1. Objectives 1. Classify costs by their behavior as variable costs, fixed costs, or mixed costs. 2. Compute the contribution margin, the contribution margin ratio, and the unit contribution margin, and explain how they may be useful to management. 3. Using the unit contribution margin, determine the break-even point and the volume necessary to achieve a target profit. Chapter 18 Cost Behavior and Cost-Volume-Profit Analysis

2. 4. Using a cost-volume profit chart and a profit- volume chart, determine the break-even point and the volume necessary to achieve a target profit. ObjectivesObjectives 5. Calculate the break-even point for a business selling more than one product. 6. Compute the margin of safety and the operating leverage, and explain how managers use this concept. 7. List the assumptions underlying cost- volume-profit analysis.

3. Jason Inc. produces stereo sound systems under the brand name of J-Sound. The parts for the stereo are purchased from an outside supplier for $10 per unit (a variable cost). Variable Cost Cost Behavior

4. Total Variable Cost Graph Total Costs $300,000 $250,000 $200,000 $150,000 $100,000 $50,000 102030 0 Units Produced (in thousands) Variable Cost Unit Variable Cost Graph $20 $15 $10 $5 0 Cost per Unit 102030 Units Produced (000)

5. Total Costs $300,000 $250,000 $200,000 $150,000 $100,000 $50,000 102030 0 $20 $15 $10 $5 0 Cost per Unit 102030 Number of Units Produced Units Produced (000) Direct Materials Cost per Unit Total Direct Materials Cost 5,000 units$10$ 50,000 10,00010l00,000 15,00010150,000 20,00010200,000 25,00010250,000 30,00010300,000 Variable Cost

6. The production supervisor for Minton Inc.’s Los Angeles plant is Jane Sovissi. She is paid $75,000 per year. The plant produces from 50,000 to 300,000 bottles of perfume. Fixed Costs

7. Number of Bottles Produced Total Salary for Jane Sovissi 50,000 bottles$75,000$1.500 100,00075,0000.750 150,00075,0000.500 200,00075,0000.375 250,00075,0000.300 300,00075,0000.250 Salary per Bottle Produced Fixed Costs

8. Total Fixed Cost Graph Total Costs $150,000 $125,000 $100,000 $75,000 $50,000 $25,000 100200300 0 Unit Fixed Cost Graph Bottles Produced (000) Number of Bottles Produced Cost per Unit $1.50 $1.25 $1.00 $.75 $.50 $.25 100200300 0 Units Produced (000) Total Salary for Jane Sovissi 50,000 bottles$75,000$1.500 100,00075,0000.750 15,00075,0000.500 20,00075,0000.375 25,00075,0000.300 30,00075,0000.250 Salary per Bottle Produced

9. Simpson Inc. manufactures sails using rented equipment. The rental charges are $15,000 per year, plus $1 for each machine hour used over 10,000 hours.

10. Mixed Costs Total Mixed Cost Graph Total Costs 0 Total Machine Hours (000) $45,000 $40,000 $35,000 $30,000 $25,000 $20,000 $15,000 $10,000 $5,000 10203040 Mixed costs are usually separated into their fixed and variable components for management analysis. Mixed costs are sometimes called semivariable or semifixed costs.

11. The high-low method is a simple way to separate mixed costs into their fixed and variable components. Mixed Costs Low High

12. Actual costs incurred ProductionTotal (Units) Cost $ High-Low Method Variable cost per unit = Highest level of activity ($) minus lowest level of activity ($) Highest level of activity (units) minus lowest level of activity (units) Activity relates to units of production June1,000$45,550 July1,50052,000 August2,10061,500 September1,80057,500 October75041,250

13. $61,500 – $41,250 2,100 – 750 Actual costs incurred ProductionTotal (Units) Cost Variable cost per unit = High-Low Method June1,000$45,550 July1,50052,000 August2,10061,500 September1,80057,500 October75041,250 = $15 $20,250 1,350 =

14. Actual costs incurred ProductionTotal (Units) Cost Variable cost per unit = $15 What is the total fixed cost (using the highest level)? Total cost = (Variable cost per unit x Units of production) + Fixed cost June1,000$45,550 July1,50052,000 August2,10061,500 September1,80057,500 October75041,250 $61,500 = ($15 x 2,100) + Fixed cost $61,500 = ($15 x 2,100) + $30,000 High-Low Method

15. Actual costs incurred ProductionTotal (Units) Cost Variable cost per unit = $15 The fixed cost is the same at the lowest level. Total cost = (Variable cost per unit x Units of production) + Fixed cost June1,000$45,550 July1,50052,000 August2,10061,500 September1,80057,500 October75041,250 $41,250 = ($15 x 750) + Fixed cost $41,250 = ($15 x 750) + $30,000 High-Low Method

16. Variable Costs Total Fixed Costs Total Units Produced Total Costs Total Units Produced Per Unit Cost Total Variable Costs Total Units Produced Unit Variable Costs Total Units Produced Total Costs Per Unit Cost Fixed Costs Review Unit Fixed Costs Unit costs remain the same regardless of activity. Total costs increase and decreases with activity level. Total costs increase and decreases proportionately with activity level. Unit costs remain the same per unit regardless of activity.

