2. ©2003 Prentice Hall Business Publishing, Cost Accounting 11/e, Horngren/Datar/Foster 3 - 1 Cost-Volume-Profit Analysis Chapter 3

3. ©2003 Prentice Hall Business Publishing, Cost Accounting 11/e, Horngren/Datar/Foster 3 - 2 Learning Objective 1 Understand the assumptions underlying cost-volume-profit (CVP) analysis.

4. ©2003 Prentice Hall Business Publishing, Cost Accounting 11/e, Horngren/Datar/Foster 3 - 3 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.

5. ©2003 Prentice Hall Business Publishing, Cost Accounting 11/e, Horngren/Datar/Foster 3 - 4 Cost-Volume-Profit Assumptions and Terminology 3. When graphed, the behavior 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.

6. ©2003 Prentice Hall Business Publishing, Cost Accounting 11/e, Horngren/Datar/Foster 3 - 5 Cost-Volume-Profit Assumptions and Terminology 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.

7. ©2003 Prentice Hall Business Publishing, Cost Accounting 11/e, Horngren/Datar/Foster 3 - 6 Cost-Volume-Profit Assumptions and Terminology Operating income = Total revenues from operations – Cost of goods sold and operating costs (excluding income taxes) Net income = Operating income – Income taxes

8. ©2003 Prentice Hall Business Publishing, Cost Accounting 11/e, Horngren/Datar/Foster 3 - 7 Learning Objective 2 Explain the features of CVP analysis.

9. ©2003 Prentice Hall Business Publishing, Cost Accounting 11/e, Horngren/Datar/Foster 3 - 8 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.

10. ©2003 Prentice Hall Business Publishing, Cost Accounting 11/e, Horngren/Datar/Foster 3 - 9 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)

11. ©2003 Prentice Hall Business Publishing, Cost Accounting 11/e, Horngren/Datar/Foster 3 - 10 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

12. ©2003 Prentice Hall Business Publishing, Cost Accounting 11/e, Horngren/Datar/Foster 3 - 11 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%

13. ©2003 Prentice Hall Business Publishing, Cost Accounting 11/e, Horngren/Datar/Foster 3 - 12 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.

14. ©2003 Prentice Hall Business Publishing, Cost Accounting 11/e, Horngren/Datar/Foster 3 - 13 Learning Objective 3 Determine the breakeven point and output level needed to achieve a target operating income using the equation, contribution margin, and graph methods.

15. ©2003 Prentice Hall Business Publishing, Cost Accounting 11/e, Horngren/Datar/Foster 3 - 14 Breakeven Point Sales Variable expenses Fixed expenses – = Total revenues = Total costs

16. ©2003 Prentice Hall Business Publishing, Cost Accounting 11/e, Horngren/Datar/Foster 3 - 15 Abbreviations SP = Selling price VCU = Variable cost per unit CMU = Contribution margin per unit CM% = Contribution margin percentage FC = Fixed costs

17. ©2003 Prentice Hall Business Publishing, Cost Accounting 11/e, Horngren/Datar/Foster 3 - 16 Abbreviations Q = Quantity of output units sold (and manufactured) OI = Operating income TOI = Target operating income TNI = Target net income

18. ©2003 Prentice Hall Business Publishing, Cost Accounting 11/e, Horngren/Datar/Foster 3 - 17 Equation Method $70Q – $42Q – $84,000 = 0 $28Q = $84,000 Q = $84,000 ÷ $28 = 3,000 units Let Q = number of units to be sold to break even (Selling price × Quantity sold) – (Variable unit cost × Quantity sold) – Fixed costs = B/E in units

19. ©2003 Prentice Hall Business Publishing, Cost Accounting 11/e, Horngren/Datar/Foster 3 - 18 Contribution Margin Method $84,000 ÷ $28 = 3,000 units (Fixed Costs ÷ CMU) = Breakeven point in units Breakeven revenues = FC ÷ CM% $84,000 ÷ [(28 ÷ 70) x 100] = $210,000

20. ©2003 Prentice Hall Business Publishing, Cost Accounting 11/e, Horngren/Datar/Foster Graph Method 3 - 19 1.Draw the Total Cost line a.Start with the point at which the fixed cost intersects the vertical axis ($84,000 in our example) b.Select a second point on the TC line. You need a second Q. For example, assume Q = 2,000. TC = 42Q + $84,000. TC = 168,000. Plot this point on the graph. Extend a line horizontally from the first point in (a) above through the second point as now calculated. This is the TC line. 2.Draw the Total Revenue line a.Begin with the point ‘0’ on the graph where the two axes intersect b.Select a quantity (you may use the same as for TC) and compute TR. Plot point on the graph and extend a line from the (a) above through this new point on the graph. This is now your TR line

