Chapter 7 Cost-Volume-Profit Analysis PDF

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CHAPTER 7 Cost-Volume-Profit Analysis ANSWERS TO REVIEW QUESTIONS 7-1

a. In the contribution-margin approach, the break-even point in units is calculated using the following formula:

Break-even point 

fixedexpenses unit contribution margin

b. In the equation approach, the following profit equation is used: sales volume   unit variable sales volume   unit fixed         0 in units   expense in units  expenses  sales price

This equation is solved for the sales volume in units. c. In the graphical approach, sales revenue and total expenses are graphed. The break-even point occurs at the intersection of the total revenue and total expense lines. 7-2

The term unit contribution margin refers to the contribution that each unit of sales makes toward covering fixed expenses and earning a profit. The unit contribution margin is defined as the sales price minus the unit variable expense.

7-3

In addition to the break-even point, a CVP graph shows the impact on total expenses, total revenue, and profit when sales volume changes. The graph shows the sales volume required to earn a particular target net profit. The firm's profit and loss areas are also indicated on a CVP graph.

7-4

The safety margin is the amount by which budgeted sales revenue exceeds breakeven sales revenue.

7-5

An increase in the fixed expenses of any enterprise will increase its break-even point. In a travel agency, more clients must be served before the fixed expenses are covered by the agency's service fees.

7-6

A decrease in the variable expense per pound of oysters results in an increase in the contribution margin per pound. This will reduce the company's break-even sales volume.

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7-7

The president is correct. A price increase results in a higher unit contribution margin. An increase in the unit contribution margin causes the break-even point to decline. The financial vice president's reasoning is flawed. Even though the break-even point will be lower, the price increase will not necessarily reduce the likelihood of a loss. Customers will probably be less likely to buy the product at a higher price. Thus, the firm may be less likely to meet the lower break-even point (at a high price) than the higher break-even point (at a low price).

7-8

When the sales price and unit variable cost increase by the same amount, the unit contribution margin remains unchanged. Therefore, the firm's break-even point remains the same.

7-9

The fixed annual donation will offset some of the museum's fixed expenses. The reduction in net fixed expenses will reduce the museum's break-even point.

7-10

A profit-volume graph shows the profit to be earned at each level of sales volume.

7-11

The most important assumptions of a cost-volume-profit analysis are as follows: (a) The behavior of total revenue is linear (straight line) over the relevant range. This behavior implies that the price of the product or service will not change as sales volume varies within the relevant range. (b) The behavior of total expenses is linear (straight line) over the relevant range. This behavior implies the following more specific assumptions: (1) Expenses can be categorized as fixed, variable, or semivariable. (2) Efficiency and productivity are constant. (c) In multiproduct organizations, the sales mix remains constant over the relevant range. (d) In manufacturing firms, the inventory levels at the beginning and end of the period are the same.

7-12

Operating managers frequently prefer the contribution income statement because it separates fixed and variable costs. This format makes cost-volume-profit relationships more readily discernible.

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7-13

The gross margin is defined as sales revenue minus all variable and fixed manufacturing expenses. The total contribution margin is defined as sales revenue minus all variable expenses, including manufacturing, selling, and administrative expenses.

7-14

East Company, which is highly automated, will have a cost structure dominated by fixed costs. West Company's cost structure will include a larger proportion of variable costs than East Company's cost structure. A firm's operating leverage factor, at a particular sales volume, is defined as its total contribution margin divided by its operating income. Since East Company has proportionately higher fixed costs, it will have a proportionately higher total contribution margin. Therefore, East Company's operating leverage factor will be higher.

7-15

When sales volume increases, Company X will have a higher percentage increase in operating than Company Y. Company X's higher proportion of fixed costs gives the firm a higher operating leverage factor. The company's percentage increase in operating income can be found by multiplying the percentage increase in sales volume by the firm's operating leverage factor.

7-16

The sales mix of a multiproduct organization is the relative proportion of sales of its products. The weighted-average unit contribution margin is the average of the unit contribution margins for a firm's several products, with each product's contribution margin weighted by the relative proportion of that product's sales.

7-17

The car rental agency's sales mix is the relative proportion of its rental business associated with each of the three types of automobiles: subcompact, compact, and full-size. In a multi-product CVP analysis, the sales mix is assumed to be constant over the relevant range of activity.

7-18

Cost-volume-profit analysis shows the effect on profit of changes in expenses, sales prices, and sales mix. A change in the hotel's room rate (price) will change the hotel's unit contribution margin. This contribution-margin change will alter the relationship between volume and profit.

