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## Cost-Volume-Profit Analysis

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### Cost-Volume-Profit Analysis

Chapter 3

Cost-Volume-Profit Assumptionsand Terminology

Cost volume profit analysis examines the behavior

of total costs and operating income as changes occur

in the output level, the selling price, the variable cost

per unit, and /or the fixed costs of a product.

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 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.

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)

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

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

margin would equal 40% × $210,000 = $84,000.

Determine the breakeven point

and output level needed to achieve

a target operating income using

the equation, contribution margin,

and graph methods.

Abbreviations

SP = Selling price

VCU = Variable cost per unit

CMU = Contribution margin per unit

= SP - VCU

CM% = Contribution margin percentage

FC = Fixed costs

Abbreviations

Q = Quantity of output units sold

(and manufactured)

OI = Operating income

TOI = Target operating income

TNI = Target net income

Equation Method

Total revenues = Total costs

(Selling price × Quantity sold) = (Variable unit cost

× Quantity sold) + Fixed costs

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

Target Operating Income

(Fixed costs + Target operating income)

/ Contribution margin (per unit or ratio)

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

Understand how income

taxes affect CVP analysis.

Target Net Incomeand 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

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

Target Net Incomeand 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

Explain CVP analysis

in decision making and

how sensitivity analysis helps

managers cope with uncertainty.

Sensitivity Analysis andUncertainty 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.

Sensitivity Analysis andUncertainty 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

Sensitivity Analysis andUncertainty 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 andUncertainty 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

Use CVP analysis to plan

fixed and variable costs.

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.

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

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

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.

Apply CVP analysis to a company

producing different products.

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.

Effects of Sales Mix on Income

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

What is the contribution margin of the mix?

$28 + (2 × $11) = $28 + $22 = $50

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

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:

PantsShirts

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

45.46%

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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