## 22 COST-VOLUME-PROFIT ANALYSIS

We find that the challenge in successfully presenting cost-volume-profit analysis is to get students to ... 3 fixed costs + operating income. Sales ...
20 COST- VOLUME-PROFIT ANALYSIS

Chapter Summary

The relationship between costs and revenue and the level of business activity is the foundation of profit planning. We begin our presentation of cost-volume-profit analysis with an introduction to cost behavior relationships. Fixed, variable and semivariable cost functions are illustrated graphically and numerically. The distinction between the behavior of total and unit costs is explained and graphically illustrated as well. With the various cost behavior patterns established, the chapter turns to the development of the basic CVP model. This analysis is initially presented graphically. Following discussion of the contribution margin concept the same results are established numerically. The model is solved for target levels of operating income and the margin of safety. A number of comparative static experiments illustrates the usefulness of the CVP model in a realistic planning situation. This example is developed form the point of view of managers of several different functional areas. The chapter concludes with an examination of the significance of sales mix and the high-low method of estimating fixed and variable components of mixed costs.

Learning Objectives

1. Explain how fixed, variable, and semivariable costs respond to changes in the volume of business activity.

2. Explain how economies of scale can reduce unit costs.

3. Prepare a cost-volume-profit graph.

4. Compute contribution margin and explain its usefulness.

5. Determine the sales volume required to earn a desired level of operating income.

6. Use the contribution margin ratio to estimate the change in operating income caused by a change in sales volume.

7. Use CVP relationships to evaluate a new marketing strategy.

Brief topical outline

A Cost-volume relationships 1. Fixed costs (and fixed expenses) 2. Variable costs (and variable expenses) 3. Semivariable costs (and semivariable expenses) - see Case in Point (page 839) 4 Cost-volume relationships: a graphic analysis 5 The behavior of per-unit costs - see Your Turn (page 842) 6. Economics of scale - see Case in Point (page 842) 7 Additional cost behavior patterns B Cost behavior and operating income - see Cash Effects (page 844) 1 Cost-volume-profit analysis: an illustration 2 Preparing and using a cost-volume-profit graph 3 Contribution margin: a key relationship a Contribution margin ratio 4. How many units must we sell? 5. How many dollars in sales must we generate? 6. What is our margin of safety? - see Management Strategy (page 849) 7. What change in operating income do we anticipate? 8. Business applications of CVP a Director of advertising b Plant manager - see Your Turn (page 851) c Vice president of sales - see Your Turn (page 852) 9. Additional considerations in CVP 10. CVP analysis when a company sells many products a Improving the "quality" of the sales mix - see Case in Point (page 853) 11. Determining semivariable cost elements: the high-low method 12. Assumptions underlying cost-volume-profit analysis 13. Summary of basic cost-volume-profit relationships C Concluding remarks - see A Second Look (page 855)

Topical coverage and suggested assignment

|Homework Assignment | |(To Be Completed Prior to Class) | |Class |Topical | | | | | | |Meetings |Outline |Discussion| | | | | |on Chapter|Coverage |Questions |Exercises |Problems |Cases |Internet | |1 |A |1, 2, 3, |1, 2, 3 | | |1 | | | |4, 5 | | | | | |2 |B |8, 9, 10, |7, 8, 9, |2, 3, 4, |1 | | | | |11 |10, 12 |5, 6 | | | |3 |B – C |7, 14, 15,|4, 5, 6, |8, 9, 12 |2 | | | | |16 |13, 16 | | | |

Teaching objectives for Chapter 20

In this chapter, we explain the patterns of cost behavior and cost-volume- profit relationships. In discussing cost behavior patterns and cost-volume- profit analysis, our teaching objectives are to:

1 Explain the importance of understanding cost-volume-profit relationships in planning and controlling business operations.

2 Define and provide examples of fixed costs, variable costs, and semivariable costs.

3 Contrast the behavior of a cost expressed on per-unit basis with that of the total cost.

4 Explain that cost behavior patterns (and cost-volume-profit analysis) serve only as useful approximations. (As part of this discussion, explore other cost behavior patterns and introduce the concept of the relevant volume range.)

5 Illustrate the preparation of a break-even graph, and explain its usefulness.

6 Define contribution margin, contribution margin ratio, and contribution margin per unit. (Stress that these concepts form the cornerstone of cost-volume-profit analysis, and also will be used extensively in later chapters.)

