1
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Cost Behavior
and CostVolume-Profit
Analysis
4
1
2
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Objective 1
4-1
Classify costs by their
behavior as variable
costs, fixed costs, or
mixed costs.
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3
Jason Inc.’s Waterloo Plant
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4-1
Jason Inc. produces stereo sound
systems under the brand name of JSound. The parts for the J-Sound
stereos are purchased from outside
suppliers for $10 per unit (a variable
cost) and assembled in Jason Inc.’s
Waterloo plant.
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Variable Cost Graphs (Cont’d)
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4-1
Total Direct
Materials Cost
Total Variable Cost Graph
$300,000
$250,000
$200,000
$150,000
$100,000
$50,000
0
10
20
30
Total Units (Model JS-12)
Produced (thousands)
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5
Variable Cost Graphs
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4-1
Unit Variable Cost Graph
Direct Materials
Cost per Unit
$20
$15
$10
$5
0
10
20
30
Total Units (Model JS-12)
Produced (thousands)
5
10
(Concluded)
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$20
$300,000
Cost per Unit
Total Costs
Unit Cost Compared to Total Cost
$250,000
$200,000
$150,000
$100,000
$50,000
4-1
$15
$10
$5
0
10
20
30
Units Produced (000)
0
10
20
30
Units Produced (000)
Number of
Units of Model
JS-12 Produced
Direct
Materials Cost
per Unit
Total Direct
Materials Cost
5,000 units
10,000
15,000
20,000
25,000
30,000
$10
10
10
10
10
10
$ 50,000
l00,000
150,000
200,000
250,000
300,000
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Minton Inc.’s Los Angeles Plant
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4-1
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 La Fleur Perfume.
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Fixed Versus Variable Cost of Jane
Sovissi’s Salary
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4-1
Salary per Bottle
Number of
of Perfume
Bottles of Perfume Total Salary for
Jane Sovissi
Produced
Produced
50,000 bottles
100,000
150,000
200,000
250,000
300,000
$75,000
75,000
75,000
75,000
75,000
75,000
$1.500
0.750
0.500
0.375
0.300
0.250
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$150,000
$1.50
$125,000
$100,000
$75,000
$50,000
$25,000
Unit Cost
Total Costs
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0 100 200 300
Bottles Produced (000)
4-1
$1.25
$1.00
$.75
$.50
$.25
0
100 200 300
Units Produced (000)
Number of
Bottles of Perfume
Produced
Total Salary
for Jane Sovissi
Salary per Bottle
of Perfume
Produced
50,000 bottles
100,000
150,000
200,000
$75,000
75,000
75,000
75,000
$1.500
0.750
0.500
0.375
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Simpson Inc. Example
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4-1
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.
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Mixed Cost Graph for Simpson Inc.’s
Equipment Rental Charges
4-1
Total Costs
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$45,000
$40,000
$35,000
$30,000
$25,000
$20,000
$15,000
$10,000
$5,000
Mixed costs are
usually separated into
their fixed and
variable components
for management
analysis.
0
10
20
30
40
Total Machine Hours (000)
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High-Low Method
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4-1
The high-low method is a
simple cost estimate
technique that may be
used for separating mixed
costs into their fixed and
variable components.
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4-1
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Example Exercise 4-1
The manufacturing cost of Alex Industries for
the first three months of the year are provided
below:
Total Cost Production
January
$80,000 1,000 units
February $125,000 2,500
March
$100,000 1,800
Using the high-low method, determine the
(a) variable cost per unit, and (b) the total fixed
cost.
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4-1
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Follow My Example 4-1
$125,000 – $80,000
a. $30 per unit =
(2,500 – 1,000)
b. $50,000 = $125,000 – ($30 x 2,500) or
$80,000 – ($30 x 1,000)
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For Practice: PE4-1A, PE4-1B
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Summary of Cost Behavior Concepts
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Total costs
increase and
decrease
proportionately
with activity level.
