1. © The McGraw-Hill Companies, Inc., 2007 McGraw-Hill/Irwin Chapter 22 Cost-Volume-Profit Analysis

2. © The McGraw-Hill Companies, Inc., 2007 McGraw-Hill/Irwin Conceptual Learning Objectives C1: Describe different types of cost behavior in relation to production and sales volume C2: Identify assumptions in cost-volume profit analysis and explain their impact C3: Describe several applications of cost- volume-profit analysis

3. © The McGraw-Hill Companies, Inc., 2007 McGraw-Hill/Irwin A1: Compare the scatter diagram, high- low, and regression methods of estimating costs A2: Compute contribution margin and describe what it reveals about a company’s cost structure A3: Analyze changes in sales using the degree of operating leverage Analytical Learning Objectives

4. © The McGraw-Hill Companies, Inc., 2007 McGraw-Hill/Irwin P1: Determine cost estimates using three different methods P2: Compute the break-even point for a single product company P3: Graph costs and sales for a single product company P4: Compute break-even point for a multiproduct company Procedural Learning Objectives

5. © The McGraw-Hill Companies, Inc., 2007 McGraw-Hill/Irwin CVP analysis is used to answer questions such as:  What sales volume is needed to earn a target income?  What is the change in income if selling prices decline and sales volume increases?  How much does income increase if we install a new machine to reduce labor costs?  What is the income effect if we change the sales mix of our products or services? CVP analysis is used to answer questions such as:  What sales volume is needed to earn a target income?  What is the change in income if selling prices decline and sales volume increases?  How much does income increase if we install a new machine to reduce labor costs?  What is the income effect if we change the sales mix of our products or services? Questions Addressed by Cost-Volume-Profit Analysis C2

6. © The McGraw-Hill Companies, Inc., 2007 McGraw-Hill/Irwin Number of Local Calls Monthly Basic Telephone Bill Total fixed costs remain unchanged when activity changes. Your monthly basic telephone bill probably does not change when you make more local calls. Total Fixed Cost C1

7. © The McGraw-Hill Companies, Inc., 2007 McGraw-Hill/Irwin Number of Local Calls Monthly Basic Telephone Bill per Local Call Fixed costs per unit decline as activity increases. Your average cost per local call decreases as more local calls are made. 1- Economic of scale 2- Learning curve Fixed Cost Per Unit C1

8. © The McGraw-Hill Companies, Inc., 2007 McGraw-Hill/Irwin Minutes Talked Total Long Distance Telephone Bill Total variable costs change when activity changes. Your total long distance telephone bill is based on how many minutes you talk. Total Variable Cost C1

9. © The McGraw-Hill Companies, Inc., 2007 McGraw-Hill/Irwin Minutes Talked Per Minute Telephone Charge Variable costs per unit do not change as activity increases. The cost per long distance minute talked is constant. For example, 7 cents per minute. Variable Cost Per Unit C1

10. © The McGraw-Hill Companies, Inc., 2007 McGraw-Hill/Irwin Cost Behavior Summary C1

11. © The McGraw-Hill Companies, Inc., 2007 McGraw-Hill/Irwin Mixed costs contain a fixed portion that is incurred even when the facility is unused, and a variable portion that increases with usage. Example: monthly electric utility charge  Fixed service fee  Variable charge per kilowatt hour used Mixed Costs C1

12. © The McGraw-Hill Companies, Inc., 2007 McGraw-Hill/Irwin Variable Utility Charge Activity (Kilowatt Hours) Total Utility Cost Total mixed cost Fixed Monthly Utility Charge Mixed Costs C1

13. © The McGraw-Hill Companies, Inc., 2007 McGraw-Hill/Irwin Activity Cost Total cost remains constant within a narrow range of activity. Step-Wise Costs C1

14. © The McGraw-Hill Companies, Inc., 2007 McGraw-Hill/Irwin Activity Cost Total cost increases to a new higher cost for the next higher range of activity. Step-Wise Costs C1