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7-19

Budgeting begins with a sales forecast. Cost-volume-profit analysis can be used to determine the profit that will be achieved at the budgeted sales volume. A CVP analysis also shows how profit will change if the sales volume deviates from budgeted sales. Cost-volume-profit analysis can be used to show the effect on profit when variable or fixed expenses change. The effect on profit of changes in variable or fixed advertising expenses is one factor that management would consider in making a decision about advertising.

7-20

The low-price company must have a larger sales volume than the high-price company. By spreading its fixed expense across a larger sales volume, the low-price firm can afford to charge a lower price and still earn the same profit as the high-price company. Suppose, for example, that companies A and B have the following expenses, sales prices, sales volumes, and profits.

Company A Sales revenue: 350 units at $10 .............................................. 100 units at $20 .............................................. Variable expenses: 350 units at $6 ................................................ 100 units at $6 ................................................ Contribution margin ............................................. Fixed expenses .................................................... Operating Profit ....................................................

Company B

$3,500 $2,000 2,100 $1,400 1,000 $ 400

600 $1,400 1,000 $ 400

7-21

The statement makes three assertions, but only two of them are true. Thus the statement is false. A company with an advanced manufacturing environment typically will have a larger proportion of fixed costs in its cost structure. This will result in a higher break-even point and greater operating leverage. However, the firm's higher break-even point will result in a reduced safety margin.

7-22

Activity-based costing (ABC) results in a richer description of an organization's cost behavior and CVP relationships. Costs that are fixed with respect to sales volume may not be fixed with respect to other important cost drivers. An ABC system recognizes these nonvolume cost drivers, whereas a traditional costing system does not.

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SOLUTIONS TO EXERCISES EXERCISE 7-23 (25 MINUTES)

1 2 3 4

Sales Revenue $160,000a 80,000 120,000 110,000

Variable Expenses $40,000 65,000 40,000 22,000

Total Contribution Margin $120,000 15,000 80,000 88,000

Fixed Operating Expenses Income $30,000 $90,000 15,000b -030,000 50,000 50,000 38,000

Break-Even Sales Revenue $40,000 80,000 45,000c 62,500d

Explanatory notes for selected items: aBreak-even

sales revenue............................................................................... Fixed expenses ................................................................................................ Variable expenses ...........................................................................................

$40,000 30,000 $10,000

Therefore, variable expenses are 25 percent of sales revenue. When variable expenses amount to $40,000, sales revenue is $160,000. b$80,000

is the break-even sales revenue, so fixed expenses must be equal to the contribution margin of $15,000 and profit must be zero. c$45,000

= $30,000  (2/3), where 2/3 is the contribution-margin ratio.

d$62,500

= $50,000/.80, where .80 is the contribution-margin ratio.

EXERCISE 7-24 (20 MINUTES) 1.

2.

Break-even point (in units) =

Contribution-margin ratio

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fixed expenses unit contribution margin

=

$40,000 = 10,000 pizzas $10  $6

=

unit contribution margin unit sales price

=

$10  $6 = .4 $10  2011 The McGraw-Hill Companies, Inc. 7-5

EXERCISE 7-24 (CONTINUED) 3.

4.

Break-even point (in sales dollars)

=

fixedexpenses contribution-margin ratio

=

$40,000 = $100,000 .4

Let X denote the sales volume of pizzas required to earn a target operating income of $80,000. $10X – $6X – $40,000 = $80,000 $4X = $120,000 X = 30,000 pizzas

EXERCISE 7-25 (25 MINUTES) 1.

2.

3.

Break-even point (in units)

=

fixed costs unit contribution margin

=

$4,000,000 = 4,000 components $3,000  $2,000

New break-even point (in units)

=

($4,000,000) (1.10) $3,000  $2,000

=

$4,400,000 = 4,400 components $1,000

Sales revenue (5,000  $3,000) ................................................. $15,000,000 Variable costs (5,000  $2,000) ........................................................ 10,000,000 Contribution margin ......................................................................... 5,000,000 Fixed costs ........................................................................................ 4,000,000 Operating income ............................................................................. $ 1,000,000

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EXERCISE 7-25 (CONTINUED) 4.

New break-even point (in units) =

$4,000,000 $2,500  $2,000

= 8,000 components 5.

Analysis of price change decision:

Sales revenue: (5,000  $3,000) ..................... (6,200  $2,500) ...................... Variable costs: (5,000  $2,000) ...................... (6,200  $2,000) ...................... Contribution margin .......................................... Fixed expenses ................................................ Operating income (loss) ...................................

Price $3,000 $2,500 $15,000,000 $15,500,000 10,000,000 12,400,000 3,100,000 5,000,000 4,000,000 4,000,000 ($900,000) $ 1,000,000

The price cut should not be made, since projected operating income will decline.

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EXERCISE 7-26 (25 MINUTES) 1.

