Chapter 8

Cost-Volume-Profit Relationships

IntroductionThis chapter examines one of the most

basic planning tools available to managers: cost-volume-profit analysis.

Cost-volume-profit analysis examines the behaviour of total revenues, total costs, and operating profit as changes occur in the output level, selling price, variable costs per unit, or fixed costs.

Learning Objectives

1 Distinguish between the general case and a special case of CVP

2 Explain the relationship between operating profit and net profit

3 Describe the assumptions underlying CVP4 Demonstrate three methods for determining the

breakeven point and target operating profit5 Explain how sensitivity analysis can help managers cope

with uncertainty6 Illustrate how CVP can assist cost planning7 Describe the effect of revenue mix on operating profit

Learning Objective 1

Distinguish between the general case and a special case of CVP

Learning Objective 1(continued)

General versus special case of CVP Using a general case of profit planning, we

realise that a business has many cost drivers and revenue streams that are fundamental to its profitability

In CVP analysis, we assume a much more simple model, where there are restrictions on these setting, as outlined in the following slides:

Learning Objective 2

Explain the relationship between operating profit and net profit

Learning Objective 1(continued)

Operating profit = Total revenues – Total costs

Operating profit = Total revenue – Variable costs - Fixed costs

Net profit = Operating profit (+/-) Non-operating revenues/costs (such as interests) – Income taxes

Learning Objective 3

Describe the assumptions underlying CVP

Learning Objective 1(continued)

• 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.

3 When graphed, the behaviour 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.

Learning Objective 1(continued)

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.

Learning Objective 3(continued)

Assumptions of Cost-Volume-Profit (CVP) Analysis Assume that the shop Dresses by Mary can

purchase dresses for £32 from a local factory; other variable costs amount to £10 per dress.

Because she plans to sell these dresses overseas, the local factory allows Mary to return all unsold dresses and receive a full £32 refund per dress within one year.

Learning Objective 3(continued)

Mary can use CVP analysis to examine changes in operating profit as a result of selling different quantities of dresses.

Assume that the average selling price per dress is £70 and total fixed costs amount to £84,000.

How much revenue will she receive if she sells 2,500 dresses? 2,500 × £70 = £175,000

How much variable costs will she incur? 2,500 × £42 = £105,000

Would she show an operating profit or an operating loss? An operating loss: £175,000 – 105,000 – 84,000 = (£14,000)

Learning Objective 3(continued)

The only numbers that change are total revenues and total variable cost.

Total revenues – total variable costs = Contribution margin

Contribution margin per unit = selling price – variable cost per unit

What is Mary’s contribution margin per unit? £70 – £42 = £28 contribution margin per unit

What is the total contribution margin when 2,500 dresses are sold? 2,500 × £28 = £70,000

Learning Objective 3(continued)

Contribution margin percentage (contribution margin ratio) is the contribution margin per unit divided by the selling price.

What is Mary’s contribution margin percentage? £28 ÷ £70 = 40%

If Mary sells 3,000 dresses, revenues will be £210,000 and contribution margin would equal 40% × £210,000 = £84,000.

Learning Objective 4

Demonstrate three methods for determining the breakeven point and target operating profit

Learning Objective 4(continued)

Breakeven Point ...– is the sales level at which operating profit is zero.

At the breakeven point, sales minus variable expenses equals fixed expenses.

Total revenues = Total costs Abbreviations

USP = Unit selling price UVC = Unit variable costs UCM = Unit contribution margin CM% = Contribution margin percentage FC = Fixed costs Q = Quantity of output (units sold or manufactured) OP = Operating profit TOP = Target operating profit TNP = Target net profit

Learning Objective 4(continued)

Methods for Determining Breakeven Point Breakeven can be computed by using either the

equation method, the contribution margin method, or the graph method.

