CHAPTER 6

COST-volume-profit analysis: Additional Issues

CHAPTER LEARNING OBJECTIVES

1. Apply basic CVP concepts. The CVP income statement classifies costs and expenses as variable or fixed and reports contribution margin in the body of the statement. Contribution margin is the amount of revenue remaining after deducting variable costs. It can be expressed as a per unit amount or as a ratio. The break-even point in sales units is fixed costs divided by unit contribution margin. The break-even point in sales dollars is fixed costs divided by the contribution margin ratio. These equations can also be used to determine sales units or sales dollars needed to achieve target net income, simply by adding target net income to fixed costs before dividing by the contribution margin. Margin of safety indicates how much sales can decline before the company is operating at a loss. It can be expressed in dollar terms or as a percentage.

2. Explain the term sales mix and its effects on break-even sales. Sales mix is the relative proportion in which each product is sold when a company sells more than one product. For a company with a small number of products, break-even sales in units is determined by using the weighted-average unit contribution margin of all the products. If the company sells many different products, then calculating the break-even point using unit information is not practical. Instead, in a company with many products, break-even point sales in dollars is calculated using the weighted-average contribution margin ratio.

3. Determine sales mix when a company has limited resources. When a company has limited resources, it is necessary to find the contribution margin per unit of limited resource. This amount is then multiplied by the units of limited resource to determine which product maximizes net income.

4. Indicate how operating leverage affects profitability. Operating leverage refers to the degree to which a company’s net income reacts to a change in sales. Operating leverage is determined by a company’s relative use of fixed versus variable costs. Companies with high fixed costs relative to variable costs have high operating leverage. A company with high operating leverage experiences a sharp increase (decrease) in net income with a given increase (decrease) in sales. The degree of operating leverage is measured by dividing contribution margin by net income.

^a5. Explain the differences between absorption costing and variable costing. Under absorption costing, fixed manufacturing costs are product costs. Under variable costing, fixed manufacturing costs are period costs. If production volume exceeds sales volume, net income under absorption costing will exceed net income under variable costing by the amount of fixed manufacturing costs included in ending inventory that results from units produced but not sold during the period. If production volume is less than sales volume, net income under absorption costing will be less than under variable costing by the amount of fixed manufacturing costs included in the units sold during the period that were not produced during the period. The use of variable costing is consistent with cost-volume-profit analysis. Net income under variable costing is unaffected by changes in production levels. Instead, it is closely tied to changes in sales. The presentation of fixed costs in the variable costing approach makes it easier to identify fixed costs and to evaluate their impact on the company’s profitability.

TRUE-FALSE STATEMENTS

1. The CVP income statement classifies costs as variable or fixed and computes a contribution margin.

2. In CVP analysis, cost includes manufacturing costs but not selling and administrative expenses.

3. When a company is in its early stages of operation, its primary goal is to generate a target net income.

4. The margin of safety tells a company how far sales can drop before it will be operating at a loss.

5. Sales mix is a measure of the percentage increase in sales from period to period.

6. Sales mix is not important to managers when different products have substantially different contribution margins.

7. The weighted-average contribution margin of all the products is computed when determining the break-even point in sales dollars for a multi-product firm.

8. If Buttercup, Inc. sells two products with a sales mix of 75%:25%, and the respective contribution margins are $80 and $240, then the weighted-average unit contribution margin is $120.

Ex. 136

Kindle, Inc. manufactures cosmetic products that are sold through a network of sales agents. The agents are paid a commission of 12.5% of sales. The income statement for the year ending December 31, 2022, is as follows (all amounts are in $000s):

KINDLE, INC.

Income Statement

Year Ending December 31, 2022

Sales $130,000

Cost of goods sold

Variable $58,500

Fixed 14,350 72,850

Gross profit 57,150

Selling and marketing expenses

Commissions $16,250

Fixed costs 17,100 33,350

Net income $ 23,800

The company is considering hiring its own sales staff to replace the network of agents. It will pay its salespeople a commission of 10% and will incur additional fixed costs of $13 million per year.

Instructions

(a) Under the current policy of using a network of sales agents, calculate Kindle, Inc.'s break-even point in sales dollars for the year 2022.

(b) Calculate the company's break-even point in sales dollars for the year 2022 if it hires its own sales force to replace the network of agents.

(c) Calculate the degree of operating leverage at sales of $130 million if (1) Kindle, Inc. uses sales agents, and (2) Kindle, Inc. employs its own sales staff.

^aSolution 136 (15–18 min.)

(a) Reformat the income statement to CVP format. All amounts are in $000s.

Sales $130,000

Variable costs ($58,500 + $16,250) 74,750

Contribution margin 55,250

Less: Fixed costs ($14,350 + $17,100) 31,450

Net income $ 23,800

Contribution margin ratio = $55,250 ÷ $130,000 = 42.5%

Break-even point = $31,450 ÷ 42.5% = $74,000

(b) If a hired workforce replaces sales agents, commissions will be reduced to 10% of sales ($13,000) but fixed costs will increase by $13,000.

Sales $130,000

Variable costs ($58,500 + $13,000) 71,500

Contribution margin 58,500

Less: Fixed costs ($31,450 + $13,000) 44,450

Net income $ 14,050

Contribution margin ratio = $58,500 ÷ $130,000 = 45%

Break-even point = $44,450 ÷ 45% = $98,778

(c) Operating leverage = contribution margin ÷ net income

Current situation: from part (a)

$55,250 ÷ $23,800 = 2.32

Proposed situation: from part (b)

$58,500 ÷ $14,050 = 4.16

Ex. 137

Qwik Service has over 200 auto-maintenance service outlets nationwide. It provides primarily two lines of service: oil changes and brake repair. Oil change-related services represent 75% of its sales and provide a contribution margin ratio of 20%. Brake repair represents 25% of its sales and provides a 60% contribution margin ratio. The company's fixed costs are $15,000,000 (or $75,000 per service outlet).

