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# Chapter 22

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1. Chapter 22 Cost-Volume-Profit Analysis

2. 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. Analytical Learning Objectives 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

4. Procedural Learning Objectives 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

5. Questions Addressed byCost-Volume-Profit Analysis C2 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?

6. Total Fixed Cost C1 Total fixed costsremain unchangedwhen activity changes. Your monthly basictelephone bill probablydoes not change whenyou make more local calls. Monthly Basic Telephone Bill Number of Local Calls

7. Fixed Cost Per Unit C1 Fixed costs per unit declineas activity increases. Your average cost perlocal call decreases asmore local calls are made. 1- Economic of scale 2- Learning curve Monthly Basic Telephone Bill per Local Call Number of Local Calls

8. Total Variable Cost C1 • Total variable costschangewhen activity changes. Your total long distancetelephone bill is basedon how many minutesyou talk. Total Long DistanceTelephone Bill Minutes Talked

9. Variable Cost Per Unit C1 Variable costs per unitdo not changeas activity increases. The cost per long distanceminute talked is constant.For example, 7cents per minute. Per MinuteTelephone Charge Minutes Talked

10. Mixed Costs C1 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 perkilowatt hour used

11. Mixed Costs C1 Total mixed cost Variable Utility Charge Total Utility Cost Fixed MonthlyUtility Charge Activity (Kilowatt Hours)

12. Step-Wise Costs C1 Total cost remainsconstant within anarrow rangeofactivity. Cost Activity

13. Step-Wise Costs C1 Total cost increases to a new higher cost for the next higher range of activity. Cost Activity

14. Curvilinear Costs C1 Costs that increase when activity increases, but in a nonlinearmanner. Total Cost Activity

15. Scatter Diagram P1 A scatter diagram of past cost behavior may be helpful in analyzing mixed costs.

16. 20 * * * * * * * * Total Cost in1,000’s of Dollars * * 10 0 0 1 2 3 4 Activity, 1,000’s of Units Produced Scatter Diagram P1 Plot the data points on a graph (total cost vs. activity).

17. 20 * * * * * * * * Total Cost in1,000’s of Dollars * * 10 0 0 1 2 3 4 Activity, 1,000’s of Units Produced Scatter Diagram P1 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

18. Δin costΔin units Unit Variable Cost = Slope = 20 * * * * * * * * Total Cost in1,000’s of Dollars * * 10 0 0 1 2 3 4 Activity, 1,000’s of Units Produced Scatter Diagram P1 Vertical distance is the change in cost. Horizontal distance is the change in activity.

19. The High-Low Method P1 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.

20. \$8,500\$50,000 Δin costΔin units • Unit variable cost = = = \$0.17/ unit The High-Low Method P1 Exh. 22-6

21. \$8,500\$50,000 Δin costΔin units • Unit variable cost = = = \$0.17/unit • Fixed cost = Total cost – Total variable The High-Low Method P1 Exh. 22-6

22. \$8,500\$50,000 Δin costΔin units • 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 The High-Low Method P1 Exh. 22-6

23. Least-Squares Regression P1 • Least-squares regression is usually covered in advanced cost accounting courses. It is commonly used with spreadsheet programs or calculators. The objective of the cost analysis remains the same: determination oftotal fixed costand thevariable unit cost.

24. Break-Even Analysis P2 Let’s extend ourknowledge ofcost behavior to break-even analysis.

25. Computing Break-Even Point P2 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.

26. Computing Break-Even Point P2 Contribution margin is amount by which revenueexceeds thevariable costsof producing the revenue.

27. Computing Break-Even Point P2 How much contribution margin must this company have to cover its fixed costs (break even)? Answer: \$24,000

28. Computing Break-Even Point P2 How manyunitsmust this company sell to cover its fixed costs (break even)? Answer: \$24,000 ÷ \$30 per unit = 800 units

29. Fixed costs Break-even point in units = Contribution margin per unit Computing Break-Even Point P2 Exh. 22-8 We have just seen one of the basic CVP relationships – the break-evencomputation. Unit sales price less unit variable cost(\$30 in previous example)

30. Fixed costs Break-even point in dollars = Contribution marginratio Computing Break-Even Point P2 Exh. 22-9 The break-even formula may also be expressed in sales dollars. Unit contribution margin Unit sales price

31. Computing Break-Even Point P2 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

32. Unit contribution = \$5.00 - \$3.00 = \$2.00 Fixed costsUnit contribution \$200,000\$2.00 per unit = = 100,000 units Computing Break-Even Point P2 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

33. Computing Break-Even Point P2 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

34. Computing Break-Even Point P2 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

35. Total costs • Draw the total cost line with a slopeequal to the unit variable cost. Preparing a CVP Chart P3 • Plot total fixed costs on the vertical axis. Total fixed costs Costs and Revenuein Dollars Volume in Units

36. Preparing a CVP Chart P3 • Starting at the origin, draw the sales line with a slope equal to the unit sales price. Sales Total fixed costs Costs and Revenuein Dollars Total costs Break-even Point Volume in Units

37. Assumptions of CVP Analysis C2 • A limited range of activity called therelevant range, where CVP relationships are linear. • Unit selling price remains constant. • Unit variable costs remain constant. • Total fixed costs remain constant. • Production = sales (no inventory changes).

38. Computing Income from Expected Sales C3 Exh. 22-12 Income (pretax) = Sales – Variable costs – Fixed costs

39. Computing Income from Expected Sales C3 Exh. 22-13 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

40. Computing Sales for a Target Income C3 Break-even formulas may be adjusted to show the sales volume needed to earn any amount of income. Fixed costs +Target income Unit sales = Contribution margin per unit Fixed costs +Target income Dollar sales = Contribution margin ratio

41. Computing Sales for a Target Income C3 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

42. Unit contribution = \$5.00 - \$3.00 = \$2.00 Fixed costs + Target income Unit contribution \$200,000 + \$40,000 \$2.00 per unit = 120,000 units Computing Sales for a Target Income C3 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

43. Target netincome is income after income tax. But we can use target income before tax in our calculations. Computing Sales (Dollars) for aTarget Net Income C3 Exh. 22-14 Fixed Target income costs before tax + Dollar sales = Contribution margin ratio

44. Computing Sales (Dollars) for aTarget Net Income C3 To convert target net income to before-tax income, use the following formula: Target net income Before-tax income = 1 - tax rate

45. Computing Sales (Dollars) for aTarget Net Income C3 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 andincome tax expense?

46. Target net income Before-tax income = 1 - tax rate \$18,000 Before-tax income = = \$24,000 1 - .25 Computing Sales (Dollars) for aTarget Net Income C3 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 andincome tax expense? Income tax = .25 × \$24,000 = \$6,000

47. Computing Sales (Dollars) for aTarget Net Income C3 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 Rydellneed to earn the target net income?

48. Fixed Target net income costs before tax + Dollar sales = Contribution margin ratio \$24,000 + \$24,000 Dollar sales = = \$160,000 30% Computing Sales (Dollars) for aTarget Net Income C3 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 Rydellneed to earn the target net income?

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