9
Cost-VolumeProfit Analysis:
A Managerial
Planning Tool
PowerPresentation® prepared by
David J. McConomy, Queen’s University
Copyright © 2004 by Nelson, a division of Thomson Canada Limited.
9-1
Learning Objectives

Determine the number of units that
must be sold to break even or to earn
a targeted profit.

Determine the amount of revenue
required to break even or to earn a
targeted profit.
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9-2
Learning Objectives
(continued)

Apply cost-volume-profit analysis in a
multiple-product setting.

Prepare a profit-volume graph and a
cost-volume-profit graph and explain
the meaning of each.
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9-3
Learning Objectives
(continued)

Explain the impact of risk, uncertainty,
and changing variables on costvolume-profit analysis.

Discuss the impact of activity-based
costing on cost-volume-profit
analysis.
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9-4
Sample Questions Raised and
Answered by CVP Analysis
1. How many units must be sold (or how much sales
revenue must be generated) in order to break even?
2. How many units must be sold to earn a before-tax
profit equal to $60,000? A before-tax profit equal to
15 percent of revenues? An after-tax profit of
$48,750?
3. Will total profits increase if the unit price is
increased by $2 and units sold decrease 15 percent?
4. What is the effect on total profit if advertising
expenditures increase by $8,000 and sales increase
from 1,600 to 1,750 units?
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9-5
Sample Questions Raised and
Answered by CVP Analysis
(continued)
5. What is the effect on total profit if the selling price is
decreased from $400 to $375 per unit and sales
increase from 1,600 units to 1,900 units?
6. What is the effect on total profit if the selling price is
decreased from $400 to $375 per unit, advertising
expenditures are increased by $8,000, and sales
increased from 1,600 units to 2,300 units?
7. What is the effect on total profit if the sales mix is
changed?
Copyright © 2004 by Nelson, a division of Thomson Canada Limited.
9-6
CVP: A Short-Term Planning
and Analysis Tool
Benefits of CVP:




Assists in establishing prices of
products.
Assists in analyzing the impact that
volume has on short-term profits.
Assists in focusing on the impact that
changes in costs (variable and fixed)
have on profits.
Assists in analyzing how the mix of
products affects profits.
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9-7
Cost-Volume-Profit Graph
Total Revenue
Revenue
Profit
Total Cost
Y
Loss
X
Units sold
X = Break-even point in units
Y = Break-even point in revenue
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9-8
Simple CVP Example
Fixed costs (F)
Selling price per unit (P)
Variable cost per unit (V)
Tax rate
=
=
=
=
$40,000
$10
$6
40%
1. What is the break-even point in units?
2. What is the break-even point in dollars?
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9-9
Simple CVP Example: BEP
1. Let X = break-even point in units
Operating income = Sales revenue -Variable expenses - Fixed
expenses
0 =$10X -$6X - $40,000
$10X - $6X =$40,000
$4X =$40,000
X =10,000 units
2. Break-even point in sales dollars is:
10,000 x $10 or $100,000
This can be shown with a variable-costing income statement.
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9-10
Variable-Costing Income
Statement
Sales (10,000 x $10)
Less: Variable costs (10,000 x $6)
Contribution margin
Less: Fixed costs
Profit before taxes
Less: Income taxes
Profit after taxes
$100,000
60,000
$ 40,000
40,000
$0
0
$
0
=====
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9-11
Sales Revenue Approach
Alternative approach: break-even point in sales dollars:
Let X equal break-even sales in dollars
Operating income = Sales revenue - Variable expenses Fixed expenses
0 = X - 0.6X - $40,000
X - 0.6X = $40,000
0.4X = $40,000
X = $100,000
Note: V is the variable cost percentage which is found by:
Variable Cost per Unit 6
Selling Price per Unit 10
Copyright © 2004 by Nelson, a division of Thomson Canada Limited.
= 0.6
9-12
CVP Example:
Targeted Pretax Income
What sales in units and dollars are needed to obtain a
targeted profit before taxes of $20,000?
Let X = break-even point in units
Sales
Less: Variable costs
Contribution margin
Less: Fixed costs
Profit before taxes
$
= $10X
=
6X
$60,000 = $ 4X
40,000
$20,000
====
Therefore,
$60,000
= $4X
15,000 units = X
Sales in dollars is (15,000 x $10) = $150,000.
Check this by completing the variable-costing income statement.
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9-13
CVP Example:
Targeted Pretax Income (continued)
Sales
Less: Variable costs
Contribution margin
Less: Fixed costs
Profit before taxes
$150,000 = 15,000 x $10
90,000 = 15,000 x $6
$ 60,000
40,000
$ 20,000
=======
It checks!
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9-14
CVP Analysis:
Targeted After-Tax Income
What sales in units and dollars are needed to obtain a
targeted profit after taxes of $24,000?
Let X = break-even point in units
Sales
Less: Variable costs
Contribution margin
Less: Fixed costs
Profit before taxes
Less income taxes
Profit after taxes
$
$
$
= $10X
= 6X
= $ 4X
40,000
$
$24,000
======
We have the same problem as PPT 9-13 assuming we are able
to find the profit before taxes.
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9-15
CVP Analysis:
Targeted After-Tax Income (continued)
The Approach:
AFTER
=
Profit after taxes
BEFORE
=
Profit before taxes
AFTER
=
(1 - tax rate) x BEFORE
$24,000
=
(1 - .4) x BEFORE
$24,000/.6
=
BEFORE
$40,000
=
BEFORE
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9-16
CVP Analysis:
Targeted After-Tax Income (continued)
Therefore,
Sales
Less: Variable costs
$
= $10X
= $ 6X
Contribution margin
$80,000 = $ 4X
Less: Fixed costs
Profit before taxes
Less: Income taxes
40,000
$40,000
16,000 = 40% of $40,000
Profit after taxes
$24,000
======
$4X = $80,000
X = $80,000/$4
X = 20,000 units
Sales in dollars is (20,000 x $10) or $200,000
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9-17
CVP Analysis:
Targeted After-Tax Income (continued)
The income statement below illustrates that $200,000 in
sales will give you an after-tax profit of $24,000.
Sales
Less: Variable costs
Contribution margin
Less: Fixed costs
Profit before taxes
Less: Income taxes
Profit after taxes
$200,000
120,000
$ 80,000
40,000
$ 40,000
16,000
$ 24,000
======
Copyright © 2004 by Nelson, a division of Thomson Canada Limited.
9-18
CVP Analysis:
Targeted Pretax Income
What sales in dollars is needed to obtain a targeted
profit before taxes equal to 20 percent of sales?
Let X = sales in dollars
Sales
Less: Variable costs
Contribution margin
Less: Fixed costs
Profit before taxes
$
=
=
$40,000 + .2X =
$40,000
1.0X
0.6X
0.4X
.2X
.4X
.2X
X
X
Copyright © 2004 by Nelson, a division of Thomson Canada Limited.
=
=
=
=
$40,000 + .2X
$40,000
$40,000/.2
$200,000
9-19
CVP Analysis:
Targeted Pretax Income (continued)
The following variable-costing income statement can be used to
check the solution.
Sales
Less: Variable costs
Contribution margin
Less: Fixed costs
Profit before taxes
$200,000
120,000 = .6 ($200,000)
$ 80,000 = .4 ($200,000)
40,000
$ 40,000
=======
$40,000 is 20% of $200,000. It checks!
Copyright © 2004 by Nelson, a division of Thomson Canada Limited.
9-20
CVP Analysis:
Targeted After-Tax Income
What sales in dollars is needed to obtain a targeted
profit after taxes equal to 6 percent of sales?
Let X = sales in dollars
Sales
Less: Variable costs
Contribution margin
Less: Fixed costs
Profit before taxes
Less: Income taxes
