Cost-Volume-Profit Analysis Chapter 3

Cost-Volume-Profit Analysis

Learning Objective 1

Understand the assumptions

underlying

cost-volume-profit

(CVP) analysis.

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.

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).

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

Cost-Volume-Profit Assumptions

and Terminology

Operating income

= Total revenues from operations

– Cost of goods sold and operating costs (excluding income taxes)

Learning Objective 2

Explain the features

of CVP analysis.

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

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

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?

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%

Essentials of Cost-Volume-Profit

(CVP) Analysis Example

If the business sells 3,000 pairs of pants, revenues will be $210,000 and contribution

Learning Objective 3

Determine the breakeven point

and output level needed to

achieve

a target operating income using

the equation, contribution

Breakeven Point

–

₌

Abbreviations

SP = Selling price

VCU = Variable cost per unit

CMU = Contribution margin per unit CM% = Contribution margin

percentage

Abbreviations

Q = Quantity of output units sold (and manufactured)

OI = Operating income

TOI = Target operating income TNI = Target net income

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

Contribution Margin Method

$84,000 ÷ $28 = 3,000 units

Graph Method

Revenue

Total costs

Breakeven

Target Operating Income

(Fixed costs + Target operating income) divided either by Contribution margin percentage or Contribution margin per unit

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

Learning Objective 4

Understand how income

taxes affect CVP analysis.

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

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

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

Learning Objective 5

Explain CVP analysis

in decision making and

how sensitivity analysis helps

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.

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

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.

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:

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%.

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.

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

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

Learning Objective 6

Use CVP analysis to plan

fixed and variable costs.

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

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%

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

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

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

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:

Operating Leverage Example

$98,000 contribution margin – $84,000 fixed costs = $14,000 operating income

$98,000 ÷ $14,000 = 7.0 New arrangement:

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

Learning Objective 7

Apply CVP analysis to a

company

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.

Effects of Sales Mix on Income

What is the contribution margin of the mix? Contribution margin per shirt: $20 – $9 = $11

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

Effects of Sales Mix on Income

What is the weighted-average budgeted contribution margin?

Pants: 1 × $28 + Shirts: 2 × $11 = $50 ÷ 3 = $16.667

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

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%

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

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

Learning Objective 8

Adapt CVP analysis to situations

in which a product has more

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.

Multiple Cost Drivers Example

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

Learning Objective 9

Distinguish between

contribution margin

Contribution Margin versus

Gross Margin

Contribution income statement emphasizes contribution margin.

Financial accounting income statement emphasizes gross margin.