0. Cost-Volume-Profit Relationships
Chapter 8
Cost-Volume-Profit Relationships

1. 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.

2. 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

3. 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

4. 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:

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

6. 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

7. Describe the assumptions underlying CVP
Learning Objective 3
Describe the assumptions underlying CVP

8. 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.

9. 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.

10. 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.

11. 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)

12. 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

13. 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.

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

15. 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

16. 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

17. 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

18. 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

19. 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.

20. Learning Objective 4(continued)
Graph Method (Dresses by Mary)
£ (000)
Revenue
245
Breakeven
Total expenses
231
210 84
Units

21. 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

22. 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

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

24. 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?

25. 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.

26. 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?

27. 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.

28. 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?

29. 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

30. Illustrate how CVP can assist cost planning
Learning Objective 6
Illustrate how CVP can assist cost planning

31. 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?

32. 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

33. 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

34. 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?

35. 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

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

37. 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?

38. 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 £?

39. 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

40. 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 %

41. 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

42. 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.