Total Costs
Total
Variable
Costs
4-1
Unit
Variable
Costs
Per Unit Cost
Total Units Produced
Unit costs remain
the same per unit
regardless of
activity.
Total Units Produced
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Summary of Cost Behavior Concepts
Total
Fixed Costs
Total Costs
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4-1
Unit costs remain
the same
regardless of
activity.
Total Units Produced
Per Unit Cost
Unit
Fixed Costs
Total costs
increase and
decrease with
activity level.
Total Units Produced
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Objective 2
4-2
Compute the contribution
margin, the contribution margin
ratio, and the unit contribution
margin, and explain how they
may be useful to managers.
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Cost-Volume-Profit Relationships
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4-2
Cost-volume-profit analysis is the
systematic examination of the
relationships among selling prices,
sales and production volume,
costs, expenses, and profits.
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4-2
The contribution margin is the
excess of sales revenues over
variable costs. It contributes first
toward covering fixed costs, then
contributes to profit.
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Contribution Margin
Income Statement
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4
Sales (50,000 units)
Variable costs
Contribution margin
Fixed costs
Income from operations
4-2
$1,000,000
600,000
$ 400,000
300,000
$ 100,000
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Contribution Margin Ratio
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Sales (50,000 units)
Variable costs
Contribution margin
Fixed costs
Income from operations
Contribution Margin Ratio =
Contribution Margin Ratio =
Contribution Margin Ratio =
$1,000,000
600,000
$ 400,000
300,000
$ 100,000
4-2
100%
60%
40%
30%
10%
Sales – Variable Costs
Sales
$1,000,000 – $600,000
$1,000,000
40%
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Unit Contribution Margin
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4-2
The unit contribution margin
is also useful for analyzing the
profit potential of proposed
projects. The unit contribution
margin is the sales price less
the variable cost per unit.
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Using Contribution Margin per
Unit as a Shortcut
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50,000
units
Sales ($20)
Variable costs ($12)
Contribution margin ($8)
Fixed costs
Income from operations
$1,000,000
600,000
$ 400,000
300,000
$ 100,000
4-2
65,000
units
$1,300,000
780,000
$ 520,000
300,000
$220,000
The increase in income from operations of
$120,000 could have been determined quickly by
multiplying the increase in unit sales (15,000) by
the contribution margin per unit ($8).
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4-2
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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%
Unit contribution margin
analyses can provide useful
information for managers.
$20
12
$ 8
24
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25
4-2
Review
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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%
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).
$20
12
$ 8
25
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4-2
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Example Exercise 4-2
Molly Company sells 20,000 units at $12 per
unit. Variable costs are $9 per unit, and fixed
costs are $25,000. Determine the (a) contribution margin ratio, (b) unit contribution margin,
and (c) income from operations.
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40
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4-2
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Follow My Example 4-2
a. 25% = ($12 – $9)/$12 or ($240,000 –
$180,000)/$240,000
b. $3 per unit = $12 – $9
c. Sales
Variable costs
Contribution margin
$240,000 (20,000 x $12)
180,000 (20,000 x $9)
$ 60,000 [20,000 x
$12 –$9)]
Fixed costs
25,000
Income from operations $ 35,000
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For Practice: PE4-2A, PE4-2B
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Objective 3
4-3
Using the unit contribution
margin, determine the break-even
point and the volume necessary to
achieve a target profit.
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Break-Even Point
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4-3
The break-even point is
the level of operations at
which a business’s
revenues and expired costs
are exactly equal.
