Cost-Volume-Profit Analysis
Chapter 3
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2009 Foster Business School
Cost Accounting
L.DuCharme
Outline
• CVP assumptions & terminology
• BEP solution
– Target operating income
– Target net income
• Margin of Safety
• Operating Leverage
• CM vs. GM
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2009 Foster Business School
Cost Accounting
L.DuCharme
Assumptions
Four assumptions
underlying cost-volume-profit
(CVP) analysis are presented
in the text.
We will assume that they hold here.
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Cost Accounting
L.DuCharme
Cost-Volume-Profit 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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Cost Accounting
L.DuCharme
(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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2009 Foster Business School
Cost Accounting
L.DuCharme
(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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2009 Foster Business School
Cost Accounting
L.DuCharme
(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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2009 Foster Business School
Cost Accounting
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(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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2009 Foster Business School
Cost Accounting
L.DuCharme
(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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2009 Foster Business School
Cost Accounting
L.DuCharme
BEPs
Determine the breakeven point
and output level needed to achieve
a target operating income using:
(1) the equation,
(2) contribution margin, and
(3) graph methods.
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2009 Foster Business School
Cost Accounting
L.DuCharme
Breakeven Point
–
Sales
Variable
expenses
=
Fixed
expenses
Total revenues = Total costs
Rev – VC – FC = 0
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2009 Foster Business School
Cost Accounting
L.DuCharme
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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2009 Foster Business School
Cost Accounting
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Abbreviations
Q = Quantity of output units sold
(and manufactured)
OI = Operating income
TOI = Target operating income
TNI = Target net income (after tax)
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Cost Accounting
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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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Cost Accounting
L.DuCharme
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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Cost Accounting
L.DuCharme
Target Operating Income
(Fixed costs + Target operating income)
divided either by Contribution Margin
percentage or Contribution Margin per unit
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Cost Accounting
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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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Income Taxes
Understand how income
taxes affect CVP analysis.
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Cost Accounting
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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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Cost Accounting
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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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2009 Foster Business School
Cost Accounting
L.DuCharme
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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Cost Accounting
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Margin of Safety (MoS)
Margin of Safety = Revenues* – BEP
(*Revenues are either budgeted or actual.)
MoS can either be expressed in # of units or $.
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MoS--question
Brie Soda has sales of $200,000; a CM of
20%; and a margin of safety of $80,000.
What is Brie’s fixed cost?
A. $16,000
B. $24,000
C. $80,000
D. $96,000
E. None of the above
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Cost Accounting
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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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Cost Accounting
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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 two different arrangements?
Existing arrangement:
3,500 × $28 = $98,000 contribution margin
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2009 Foster Business School
Cost Accounting
L.DuCharme
Operating Leverage Example
$98,000 contribution margin – $84,000 fixed costs
= $14,000 operating income
$98,000 ÷ $14,000 = 7.0
New arrangement:
Assume Unit Variable Costs = $35 and Fixed Cost = $114,000
3,500 × $35 = $122,500 contribution margin
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2009 Foster Business School
Cost Accounting
L.DuCharme
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.
E.g., above: a 10% increase in sales will yield a 144% increase in op. income!
What is operating leverage if fixed costs = 0?
As sales increase, what happens to op. leverage?
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Cost Accounting
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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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Cost Accounting
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GM versus CM
• The difference between GM and CM all is
in how you account for:
– Fixed mfg. costs (in CoGS, NOT in VC)
– Variable non-mfg. costs (in VC, NOT in CoGS)
GM = Rev. – CoGS
CM = Rev. – VC
“Margins” are usually referred to in finance. What margins are they usually referring to?
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2009 Foster Business School
Cost Accounting
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End of Chapter 3
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2009 Foster Business School
Cost Accounting
L.DuCharme