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Chapter 20
Cost Behavior and CostVolume-Profit Analysis
Accounting, 21st Edition
Warren Reeve Fess
PowerPoint Presentation by Douglas Cloud
Professor Emeritus of Accounting
Pepperdine University
© Copyright 2004 South-Western, a division
of Thomson Learning. All rights reserved.
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Objectives
1. Classify costs by their behavior as
After studying this
variable costs, fixed costs, or mixed
chapter, you should
costs.
be able to: margin, the
2. Compute the contribution
contribution margin ratio, and the unit
contribution margin, and explain how
they may be useful to management.
3. Using the unit contribution margin,
determine the break-even point and the
volume necessary to achieve a target
profit.
Objectives
4. Using a cost-volume profit chart and a profitvolume chart, determine the break-even point
and the volume necessary to achieve a
target profit.
5. Calculate the break-even point for a business
selling more than one product.
6. Compute the margin of safety and the
operating leverage, and explain how
managers use this concept.
7. List the assumptions underlying cost-volumeprofit analysis.
Cost Behavior
Variable Cost
Jason Inc. produces stereo sound systems
under the brand name of J-Sound. The parts
for the stereo are purchased from an outside
supplier for $10 per unit (a variable cost).
Variable Cost
Total Costs
Total Variable Cost Graph
$300,000
$250,000
$200,000
$150,000
$100,000
$50,000
0 10 20 30
Units Produced
(in thousands)
Variable Cost
Unit Variable Cost Graph
Cost per Unit
$20
$15
$10
$5
0
10 20 30
Units Produced
(000)
$300,000
$250,000
$200,000
$150,000
$100,000
$50,000
Cost per Unit
Total Costs
Variable Cost
$20
$15
$10
$5
0
10
20
30
Units Produced (000)
0
10
20
30
Units Produced (000)
Number of
Units
Produced
5,000 units
10,000
15,000
20,000
25,000
30,000
Direct
Materials
Cost per Unit
Total Direct
Materials
Cost
$10
10
10
10
10
10
$ 50,000
l00,000
150,000
200,000
250,000
300,000
Fixed Costs
The production
supervisor for Minton
Inc.’s Los Angeles plant
is Jane Sovissi. She is
paid $75,000 per year.
The plant produces from
50,000 to 300,000
bottles of perfume.
La Fleur
Fixed Costs
Number of
Bottles
Produced
Total Salary
for Jane
Sovissi
50,000 bottles
100,000
15,000
20,000
25,000
30,000
$75,000
75,000
75,000
75,000
75,000
75,000
Salary per
Bottle
Produced
$1.500
0.750
0.500
0.375
0.300
0.250
Fixed Costs
Unit Fixed Cost Graph
$150,000
$125,000
$100,000
$75,000
$50,000
$25,000
Cost per Unit
Total Costs
Total Fixed Cost Graph
0
100 200 300
Bottles Produced (000)
Number of
Bottles
Produced
50,000 bottles
100,000
15,000
20,000
25,000
30,000
$1.50
$1.25
$1.00
$.75
$.50
$.25
0
100 200 300
Units Produced (000)
Total Salary
for Jane
Sovissi
Salary per
Bottle
Produced
$75,000
75,000
75,000
75,000
75,000
75,000
$1.500
0.750
0.500
0.375
0.300
0.250
Simpson Inc. manufactures
sails using rented equipment.
The rental charges are
$15,000 per year, plus $1 for
each machine hour used over
10,000 hours.
Mixed Costs
Total Costs
Total Mixed Cost Graph
$45,000
$40,000
$35,000
$30,000
$25,000
$20,000
$15,000
$10,000
$5,000
0
10 20
30
40
Total Machine Hours (000)
Mixed costs are
sometimes called
semivariable or
semifixed costs.
Mixed costs are
usually separated into
their fixed and
variable components
for management
analysis.
Mixed Costs
The high-low method is a simple way
to separate mixed costs into their
fixed and variable components.
