# volume-profit relationships

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1 Slide Accounting for decision making 1.3 Cost-volume volume-profit relationships

2 Slide Introduction This chapter examines one of the most basic planning tools available to managers: cost volume profit (CVP) analysis. Cost volume 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.

3 Slide 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 CVP 4 Demonstrate three methods for determining the breakeven point and target operating profit

4 Slide Learning Objectives (Continued) 5 Explain how sensitivity analysis can help managers cope with uncertainty

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

6 Slide General case 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.

7 Slide Cost Volume 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.

8 Slide Cost Volume Volume Profit Assumptions and Terminology (Continued) 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.

9 Slide Cost Volume Volume Profit Assumptions and Terminology (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.

10 Slide Cost Volume Volume Profit Assumptions and Terminology (Continued) Operating profit = Total revenues Total Cost Net Profit = Operating profit + Non-operating operating revenues (such as interest revenue) Non-operating operating costs (such as interest cost) Profit taxes

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

12 Slide Operating Profit versus Net Profit Operating profit statement emphasises operating profit (contribution margin). Revenues Variable cost of goods sold Variable operating costs Fixed operating costs = Operating profit Operating profit Taxes = Net profit

13 Slide Operating Profit versus Net Profit (Continued) Financial accounting profit statement emphasises operating profit. Revenues Cost of goods sold = Gross Profit Gross Profit Operating costs = Operating Profit

14 Slide Learning Objective 3 Describe the assumptions underlying CVP

15 Slide Assumptions of 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.

16 Slide Assumptions of CVP Analysis (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?

17 Slide Assumptions of CVP Analysis (Continued) 2, = 175,000 How much variable costs will she incur? 2, = 105,000 Would she show an operating profit or an operating loss? An operating loss 175, ,000 84,000 = ( 14,000)

18 Slide Assumptions of CVP Analysis (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 s contribution margin per unit?

19 Slide Assumptions of CVP Analysis (Continued) = 28 contribution margin per unit What is the total contribution margin when 2,500 dresses are sold? 2, = 70,000

20 Slide Assumptions of CVP Analysis (Continued) Contribution margin percentage (contribution margin ratio) is the contribution margin per unit divided by the selling price. What is Mary s s contribution margin percentage? = 40%

21 Slide Assumptions of CVP Analysis (Continued) If Mary sells 3,000 dresses, revenues will be 210,000 and contribution margin would equal 40% 210,000 = 84,000.

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

23 Slide Breakeven Point 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

24 Slide Abbreviations USP = Unit selling price UVC = Unit variable costs UCM = Unit contribution margin CM% = Contribution margin percentage FC = Fixed costs

25 Slide Abbreviations (Continued) Q = Quantity of output (units sold or manufactured) OP = Operating profit TOP = Target operating profit TNP = Target net profit

26 Slide Methods for Determining Breakeven Point Breakeven can be computed by using either the equation method, the contribution margin method or the graph method.

27 Slide 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

28 Slide Equation Method (Continued) Using the equation approach, compute the breakeven for Dresses by Mary. 70Q 42Q 84,000 = 0 28Q = 84,000 Q = 84, Q = 3,000 units

29 Slide 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, = 3,000 units

30 Slide Contribution Margin Method (Continued) Using the contribution margin percentage, what is the breakeven point for Dresses by Mary? 84,000 40% = 210,000

31 Slide 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.

32 Slide Graph Method Dresses by Mary (000) 245 Revenue 231 Breakeven Total expenses ,000 3,500 Units

33 Slide Target Operating Profit Target operating profit can be determined by using any of three methods: 1 The equation method 2 The contribution margin method 3 The graph method.

34 Slide Target Operating Profit (Continued) 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.

35 Slide Target Operating Profit (Continued) Assume that Mary wants to have an operating profit of 14,000. How many dresses must she sell? ( 84, ,000) 28 = 3,500 What sales are needed to achieve this profit? ( 84, ,000) 40% = 245,000

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

37 Slide 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?

38 Slide Using CVP Analysis (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

39 Slide Using CVP Analysis (Continued) 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.

40 Slide Using CVP Analysis (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?

41 Slide Using CVP Analysis (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

42 Slide Using CVP Analysis (Continued) The selling price should not be reduced to 61. Operating profit decreases from 5,600 to 1,500.

43 Slide 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.

44 Slide Sensitivity Analysis and Uncertainty (Continued) 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.

45 Slide Sensitivity Analysis and Uncertainty (Continued) To satisfy a demand for 4,000 dresses, management must acquire additional space for 6,000. Should the additional space be acquired?

46 Slide Sensitivity Analysis and Uncertainty (Continued) Revenues at breakeven with existing space are 84, = 210,000. Revenues at breakeven with additional space are 90, = 225,000.

47 Slide Sensitivity Analysis and Uncertainty (Continued) Operating profit at 245,000 revenues with existing space = ( 245, ) 84,000 = 14,000. (3,500 dresses 28) 84,000 = 14,000.

48 Slide Sensitivity Analysis and Uncertainty (Continued) Operating profit at 280,000 revenues with additional space = ( 280, ) 90,000 = 22,000. (4,000 dresses 28 contribution margin) 90,000 = 22,000.

49 Slide End of Chapter 1.3

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