Equation Method With the equation approach, breakeven sales

in units is calculated as follows: (Unit sales price × Units sold) – (Variable unit

cost × units sold) – Fixed expenses = Operating profit

Learning Objective 4(continued)

Using the equation approach, compute the breakeven for Dresses by Mary. £70Q – £42Q – £84,000 = 0 £28Q = £84,000 Q = £84,000 ÷ £28 Q = 3,000 units

Learning Objective 4(continued)

Contribution Margin Method With the contribution margin method,

breakeven is calculated by using the following relationship:

(USP – UVC) × Q = FC + OP UCM × Q = FC + OP Q = (FC + OP) ÷ UCM £84,000 ÷ £28 = 3,000 units

Using the contribution margin percentage, what is the breakeven point for Dresses by Mary?

£84,000 ÷ 40% = £210,000

Learning Objective 4(continued)

Graph Method In this method, we plot a line for total revenues

and total costs. The breakeven point is the point at which the

total revenue line intersects the total cost line. The area between the two lines to the right of

the breakeven point is the operating profit area.

Learning Objective 4(continued)

Breakeven

210

84

Revenue

Total expenses

3000 3500

245

231

£ (000)

Units

Graph Method (Dresses by Mary)

Learning Objective 4(continued)

• Target Operating Profit ...– can be determined by using any of three methods:

1 The equation method2 The contribution margin method 3 The graph method

Insert the target operating profit in the formula and solve for target sales either in pounds or units.

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

Learning Objective 4(continued)

Assume that Mary wants to have an operating profit of £14,000.

How many dresses must she sell? (£84,000 + £14,000) ÷ £28 = 3,500

What £ sales are needed to achieve this profit? (£84,000 + £14,000) ÷ 40% = £245,000

Learning Objective 5

Explain how sensitivity analysis can help managers cope with uncertainty

Learning Objective 5(continued)

Using CVP Analysis Suppose the management of Dresses by Mary

anticipates selling 3,200 dresses. Management is considering an advertising

campaign that would cost £10,000. It is anticipated that the advertising will increase

sales to 4,000 dresses. Should Mary advertise?

Learning Objective 5(continued)

3,200 dresses sold with no advertising: Contribution margin £89,600 Fixed

costs 84,000 Operating profit£ 5,600

4,000 dresses sold with advertising: Contribution margin £112,000 Fixed

costs 94,000 Operating profit£ 18,000

Mary should advertise. Operating profit increases by £12,400. The £10,000 increase in fixed costs is offset by

the £22,400 increase in the contribution margin.

Learning Objective 5(continued)

Instead of advertising, management is considering reducing the selling price to £61 per dress.

It is anticipated that this will increase sales to 4,500 dresses.

Should Mary decrease the selling price per dress to £61?

Learning Objective 5(continued)

3,200 dresses sold with no change in the selling price: Operating profit £ 5,600

4,500 dresses sold at a reduced selling price:Contribution margin: (4,500 × £19)£85,500 Fixed costs 84,000 Operating profit £ 1,500

The selling price should not be reduced to £61. Operating profit decreases from £5,600 to

£1,500.

Learning Objective 5(continued)

Sensitivity Analysis and Uncertainty Sensitivity analysis is a “what if” technique that

examines how a result will change if the original predicted data are not achieved or if an underlying assumption changes.

Assume that Dresses by Mary can sell 4,000 dresses. Fixed costs are £84,000. Contribution margin ratio is 40%. At the present time Dresses by Mary cannot handle

more than 3,500 dresses. To satisfy a demand for 4,000 dresses, management

must acquire additional space for £6,000. Should the additional space be acquired?

Learning Objective 5(continued)

Revenues at breakeven with existing space are £84,000 ÷ 0.40 = £210,000.

Revenues at breakeven with additional space are £90,000 ÷ 0.40 = £225,000.

Operating profit at £245,000 revenues with existing space = (£245,000 × 0.40) – £84,000 = £14,000.

(3,500 dresses × £28) – £84,000 = £14,000 Operating profit at £280,000 revenues with additional

space = (£280,000 × 0.40) – £90,000 = £22,000. (4,000 dresses × £28 contribution margin) – £90,000 =

£22,000

Learning Objective 6

Illustrate how CVP can assist cost planning

Learning Objective 6(continued)

Alternative Fixed/Variable Cost Structures Suppose that the factory Dresses by Mary uses

to obtain the merchandise offers Mary the following:

Decrease the price they charge Mary from £32 to £25 and charge an annual administrative fee of £30,000.