15. © The McGraw-Hill Companies, Inc., 2007 McGraw-Hill/Irwin Costs that increase when activity increases, but in a nonlinear manner. Activity Total Cost Curvilinear Costs C1

16. © The McGraw-Hill Companies, Inc., 2007 McGraw-Hill/Irwin A scatter diagram of past cost behavior may be helpful in analyzing mixed costs. Scatter Diagram P1

17. © The McGraw-Hill Companies, Inc., 2007 McGraw-Hill/Irwin Plot the data points on a graph (total cost vs. activity). 0 1 2 3 4 * Total Cost in 1,000’s of Dollars 10 20 0 * * * * * * * * * Activity, 1,000’s of Units Produced P1 Scatter Diagram

18. © The McGraw-Hill Companies, Inc., 2007 McGraw-Hill/Irwin Draw a line through the plotted data points so that about equal numbers of points fall above and below the line. Estimated fixed cost = 10,000 0 1 2 3 4 * Total Cost in 1,000’s of Dollars 10 20 0 * * * * * * * * * Activity, 1,000’s of Units Produced P1 Scatter Diagram

19. © The McGraw-Hill Companies, Inc., 2007 McGraw-Hill/Irwin Vertical distance is the change in cost. Horizontal distance is the change in activity. Unit Variable Cost = Slope = Δ  in cost Δ  in units 0 1 2 3 4 * Total Cost in 1,000’s of Dollars 10 20 0 * * * * * * * * * Activity, 1,000’s of Units Produced P1 Scatter Diagram

20. © The McGraw-Hill Companies, Inc., 2007 McGraw-Hill/Irwin The following relationships between units produced and costs are observed: Using these two levels of activity, compute:  the variable cost per unit.  the total fixed cost. The High-Low Method P1

21. © The McGraw-Hill Companies, Inc., 2007 McGraw-Hill/Irwin  Unit variable cost = = = $0.17/ unit Δ  in cost Δ  in units $8,500 $50,000 Exh. 22-6 P1 The High-Low Method

22. © The McGraw-Hill Companies, Inc., 2007 McGraw-Hill/Irwin  Unit variable cost = = = $0.17/unit  Fixed cost = Total cost – Total variable Δ  in cost Δ  in units $8,500 $50,000 Exh. 22-6 P1 The High-Low Method

23. © The McGraw-Hill Companies, Inc., 2007 McGraw-Hill/Irwin  Unit variable cost = = = $0.17 /unit  Fixed cost = Total cost – Total variable cost Fixed cost = $29,000 – ($0.17 per unit × $67,500) Fixed cost = $29,000 – $11,475 = $17,525 Δ  in cost Δ  in units $8,500 $50,000 Exh. 22-6 P1 The High-Low Method

24. © The McGraw-Hill Companies, Inc., 2007 McGraw-Hill/Irwin The objective of the cost analysis remains the same: determination of total fixed cost and the variable unit cost. Least-squares regression is usually covered in advanced cost accounting courses. It is commonly used with spreadsheet programs or calculators. Least-Squares Regression P1

25. © The McGraw-Hill Companies, Inc., 2007 McGraw-Hill/Irwin Let’s extend our knowledge of cost behavior to break-even analysis. Break-Even Analysis P2

26. © The McGraw-Hill Companies, Inc., 2007 McGraw-Hill/Irwin The break-even point (expressed in units of product or dollars of sales) is the unique sales level at which a company earns neither a profit nor incurs a loss. Computing Break-Even Point P2

27. © The McGraw-Hill Companies, Inc., 2007 McGraw-Hill/Irwin Contribution margin is amount by which revenue exceeds the variable costs of producing the revenue. Computing Break-Even Point P2

28. © The McGraw-Hill Companies, Inc., 2007 McGraw-Hill/Irwin How much contribution margin must this company have to cover its fixed costs (break even)? Answer: $24,000 P2 Computing Break-Even Point

29. © The McGraw-Hill Companies, Inc., 2007 McGraw-Hill/Irwin How many units must this company sell to cover its fixed costs (break even)? Answer: $24,000 ÷ $30 per unit = 800 units P2 Computing Break-Even Point

