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**Cost-Volume-Profit Relationships**

Chapter 8 Cost-Volume-Profit Relationships

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Introduction This 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.

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Learning Objectives Distinguish between the general case and a special case of CVP Explain the relationship between operating profit and net profit Describe the assumptions underlying CVP Demonstrate three methods for determining the breakeven point and target operating profit Explain how sensitivity analysis can help managers cope with uncertainty Illustrate how CVP can assist cost planning Describe the effect of revenue mix on operating profit

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

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

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**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:

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**Explain the relationship between operating profit and net profit**

Learning Objective 2 Explain the relationship between operating profit and net profit

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**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

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**Describe the assumptions underlying CVP**

Learning Objective 3 Describe the assumptions underlying CVP

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**Learning Objective 1(continued)**

Cost-Volume-Profit Assumptions and Terminology Changes in the level of revenues and costs arise only because of changes in the number of product (or service) units produced and sold. Total costs can be divided into a fixed component and a component that is variable with respect to the level of output. 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). The unit selling price, unit variable costs, and fixed costs are known and constant.

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**Learning Objective 1(continued)**

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. All revenues and costs can be added and compared without taking into account the time value of money.

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**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.

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**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)

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**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

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**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.

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Learning Objective 4 Demonstrate three methods for determining the breakeven point and target operating profit

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**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

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**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

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**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

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**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

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**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.

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**Learning Objective 4(continued)**

Graph Method (Dresses by Mary) £ (000) Revenue 245 Breakeven Total expenses 231 210 84 Units

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**Learning Objective 4(continued)**

Target Operating Profit ... can be determined by using any of three methods: The equation method The contribution margin method 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

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**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

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Learning Objective 5 Explain how sensitivity analysis can help managers cope with uncertainty

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**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?

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**Learning Objective 5(continued)**

3,200 dresses sold with no advertising: Contribution margin £89, Fixed costs , Operating profit £ 5,600 4,000 dresses sold with advertising: Contribution margin £112, Fixed costs , 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.

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**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?

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**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, Fixed costs , Operating profit £ 1,500 The selling price should not be reduced to £61. Operating profit decreases from £5,600 to £1,500.

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**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?

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**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

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**Illustrate how CVP can assist cost planning**

Learning Objective 6 Illustrate how CVP can assist cost planning

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**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?

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**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

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**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

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**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?

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**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

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**Describe the effect of revenue mix on operating profit**

Learning Objective 7 Describe the effect of revenue mix on operating profit

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**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?

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**Learning Objective 7(continued)**

The contribution margin per dress is £ (£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 ,680 × 1 = 1,680 dresses Total units = 5,040 What is the breakeven in £?

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**Learning Objective 7(continued)**

1,680 × 2 = 3,360 blouses × £20 = £ 67, ,680 × 1 = 1,680 dresses × £70 = 117, £184,800 What is the weighted average budgeted contribution margin? Dresses Blouses × £ × £11 = £50 ÷ 3 = £16.667 Breakeven point for the two products is: £84,000 ÷ £ = 5,040 units 5,040 × 1/3 = 1,680 dresses 5,040 × 2/3 = 3,360 blouses

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**Learning Objective 7(continued)**

Revenue mix can be stated in sales £: Dresses Blouses Sales price £70 £ Variable costs Contribution margin £28 £22 Contribution margin ratio 40% % Assume the revenue mix in £ is 63.6% dresses and 36.4% blouses. Weighted contribution would be: % × 63.6% = 25.44% dresses % × 36.4% = 20.02% blouses %

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**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

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**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.

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