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4-3
Barker Corporation’s fixed costs are
estimated to be $90,000. The unit
contribution margin is calculated as
follows:
Unit selling price
Unit variable cost
Unit contribution margin
$25
15
$10
30
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4-3
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The break-even point is calculated using the
following equation:
Break-Even Sales (units) =
Fixed Costs
Unit Contribution Margin
$90,000
Break-Even Sales (units) =
$10
Break-Even Sales (units) = 9,000 units
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Proof of the Preceding
Computation
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Sales ($25 x 9,000)
Variable costs ($15 x 9,000)
Contribution margin
Fixed costs
Income from operations
4-3
$225,000
135,000
$ 90,000
90,000
$
0
Income from operations is zero when
9,000 units are sold—hence, breakeven is 9,000 units.
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Effect of Changes in Fixed Costs
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If
Fixed
Costs
Then
BreakEven
If
Fixed
Costs
Then
BreakEven
4-3
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4-3
Bishop Co. is evaluating a proposal
to budget an additional $100,000 for
advertising. Fixed costs before the
additional advertising are estimated
at $600,000, and the unit
contribution margin is $20.
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4-3
Without additional advertising:
Fixed Costs
Break-Even in Sales (units) =
Unit Contribution Margin
$600,000
Break-Even in Sales (units) =
$20
30,000
=
units
With additional advertising:
$700,000
Break-Even in Sales (units) =
$20
=
35,000
units
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Effect of Changes in Unit
Variable Costs
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If
Unit
Variable
Cost
If
Unit
Variable
Costs
Then
BreakEven
Then
BreakEven
4-3
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4-3
Park Co. is evaluating a proposal to pay an
additional 2% commission on sales to its
salespeople (a variable cost) as an incentive
to increase sales. Fixed costs are estimated at
$840,000. The unit contribution margin
before the additional 2% commission is
determined as follows:
Unit selling price
Unit variable cost
Unit contribution margin
$250
145
$105
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4-3
Without additional 2% commission:
Fixed Costs
Break-Even in Sales (units) =
Unit Contribution Margin
$840,000
Break-Even in Sales (units) =
$105
8,000
=
units
With additional 2% commission:
$840,000
Break-Even in Sales (units) =
$100
$250 – [$145 + ($250 x 2%)] = $100
=
8,400
units
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Effect of Changes in the Unit
Selling Price
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If
Unit
Selling
Price
Then
If
Unit
Selling
Price
Then
4-3
BreakEven
BreakEven
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4-3
Graham Co. is evaluating a proposal to increase the
unit selling price of a product from $50 to $60.
The following data have been gathered:
Current
Unit selling price
$50
Unit variable cost
30
Unit contribution margin
$20
Total fixed costs
Proposed
$60
30
$30
$600,000 $600,000
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4-3
Without price increase:
Fixed Costs
Break-Even in Sales (units) =
Unit Contribution Margin
$600,000
Break-Even in Sales (units) =
$20
30,000
=
units
With price increase:
$600,000
Break-Even in Sales (units) =
$30
=
20,000
units
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Summary of Effects of Changes
on Break-Even Point
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Type of Change
4-3
Effect of Change
Direction of on Break-Even
Change
Sales (Units)
Fixed cost
Increase
Decrease
Increase
Decrease
Variable cost per unit
Increase
Decrease
Increase
Decrease
Unit sales price
Increase
Decrease
Decrease
Increase
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4-3
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Example Exercise 4-3
Nicholas Enterprises sells a product for $60 per unit.
The variable cost is $35 per unit, while fixed costs are
$80,000. Determine the (a) break-even point in sales
units, and (b) break-even point if the selling price were
increased to $67 per unit.
Follow My Example 4-3
a. 3,200 units = $80,000/($60 – $35)
b. 2,500 units = $80,000/($67 – $35)
For Practice: PE4-3A, PE4-3B
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Target Profit
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4-3
The sales volume required to earn a
target profit is determined by modifying
the break-even equation.
Sales (units) =
Fixed Costs + Target Profit
Unit Contribution Margin
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Units Required for Target Profit
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4-3
Fixed costs are estimated at $200,000, and the
desired profit is $100,000. Unit contribution
margin is $30.