30. © The McGraw-Hill Companies, Inc., 2007 McGraw-Hill/Irwin We have just seen one of the basic CVP relationships – the break-even computation. Break-even point in units = Fixed costs Contribution margin per unit Computing Break-Even Point Unit sales price less unit variable cost ($30 in previous example) Exh. 22-8 P2

31. © The McGraw-Hill Companies, Inc., 2007 McGraw-Hill/Irwin The break-even formula may also be expressed in sales dollars. Break-even point in dollars = Fixed costs Contribution margin ratio Unit contribution margin Unit sales price Exh. 22-9 P2 Computing Break-Even Point

32. © The McGraw-Hill Companies, Inc., 2007 McGraw-Hill/Irwin ABC Co. sells product XYZ at $5.00 per unit. If fixed costs are $200,000 and variable costs are $3.00 per unit, how many units must be sold to break even? a. 100,000 units b. 40,000 units c. 200,000 units d. 66,667 units ABC Co. sells product XYZ at $5.00 per unit. If fixed costs are $200,000 and variable costs are $3.00 per unit, how many units must be sold to break even? a. 100,000 units b. 40,000 units c. 200,000 units d. 66,667 units P2 Computing Break-Even Point

33. © The McGraw-Hill Companies, Inc., 2007 McGraw-Hill/Irwin ABC Co. sells product XYZ at $5.00 per unit. If fixed costs are $200,000 and variable costs are $3.00 per unit, how many units must be sold to break even? a. 100,000 units b. 40,000 units c. 200,000 units d. 66,667 units ABC Co. sells product XYZ at $5.00 per unit. If fixed costs are $200,000 and variable costs are $3.00 per unit, how many units must be sold to break even? a. 100,000 units b. 40,000 units c. 200,000 units d. 66,667 units Unit contribution = $5.00 - $3.00 = $2.00 Fixed costs Unit contribution = $200,000 $2.00 per unit = 100,000 units P2 Computing Break-Even Point

34. © The McGraw-Hill Companies, Inc., 2007 McGraw-Hill/Irwin Use the contribution margin ratio formula to determine the amount of sales revenue ABC must have to break even. All information remains unchanged: fixed costs are $200,000; unit sales price is $5.00; and unit variable cost is $3.00. a. $200,000 b. $300,000 c. $400,000 d. $500,000 Use the contribution margin ratio formula to determine the amount of sales revenue ABC must have to break even. All information remains unchanged: fixed costs are $200,000; unit sales price is $5.00; and unit variable cost is $3.00. a. $200,000 b. $300,000 c. $400,000 d. $500,000 P2 Computing Break-Even Point

35. © The McGraw-Hill Companies, Inc., 2007 McGraw-Hill/Irwin Use the contribution margin ratio formula to determine the amount of sales revenue ABC must have to break even. All information remains unchanged: fixed costs are $200,000; unit sales price is $5.00; and unit variable cost is $3.00. a. $200,000 b. $300,000 c. $400,000 d. $500,000 Use the contribution margin ratio formula to determine the amount of sales revenue ABC must have to break even. All information remains unchanged: fixed costs are $200,000; unit sales price is $5.00; and unit variable cost is $3.00. a. $200,000 b. $300,000 c. $400,000 d. $500,000 Unit contribution = $5.00 - $3.00 = $2.00 Contribution margin ratio = $2.00 ÷ $5.00 =.40 Break-even revenue = $200,000 ÷.4 = $500,000 P2 Computing Break-Even Point

36. © The McGraw-Hill Companies, Inc., 2007 McGraw-Hill/Irwin Volume in Units Costs and Revenue in Dollars Total fixed costs Total costs  Draw the total cost line with a slope equal to the unit variable cost.  Plot total fixed costs on the vertical axis. Preparing a CVP Chart P3