High-Low Method
Actual costs incurred
ProductionTotal
(Units) Cost
June
July
August
September
October
1,000 $45,550
1,500 52,000
2,100 61,500
1,800 57,500
750 41,250
What month has
the highest level
of activity in
terms of cost?
Highest level of activity ($) minus
lowest level of activity ($)
Variable cost per unit =
Highest level of activity (n) minus
lowest level of activity (n)
High-Low Method
Actual costs incurred
ProductionTotal
(Units) Cost
June
July
August
September
October
1,000 $45,550
1,500 52,000
2,100 61,500
1,800 57,500
750 41,250
What month has
the highest level
of activity in
terms of cost?
$61,500 minus lowest level of
activity ($)
Variable cost per unit =
Highest level of activity (n) minus
lowest level of activity (n)
High-Low Method
Actual costs incurred
ProductionTotal
(Units) Cost
June
July
August
September
October
1,000 $45,550
1,500 52,000
2,100 61,500
1,800 57,500
750 41,250
For the highest
level of cost,
what is the level
of production?
$61,500 minus lowest level of
activity ($)
Variable cost per unit =
Highest
of lowest
activitylevel
(n) minus
2,100level
minus
of
lowestactivity
level of(n)
activity (n)
High-Low Method
Actual costs incurred
ProductionTotal
(Units) Cost
June
July
August
September
October
1,000 $45,550
1,500 52,000
2,100 61,500
1,800 57,500
750 41,250
What month has
the lowest level of
activity in terms
of cost?
$61,500 minus lowest level of
$57,500
– $41,250
activity
($)
Variable cost per unit =
2,100 2,100
minus –
lowest
750 level of
activity (n)
High-Low Method
Actual costs incurred
ProductionTotal
(Units) Cost
June
July
August
September
October
1,000 $45,550
1,500 52,000
2,100 61,500
1,800 57,500
750 41,250
What is the
variable cost per
unit?
$20,250
$57,500 – $41,250
Variable cost per unit = $15
1,350
2,100
– 750
High-Low Method
Actual costs incurred
ProductionTotal
(Units) Cost
June
July
August
September
October
1,000 $45,550
1,500 52,000
2,100 61,500
1,800 57,500
750 41,250
Variable cost per unit = $15
What is the total
fixed cost (using the
highest level)?
Total cost = (Variable cost per unit x Units of production)
+ Fixed cost
$61,500 = ($15 x 2,100) + Fixed cost
$61,500 = ($15 x 2,100) + $30,000
High-Low Method
Actual costs incurred
ProductionTotal
(Units) Cost
June
July
August
September
October
1,000 $45,550
1,500 52,000
2,100 61,500
1,800 57,500
750 41,250
Variable cost per unit = $15
The fixed cost is
the same at the
lowest level.
Total cost = (Variable cost per unit x Units of production)
+ Fixed cost
$41,250 = ($15 x 750) + Fixed cost
$41,250 = ($15 x 750) + $30,000
Variable Costs
Fixed Costs
Unit costs remain the
sameTotal
per Units
unit Produced
regardless
Review
of activity.
Total costs
increase and
Per Unit Cost
decreases
proportionately
Unit Variable
Costs
with activity level.
Total Costs
Total Fixed Costs
Total costs increase
and decreases with
Total
Units level.
Produced
activity
Unit
Unitcosts
Fixedremain
Costs the
same regardless of
activity.
Per Unit Cost
Total Costs
Total Variable Costs
Total Units Produced
Total Units Produced
Contribution Margin Income Statement
Sales (50,000 units)
Variable costs
Contribution margin
Fixed costs
Income from operations
The contribution
margin is
available to cover
the fixed costs
and income from
operations.