18. Contribution Margin Income Statement Sales (50,000 units)$1,000,000 Variable costs 600,000 Contribution margin$ 400,000 Fixed costs 300,000 Income from operations$ 100,000 The contribution margin is available to cover the fixed costs and income from operations. FIXED COSTS Contribution margin Income from Operations

19. Contribution Margin Income Statement Sales Sales Variable VariablecostsContributionmargin –= Sales (50,000 units)$1,000,000 Variable costs 600,000 Contribution margin$ 400,000 Fixed costs 300,000 Income from operations$ 100,000

20. Contribution Margin Ratio 100% 60% 40% 30% 10% Contribution margin ratio = Sales – Variable costs Sales Contribution margin ratio = $1,000,000 – $600,000 $1,000,000 Contribution margin ratio = 40% Sales (50,000 units)$1,000,000 Variable costs 600,000 Contribution margin$ 400,000 Fixed costs 300,000 Income from operations$ 100,000

21. 100% 60% 40% 30% 10% The contribution margin can be expressed three ways: 1. Total contribution margin in dollars. 3. Contribution margin ratio (percentage). 3. Unit contribution margin (dollars per unit). The contribution margin can be expressed three ways: 1. Total contribution margin in dollars. 3. Contribution margin ratio (percentage). 3. Unit contribution margin (dollars per unit). $20 12 $ 8 Sales (50,000 units)$1,000,000 Variable costs 600,000 Contribution margin$ 400,000 Fixed costs 300,000 Income from operations$ 100,000 Contribution Margin Ratio

22. What is the break-even point? RevenuesCosts = Break-even

23. Calculating the Break-Even Point At the break-even point, fixed costs and the contribution margin are equal. Sales (? units)$ ? Variable costs ? Contribution margin$ 90,000 Fixed costs 90,000 Income from operations$ 0 $25 15 $10

24. 9,000 units Sales ($25 x ? units)$ ? Variable costs ($15 x ? units) ? Contribution margin$ 90,000 Fixed costs 90,000 Income from operations$ 0 $25 15 $10 Break-even sales (units) = Unit contribution margin Fixed costs $90,000 $10 Sales ($25 x 9,000)$225,000 Variable costs ($15 x 9,000) 135,000 Contribution margin$ 90,000 Fixed costs 90,000 Income from operations$ 0 Calculating the Break-Even Point In Units = =

25. Sales ($250 x ? units)$ ? Variable costs ($145 x ? units) ? Contribution margin$ ? Fixed costs 840,000 Income from operations$ 0 $250 145 $105 Break-even sales (units) = Unit contribution margin Fixed costs $840,000 $105 8,000 units Calculating the Break-Even Point In Units The unit selling price is $250 and unit variable cost is $145. Fixed costs are $840,000.

26. Sales ($25 x ? units)$ ? Variable costs ($15 x ? units) ? Contribution margin$ ? Fixed costs 840,000 Income from operations$ 0 $250 145 $105 Break-even sales (units) = Unit contribution margin Fixed costs $840,000 $100 8,400 units $250 150 $100 Next, assume variable costs is increased by $5. Calculating the Break-Even Point In Units The unit selling price is $250 and unit variable cost is $145. Fixed costs are $840,000.

27. Sales $ ? Variable costs ? Contribution margin$ ? Fixed costs $600,000 Income from operations$ 0 Break-even sales (units) = Unit contribution margin Fixed costs $600,000 $20 30,000 units $50 30 $20 Calculating the Break-Even Point In Units A firm currently sells their product at $50 per unit and it has a related unit variable cost of $30. The fixed costs are $600,000.

28. Sales $ ? Variable costs ? Contribution margin$ ? Fixed costs $600,000 Income from operations$ 0 Break-even sales (units) = Unit contribution margin Fixed costs $600,000 $30 20,000 units $50 30 $20 $60 30 $30 Calculating the Break-Even Point In Units Management increases the selling price from $50 to $60.