37. © The McGraw-Hill Companies, Inc., 2007 McGraw-Hill/Irwin Sales Volume in Units Costs and Revenue in Dollars  Starting at the origin, draw the sales line with a slope equal to the unit sales price. Preparing a CVP Chart Break- even Point Total costs Total fixed costs P3

38. © The McGraw-Hill Companies, Inc., 2007 McGraw-Hill/Irwin  A limited range of activity called the relevant range, where CVP relationships are linear. 4 Unit selling price remains constant. 4 Unit variable costs remain constant. 4 Total fixed costs remain constant.  Production = sales (no inventory changes). Assumptions of CVP Analysis C2

39. © The McGraw-Hill Companies, Inc., 2007 McGraw-Hill/Irwin Income (pretax) = Sales – Variable costs – Fixed costs Computing Income from Expected Sales Exh. 22-12 C3

40. © The McGraw-Hill Companies, Inc., 2007 McGraw-Hill/Irwin Rydell expects to sell 1,500 units at $100 each next month. Fixed costs are $24,000 per month and the unit variable cost is $70. What amount of income should Rydell expect? Income (pretax) = Sales – Variable costs – Fixed costs = [ 1,500 units × $100 ] – [ 1,500 units × $70 ] – $24,000 = $21,000 Income (pretax) = Sales – Variable costs – Fixed costs = [ 1,500 units × $100 ] – [ 1,500 units × $70 ] – $24,000 = $21,000 Computing Income from Expected Sales Exh. 22-13 C3

41. © The McGraw-Hill Companies, Inc., 2007 McGraw-Hill/Irwin Break-even formulas may be adjusted to show the sales volume needed to earn any amount of income. Unit sales = Fixed costs + Target income Contribution margin per unit Dollar sales = Fixed costs + Target income Contribution margin ratio Computing Sales for a Target Income C3

42. © The McGraw-Hill Companies, Inc., 2007 McGraw-Hill/Irwin ABC Co. sells product XYZ at $5.00 per unit. If fixed costs are $200,000 and variable costs are $3.00 per unit, how many units must be sold to earn income of $40,000? a. 100,000 units b. 120,000 units c. 80,000 units d. 200,000 units ABC Co. sells product XYZ at $5.00 per unit. If fixed costs are $200,000 and variable costs are $3.00 per unit, how many units must be sold to earn income of $40,000? a. 100,000 units b. 120,000 units c. 80,000 units d. 200,000 units C3 Computing Sales for a Target Income

43. © The McGraw-Hill Companies, Inc., 2007 McGraw-Hill/Irwin ABC Co. sells product XYZ at $5.00 per unit. If fixed costs are $200,000 and variable costs are $3.00 per unit, how many units must be sold to earn income of $40,000? a. 100,000 units b. 120,000 units c. 80,000 units d. 200,000 units ABC Co. sells product XYZ at $5.00 per unit. If fixed costs are $200,000 and variable costs are $3.00 per unit, how many units must be sold to earn income of $40,000? a. 100,000 units b. 120,000 units c. 80,000 units d. 200,000 units = 120,000 units Unit contribution = $5.00 - $3.00 = $2.00 Fixed costs + Target income Unit contribution $200,000 + $40,000 $2.00 per unit C3 Computing Sales for a Target Income

44. © The McGraw-Hill Companies, Inc., 2007 McGraw-Hill/Irwin Target net income is income after income tax. But we can use target income before tax in our calculations. Dollar sales = Fixed Target income costs before tax Contribution margin ratio + Computing Sales (Dollars) for a Target Net Income Exh. 22-14 C3

45. © The McGraw-Hill Companies, Inc., 2007 McGraw-Hill/Irwin To convert target net income to before-tax income, use the following formula: Before-tax income = Target net income 1 - tax rate C3 Computing Sales (Dollars) for a Target Net Income

46. © The McGraw-Hill Companies, Inc., 2007 McGraw-Hill/Irwin Rydell has a monthly target net income of $18,000. The unit selling price is $100. Monthly fixed costs are $24,000, the unit variable cost is $70, and the tax rate is 25 percent.  What is Rydell’s before-tax income and income tax expense? C3 Computing Sales (Dollars) for a Target Net Income