Cost-volume-profit graph:

Dollars per year Total revenue $300,000

Total expenses

Break-even point: 20,000 tickets

$250,000

Profit area Variable expense (at 30,000 tickets)



$200,000

$150,000 Loss area $100,000

Annual fixed expenses

$50,000

5,000

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10,000

15,000

20,000

25,000

Tickets sold per 30,000 year

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EXERCISE 7-26 (CONTINUED) 2.

Stadium capacity ................................................ Attendance rate ................................................... Attendance per game .........................................

10,000  50% 5,000

Break-even point (tickets) 20,000  4 Attendanceper game 5,000 The team must play 4 games to break even.

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EXERCISE 7-27 (25 MINUTES) 1.

Profit-volume graph:

Dollars per year $150,000

$100,000

$50,000 Break-even point: 20,000 tickets 0

$(50,000)

5,000

10,000

15,000

Profit area



20,000

25,000

Tickets sold per year

Loss area

$(100,000) Annual fixed expenses $(150,000) $(180,000)

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EXERCISE 7-27 (CONTINUED) 2.

Safety margin: Budgeted sales revenue (12 games  10,000 seats  .30 full  $10) ............................................. Break-even sales revenue (20,000 tickets  $10) ............................................................................... Safety margin .................................................................................................

3.

$360,000 200,000 $160,000

Let P denote the break-even ticket price, assuming a 12-game season and 50 percent attendance: (12)(10,000)(.50)P – (12)(10,000)(.50)($1) – $180,000 = 0 60,000P = $240,000 P = $4 per ticket

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EXERCISE 7-28 (25 MINUTES) 1.

(a) Traditional income statement: EUROPA PUBLICATIONS, INC. INCOME STATEMENT FOR THE YEAR ENDED DECEMBER 31, 20XX Sales ......................................................................... Less: Cost of goods sold ......................................... Gross margin ............................................................... Less: Operating expenses: Selling expenses ............................................ Administrative expenses ............................... Operating income ........................................................

$2,200,000 1,500,000 $ 700,000 $150,000 150,000

300,000 $ 400,000

(b) Contribution income statement: EUROPA PUBLICATIONS, INC. INCOME STATEMENT FOR THE YEAR ENDED DECEMBER 31, 20XX Sales ......................................................................... Less: Variable expenses: Variable manufacturing.................................. Variable selling ............................................... Variable administrative .................................. Contribution margin .................................................... Less: Fixed expenses: Fixed manufacturing ...................................... Fixed selling ................................................... Fixed administrative ....................................... Operating income ........................................................ 2.

$2,200,000 $1,000,000 100,000 30,000

1,130,000 $ 1,070,000

$ 500,000 50,000 120,000

670,000 $ 400,000

contribution margin operating income $1,070,000   2.6 $400,000

Operating leverage factor (at $2,200,000 sales level) 

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EXERCISE 7-28 (CONTINUED) 3.

 percentage increase    Percentage increase in operating income    in sales revenue 

 operating     leverage factor 

= 10%  2.6 = 26% 4.

Most operating managers prefer the contribution income statement for answering this type of question. The contribution format highlights the contribution margin and separates fixed and variable expenses.

EXERCISE 7-29 (30 MINUTES) 1. Bicycle Type High-quality Medium-quality 2.

Sales Price $500 300

Unit Variable Cost $300 ($275 + $25) 150 ($135 + $15)

Unit Contribution Margin $200 150

Sales mix: High-quality bicycles ........................................................................................ Medium-quality bicycles ...................................................................................

3.

Weighted-average unit contribution margin

25% 75%

= ($200  25%) + ($150  75%) = $162.50

4.

Break-even point (in units)  

Bicycle Type High-quality bicycles Medium-quality bicycles Total

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fixed expenses weighted-average unit contribution margin $65,000  400 bicycles $162.50 Break-Even Sales Volume 100 (400  .25) 300 (400  .75)

Sales Price $500 300

Sales Revenue $ 50,000 90,000 $140,000

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EXERCISE 7-29 (CONTINUED) 5.

Target operating income:

$65,000  $48,750 $162.50  700 bicycles

Sales volume required to earn target operating income of $48,750 

This means that the shop will need to sell the following volume of each type of bicycle to earn the target operating income: High-quality ........................................................................... Medium-quality .....................................................................

175 (700  .25) 525 (700  .75)

EXERCISE 7-30 (30 MINUTES) Answers will vary on this question, depending on the airline selected as well as the year of the inquiry. All publicly-owned airlines disclose load factors; some disclose break-even load factors. In a typical year, most airlines report a load factor of about 80% and a breakeven load factor of around 65 percent, though it can vary quite dramatically from company to company and year to year. EXERCISE 7-31 (25 MINUTES) 1.

The following income statement, often...