Cost-Volume-Profit Analysis Chapter 3

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Cost-Volume-Profit Analysis Cost-Volume-Profit Analysis

Chapter 3

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Learning Objective 1 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 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.

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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.

FEDER AL RE SE RVE NOTE THE UNITED STAT ES OF AMERICA THE UNITED STATES OF AMERICA

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THIS NOTE IS LEGAL TENDER FOR ALL DEBTS, PUBLIC AND PRIVATE

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Learning Objective 3 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 Breakeven Point

Sales Variable

expenses

Fixed expenses

– =

Total revenues = Total costs

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Abbreviations 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 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 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 Contribution Margin Method

$84,000 ÷ $28 = 3,000 units

$84,000 ÷ 40% = $210,000

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Graph Method Graph Method

42 0 126 84 168 210 252 294 336 378

0 1000 2000 3000 4000 5000 Units

$( 00 0) ^Rev

enu e

Total costs Breakeven

Fixed costs

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Target Operating Income 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 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 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 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

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Target Net Income

and Income Taxes Example 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 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 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 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

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Using CVP Analysis Example 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 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

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Sensitivity Analysis and Uncertainty Example 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 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.

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Sensitivity Analysis and Uncertainty Example 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 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 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

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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

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 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 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 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 Learning Objective 7

Apply CVP analysis to a company

producing different products.

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Effects of Sales Mix on Income 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 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 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 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 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 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 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 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 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 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 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 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

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Multiple Cost Drivers Multiple Cost Drivers

Would the operating income of the Pants Shop be lower or higher if the business sells pants