47. © The McGraw-Hill Companies, Inc., 2007 McGraw-Hill/Irwin Before-tax income = Target net income 1 - tax rate Before-tax income = = $24,000 $18,000 1 -.25 Income tax =.25 × $24,000 = $6,000 Rydell has a monthly target net income of $18,000. The unit selling price is $100. Monthly fixed costs are $24,000, the unit variable cost is $70, and the tax rate is 25 percent.  What is Rydell’s before-tax income and income tax expense? C3 Computing Sales (Dollars) for a Target Net Income

48. © The McGraw-Hill Companies, Inc., 2007 McGraw-Hill/Irwin Rydell has a monthly target net income of $18,000. The unit selling price is $100. Monthly fixed costs are $24,000, the unit variable cost is $70, and the tax rate is 25 percent.  What monthly sales revenue will Rydell need to earn the target net income? C3 Computing Sales (Dollars) for a Target Net Income

49. © The McGraw-Hill Companies, Inc., 2007 McGraw-Hill/Irwin Dollar sales = Fixed Target net income costs before tax Contribution margin ratio + Dollar sales = = $160,000 $24,000 + $24,000 30% Rydell has a monthly target net income of $18,000. The unit selling price is $100. Monthly fixed costs are $24,000, the unit variable cost is $70, and the tax rate is 25 percent.  What monthly sales revenue will Rydell need to earn the target net income? C3 Computing Sales (Dollars) for a Target Net Income

50. © The McGraw-Hill Companies, Inc., 2007 McGraw-Hill/Irwin The formula for computing dollar sales may be used to compute unit sales by substituting contribution per unit in the denominator. Contribution margin per unit Unit sales = Fixed Target net income taxesbefore taxes ++ Unit sales = = 1,600 units $24,000 + $24,000 $30 per unit Formula for Computing Sales (Units) for a Target Net Income Exh. 22-16 C3

51. © The McGraw-Hill Companies, Inc., 2007 McGraw-Hill/Irwin Margin of safety is the amount by which sales can drop before the company incurs a loss. Margin of safety may be expressed as a percentage of expected sales. Computing the Margin of Safety Exh. 22-17 Margin of safety Expected sales - Break-even sales percentage Expected sales = C3

52. © The McGraw-Hill Companies, Inc., 2007 McGraw-Hill/Irwin Margin of safety Expected sales - Break-even sales percentage Expected sales = If Rydell’s sales are $100,000 and break- even sales are $80,000, what is the margin of safety in dollars and as a percentage? Exh. 22-17 C3 Computing the Margin of Safety

53. © The McGraw-Hill Companies, Inc., 2007 McGraw-Hill/Irwin If Rydell’s sales are $100,000 and break-even sales are $80,000, what is the margin of safety in dollars and as a percentage? Margin of safety = $100,000 - $80,000 = $20,000 Margin of safety Expected sales - Break-even sales percentage Expected sales = Margin of safety $100,000 - $80,000 percentage $100,000 = = 20% Exh. 22-17 C3 Computing the Margin of Safety

54. © The McGraw-Hill Companies, Inc., 2007 McGraw-Hill/Irwin The basic CVP relationships may be used to analyze a number of situations such as changing sales price, changing variable cost, or changing fixed cost. Consider the following example. The basic CVP relationships may be used to analyze a number of situations such as changing sales price, changing variable cost, or changing fixed cost. Consider the following example. Sensitivity Analysis C3

55. © The McGraw-Hill Companies, Inc., 2007 McGraw-Hill/Irwin Rydell Company is considering buying a new machine that would increase monthly fixed costs from $24,000 to $30,000, but decrease unit variable costs from $70 to $60. The $100 per unit selling price would remain unchanged. What is the new break-even point in dollars? Sensitivity Analysis Example C3