What is the new contribution margin?

Learning Objective 6(continued)

£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

Learning Objective 6(continued)

Management questions what sales volume would yield an identical operating profit regardless of the arrangement. 28X – 84,000 = 35X – 114,000 114,000 – 84,000 = 35X – 28X 7X = 30,000 X = 4,286 dresses

Cost with existing arrangement = Cost with new arrangement .60X + 84,000 = 0.50X + 114,000 0.10X = £30,000 X = £300,000 (£300,000 × 0.40) – £ 84,000 = £36,000 (£300,000 × 0.50) – £114,000 = £36,000

Learning Objective 6(continued)

Operating Leverage ...– measures the relationship between a company’s

variable and fixed expenses. It is greatest in organisations that have high fixed

expenses and low per unit variable expenses. The degree of operating leverage shows how a

percentage change in sales volume affects profit. Degree of operating leverage = Contribution margin ÷

Operating profit What is the degree of operating leverage of

Dresses by Mary at the 3,500 sales level under both arrangements?

Learning Objective 6(continued)

Existing arrangement: 3,500 × £28 = £98,000 contribution margin £98,000 contribution margin – £84,000 fixed

costs = £14,000 operating profit £98,000 ÷ £14,000 = 7.0

New arrangement: 3,500 × £35 = £122,500 contribution margin £122,500 contribution margin – £114,000 fixed

costs = £8,500 £122,500 ÷ £8,500 = 14.4

Learning Objective 7

Describe the effect of revenue mix on operating profit

Learning Objective 7(continued)

Effects of Revenue Mix on Profit Revenue mix (or Sales mix) is the combination

of product that a business sells.Assume that Dresses by Mary is

considering selling blouses. This will not require any additional fixed costs. It expects to sell 2 blouses at £20 each for

every dress it sells. The variable cost per blouse is £9.

What is the new breakeven point?

Learning Objective 7(continued)

The contribution margin per dress is £28 (£70 selling price – £42 variable cost).

The contribution margin per blouse is

£20 – £9 = £11. The contribution margin of the mix is

£28 + (2 × £11) = £28 + £22 = £50. £84,000 fixed costs ÷ £50 = 1,680 packages 1,680 × 2 = 3,360 blouses

1,680 × 1 = 1,680 dresses Total units = 5,040

What is the breakeven in £?

Learning Objective 7(continued)

1,680 × 2 = 3,360 blouses × £20 =£ 67,200 1,680 × 1 = 1,680 dresses × £70 =

117,600 £184,800

What is the weighted average budgeted contribution margin? Dresses Blouses 1

× £28 + 2 × £11 = £50 ÷ 3 = £16.667 Breakeven point for the two products is: £84,000 ÷

£16.667 = 5,040 units 5,040 × 1/3 = 1,680 dresses 5,040 × 2/3 = 3,360 blouses

Learning Objective 7(continued)

Revenue mix can be stated in sales £: Dresses Blouses

Sales price £70£40 Variable costs 42 18 Contribution margin

£28 £22 Contribution margin ratio 40% 55%

Assume the revenue mix in £ is 63.6% dresses and 36.4% blouses. Weighted contribution would be: 40% ×

63.6% = 25.44% dresses 55% × 36.4% = 20.02% blouses

45.46%

Learning Objective 7(continued)

Breakeven sales £ is £84,000 ÷ 45.46% = £184,778 (rounding).

£184,778 × 63.6% = £117,519 dress sales £184,778 × 36.4% = £67,259 blouse sales

Learning Objective 7(continued)

CVP Analysis in Service and Non-profit Organisations CVP can also be applied to decisions by

manufacturing, service, and non-profit organisations.

The key to applying CVP analysis in service and non-profit organisations is measuring their output.