Contribution
$1,000,000
600,000
$ 400,000
300,000
$ 100,000
margin
FIXED
COSTS
Income from
Operations
Contribution Margin Income Statement
Sales (50,000 units)
Variable costs
Contribution margin
Fixed costs
Income from operations
Sales
Sales
$1,000,000
600,000
$ 400,000
300,000
$ 100,000
=
Variable
costs
–
Variable
costs
Income
from
operations
+
Fixed
+
costs
=
Contribution
margin
Contribution Margin Ratio
Sales (50,000 units)
Variable costs
Contribution margin
Fixed costs
Income from operations
$1,000,000
600,000
$ 400,000
300,000
$ 100,000
100%
60%
40%
30%
10%
Sales – Variable costs
Contribution margin ratio =
Sales
$1,000,000 – $600,000
Contribution margin ratio =
$1,000,000
Contribution margin ratio = 40%
Contribution Margin Ratio
Sales (50,000 units)
Variable costs
Contribution margin
Fixed costs
Income from operations
$1,000,000
600,000
$ 400,000
300,000
$ 100,000
100%
60%
40%
30%
10%
$20
12
$ 8
The contribution margin can be expressed three ways:
1. Total contribution margin in dollars.
2. Contribution margin ratio (percentage).
3. Unit contribution margin (dollars per unit).
What is the
break-even
point?
Revenues
=
Break-even
Costs
Calculating the Break-Even Point
Sales (? units)
Variable costs
Contribution margin
Fixed costs
Income from operations
$
?
?
$ 90,000
90,000
$
0
$25
15
$10
At the break-even point, fixed
costs and the contribution
margin are equal.
Calculating the Break-Even Point
In Units
Sales($25
($25xx?9,000)
Sales
units)
$
Variablecosts
costs($15
($15xx?9,000)
Variable
units)
Contributionmargin
margin
Contribution
$
Fixedcosts
costs
Fixed
Incomefrom
fromoperations
operations
Income
$
$225,000
?
135,000
?
$90,000
90,000
90,000
90,000
$
00
$25
15
$10
$90,000
Fixed
costs
Break-even sales (units) = 9,000 units
$10 margin
Unit contribution
PROOF!
Calculating the Break-Even Point
In Units
Sales ($250 x ? units)
$
?
Variable costs ($145 x ? units)
?
Contribution margin
$
?
Fixed costs
840,000
Income from operations
$
0
$250
145
$105
$840,000
Fixed
costs
Break-even sales (units) = 8,000 units
$105 margin
Unit contribution
The unit selling price is $250 and unit variable
cost is $145. Fixed costs are $840,000.
Calculating the Break-Even Point
In Units
Sales ($25 x ?Next,
units) assume$
?
variable
Variable costs
($15 x ?costs
units) is
?
Contribution
margin by $5.
$
?
increased
Fixed costs
840,000
Income from operations
$
0
$250
145
150
$105
$100
$840,000
Fixed
costs
Break-even sales (units) = 8,400 units
$100 margin
Unit contribution
The unit selling price is $250 and unit variable
cost is $145. Fixed costs are $840,000.
Calculating the Break-Even Point
In Units
Sales
Variable costs
Contribution margin
Fixed costs
Income from operations
$
?
?
$
?
$600,000
$
0
$50
30
$20
$600,000
Fixed
costs
Break-even sales (units) = 30,000 units
$20 margin
Unit contribution
A firm currently sells their product at $50 per
unit and it has a related unit variable cost of
$30. The fixed costs are $600,000.
Calculating the Break-Even Point
In Units
Management increases
Salesthe selling price from
$
Variable costs
$50 to $60.
Contribution margin
Fixed costs
Income from operations
?
?
$
?
$600,000
$
0
$60
$50
30
$30
$20
$600,000
Fixed
costs
Break-even sales (units) = 20,000 units
$30 margin
Unit contribution
Summary of Effects of Changes on
Break-Even Point
Target Profit
Sales (? units)
Variable costs
Contribution margin
Fixed costs
Income from operations
$
?
?
$
?
200,000
$
0
In
Units
$75
45
$35
Fixed costs are estimated at $200,000, and the
desired profit is $100,000. The unit selling
price is $75 and the unit variable cost is $45.
The firm wishes to make a $100,000 profit.
Target Profit
Sales (? units)
Variable costs
Contribution margin
Fixed costs
Income from operations
$
?
?
$
?
