12009 Foster Business School Cost Accounting L.DuCharme

Cost-Volume-Profit Analysis

Chapter 3

22009 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

32009 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.

42009 Foster Business School 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

52009 Foster Business School Cost Accounting L.DuCharme

(CVP) Analysis Example

Assume that the Pants Shop can purchase pantsfor $32 from a local factory; other variable costs

amount to $10 per unit.

The local factory allows the Pants Shop toreturn 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 $70and total fixed costs amount to $84,000.

62009 Foster Business School Cost Accounting L.DuCharme

(CVP) Analysis Example

How much revenue will the business receive if2,500 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)

72009 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 when2,500 pairs of pants are sold?

2,500 × $28 = $70,000

82009 Foster Business School Cost Accounting L.DuCharme

(CVP) Analysis Example

Contribution margin percentage (contributionmargin ratio) is the contribution margin per

unit divided by the selling price.

What is the contribution margin percentage?

$28 ÷ $70 = 40%

92009 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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102009 Foster Business School Cost Accounting L.DuCharme

BEPs

Determine the breakeven pointand output level needed to achievea target operating income using: (1) the equation, (2) contribution margin, and(3) graph methods.

112009 Foster Business School Cost Accounting L.DuCharme

Breakeven Point

SalesVariableexpenses

Fixedexpenses

– =

Total revenues = Total costsRev – VC – FC = 0

122009 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

132009 Foster Business School Cost Accounting L.DuCharme

Abbreviations

Q = Quantity of output units sold(and manufactured)

OI = Operating income

TOI = Target operating income

TNI = Target net income (after tax)

142009 Foster Business School Cost Accounting L.DuCharme

Equation Method

$70Q – $42Q – $84,000 = 0$28Q = $84,000

Q = $84,000 ÷ $28 = 3,000 units

Let Q = number of units to be sold to break even

(Selling price × Quantity sold) – (Variable unit cost× Quantity sold) – Fixed costs = Operating income

152009 Foster Business School Cost Accounting L.DuCharme

Contribution Margin Method

$84,000 ÷ $28 = 3,000 units

$84,000 ÷ 40% = $210,000

162009 Foster Business School Cost Accounting L.DuCharme

Graph Method

04284

126168210252294336378

0 1000 2000 3000 4000 5000

Units

$(00

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Revenue

Total costs

Breakeven

Fixed costs

172009 Foster Business School Cost Accounting L.DuCharme

Target Operating Income

(Fixed costs + Target operating income)divided either by Contribution Margin

percentage or Contribution Margin per unit

182009 Foster Business School Cost Accounting L.DuCharme

Target Operating Income

Assume that management wants to have anoperating 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

192009 Foster Business School Cost Accounting L.DuCharme

Income Taxes

Understand how incometaxes affect CVP analysis.

202009 Foster Business School Cost Accounting L.DuCharme

Target Net Incomeand Income Taxes Example

Management would like to earnan 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

212009 Foster Business School Cost Accounting L.DuCharme

Target Net Incomeand 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

222009 Foster Business School Cost Accounting L.DuCharme

Target Net Incomeand Income Taxes Example

Proof:Revenues: 4,822 × $70 $337,540Variable costs: 4,822 × $42 202,524Contribution margin $135,016Fixed costs 84,000Operating income 51,016Income taxes: $51,016 × 30% 15,305Net income $ 35,711

232009 Foster Business School Cost Accounting L.DuCharme

Margin of Safety (MoS)

Margin of Safety = Revenues* – BEP (*Revenues are either budgeted or actual.)

MoS can either be expressed in # of units or $.

242009 Foster Business School Cost Accounting L.DuCharme

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. $16,000B. $24,000C. $80,000D. $96,000E. None of the above

252009 Foster Business School Cost Accounting L.DuCharme

Operating Leverage

Operating leverage describes the effects thatfixed costs have on changes in operatingincome as changes occur in units sold.

Organizations with a high proportion of fixedcosts have high operating leverage.

262009 Foster Business School Cost Accounting L.DuCharme

Operating Leverage Example

Degree of operating leverage= Contribution margin ÷ Operating income

What is the degree of operating leverageof the Pants Shop at the 3,500 sales level

under two different arrangements?

Existing arrangement:3,500 × $28 = $98,000 contribution margin

272009 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

282009 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 levelof 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?

292009 Foster Business School Cost Accounting L.DuCharme

Contribution Margin versusGross Margin

Contribution income statement emphasizescontribution margin.

Financial accounting income statementemphasizes gross margin.

302009 Foster Business School Cost Accounting L.DuCharme

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?

312009 Foster Business School Cost Accounting L.DuCharme

End of Chapter 3