Cost-Volume-Profit Analysis
Chapter 3
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Learning Objective 1
Understand the assumptions
underlying cost-volume-profit
(CVP) analysis.
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Cost-Volume-Profit Assumptions
and Terminology
1. Changes in the level of revenues and costs arise
only because of changes in the number of product
(or service) units produced and sold.
2. Total costs can be divided into a fixed component
and a component that is variable with respect to
the level of output.
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Cost-Volume-Profit Assumptions
and Terminology
3. When graphed, the behavior of total revenues
and total costs is linear (straight-line) in relation
to output units within the relevant range
(and time period).
4. The unit selling price, unit variable costs, and
fixed costs are known and constant.
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Cost-Volume-Profit Assumptions
and Terminology
5. The analysis either covers a single product or
assumes that the sales mix when multiple
products are sold will remain constant as the
level of total units sold changes.
6. All revenues and costs can be added and
compared without taking into account the time
value of money.
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Cost-Volume-Profit Assumptions
and Terminology
Operating income
= Total revenues from operations
– Cost of goods sold and operating costs
(excluding income taxes)
Net income = Operating income – Income taxes
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Learning Objective 2
Explain the features
of CVP analysis.
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Essentials of Cost-Volume-Profit
(CVP) Analysis Example
Assume that the Pants Shop can purchase pants
for $32 from a local factory; other variable costs
amount to $10 per unit.
The local factory allows the Pants Shop to
return all unsold pants and receive a full $32
refund per pair of pants within one year.
The average selling price per pair of pants is $70
and total fixed costs amount to $84,000.
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Essentials of Cost-Volume-Profit
(CVP) Analysis Example
How much revenue will the business receive if
2,500 units are sold?
2,500 × $70 = $175,000
How much variable costs will the business incur?
2,500 × $42 = $105,000
$175,000 – 105,000 – 84,000 = ($14,000)
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Essentials of Cost-Volume-Profit
(CVP) Analysis Example
What is the contribution margin per unit?
$70 – $42 = $28 contribution margin per unit
What is the total contribution margin when
2,500 pairs of pants are sold?
2,500 × $28 = $70,000
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Essentials of Cost-Volume-Profit
(CVP) Analysis Example
Contribution margin percentage (contribution
margin ratio) is the contribution margin per
unit divided by the selling price.
What is the contribution margin percentage?
$28 ÷ $70 = 40%
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Essentials of Cost-Volume-Profit
(CVP) Analysis Example
If the business sells 3,000 pairs of pants,
revenues will be $210,000 and contribution
margin would equal 40% × $210,000 = $84,000.
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Learning Objective 3
Determine the breakeven point
and output level needed to achieve
a target operating income using
the equation, contribution margin,
and graph methods.
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Breakeven Point
Sales
–
Variable
expenses
=
Fixed
expenses
Total revenues = Total costs
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Abbreviations
SP = Selling price
VCU = Variable cost per unit
CMU = Contribution margin per unit
CM% = Contribution margin percentage
FC = Fixed costs
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Abbreviations
Q = Quantity of output units sold
(and manufactured)
OI = Operating income
TOI = Target operating income
TNI = Target net income
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Equation Method
(Selling price × Quantity sold) – (Variable unit cost
× Quantity sold) – Fixed costs = Operating income
Let Q = number of units to be sold to break even
$70Q – $42Q – $84,000 = 0
$28Q = $84,000
Q = $84,000 ÷ $28 = 3,000 units
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Contribution Margin Method
$84,000 ÷ $28 = 3,000 units
$84,000 ÷ 40% = $210,000
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$(000)
Graph Method
Breakeven
378
336
294
252
210
168
126
84
42
0
Fixed costs
0
1000
2000
3000
4000
5000
Units
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Target Operating Income
(Fixed costs + Target operating income)
divided either by Contribution margin
percentage or Contribution margin per unit
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Target Operating Income
Assume that management wants to have an
operating income of $14,000.
How many pairs of pants must be sold?
($84,000 + $14,000) ÷ $28 = 3,500
What dollar sales are needed to achieve this income?
($84,000 + $14,000) ÷ 40% = $245,000
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Learning Objective 4
Understand how income
taxes affect CVP analysis.