56. © The McGraw-Hill Companies, Inc., 2007 McGraw-Hill/Irwin Rydell Company is considering buying a new machine that would increase monthly fixed costs from $24,000 to $30,000, but decrease unit variable costs from $70 to $60. The $100 per unit selling price would remain unchanged. Revised Break-even point in dollars Revised fixed costs Revised contribution margin ratio Revised Break-even point in dollars $30,000 40% = $75,000= = Exh. 22-18 C3 Sensitivity Analysis Example

57. © The McGraw-Hill Companies, Inc., 2007 McGraw-Hill/Irwin The CVP formulas may be modified for use when a company sells more than one product.  The unit contribution margin is replaced with the contribution margin for a composite unit.  A composite unit is composed of specific numbers of each product in proportion to the product sales mix.  Sales mix is the ratio of the volumes of the various products. Computing Multiproduct Break-Even Point P4

58. © The McGraw-Hill Companies, Inc., 2007 McGraw-Hill/Irwin The resulting break-even formula for composite unit sales is: Break-even point in composite units Fixed costs Contribution margin per composite unit = Consider the following example: Continue Exh. 22-19 P4 Computing Multiproduct Break-Even Point

59. © The McGraw-Hill Companies, Inc., 2007 McGraw-Hill/Irwin Hair-Today offers three cuts as shown below. Annual fixed costs are $96,000. Compute the break-even point in composite units and in number of units for each haircut at the given sales mix. P4 Computing Multiproduct Break-Even Point

60. © The McGraw-Hill Companies, Inc., 2007 McGraw-Hill/Irwin Hair-Today offers three cuts as shown below. Annual fixed costs are $96,000. Compute the break-even point in composite units and in number of units for each haircut at the given sales mix. A 4:2:1 sales mix means that if there are 500 budget cuts, then there will be 1,000 ultra cuts, and 2,000 basic cuts. P4 Computing Multiproduct Break-Even Point

61. © The McGraw-Hill Companies, Inc., 2007 McGraw-Hill/Irwin Step 1: Compute contribution margin per composite unit. P4 Computing Multiproduct Break-Even Point

62. © The McGraw-Hill Companies, Inc., 2007 McGraw-Hill/Irwin Contribution margin per composite unit Step 1: Compute contribution margin per composite unit. P4 Computing Multiproduct Break-Even Point

63. © The McGraw-Hill Companies, Inc., 2007 McGraw-Hill/Irwin Break-even point in composite units Fixed costs Contribution margin per composite unit = Step 2: Compute break-even point in composite units. Exh. 22-19 P4 Computing Multiproduct Break-Even Point

64. © The McGraw-Hill Companies, Inc., 2007 McGraw-Hill/Irwin Break-even point in composite units Fixed costs Contribution margin per composite unit = Step 2: Compute break-even point in composite units. Break-even point in composite units $96,000 $32.00 per composite unit = Break-even point in composite units = 3,000 composite units Exh. 22-19 P4 Computing Multiproduct Break-Even Point

65. © The McGraw-Hill Companies, Inc., 2007 McGraw-Hill/Irwin Step 3: Determine the number of each haircut that must be sold to break even. P4 Computing Multiproduct Break-Even Point

66. © The McGraw-Hill Companies, Inc., 2007 McGraw-Hill/Irwin Step 4: Verify the results. Multiproduct Break-Even Income Statement Exh. 22-20 P4

67. © The McGraw-Hill Companies, Inc., 2007 McGraw-Hill/Irwin A measure of the extent to which fixed costs are being used in an organization. A measure of how a percentage change in sales will affect profits. Contribution margin Net income = Degree of operating leverage Operating Leverage A3

68. © The McGraw-Hill Companies, Inc., 2007 McGraw-Hill/Irwin $36,000 $12,000 = 3.0 Contribution margin Net income = Degree of operating leverage If Rydell increases sales by 10 percent, what will the percentage increase in income be? Operating Leverage A3

69. © The McGraw-Hill Companies, Inc., 2007 McGraw-Hill/Irwin Operating Leverage A3

70. © The McGraw-Hill Companies, Inc., 2007 McGraw-Hill/Irwin End of Chapter 22