Unit selling price
Unit variable cost
Unit contribution margin
Sales (units) =
$75
45
$30
$200,000
$100,000
Fixed
Costs + Target
Profit
Unit Contribution
Margin
$30
Sales (units) = 10,000 units
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Sales (10,000 units x $75)
Variable costs (10,000 x $45)
Contribution margin (10,000
x $30)
Fixed costs
Income from operations
4-3
$750,000
450,000
$300,000
200,000
$100,000
Proof that sales of 10,000 units will
provide a profit of $100,000.
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4-3
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Example Exercise 4-4
The Forest Company sells a product for $140 per unit.
The variable cost is $60 per unit, and fixed costs are
$240,000. Determine the (a) break-even point in sales
units, and (b) break-even point in sales units if the
company desires a target profit of $50,000.
Follow My Example 4-4
a. 3,000 units = $240,000/($140 – $60)
b. 3,625 units = ($240,000 + $50,000)/($140 – $60)
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For Practice: PE4-4A, PE4-4B
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Objective 4
4-4
Using a cost-volume-profit chart
and a profit-volume chart,
determine the break-even point
and the volume necessary to
achieve a target profit.
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Cost-Volume-Profit (BreakEven) Chart
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4-4
A cost-volume-profit chart,
sometimes called a breakeven chart, may assist
management in
understanding relationships
among costs, sales, and
operating profit or loss.
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4-4
The cost-volume-profit chart in Exhibit 5
(Slides 65-73) is based on the following
data:
Unit selling price
$ 50
Unit variable cost
30
Unit contribution margin $ 20
Total fixed costs
$100,000
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Cost-Volume-Profit
Chart
Dollar
amounts
are
indicated
along the
vertical
axis.
Sales and Costs (in thousands)
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4-4
$500
$450
$400
$350
$300
$250
$200
$150
$100
$ 50
0
1
2
3
4
5
6
7
8
9 10
Units of Sales (in thousands)
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Volume is shown on the horizontal axis.
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Cost-Volume-Profit
Chart (Continued)
Sales and Costs (in thousands)
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4-4
$500
$450
$400
$350
$300
$250
$200
$150
$100
$ 50
0
1
2
3
4
5
6
7
8
9 10
Units of Sales (in thousands)
A sales line is plotted by determining one value ($500,000 in 52
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sales divided by the $50 selling price equals 10,000 units).
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Cost-Volume-Profit
Chart (Continued)
Sales and Costs (in thousands)
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4-4
$500
$450
$400
$350
$300
$250
$200
$150
$100
$ 50
0
1
2
3
4
5
6
7
8
9 10
Units of Sales (in thousands)
Now, beginning at zero on the left corner of the graph,
connect a straight line to the dot.
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Cost-Volume-Profit
Chart (Continued)
Sales and Costs (in thousands)
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4-4
$500
$450
$400
$350
$300
$250
$200
$150
$100
$ 50
0
1
2
3
4
5
6
7
8
9 10
Units of Sales (in thousands)
Fixed cost of $100,00 is a horizontal line.
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Cost-Volume-Profit
Chart (Continued)
Sales and Costs (in thousands)
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4-4
$500
$450
$400
$350
$300
$250
$200
$150
$100
$ 50
0
1
2
3
4
5
6
7
8
9 10
Units of Sales (in thousands)
Similar to the sales line, a point is determined on the cost
line (10,000 @ $30 = $300,000 + $100,000 = $400,000)
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Cost-Volume-Profit
Chart (Continued)
Sales and Costs (in thousands)
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4-4
$500
$450
$400
$350
$300
$250
$200
$150
$100
$ 50
0
1
2
3
4
5
6
7
8
9 10
Units of Sales (in thousands)
Beginning with the total fixed cost at the vertical axis
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($100,000), draw a line to the red dot. This is the total cost line.