21. ©2003 Prentice Hall Business Publishing, Cost Accounting 11/e, Horngren/Datar/Foster 3 - 20 Graph Method Revenue Total costs Breakeven Fixed costs

22. ©2003 Prentice Hall Business Publishing, Cost Accounting 11/e, Horngren/Datar/Foster 3 - 21 Target Operating Income (Fixed costs + Target operating income) divided either by Contribution margin percentage or Contribution margin per unit

23. ©2003 Prentice Hall Business Publishing, Cost Accounting 11/e, Horngren/Datar/Foster 3 - 22 Target Operating Income Assume that management wants to have an operating income of $14,000. How many pairs of pants must be sold? Units to be sold = (Fixed Costs + Target Income) ÷ CMU ($84,000 + $14,000) ÷ $28 = 3,500 What dollar sales are needed to achieve this income? Revenue needed = (Fixed Costs + Target Income) ÷ CM% ($84,000 + $14,000) ÷ 40% = $245,000 ** Remember CM% = (Price – VC per unit) x 100**

24. ©2003 Prentice Hall Business Publishing, Cost Accounting 11/e, Horngren/Datar/Foster 3 - 23 Learning Objective 4 Understand how income taxes affect CVP analysis.

25. ©2003 Prentice Hall Business Publishing, Cost Accounting 11/e, Horngren/Datar/Foster 3 - 24 Target Net Income and 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

26. ©2003 Prentice Hall Business Publishing, Cost Accounting 11/e, Horngren/Datar/Foster 3 - 25 Target Net Income and Income Taxes Example How many units must be sold? (FC + [Target Net Income ÷ (1 – Tax rate)]) CMU (84,000 + [35,711 ÷ (1- 0.3) ] ) (70 – 42) (84,000 + 51,016) ÷ $28 Q = $135,016 ÷ $28 = 4,822 pairs of pants

27. ©2003 Prentice Hall Business Publishing, Cost Accounting 11/e, Horngren/Datar/Foster 3 - 26 Target Net Income and 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

28. ©2003 Prentice Hall Business Publishing, Cost Accounting 11/e, Horngren/Datar/Foster 3 - 27 Learning Objective 5 Explain CVP analysis in decision making and how sensitivity analysis helps managers cope with uncertainty.

29. ©2003 Prentice Hall Business Publishing, Cost Accounting 11/e, Horngren/Datar/Foster 3 - 28 Using CVP Analysis Example Suppose the management anticipates selling 3,200 pairs of pants. Management is considering an advertising campaign that would cost $10,000. It is anticipated that the advertising will increase sales to 4,000 units. Should the business advertise?

30. ©2003 Prentice Hall Business Publishing, Cost Accounting 11/e, Horngren/Datar/Foster 3 - 29 Using CVP Analysis Example 3,200 pairs of pants sold with no advertising: Contribution margin$89,600 Fixed costs 84,000 Operating income$ 5,600 4,000 pairs of pants sold with advertising: Contribution margin$112,000 Fixed costs 94,000 Operating income$ 18,000

31. ©2003 Prentice Hall Business Publishing, Cost Accounting 11/e, Horngren/Datar/Foster 3 - 30 Using CVP Analysis Example Instead of advertising, management is considering reducing the selling price to $61 per pair of pants. It is anticipated that this will increase sales to 4,500 units. Should management decrease the selling price per pair of pants to $61?

32. ©2003 Prentice Hall Business Publishing, Cost Accounting 11/e, Horngren/Datar/Foster 3 - 31 Using CVP Analysis Example 3,200 pairs of pants sold with no change in the selling price: Operating income = $5,600 4,500 pairs of pants sold at a reduced selling price: Contribution margin: (4,500 × $19)$85,500 Fixed costs 84,000 Operating income$ 1,500

33. ©2003 Prentice Hall Business Publishing, Cost Accounting 11/e, Horngren/Datar/Foster 3 - 32 Sensitivity Analysis and Uncertainty 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.