29. Summary of Effects of Changes on Break-Even Point

30. Target Profit Fixed costs are estimated at $200,000, and the desired profit is $100,000. The unit selling price is $75 and the unit variable cost is $45. The firm wishes to make a $100,000 profit. Sales (? units)$ ? Variable costs ? Contribution margin$ ? Fixed costs 200,000 Income from operations$ 0 $75 45 $35 In Units

31. Sales (? units)$ ? Variable costs ? Contribution margin$ ? Fixed costs 200,000 Income from operations$ 0 Sales (units) = Unit contribution margin Fixed costs + target profit $200,000 + $100,000 $30 10,000 units Target Profit In Units $75 45 $30

32. $75 45 $30 Sales (10,000 units x $75)$750,000 Variable costs (10,000 x $45) 450,000 Contribution margin$300,000 Fixed costs 200,000 Income from operations$100,000 Proof that sales of 10,000 units will provide a profit of $100,000. Target Profit

33. Graphic Approach to Cost-Volume-Profit Analysis

34. Cost-Volume-Profit Chart Sales and Costs ($000) 0 Units of Sales (000) $500 $450 $400 $350 $300 $250 $200 $150 $100 $ 50 Unit selling price$ 50 Unit variable cost 30 Unit contribution margin$ 20 Total fixed costs$100,000 Unit selling price$ 50 Unit variable cost 30 Unit contribution margin$ 20 Total fixed costs$100,000 60% Total SalesVariable Costs 12345678910

35. Cost-Volume-Profit Chart Sales and Costs ($000) 0 Units of Sales (000) $500 $450 $400 $350 $300 $250 $200 $150 $100 $ 50 Unit selling price$ 50 Unit variable cost 30 Unit contribution margin$ 20 Total fixed costs$100,000 Unit selling price$ 50 Unit variable cost 30 Unit contribution margin$ 20 Total fixed costs$100,000 60% 40% Contribution Margin 100% 60% 40% 12345678910

36. Cost-Volume-Profit Chart Sales and Costs ($000) 0 Units of Sales (000) $500 $450 $400 $350 $300 $250 $200 $150 $100 $ 50 Unit selling price$ 50 Unit variable cost 30 Unit contribution margin$ 20 Total fixed costs$100,000 Unit selling price$ 50 Unit variable cost 30 Unit contribution margin$ 20 Total fixed costs$100,000 Fixed Costs 100% 60% 40%TotalCosts 12345678910

37. Cost-Volume-Profit Chart Sales and Costs ($000) 0 $500 $450 $400 $350 $300 $250 $200 $150 $100 $ 50 12345678910 Break-Even Point Units of Sales (000) Unit selling price$ 50 Unit variable cost 30 Unit contribution margin$ 20 Total fixed costs$100,000 Unit selling price$ 50 Unit variable cost 30 Unit contribution margin$ 20 Total fixed costs$100,000 100% 60% 40% $100,000 $20 = 5,000 units

38. Cost-Volume-Profit Chart Sales and Costs ($000) 0 Units of Sales (000) $500 $450 $400 $350 $300 $250 $200 $150 $100 $ 50 Unit selling price$ 50 Unit variable cost 30 Unit contribution margin$ 20 Total fixed costs$100,000 Unit selling price$ 50 Unit variable cost 30 Unit contribution margin$ 20 Total fixed costs$100,000 100% 60% 40% Operating Profit AreaOperating Loss Area

40. $100 $75 $50 $25 $ 0 $(25) $(50) $(75) $(100) Sales (10,000 units x $50)$500,000 Variable costs (10,000 units x $30) 300,000 Contribution margin (10,000 units x $20)$200,000 Fixed costs 100,000 Operating profit$100,000 Sales (10,000 units x $50)$500,000 Variable costs (10,000 units x $30) 300,000 Contribution margin (10,000 units x $20)$200,000 Fixed costs 100,000 Operating profit$100,000 Units of Sales (000’s) 12345678910 Relevant range is 10,000 units Operating Profit (Loss) $000’s

41. Units of Sales (000’s) 12345678910 Maximum loss is equal to the total fixed costs. Profit Line Operating loss Operating profit $100 $75 $50 $25 $ 0 $(25) $(50) $(75) $(100) Sales (10,000 units x $50)$500,000 Variable costs (10,000 units x $30) 300,000 Contribution margin (10,000 units x $20)$200,000 Fixed costs 100,000 Operating profit$100,000 Sales (10,000 units x $50)$500,000 Variable costs (10,000 units x $30) 300,000 Contribution margin (10,000 units x $20)$200,000 Fixed costs 100,000 Operating profit$100,000 Maximum profit within the relevant range. Operating Profit (Loss) $000’s