200,000
$
0
In
Units
Target profit is
$75 here to refer
used
to45“Income from
$35
operations.”
Fixed
costs ++desired
profit
$200,000
$100,000
Sales (units) = 10,000 units
Unit contribution
margin
$30
Target Profit
Sales (10,000 units x $75)
$750,000
Variable costs (10,000 x $45) 450,000
Contribution margin
$300,000
Fixed costs
200,000
Income from operations
$100,000
$75
45
$30
Proof that sales of 10,000 units
will provide a profit of $100,000.
Graphic Approach to
Cost-Volume-Profit
Analysis
Sales and Costs ($000)
Cost-Volume-Profit Chart
$500
$450
$400
$350
$300
$250
$200
$150
$100
$ 50
0
Total Sales
Variable
Costs
60%
1
2
3
4
5
6
7
Units of Sales (000)
Unit selling price
$ 50
Unit variable cost
30
Unit contribution margin
$ 20
Total fixed costs
$100,000
8
9 10
Sales and Costs ($000)
Cost-Volume-Profit Chart
$500
$450
$400
$350
$300
$250
$200
$150
$100
$ 50
0
Contribution
Margin
40%
60%
1
2
3
4
5
6
7
Units of Sales (000)
Unit selling price
$ 50 100%
Unit variable cost
30 60%
Unit contribution margin
$ 20 40%
Total fixed costs
$100,000
8
9 10
Sales and Costs ($000)
Cost-Volume-Profit Chart
$500
$450
$400
$350
$300
$250
$200
$150
$100
$ 50
0
Total
Costs
Fixed Costs
1
2
3
4
5
6
7
Units of Sales (000)
Unit selling price
$ 50 100%
Unit variable cost
30 60%
Unit contribution margin
$ 20 40%
Total fixed costs
$100,000
8
9 10
Sales and Costs ($000)
Cost-Volume-Profit Chart
$500
$450
$400
$350
$300
$250
$200
$150
$100
$ 50
0
Break-Even Point
1
2
3
4
5
6
7
Units of Sales (000)
Unit selling price
$ 50 100%
Unit variable cost
30 60%
Unit contribution margin
$ 20 40%
Total fixed costs
$100,000
8
9 10
$100,000
= 5,000 units
$20
Sales and Costs ($000)
Cost-Volume-Profit Chart
$500
$450
$400
$350
$300
$250
$200
$150
$100
$ 50
0
Operating Profit Area
Operating Loss Area
Units of Sales (000)
Unit selling price
$ 50 100%
Unit variable cost
30 60%
Unit contribution margin
$ 20 40%
Total fixed costs
$100,000
Operating Profit
(Loss) $000’s
$100
$75
$50
$25
$ 0
$(25)
$(50)
$(75)
$(100)
1
2
3
4
5
6
7
Relevant
range is
8 10,000
9 10 units
Units of Sales (000’s)
Sales (10,000 units x $50)
Variable costs (10,000 units x $30)
Contribution margin (10,000 units x $20)
Fixed costs
Operating profit
$500,000
300,000
$200,000
100,000
$100,000
Operating Profit
(Loss) $000’s
$100
$75
$50
$25
$ 0
$(25) Operating
loss
$(50)
$(75)
$(100)
1
2 3
Profit Line
Operating
profit
4
5
6
7
Units of Sales (000’s)
Maximum loss is
equal (10,000
to the total
Sales
units x $50)
fixed costs.
Variable
costs (10,000 units x $30)
Contribution margin (10,000 units x $20)
Fixed costs
Operating profit
8
9
Maximum
profit within
the relevant
10 range.
$500,000
300,000
$200,000
100,000
$100,000
Operating Profit
(Loss) $000’s
$100
$75
$50
$25
$ 0
$(25) Operating
loss
$(50)
$(75)
$(100)
1
2 3
Operating
profit
Break-Even Point
4
5
6
7
8
9 10
Units of Sales (000’s)
Sales (10,000 units x $50)
Variable costs (10,000 units x $30)
Contribution margin (10,000 units x $20)
Fixed costs
Operating profit
$500,000
300,000
$200,000
100,000
$100,000
Sales Mix
Considerations
Cascade Company sold 8,000 units of Product A
and 2,000 units of Product B during the past year.