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Cost-Volume-Profit
Chart (Continued)
Sales and Costs (in thousands)
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4-4
$500
$450
$400
$350
$300
$250
$200
$150
$100
$ 50
0
1
2
3
4
5
6
7
8
9 10
Units of Sales (in thousands)
Horizontal and vertical lines are drawn at the intersection
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point of the sales and cost lines, which is the break-even point.
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Cost-Volume-Profit
Chart (Continued)
Sales and Costs (in thousands)
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4-4
$500
$450
$400
$350
$300
$250
$200
$150
$100
$ 50
0
1
2
3
4
5
6
7
8
9 10
Units of Sales (in thousands)
Break-even is sales of 5,000 units or $250,000.
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Cost-Volume-Profit
Chart (Concluded)
Sales and Costs (in thousands)
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$500
$450
$400
$350
$300
$250
$200
$150
$100
$ 50
4-4
Profit area
0
1
2
3
4
5
6
7
8
9 10
Units of Sales (in thousands)
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60
Revised Cost-Volume-Profit Chart
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4-4
Using the data from Slide 64, assume
that a proposal to reduced fixed cost by
$20,000 is to be evaluated. A costvolume-profit chart can be created to
assist in this evaluation.
Click this button to go to Slide 64. Return to
this slide by typing “74” and striking “Enter.”
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Revised Cost-VolumeProfit Chart
Sales and Costs (in thousands)
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$500
$450
$400
$350
$300
$250
$200
$150
$100
$ 50
4-4
$80,000
0
1
2
3
4
5
6
7
8
9 10
Units of Sales (in thousands)
If fixed costs can be reduced to $80,000, the new breakeven point is sales of $200,000 or 4,000 units.
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Profit-Volume Chart
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4-4
Another graphic approach to cost-volumeprofit analysis, the profit-volume chart, plots
only the difference between total sales and
total costs (or profits). Again, the data from
Slide 64 (shown below) will be used.
Unit selling price
$ 50
Unit variable cost
30
Unit contribution margin $ 20
Total fixed costs
$100,000
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to
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The maximum operating loss is equal to the
4-4
fixed costs of $100,000. Assuming that the
maximum unit sales within the relevant range is
10,000 units, the maximum operating profit is
$100,000, computed as follows:
Sales (10,000 units x $50)
$500,000
Variable costs (10,000 units x $30)
300,000
Contribution margin (10,000 units x $20) $200,000
Fixed costs
100,000
Operating profit
$100,000
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Maximum profit
64
Profit-Volume Chart
Operating Profit (Loss)
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$100,000
$75,000
$50,000
$25,000
$ 0
$(25,000)
$(50,000)
$(75,000)
$(100,000)
4-4
Profit Line
Operating
profit
Operating
loss
1
2
Break-Even Point
3
4
5
6
7
8
9 10
Units of Sales (in thousands)
Maximum loss is $100,000,
the fixed costs.
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Assumptions of Cost-Volume-Profit
Analysis
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4-4
The primary assumptions are:
1. Total sales and total costs can be represented by a
straight line.
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.
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4-5
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Objective 5
Compute the break-even point for a
business selling more than one
product, the operating leverage, and
the margin of safety, and explain how
managers use these concepts.
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Sales Mix Considerations
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4-5
The sales volume necessary to
break even or to earn a target profit
for a business selling two or more
products depends upon the sales
mix. The sales mix is the relative
distribution of sales among the
various products sold by a business.
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4-5
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:
Product
A
B
Unit
Selling
Price
$ 90
140
Unit
Variable
Cost
$70
95
Unit
Contribution
Margin
$20
45
Sales
Mix
%
20%
80%
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Cascade Company Example
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4-5
For Cascade Company, the overall enterprise
product is called E.
