
$20 per unit
20,000 units to break-even
Sales
Variable costs
Contribution margin
Fixed costs
Net income
P2
Units
20,000
20,000
per unit
Total
$170 $3,400,000
$150 3,000,000
$20
400,000
400,000
$0
30
NEED-TO-KNOW
A manufacturer predicts fixed costs of $400,000 for the next year. Its one product sells for $170 per unit,
and it incurs variable costs of $150 per unit. The company predicts total sales of 25,000 units for the next
year.
1. Compute the contribution margin per unit.
$20 per unit
2. Compute the break-even point (in units).
20,000 units
3. Compute the margin of safety (in dollars).
$850,000
The excess of expected sales over the break-even sales
level is called a company’s margin of safety
Expected sales
Break-even sales
Margin of safety
P2
Units
25,000
20,000
per unit
Total
$170 $4,250,000
$170 3,400,000
$850,000
31
18-P3: Preparing a Cost-VolumeProfit Chart
32
Preparing a CVP Chart
P3
33
Working with Changes
in Estimates
P3
34
18-C2: Applying Cost-VolumeProfit Analysis
35
Computing Income
from Sales and Costs
C2
36
Computing Sales
for a Target Income
C2
37
Computing Sales
for a Target Income
C2
38
Computing Sales
for a Target Income
C2
39
NEED-TO-KNOW
A manufacturer predicts fixed costs of $502,000 for the next year. Its one product sells for $180 per unit,
and it incurs variable costs of $126 per unit. Its target income (pretax) is $200,000.
1. Compute the contribution margin ratio. 30%
2. Compute the dollar sales needed to yield the target income.
3. Compute the unit sales needed to yield the target income.
The contribution margin ratio is the percent of a unit’s selling price that exceeds total
unit variable cost.
Contribution margin ratio =
Contribution margin per unit
Selling price per unit
$180 - $126
$180
$54
$180
30%
Sales
Variable costs
Contribution margin
C2
per unit
$180
126
$54
Ratio
100%
70%
30%
40
NEED-TO-KNOW
A manufacturer predicts fixed costs of $502,000 for the next year. Its one product sells for $180 per unit,
and it incurs variable costs of $126 per unit. Its target income (pretax) is $200,000.
1. Compute the contribution margin ratio. 30%
2. Compute the dollar sales needed to yield the target income. $2,340,000
3. Compute the unit sales needed to yield the target income.
Dollar sales to achieve target income = Fixed costs + Pretax Income
Contribution margin ratio
$502,000 + $200,000
.30
$2,340,000
Sales
Variable costs
Contribution margin
Fixed costs
Net income
C2
per unit
$180
$126
$54
Ratio
100%
70%
30%
Total
$2,340,000
1,638,000
702,000
502,000
$200,000
41
NEED-TO-KNOW
A manufacturer predicts fixed costs of $502,000 for the next year. Its one product sells for $180 per unit,
and it incurs variable costs of $126 per unit. Its target income (pretax) is $200,000.
1. Compute the contribution margin ratio. 30%
2. Compute the dollar sales needed to yield the target income. $2,340,000
3. Compute the unit sales needed to yield the target income. 13,000 units (or $2,340,000 / $180)
Units
to yield
target
income
Break-even
point
in units
==
Fixed costs
target (pretax) income
Fixed +costs
Contribution
margin
unit
Contribution
margin
perper
unit
$502,000 + $200,000
$180 - $126
$702,000
$54
13,000 units
Sales
Variable costs
Contribution margin
Fixed costs
Net income
C2
Units
13,000
13,000
per unit
$180
$126
$54
Total
$2,340,000
1,638,000
702,000
502,000
$200,000
42
Using Sensitivity Analysis
C2
43
18-P4: Computing a
Multiproduct Break-Even Point
44
Computing a Multiproduct
Break-Even Point
The CVP formulas can be modified for use
when a company sells more than one product.
 The unit contribution margin is replaced with the
contribution margin for a composite unit.
 A composite unit is composed of specific numbers
of each product in proportion to the product sales
mix.
 Sales mix is the ratio of the volumes of the various
products.
P4
45
Computing a Multiproduct
Break-Even Point
The resulting break-even formula
for composite unit sales is:
Break-even point
in composite units
=
Fixed costs
Contribution margin
per composite unit
Continue
P4
46
Computing a Multiproduct
Break-Even Point
Hair-Today offers three cuts as shown below. Annual fixed
costs are $192,000. Compute the break-even point in
composite units and in number of units for each haircut at the
given sales mix.
