Cost Volume Profit Analysis

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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

$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

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Contribution Margin Method

$84,000 ÷ $28 = 3,000 units

$84,000 ÷ 40% = $210,000

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Graph Method

Revenue

Total costs

Breakeven

Fixed costs

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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 $337,540

Variable costs: 4,822 × $42 202,524

Contribution margin $135,016

Fixed costs 84,000

Operating income 51,016

Income taxes: $51,016 × 30% 15,305

Net income $ 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 $112,000

Fixed costs 94,000

Operating income $ 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) $85,500

Fixed costs 84,000

Operating income $ 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

What is the new contribution margin?

Decrease the price they charge from $32 to $25 and

charge an annual administrative fee of $30,000.

Suppose that the factory the Pants Shop is using to

obtain the merchandise offers the following:

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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

What is the contribution margin of the mix?

Contribution margin per shirt: $20 – $9 = $11

$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:

Pants Shirts

Sales price $70 $40

Variable costs 42 18

Contribution margin $28 $22

Contribution margin ratio 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 $245,000

Variable costs:

Pants: 3,500 × $42 147,000

Documents: 100 × $10 1,000

Total 148,000

Contribution margin 97,000

Fixed costs 84,000

Operating income $ 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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