7 Show how contribution margin ratio and/or contribution margin per unit are used to determine the sales volume necessary to earn a specified level of operating income.

8 Illustrate the importance of sales mix and the relative contribution margin ratios of different products.

9 Illustrate and explain the high-low method of determining the fixed and variable components of a semivariable cost.

10 Review the assumptions underlying cost-volume-profit analysis.

11 Review the summary of basic cost-volume-profit relationships.

New features in Chapter 20

This chapter parallels the coverage of cost-volume-profit (CVP) analysis in our previous edition.

We find that the challenge in successfully presenting cost-volume-profit analysis is to get students to understand the significance of contribution margin, rather than to commit numerous formulas to memory. Memorizing formulas serves little purpose beyond the next exam; an understanding of the concept of contribution margin, however, can serve students well through a lifetime of managerial and personal financial decisions. Contribution margin is merely that portion of revenue that "contributes" to fixed costs and (after covering the fixed costs) to operating income. In short, all revenue except for the contribution margin is consumed by the variable costs relating to the revenue. Once students grasp the fact that only the contribution margin "contributes" to covering fixed costs and to providing a profit, most of the formulas presented in this chapter will "fall into place." We recommend that in approaching any cost-volume-profit problem (homework assignment or exam question), students jot down in the margin of the paper the contribution margin ratio and contribution margin per unit. One of these measurements is usually the key to solving the problem.

Supplementary Exercises

In "Retail: Discounters Get Their Day”, Business Week, January 14, 2002, the authors suggest that consumers will try to stretch their dollars. So discounters and value-oriented retailers such as Wal-Mart Stores Inc. and Target Stores will continue to take market share away from mall-based department stores and specialty stores. The authors also suggest retailers will have “to keep an eye on inventory and other expenses”. How could an excessive build up of inventory hurt a retailer’s bottom line?

Group Exercise

Suppose a company faces two technologies for manufacturing its single product. The first requires significantly higher fixed costs but much smaller unit variable costs than does the second. Prepare a cost-volume- profit graph for each of the technologies. Using the graphs, discuss the economic circumstances that would lead to a choice of one technology over the other.

Internet Exercise

Research the Dell Computer website at http://www.dell.com/ and the Hewlett Packard website at http://www.hewlettpackard.com/ to see how these corporations differ in their approach to manufacturing and selling personal computers. CHAPTER 20 NAME #

10-MINUTE QUIZ A SECTION

Information regarding a product manufactured and sold by Cousins Mfg. is shown below:

Maximum capacity with existing facilities 4,000 units Total fixed costs per month \$60,000 Variable cost per unit \$41.25 Sales price per unit \$55.00

1 Refer to the above data. The contribution margin ratio for this product is: a 20%. c 30%. b 25%. d 40%. 2 Refer to the above data. The number of units Cousins must sell to break even is: (rounded) a 3,927. c 4,823. b 4,364. d 5,140. 3 Refer to the above data. The dollar sales volume necessary to produce monthly operating income of \$12,000 before taxes is: a \$188,000. c \$249,000. b \$186,000. d \$288,000.

Use the following data for questions 4 and 5.

The monthly high and low levels of units and total manufacturing overhead for Arista Company are shown below:

Highest observed level 78,000 \$204,000 Lowest observed level 54,000 156,000

4 Refer to the above data. The cost formula for Arista’s monthly overhead cost can be expressed as: a \$2.65 average cost per unit. b \$1.75 average cost per unit. c \$24,000 fixed cost plus \$1.00 per unit. d \$48,000 fixed cost + \$2.00 per unit. 5 Refer to the above data. In a month in which 30,000 equivalent full units are produced, Arista’s manufacturing overhead should be approximately: a \$52,500. c \$108,000. b \$79,500. d \$ 90,500. CHAPTER 20 NAME #

10-MINUTE QUIZ B SECTION

1 Management predicts total sales for June to be \$3,000,000, yielding a margin of safety of \$1,000,000 and a contribution margin ratio of 25%. Which of the following amounts is not consistent with this information? a Fixed costs, \$500,000. b Variable costs, \$750,000. c Operating income, \$250,000. d Break-even sales volume, \$2,000,000.

Use the following data for questions 2 through 4.