Unit selling price of E: ($90 x 0.8) + ($140 x 0.2)
= $100
Unit variable cost of E: ($70 x 0.8) + ($ 95 x 0.2)
= $ 75
Unit contribution margin of E: ($20 x .08) + ($45
x .02) = $ 25
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Break-Even Point of 8,000 Units of E
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4-5
Fixed Costs
Break-Even Sales (units) = Unit Contribution
Margin
Break-Even Sales (units) =
$200,000
$25
Break-Even Sales (units) =
8,000 units
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4-5
Verification of Analysis
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Break-even point
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4-5
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to
edit
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title
style
Example Exercise 4-5
Megan Company has fixed cost of $180,000. The unit
selling price, variable cost per unit, and contribution
margin per unit for the company’s two products are
provided below:
Product
Q
Z
Selling
Price
$ 160
140
Variable
Cost per
Unit
$100
95
Contribution
Margin per
Unit
$20
45
Sales
Mix
%
75%
25%
Determine the break-even point in units of Q and Z.
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4-5
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Follow My Example 4-5
Unit selling price of E: ($160 x .75) + ($100 x .25) = $145
Unit variable cost of E: ($100 x .75) + ($80 x .25) = $95
Unit contribution margin
of E: ($60 x .75) + ($20 x .25), or $145 – $95 = $50
Break-even sales (units) = 3,600 units = $180,000/$50
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For Practice: PE4-5A, PE4-5B
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Operating Leverage
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4-5
The relative mix of a business’s variable costs
and fixed costs is measured by the operating
leverage. It is computed as follows:
Contribution Margin
Operating Leverage =
Income from
Operations
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Operating Leverage Example
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Sales
Variable costs
Contribution margin
Fixed costs
Income from operations
Operating leverage
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.
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4-5
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Sales
Variable costs
Contribution margin
Fixed costs
Income from operations
Operating leverage
Jones Inc.:
Jones Inc.
$400,000
300,000
$100,000
80,000
$ 20,000
5?
$100,000Margin
Contribution
Wilson Inc.
$400,000
300,000
$100,000
50,000
$ 50,000
?
=5
Income from
Operations
$20,000
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4-5
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Sales
Variable costs
Contribution margin
Fixed costs
Income from operations
Operating leverage
Wilson Inc.:
Jones Inc.
$400,000
300,000
$100,000
80,000
$ 20,000
5?
$100,000Margin
Contribution
Wilson Inc.
$400,000
300,000
$100,000
50,000
$ 50,000
?2
=2
Income from
Operations
$50,000
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High Versus Low Operating Leverage
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4-5
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4-5
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Example Exercise 4-6
The Tucker Company reports the following data.
Sales
Variable costs
Fixed costs
$750,000
$500,000
$187,500
Determine Tucker Company’s operating leverage.
Follow My Example 4-6
4.0 = ($750,000 – $500,000)/($750,000 – $500,000 –
$187,500) = $250,000/$62,500
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For Practice: PE4-6A, PE4-6B
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Margin of Safety
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4-5
The difference between the
current sales revenue and the
sales revenue at the breakeven point is called the
margin of safety.
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4-5
If sales are $250,000, the unit selling price is $25, and the
sales at the break-even point are $200,000, the margin of
safety is 20%, computed as follows:
Sales – Sales at Break-Even Point
Margin of Safety =
Sales
$250,000 – $200,000
Margin of Safety =
$250,000
Margin of Safety = 20%
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Example Exercise 4-7
The Rachel Company has sales of $400,000, and the
break-even point in sales dollars is $300,000.
Determine the company’s margin of safety.
Follow My Example 4-7
25% = ($400,000 – $300,000)/$400,000
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For Practice: PE4-7A, PE4-7B
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Preparing a Variable Costing Income
Statement
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Total Cost
Manufacturing costs:
Variable
Fixed
Total
Selling and administrative
expenses:
Variable ($5 per unit sold)
Fixed
Total
$375,000
150,000
$525,000
Number
of Units
Unit
Cost
15,000
15,000
$25
10
$35
4-5
$ 75,000
50,000
$125,000
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