Selling Price
Variable Cost
Unit Contribution
Sales Mix Ratio
P4
Haircuts
Basic
Ultra
Budget
$ 20.00 $ 32.00 $ 16.00
13.00
18.00
8.00
$ 7.00 $ 14.00 $ 8.00
4
2
1
47
Computing a Multiproduct
Break-Even Point
Haircuts
Basic
Ultra
Selling Price
$ 20.00 $ 32.00
Sales Mix Ratio
4.00
2.00
Selling Price/cut
$ 80.00 $ 64.00
Total Selling Price/Composite Unit
P4
Budget
$ 16.00
1.00
$ 16.00
$ 160.00
48
Computing a Multiproduct
Break-Even Point
Haircuts
Basic
Ultra
Variable Costs
$ 13.00 $ 18.00
Sales Mix Ratio
4.00
2.00
Selling Price/cut
$ 52.00 $ 36.00
Total Variable Cost/Composite Unit
P4
Budget
$
8.00
1.00
$
8.00
$ 96.00
49
Computing a Multiproduct
Break-Even Point
=
Fixed costs
Contribution margin
per composite unit
Break-even point
in composite units
=
$192,000
$64.00 per
composite unit
Break-even point
in composite units
=
3,000 composite units
Break-even point
in composite units
P4
50
Computing a Multiproduct
Break-Even Point
Sales Composite
Product Mix
Cuts
Haircuts
Basic
4
×
3,000
= 12,000
Ultra
2
×
3,000
=
6,000
Budget
1
×
3,000
=
3,000
Total
21,000
P4
51
Multiproduct Break-Even
Income Statement
P4
52
NEED-TO-KNOW
The sales mix of a company’s two products, X and Y, is 2:1. Unit variable costs for both products
are $2, and unit selling prices are $5 for X and $4 for Y. The company has $640,000 of fixed costs.
1. What is the contribution margin per composite unit? $8
2. What is the break-even point in composite units?
3. How many units of X and how many units of Y will be sold at the break-even point?
Selling price per composite unit
Product X
Product Y
Total
Units
2
1
3
per unit
$5
$4
Total
$10
4
$14
Variable cost per composite unit
Product X
Product Y
Total
Units
2
1
3
per unit
$2
$2
Total
$4
2
$6
Contribution margin per composite unit ($14 - $6)
P4
$8
53
NEED-TO-KNOW
The sales mix of a company’s two products, X and Y, is 2:1. Unit variable costs for both products
are $2, and unit selling prices are $5 for X and $4 for Y. The company has $640,000 of fixed costs.
1. What is the contribution margin per composite unit? $8
2. What is the break-even point in composite units?
80,000 composite units
3. How many units of X and how many units of Y will be sold at the break-even point?
Break-even point in composite units =
Fixed costs
Contribution margin per composite unit
$640,000
$8 per composite unit
80,000 composite units to break even
P4
54
NEED-TO-KNOW
The sales mix of a company’s two products, X and Y, is 2:1. Unit variable costs for both products
are $2, and unit selling prices are $5 for X and $4 for Y. The company has $640,000 of fixed costs.
1. What is the contribution margin per composite unit? $8
2. What is the break-even point in composite units?
80,000 composite units
3. How many units of X and how many units of Y will be sold at the break-even point?
Units of each product at break-even
Product X 80,000 composite units x 2 units per composite unit
Product Y
80,000 composite units x 1 unit per composite unit
Total Sales
Product X
Product Y
Total
Units
160,000
80,000
240,000
per unit
$5
$4
Total
$800,000
320,000
$1,120,000
Total Variable Costs
Product X
Product Y
Total
Units
160,000
80,000
240,000
per unit
$2
$2
Total
$320,000
160,000
$480,000
Composite units
80,000
80,000
per unit
$14
$6
$8
Total
$1,120,000
480,000
640,000
640,000
$0
Sales
Variable costs
Contribution margin
Fixed costs
Net income
P4
Total
160,000
80,000
240,000
55
Global View
Over 90 percent of German companies
surveyed report their cost accounting systems
focus on contribution margin. This focus helps
German companies like Volkswagen control
costs and plan their production levels.
56
18-A2: Degree of Operating
Leverage
57
Degree of Operating Leverage
A measure of the extent to which fixed costs
are being used in an organization.
A measure of how a percentage change in
sales will affect profits.
A2
58
Operating Leverage
Rydell Company
Sales (1,200 units)
Less: variable expenses
Contribution margin
Less: fixed expenses
Pretax income
$120,000
84,000
36,000
24,000
$ 12,000
If Rydell increases sales by 10 percent, what will the
percentage increase in income be?
A2
59
Appendix 18A: Using Excel to
Estimate Least-Squares Regression
60
End of Chapter 18
61