Cascade Company’s fixed costs are $200,000.
Other relevant data are as follows:
Products
A
B
Sales
$ 90 $140
Variable costs
70
95
Contribution margin
$ 20 $ 45
Sales mix
80% 20%
Sales Mix Considerations
Sales
Variable costs
Contribution margin
Sales mix
Product contribution
margin
Products
A
B
$ 90 $140
70
95
$ 20 $ 45
80% 20%
$16
$ 9
$25
Fixed costs, $200,000
Sales Mix Considerations
Product contribution
margin
Products
A
B
$16
$ 9
$25
Break-even sales units
$200,000
$25
Fixed costs, $200,000
Sales Mix Considerations
Product contribution
margin
Products
A
B
$16
$ 9
$25
Break-even sales units
$200,000
$25
= 8,000 units
Fixed costs, $200,000
Sales Mix Considerations
Product contribution
margin
Products
A
B
$16
$ 9
$25
A: 8,000 units x Sales Mix (80%) =
B: 8,000 units x Sales Mix (20%) =
6,400
1,600
Product A Product B
Sales:
6,400 units x $90
1,600 units x $140
Total sales
Variable costs:
6,400 x $70
1,600 x $95
Total variable costs
Contribution margin
Fixed costs
Income from operations
$576,000
$576,000
$224,000
$224,000
$576,000
224,000
$800,000
$152,000
$152,000
$ 72,000
$448,000
152,000
$600,000
$200,000
$448,000
$448,000
$128,000
Break-even point
PROOF
Total
200,000
$
0
Margin
of Safety
Margin of Safety =
Sales – Sales at break-even point
Margin of Safety =
Sales
$250,000 – $200,000
$250,000
Margin of Safety = 20%
The margin of safety indicates the
possible decrease in sales that may occur
before an operating loss results.
Operating Leverage
Operating Leverage
Sales
Variable costs
Contribution margin
Fixed costs
Income from operations
Contribution margin
Jones Inc.
$400,000
300,000
$100,000
80,000
$ 20,000
?
Wilson Inc.
$400,000
300,000
$100,000
50,000
$ 50,000
?
Both companies have the same contribution margin.
Contribution margin
Income from operations
Operating Leverage
Sales
Variable costs
Contribution margin
Fixed costs
Income from operations
Contribution margin
Jones Inc.:
Jones Inc.
$400,000
300,000
$100,000
80,000
$ 20,000
5.0
$100,000margin
Contribution
Income $20,000
from operations
Wilson Inc.
$400,000
300,000
$100,000
50,000
$ 50,000
?
= 5.0
Operating Leverage
Sales
Variable costs
Contribution margin
Fixed costs
Income from operations
Contribution margin
Jones Inc.
Jones Inc.
$400,000
300,000
$100,000
80,000
$ 20,000
5.0
$100,000margin
Contribution
Income $20,000
from operations
Wilson Inc.
$400,000
300,000
$100,000
50,000
$ 50,000
?
= 5.0
Operating Leverage
Sales
Variable costs
Contribution margin
Fixed costs
Income from operations
Contribution margin
Jones Inc.
$400,000
300,000
$100,000
80,000
$ 20,000
5.0
Wilson Inc.
$400,000
300,000
$100,000
50,000
$ 50,000
2.0
Capital
intensive?
Wilson Inc.:
Contribution
$100,000margin
Income $50,000
from operations
Labor
intensive?
= 2.0
Assumptions of Cost-Volume-Profit Analysis
The reliability of cost-volume-profit analysis
depends upon several assumptions.
1. Total sales and total costs can be represented
by straight lines.
2. Within the relevant range of operating
activity, the efficiency of operations does
not change.
3. Costs can be accurately divided into fixed
and variable components.
4. The sales mix is constant.
5. There is no change in the inventory
quantities during the period.
Chapter 20
The End