34. ©2003 Prentice Hall Business Publishing, Cost Accounting 11/e, Horngren/Datar/Foster 3 - 33 Sensitivity Analysis and Uncertainty 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

35. ©2003 Prentice Hall Business Publishing, Cost Accounting 11/e, Horngren/Datar/Foster 3 - 34 Sensitivity Analysis and Uncertainty 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

36. ©2003 Prentice Hall Business Publishing, Cost Accounting 11/e, Horngren/Datar/Foster 3 - 35 Sensitivity Analysis and Uncertainty 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

37. ©2003 Prentice Hall Business Publishing, Cost Accounting 11/e, Horngren/Datar/Foster 3 - 36 Learning Objective 6 Use CVP analysis to plan fixed and variable costs.

38. ©2003 Prentice Hall Business Publishing, Cost Accounting 11/e, Horngren/Datar/Foster 3 - 37 Alternative Fixed/Variable Cost Structures Example What is the new contribution margin? Decrease the price they charge from $32 to $25 and charge an annual administrative fee of $30,000. Suppose that the factory the Pants Shop is using to obtain the merchandise offers the following:

39. ©2003 Prentice Hall Business Publishing, Cost Accounting 11/e, Horngren/Datar/Foster 3 - 38 Alternative Fixed/Variable Cost Structures Example $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

40. ©2003 Prentice Hall Business Publishing, Cost Accounting 11/e, Horngren/Datar/Foster 3 - 39 Alternative Fixed/Variable Cost Structures Example Management questions what sales volume would yield an identical operating income regardless of the arrangement. 28x – 84,000 = 35x – 114,000 114,000 – 84,000 = 35x – 28x 7x = 30,000 x = 4,286 pairs of pants

41. ©2003 Prentice Hall Business Publishing, Cost Accounting 11/e, Horngren/Datar/Foster 3 - 40 Alternative Fixed/Variable Cost Structures Example Cost with existing arrangement = Cost with new arrangement.60x + 84,000 =.50x + 114,000.10x = $30,000  x = $300,000 ($300,000 ×.40) – $ 84,000 = $36,000 ($300,000 ×.50) – $114,000 = $36,000

42. ©2003 Prentice Hall Business Publishing, Cost Accounting 11/e, Horngren/Datar/Foster 3 - 41 Learning Objective 7 Apply CVP analysis to a company producing different products.

43. ©2003 Prentice Hall Business Publishing, Cost Accounting 11/e, Horngren/Datar/Foster 3 - 42 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.

44. ©2003 Prentice Hall Business Publishing, Cost Accounting 11/e, Horngren/Datar/Foster 3 - 43 Effects of Sales Mix on Income What is the contribution margin of the mix? Contribution margin per shirt: Price – VC per unit $20 – $9 = $11 CMU for pants + CMU for shirts $28 + (2 × $11) = $28 + $22 = $50 *** The $28 is from the previous slides**

45. ©2003 Prentice Hall Business Publishing, Cost Accounting 11/e, Horngren/Datar/Foster 3 - 44 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

46. ©2003 Prentice Hall Business Publishing, Cost Accounting 11/e, Horngren/Datar/Foster 3 - 45 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

47. ©2003 Prentice Hall Business Publishing, Cost Accounting 11/e, Horngren/Datar/Foster 3 - 46 Effects of Sales Mix on Income What is the weighted-average budgeted contribution margin? Pants: 1 × $28 + Shirts: 2 × $11 = $50 ÷ 3 = $16.667

48. ©2003 Prentice Hall Business Publishing, Cost Accounting 11/e, Horngren/Datar/Foster 3 - 47 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

49. ©2003 Prentice Hall Business Publishing, Cost Accounting 11/e, Horngren/Datar/Foster 3 - 48 Effects of Sales Mix on Income Sales mix can be stated in sales dollars: Pants Shirts Sales price$70$40 Less: Variable costs 42 18 Contribution margin$28$22 Contribution margin ratio 40% 55%

50. ©2003 Prentice Hall Business Publishing, Cost Accounting 11/e, Horngren/Datar/Foster 3 - 49 Effects of Sales Mix on Income Now, let’s 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%

51. ©2003 Prentice Hall Business Publishing, Cost Accounting 11/e, Horngren/Datar/Foster 3 - 50 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

52. ©2003 Prentice Hall Business Publishing, Cost Accounting 11/e, Horngren/Datar/Foster 3 - 51 Contribution Margin versus Gross Margin Contribution income statement emphasizes contribution margin. Financial accounting income statement emphasizes gross margin.

53. ©2003 Prentice Hall Business Publishing, Cost Accounting 11/e, Horngren/Datar/Foster 3 - 52 End of Module 3