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Target Net Income
and Income Taxes Example
Management would like to earn
an after tax income of $35,711.
The tax rate is 30%.
What is the target operating income?
Target operating income
= Target net income ÷ (1 – tax rate)
TOI = $35,711 ÷ (1 – 0.30) = $51,016
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Target Net Income
and Income Taxes Example
How many units must be sold?
Revenues – Variable costs – Fixed costs
= Target net income ÷ (1 – tax rate)
$70Q – $42Q – $84,000 = $35,711 ÷ 0.70
$28Q = $51,016 + $84,000
Q = $135,016 ÷ $28 = 4,822 pairs of pants
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Target Net Income
and Income Taxes Example
Proof:
Revenues: 4,822 × $70
Variable costs: 4,822 × $42
Contribution margin
Fixed costs
Operating income
Income taxes: $51,016 × 30%
Net income
$337,540
202,524
$135,016
84,000
51,016
15,305
$ 35,711
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Learning Objective 5
Explain CVP analysis
in decision making and
how sensitivity analysis helps
managers cope with uncertainty.
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Using CVP Analysis Example
Suppose the management anticipates
selling 3,200 pairs of pants.
Management is considering an advertising
campaign that would cost $10,000.
It is anticipated that the advertising will
increase sales to 4,000 units.
Should the business advertise?
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Using CVP Analysis Example
3,200 pairs of pants sold with no advertising:
Contribution margin
$89,600
Fixed costs
84,000
Operating income
$ 5,600
4,000 pairs of pants sold with advertising:
Contribution margin
Fixed costs
Operating income
$112,000
94,000
$ 18,000
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Using CVP Analysis Example
Instead of advertising, management is
considering reducing the selling price
to $61 per pair of pants.
It is anticipated that this will increase
sales to 4,500 units.
Should management decrease the selling
price per pair of pants to $61?
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Using CVP Analysis Example
3,200 pairs of pants sold with no change
in the selling price:
Operating income = $5,600
4,500 pairs of pants sold at a reduced selling price:
Contribution margin: (4,500 × $19)
Fixed costs
Operating income
©2003 Prentice Hall Business Publishing, Cost Accounting 11/e, Horngren/Datar/Foster
$85,500
84,000
$ 1,500
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Sensitivity Analysis and
Uncertainty Example
Assume that the Pants Shop can sell
4,000 pairs of pants.
Fixed costs are $84,000.
Contribution margin ratio is 40%.
At the present time the business cannot
handle more than 3,500 pairs of pants.
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Sensitivity Analysis and
Uncertainty Example
To satisfy a demand for 4,000 pairs, management
must acquire additional space for $6,000.
Should the additional space be acquired?
Revenues at breakeven with existing space are
$84,000 ÷ .40 = $210,000.
Revenues at breakeven with additional space are
$90,000 ÷ .40 = $225,000
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Sensitivity Analysis and
Uncertainty Example
Operating income at $245,000 revenues with
existing space = ($245,000 × .40)
– $84,000 = $14,000.
(3,500 pairs of pants × $28) – $84,000 = $14,000
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Sensitivity Analysis and
Uncertainty Example
Operating income at $280,000 revenues with
additional space = ($280,000 × .40) – $90,000
= $22,000.
(4,000 pairs of pants × $28 contribution margin)
– $90,000 = $22,000
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Learning Objective 6
Use CVP analysis to plan
fixed and variable costs.
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Alternative Fixed/Variable Cost
Structures Example
Suppose that the factory the Pants Shop is using to
obtain the merchandise offers the following:
Decrease the price they charge from $32 to $25 and
charge an annual administrative fee of $30,000.
What is the new contribution margin?
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Alternative Fixed/Variable Cost
Structures Example
$70 – ($25 + $10) = $35
Contribution margin increases from $28 to $35.
What is the contribution margin percentage?
$35 ÷ $70 = 50%
What are the new fixed costs?
$84,000 + $30,000 = $114,000
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Alternative Fixed/Variable Cost
Structures Example
Management questions what sales volume
would yield an identical operating income
regardless of the arrangement.