42. Operating Profit (Loss) $000’s Units of Sales (000’s) 12345678910 Operating loss Operating profit Break-Even Point Sales (10,000 units x $50)$500,000 Variable costs (10,000 units x $30) 300,000 Contribution margin (10,000 units x $20)$200,000 Fixed costs 100,000 Operating profit$100,000 Sales (10,000 units x $50)$500,000 Variable costs (10,000 units x $30) 300,000 Contribution margin (10,000 units x $20)$200,000 Fixed costs 100,000 Operating profit$100,000 $100 $75 $50 $25 $ 0 $(25) $(50) $(75) $(100)

43. Sales Mix Considerations

44. Cascade Company sold 8,000 units of Product A and 2,000 units of Product B during the past year. Cascade Company’s fixed costs are $200,000. Other relevant data are as follows: Sales$ 90 $140 Variable costs70 95 Contribution margin$ 20 $ 45 Sales mix 80% 20% Products A B

45. Sales$ 90 $140 Variable costs70 95 Contribution margin$ 20 $ 45 Sales mix 80% 20% Sales Mix Considerations Sales Mix Considerations Products A B Product contribution margin$16 $ 9 $25 Fixed costs, $200,000

46. Sales Mix Considerations Sales Mix Considerations Products A B Product contribution margin$16 $ 9 $25 Break-even sales units $200,000 $25 Fixed costs, $200,000

47. Sales Mix Considerations Sales Mix Considerations Products A B Product contribution margin$16 $ 9 $25 Break-even sales units $200,000 $25 Fixed costs, $200,000 = 8,000 units

48. Sales Mix Considerations Sales Mix Considerations Products A B Product contribution margin$16 $ 9 $25 A: A: 8,000 units x Sales Mix (80%) =6,400 B: B: 8,000 units x Sales Mix (20%) =1,600

49. PROOF Product A Product B Total Sales: 6,400 units x $90$576,000$576,000 1,600 units x $140$224,000 224,000 Total sales$576,000$224,000$800,000 Variable costs: 6,400 x $70$448,000$448,000 1,600 x $95$152,000 152,000 Total variable costs$448,000$152,000$600,000 Contribution margin$128,000$ 72,000$200,000 Fixed costs 200,000 Income from operations$ 0 Break-even point

50. Margin of Safety

51. Margin of Safety = Sales – Sales at break-even point Sales The margin of safety indicates the possible decrease in sales that may occur before an operating loss results. Margin of Safety = $250,000 – $200,000 $250,000 Margin of Safety = 20%

52. Operating Leverage

53. Both companies have the same contribution margin. Operating Leverage Jones Inc. Wilson Inc. Contribution margin Income from operations Sales$400,000$400,000 Variable costs 300,000 300,000 Contribution margin$100,000$100,000 Fixed costs 80,000 50,000 Income from operations$ 20,000$ 50,000 Contribution margin? ?

54. Contribution margin Income from operations Jones Inc. Wilson Inc. $100,000 $20,000 = 5.0 Jones Inc.: Operating Leverage 5.0 Sales$400,000$400,000 Variable costs 300,000 300,000 Contribution margin$100,000$100,000 Fixed costs 80,000 50,000 Income from operations$ 20,000$ 50,000 Contribution margin?

55. Contribution margin Income from operations Jones Inc. Wilson Inc. = 5.0 $100,000 $20,000 Jones Inc. Operating Leverage Sales$400,000$400,000 Variable costs 300,000 300,000 Contribution margin$100,000$100,000 Fixed costs 80,000 50,000 Income from operations$ 20,000$ 50,000 Contribution margin5.0 ?

56. Contribution margin Income from operations Jones Inc. Wilson Inc. = 2.0 $100,000 Wilson Inc.: Capital intensive? Labor intensive? 2.0 Operating Leverage Sales$400,000$400,000 Variable costs 300,000 300,000 Contribution margin$100,000$100,000 Fixed costs 80,000 50,000 Income from operations$ 20,000$ 50,000 Contribution margin5.0 $50,000

57. Assumptions of Cost-Volume-Profit Analysis 1.Total sales and total costs can be represented by straight lines. 2.Within the relevant range of operating activity, the efficiency of operations does not change. 3.Costs can be accurately divided into fixed and variable components. 4.The sales mix is constant. 5.There is no change in the inventory quantities during the period. The reliability of cost-volume-profit analysis depends upon several assumptions.

58. The End Chapter 18