Profit after taxes
$
=
=
=
$
1.0X
0.6X
0.4X
40,000
$
$ .06X
=====
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9-21
CVP Analysis:
Targeted After-Tax Income (continued)
Use the method from PPT 9-16
AFTER = (1- tax rate) x BEFORE
0.06X = (1 - .4) x BEFORE
0.06X / 0.6 = BEFORE
0.1X = BEFORE
Therefore,
Sales
Less: Variable costs
Contribution margin
Less: Fixed costs
Profit before taxes
Less: Income taxes
Profit after taxes
$
=
=
$ 40,000 + .1X =
40,000
0.10X
0.04X
0.06X
1.0X
0.6X
0.4X
======
.4X
.3X
X
X
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=
=
=
=
40,000 + .1X
40,000
$40,000/.3
$133,333
9-22
CVP Analysis:
Targeted After-Tax Income (continued)
The following income statement checks the solution:
Sales
Less: Variable costs
Contribution margin
Less: Fixed costs
Profit before taxes
Less: Income taxes
Profit after taxes
$133,333
80,000 = .6 x $133,333
$ 53,333
40,000
$ 13,333
5,333 = .4 x $13,333
$ 8,000
=======
$8,000 is 6% of $133,333. It Checks!
Copyright © 2004 by Nelson, a division of Thomson Canada Limited.
9-23
Multiple-Product Example
Product
A
B
P
$10
-
V
$6
=
=
CM
$4
x
x
Mix
3
8
-
5
=
3
x
2
Total CM per package
= Total CM
=
$12
=
6
$18
===
Total fixed expenses = $180,000
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9-24
Multiple-Product Example
(continued)
Break-even point:
X
= Fixed cost / Unit contribution margin
= $180,000 / $18
= 10,000 packages to break even
Each package contains 3 units of A and 2 units of B. Therefore, to break
even, we need to sell the following units of A and B:
A: 3
x10,000
=
30,000 units
B: 2
x10,000
=
20,000 units
Copyright © 2004 by Nelson, a division of Thomson Canada Limited.
9-25
Another Multiple-Product
Example
Assume the following:
Regular
Units sold
Sales price per unit
Sales
Less: Variable expenses
Contribution margin
Less: Fixed expenses
Net income
1.
2.
Deluxe
Total Percent
400
200
600
$500
$750
---$200,000 $150,000 $350,000
120,000
60,000 180,000
$ 80,000 $ 90,000 $170,000
------100.0%
51.4
48.6%
130,000
$ 40,000
=======
What is the break-even point?
How much sales-revenue of each product must be generated to earn
a before tax profit of $50,000?
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9-26
Another Multiple-Product
Example: BEP
BEP =
=
=
Fixed cost / CM ratio for sales mix
$130,000 / 0.486
$267,490 for the firm
BEP for Regular Model:
(400/600) x $267,490 = $178,327
BEP for Deluxe Model:
(200/600) x $267,490 = $89,163
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9-27
Another Multiple-Product
Example: Targeted Revenue
BEP
= (Fixed Costs + Targeted income) / CM ratio per sales mix
= ($130,000 + $50,000) / 0.486
= $370,370 for the firm
BEP for Regular Model:
(400/600) x $370,370 = $246,913
BEP for Deluxe Model:
(200/600) x 370,370 = $123,457
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9-28
Profit-Volume Graph
Profit
I = (P-V)X-F
Slope = P-V
Profit
loss
break-even point
UNITS
in units
-F
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9-29
The Limitations of CVP
Analysis
A number of limitations are commonly mentioned with respect to
CVP analysis:
1.
The analysis assumes a linear revenue function and a linear
cost function.
2.
The analysis assumes that price, total fixed costs, and unit
variable costs can be accurately identified and remain constant
over the relevant range.
3.
The analysis assumes that what is produced is sold.
4.
For multiple-product analysis, the sales mix is assumed to be
known.
5.
The selling prices and costs are assumed to be known with
certainty.
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9-30
Margin of Safety
Assume that a company has the following projected income statement:
Sales
Less: Variable expenses
Contribution margin
Less: Fixed expenses
Income before taxes
$100,000
60,000
$ 40,000
30,000
$ 10,000
=======
Break-even point in dollars (R):
R = $30,000/.4
= $75,000
Safety margin = $100,000 - $75,000
= $25,000
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9-31
Degree of Operating Leverage
(DOL)
DOL = $40,000/$10,000 = 4.0
Now suppose that sales are 25% higher than projected.
What is the percentage change in profits?
Percentage change in profits = DOL x percentage change in sales
Percentage change in profits = 4.0 x 25% = 100%
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9-32
DOL (continued)
Proof:
Sales
Less: Variable expenses
Contribution margin
Less: Fixed expenses
Income before taxes
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$125,000
75,000
$ 50,000
30,000
$ 20,000
======
9-33
CVP and ABC
Assume the following:
Sales price per unit
Variable cost
Fixed costs (conventional)
Fixed costs (ABC)
analysis
$15
5
$180,000
100,000 with $80,000 subject to ABC
Other Data:
Activity Driver
Setups
Inspections
Unit
Variable
Costs
$500
50
Level of
Activity
Driver
100
600
1. What is the BEP under conventional analysis?
2. What is the BEP under ABC analysis?
3. What is the BEP if setup cost could be reduced to $450 and inspection cost
reduced to $40?
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9-34
CVP and ABC (continued)
1. Break-even units (conventional analysis)
BEP
= $180,000/$10
= 18,000 units
2. Break-even units (ABC analysis)
BEP
= [$100,000 + (100 x $500) + (600 x $50)]/$10
= 18,000 units
3. BEP
= [$100,000 + (100 x $450) + (600 x $40)]/$10
= 16,900 units
What implications does ABC have for improving
performance?
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9-35