28x – 84,000 = 35x – 114,000
114,000 – 84,000 = 35x – 28x
7x = 30,000
x = 4,286 pairs of pants
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Alternative Fixed/Variable Cost
Structures Example
Cost with existing arrangement
= Cost with new arrangement
.60x + 84,000 = .50x + 114,000
.10x = $30,000  x = $300,000
($300,000 × .40) – $ 84,000 = $36,000
($300,000 × .50) – $114,000 = $36,000
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Operating Leverage
Operating leverage describes the effects that
fixed costs have on changes in operating
income as changes occur in units sold.
Organizations with a high proportion of fixed
costs have high operating leverage.
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Operating Leverage Example
Degree of operating leverage
= Contribution margin ÷ Operating income
What is the degree of operating leverage
of the Pants Shop at the 3,500 sales level
under both arrangements?
Existing arrangement:
3,500 × $28 = $98,000 contribution margin
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Operating Leverage Example
$98,000 contribution margin – $84,000 fixed costs
= $14,000 operating income
$98,000 ÷ $14,000 = 7.0
New arrangement:
3,500 × $35 = $122,500 contribution margin
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Operating Leverage Example
$122,500 contribution margin
– $114,000 fixed costs = $8,500
$122,500 ÷ $8,500 = 14.4
The degree of operating leverage at a given level
of sales helps managers calculate the effect of
fluctuations in sales on operating income.
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Learning Objective 7
Apply CVP analysis to a company
producing different products.
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Effects of Sales Mix on Income
Pants Shop Example
Management expects to sell 2 shirts at $20 each
for every pair of pants it sells.
This will not require any additional fixed costs.
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Effects of Sales Mix on Income
Contribution margin per shirt: $20 – $9 = $11
What is the contribution margin of the mix?
$28 + (2 × $11) = $28 + $22 = $50
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Effects of Sales Mix on Income
$84,000 fixed costs ÷ $50 = 1,680 packages
1,680 × 2 = 3,360 shirts
1,680 × 1 = 1,680 pairs of pants
Total units = 5,040
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Effects of Sales Mix on Income
What is the breakeven in dollars?
3,360 shirts × $20
= $ 67,200
1,680 pairs of pants × $70 = 117,600
$184,800
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Effects of Sales Mix on Income
What is the weighted-average budgeted
contribution margin?
Pants: 1 × $28 + Shirts: 2 × $11
= $50 ÷ 3 = $16.667
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Effects of Sales Mix on Income
The breakeven point for the two products is:
$84,000 ÷ $16.667 = 5,040 units
5,040 × 1/3 = 1,680 pairs of pants
5,040 × 2/3 = 3,360 shirts
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Effects of Sales Mix on Income
Sales mix can be stated in sales dollars:
Sales price
Variable costs
Contribution margin
Contribution margin ratio
Pants Shirts
$70
$40
42
18
$28
$22
40%
55%
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Effects of Sales Mix on Income
Assume the sales mix in dollars
is 63.6% pants and 36.4% shirts.
Weighted contribution would be:
40% × 63.6% = 25.44% pants
55% × 36.4% = 20.02% shirts
45.46%
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Effects of Sales Mix on Income
Breakeven sales dollars is $84,000
÷ 45.46% = $184,778 (rounding).
$184,778 × 63.6% = $117,519 pants sales
$184,778 × 36.4% = $ 67,259 shirt sales
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Learning Objective 8
Adapt CVP analysis to situations
in which a product has more
than one cost driver.
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Multiple Cost Drivers Example
Suppose that the business will incur an additional
cost of $10 for preparing documents associated
with the sale of pants to various customers.
Assume that the business sells 3,500
pants to 100 different customers.
What is the operating income from this sale?
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Multiple Cost Drivers Example
Revenues: 3,500 × $70
Variable costs:
Pants: 3,500 × $42
Documents: 100 × $10
Total
Contribution margin
Fixed costs
Operating income
$245,000
147,000
1,000
148,000
97,000
84,000
$ 13,000
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Multiple Cost Drivers
Would the operating income of the Pants Shop
be lower or higher if the business sells pants
to more customers?
The cost structure depends on two cost drivers:
1. Number of units
2. Number of customers
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Learning Objective 9
Distinguish between
contribution margin
and gross margin.
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Contribution Margin versus
Gross Margin
Contribution income statement emphasizes
contribution margin.
Financial accounting income statement
emphasizes gross margin.
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End of Chapter 3
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