The recent high and low levels of hours operated and monthly repair cost for heavy equipment for Master Mfg. are shown below:

Hours Operated Repair Cost

Highest observed level 24,000 \$7,450 Lowest observed level 21,500 6,700

2 Refer to the above data. Using the high-low method, compute the variable element of repair cost per hour of operation for Master’s equipment: a \$750 c \$0.30. b \$3.33. d \$0.34.

3 Refer to the above data. Using the high-low method, compute the fixed element of Master’s monthly repair cost: a \$150. c \$6,300. b \$250. d \$6,450.

4 Refer to the above data. The total estimated repair cost for a month in which Master operates equipment for 19,000 hours is: a \$5,950. c \$6,450. b \$6,300. d \$5,700.

5 Perry Corporation manufactures two products; data are shown below: Contribution Relative Margin Ratio Sales Mix Product A 40% 40% Product B 30% 60% If Perry’s monthly fixed costs average \$425,000, what is its break-even point expressed in sales dollars? a \$1,320,000. c \$1,250,000. b \$1,400,000. d \$990,000.

CHAPTER 20 NAME #

10-MINUTE QUIZ C SECTION

Sanchez Company sells only one product. The regular selling price is \$30. Variable costs are 70% of this selling price, and fixed costs are \$4,500 per month. Management decides to increase the selling price from \$30 to \$35 per unit. Assume that the cost of the product and the fixed operating expenses are not changed by this pricing decision.

1 Refer to the above data. At the original selling price of \$30 per unit, what is the contribution margin ratio? ____________%

2 Refer to the above data. At the original selling price of \$30 per unit, how many units must Sanchez sell to break even? ____________units

3 Refer to the above data. At the original selling price of \$30 per unit, what dollar volume of sales per month is required for Sanchez to earn a monthly operating income of \$3,000? \$____________

4 Refer to the above data. At the increased selling price of \$35 per unit, what is the contribution margin ratio? ____________%

5 Refer to the above data. At the increased selling price of \$35 per unit, what dollar volume of sales per month is required to break even? \$_____________

CHAPTER 20 NAME #

10-MINUTE QUIZ D SECTION

Torrere brews reduced calorie beer and regular beer. Sales of its reduced calorie beer represent 25% of the company’s total revenue. Sales of regular beer represent the remaining 75%. Reduced calorie beer has a contribution margin ratio of 80%, whereas the contribution margin ratio of regular beer is only 60%. Torrere’s monthly fixed costs average \$812,500.

1 What is the company’s monthly break-even point expressed in sales dollars? \$__________

2 What monthly sales level must be achieved for Torrere to earn a monthly operating income of \$325,000? \$__________

3 If Torrere generates \$1,350,000 in monthly sales, it will earn a monthly operating income of \$__________.

4 Assume Torrere’s margin of safety was \$250,000 in May. What was the company’s operating income in May? \$__________.

5 If Torrere’s monthly fixed costs increase by \$6,500, what level of monthly sales revenue will be required to break-even? \$__________.

SOLUTIONS TO CHAPTER 20 10-MINUTE QUIZZES

QUIZ A QUIZ B 1 B 1 B 2 B 2 C 3 D 3 B 4 D 4 A 5 C 5 C

QUIZ C 1 Sales price (100%) minus variable costs (70%) = 30%

2 Sales volume (units) = fixed costs / contribution margin \$4,500 / (\$30 x 30%) = 500 units 3 fixed costs + operating income Sales volume (dollars) = ___________________________ contribution margin ratio

\$4,500 + 3,000 = ______________ = \$25,000 30% 4 \$35 sales price - \$21 variable cost per unit (\$30 x 70%) ___________________________________________________ = 40% \$35 sales price 5 Sales volume (dollars) = fixed costs / contribution margin ratio = \$4,500 / 40% = \$11,250

QUIZ D 1 \$812,500/[(75% x 60%) + (25% x 80%)] = \$1,250,000

2 (\$812,500 + \$325,000)/[75% x 60%) + (25% x 80%)] = \$1,750,000

3 \$1,350,000 x [(75% x 60%) + \$1,350,000 (25% x 80%)] = \$877,500; Thus, operating income = \$877,500 - \$812,500 = \$65,000

4 \$250,000 x [(75% x 60%) + (25% x 80%)] = \$162,500

5 (\$812,500 + \$6,500)/[(75% x 60%) + (25% x 80%)] = \$1,260,000