Instructions

(a) Calculate the dollar amount of each type of service that the company must provide in order to break even.

(b) The company has a desired net income of $45,000 per service outlet. What is the dollar amount of each type of service that must be provided by each service outlet to meet its target net income?

Ex. 138

Seaver Corporation manufactures mountain bikes. It has fixed costs of $4,140,000. Seaver’s sales mix and unit contribution margin are shown as follows:

Sales Mix Unit Contribution Margin

Green Demon 25% $120

Brown Beast 45% $ 60

Blue Bear 30% $ 40

Instructions

Compute the number of each type of bike that the company would need to sell in order to break even under this product mix.

Ex. 139

DeMont Tax Services provides primarily two lines of service: accounting compilation and tax return preparation. Accounting compilation services represent 60% of its revenue and provide a contribution margin ratio of 30%. Tax return preparation services represent 40% of its revenue and provide a 40% contribution margin ratio. The company’s fixed costs are $4,590,000.

Instructions

(a) Calculate the revenue from each type of service that the company must achieve to break even.

(b) The company has a desired net income of $1,700,000. What amount of revenue would DeMont earn from tax return preparation services if it achieves this goal with the current sales mix?

Ex. 140

Blue Chance Co. sells computers and video game systems. The business is divided into two divisions along product lines. Variable costing income statements for the current year are presented below:

Computers VG Systems Total

Sales $700,000 $300,000 $1,000,000

Variable costs 420,000 210,000 630,000

Contribution margin $280,000 $ 90,000 370,000

Fixed costs 296,000

Net income $ 74,000

Instructions

(a) Determine the sales mix and contribution margin ratio for each division.

(b) Calculate the company’s weighted-average contribution margin ratio.

(c) Calculate the company’s break-even point in sales dollars.

(d) Determine the sales level, in dollars, for each division at the break-even point.

Ex. 141

Hewitt Co. has 4,000 machine hours available to produce either Product 22 or Product 44. The cost accounting department developed the following unit information for each product:

Product 22 Product 44

Sales price $27 $50

Direct materials 6 8

Direct labor 3 2

Variable manufacturing overhead 4 5

Fixed manufacturing overhead 3 5

Machine time required 20 minutes 60 minutes

Instructions

Management wants to know which product to produce in order to maximize the company’s net income. Taking into consideration the constraints under which the company operates, prepare a report to show which product should be produced and sold.

Ex. 142

Reynolds, Inc. manufactures and sells two products, Standard and Deluxe. Relevant per unit data for each product are given below:

Product

Standard Deluxe

Selling price $50 $75

Variable costs $26 $33

Machine hours 2 3

Instructions

(a) Compute the contribution margin per unit of limited resource for each product.

(b) If 1,000 additional machine hours are available, which product should be manufactured?

Ex. 143

Oscar Corporation produces and sells three products. Unit data concerning each product is shown below.

Product

X Y Z  

Selling price $200 $300 $250

Direct labor costs 45 75 60

Other variable costs 110 130 102

The company has 2,000 hours of labor available to build inventory in anticipation of the company's peak season. Management is trying to decide which product should be produced. The direct labor hourly rate is $15.

Instructions

(a) Determine the number of direct labor hours per unit.

(b) Determine the contribution margin per direct labor hour.

(c) Determine which product should be produced and the total contribution margin for that product.

Ex. 144

Shanahan Co. is contemplating a major change in its cost structure. Currently, all of its drafting work is performed by skilled drafters. Mike Shanahan the owner, is considering replacing the drafters with a computerized drafting system.

However, before making the change, Mike would like to know the consequences of the change, since the volume of business varies significantly from year to year. Shown below are CVP income statements for each alternative.

Manual System Computerized System

Sales $1,500,000 $1,500,000

Variable costs 1,200,000 900,000

Contribution margin 300,000 600,000

Fixed costs 150,000 450,000

Net income $150,000 $150,000

Instructions

(a) Determine the degree of operating leverage for each alternative.

(b) Which alternative would produce the higher net income if sales increased by $300,000?

Ex. 145

The following CVP income statements are available for Chantal Corp. and Mantle, Inc.

Chantal Corp. Mantle, Inc.

Sales revenue $700,000 $700,000

Variable costs 350,000 210,000

Contribution margin 350,000 490,000

Fixed costs 225,000 365,000

Net income $125,000 $125,000

Instructions

(a) Compute the degree of operating leverage for each company.

(b) Assume that sales revenue decreases by 20%. Prepare a CVP income statement for each company.

Ex. 146

An investment banker is analyzing two companies that specialize in the production and sale of gourmet cappuccino and chai mixes. Roasted Beans Co. uses a labor-intensive approach and Monat Industries uses a mechanized system. Variable costing income statements for the two companies are shown below:

Roasted Beans Monat Industries

Sales $1,000,000 $1,000,000

Variable costs 650,000 300,000

Contribution margin 350,000 700,000

Fixed costs 175,000 525,000

Net Income $ 175,000 $ 175,000

The investment banker is interested in acquiring one of these companies. However, she is concerned about the impact that each company’s cost structure might have on its profitability.

Instructions

(a) Calculate each company’s degree of operating leverage.

(b) Determine the effect on each company’s net income if sales decrease by 10% and if sales increase by 15%. Do not prepare income statements.