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 

fixed expenses 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 b 15,000 -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)

=

fixed expenses 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: Price $3,000 $15,000,000 Sales revenue: (5,000  $3,000) ................................ (6,200  $2,500) ................................ 10,000,000 Variable costs: (5,000  $2,000) ................................ (6,200  $2,000) ................................ Contribution margin....................................................5,000,000 Fixed expenses ...........................................................4,000,000 $ 1,000,000 Operating income (loss) .............................................

$2,500 $15,500,000 12,400,000 3,100,000 4,000,000 ($900,000)

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 $ 500,000 50,000 120,000

1,130,000 $ 1,070,000

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

fixed expenses weighted-average unit contribution margin $65,000   400 bicycles $162.50

Break-even point (in units) 

Bicycle Type High-quality bicycles Medium-quality bicycles Total

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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 called a common-size income statement, provides a convenient way to show the cost structure. Amount Revenue .............................................................. Variable expenses .............................................. Contribution margin........................................... Fixed expenses .................................................. Operating income...............................................

$550,000 300,000 $250,000 200,000 $ 50,000

Percent (rounded) 100.0 54.5 45.5 36.4 9.1

2. Decrease in Revenue $55,000*



Contribution Margin Percentage 45.5%†

=

Decrease in Operating Income $25,025

*$55,000 = $550,000  10% †45.5%

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EXERCISE 7-31 (CONTINUED)

contribution margin operating income $250,000  5 $50,000

3.

Operating leverage factor (at revenueof $550,000) 

4.

Percentage changein operating income  

 percentageincrease  operating leverage     in revenue factor    

20 % 5  100%

EXERCISE 7-32 (10 MINUTES) Revenue ....................................................... Less: Variable expenses........................... Contribution margin ................................... Less: Fixed expenses ............................... Operating Income (loss) .............................

Requirement (1) $660,000 360,000 $300,000 280,000 $ 20,000

Requirement (2) $ 550,000 600,000 $ (50,000) 175,000 $ (225,000)

EXERCISE 7-33 (20 MINUTES)

fixed expenses contribution margin ratio $120,000   $600,000 .20

1.

Break - even volume of service revenue 

2.

Target pre - tax income 

target after - tax net income 1  tax rate $48,000   $80,000 1  .40

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EXERCISE 7-33 (CONTINUED)

target after - tax net income (1  t )  contribution margin ratio $48,000 $120,000  1  .40  $1,000,000  .20 fixed expenses 

3.

Service revenue required to earn target after-tax income of $48,000

4.

A change in the tax rate will have no effect on the firm's break-even point. At the breakeven point, the firm has no profit and does not have to pay any income taxes.

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SOLUTIONS TO PROBLEMS PROBLEM 7-34 (30 MINUTES) 1.

Break-even point in units, using the equation approach: $16X – ($10 + $2)X – $600,000 = 0 $4X = $600,000 X =

$600,000 $4

= 150,000 units 2.

New projected sales volume = 200,000  110% = 220,000 units Operating income = (220,000)($16 – $12) – $600,000 = (220,000)($4) – $600,000 = $880,000 – $600,000 = $280,000

3.

Target operating income = $200,000 (from original problem data) New disk purchase price = $10  130% = $13 Volume of sales dollars required: Volume of sales dollars required

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fixed expenses  target operating income contribution - margin ratio $600,000  $200,000 $800,000   $16  $13  $2 .0625 $16  $12,800,000 

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PROBLEM 7-34 (CONTINUED) 4.

Let P denote the selling price that will yield the same contribution-margin ratio:

$16  $10  $2 P  $13  $2  $16 P .25 

P  $15 P

.25P  P  $15 $15  .75P P  $15/.75 P  $20 Check: New contribution-margin ratio is:

$20  $15  .25 $20

5. In the electronic version of the solutions manual, press the CTRL key and click on the following link: Build a Spreadsheet 07-34.xls

PROBLEM 7-35 (30 MINUTES) 1.

Break-even point in sales dollars, using the contribution-margin ratio:

fixed expenses contribution - margin ratio $180,000  $72,000 $252,000   $20  $8  $2 .5 $20  $504,000

Break - even point 

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PROBLEM 7-35 (CONTINUED) 2.

Target operating income, using contribution-margin approach:

fixed expenses  target operating income unit contribution margin $252,000  $180,000 $432,000   $20  $8  $2 $10  43,200 units

Sales units to earn operating income of $180,000 

3.

New unit variable manufacturing cost

= $8  110% = $8.80

Break-even point in sales dollars: $252,000 $252,000  $20.00  $8.80  $2.00 .46 $20  $547,826 (rounded)

Break - even point 

4.

Let P denote the selling price that will yield the same contribution-margin ratio: $20.00  $8.00  $2.00 P  $8.80  $2.00  $20.00 P P  $10.80 .5  P .5P  P  $10.80 $10.80  .5P P  $10.80/.5 P  $21.60

Check: New contribution-margin ratio is: $21.60  $8.80  $2.00  .5 $21.60

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PROBLEM 7-36 (30 MINUTES) 1.

Unit contribution margin: Sales price………………………………… Less variable costs: Sales commissions ($64 x 5%)…… $ 3.20 System variable costs……………… 16.00 Unit contribution margin………………..

$64.00 19.20 $44.80

Break-even point = fixed costs ÷ unit contribution margin = $985,600 ÷ $44.80 = 22,000 units 2.

Model no. 4399 is more profitable when sales and production average 46,000 units.

Sales revenue (46,000 units x $64.00)……... Less variable costs: Sales commissions ($2,944,000 x 5%)… System variable costs:…………………… 46,000 units x $16.00…………………. 46,000 units x $12.80…………………. Total variable costs……………………….. Contribution margin…………………………... Less: Annual fixed costs…………………….. Operating income.……………..……………… 3.

Model No. 6754

Model No. 4399

$2,944,000

$2,944,000

$ 147,200

$ 147,200

736,000 $ 883,200 $2,060,800 985,600 $1,075,200

588,800 $ 736,000 $2,208,000 1,113,600 $1,094,400

Annual fixed costs will increase by $90,000 ($450,000 ÷ 5 years) because of straightline depreciation associated with the new equipment, to $1,203,600 ($1,113,600 + $90,000). The unit contribution margin is $48 ($2,208,000 ÷ 46,000 units). Thus: Required sales = (fixed costs + target net profit) ÷ unit contribution margin = ($1,203,600 + $956,400) ÷ $48 = 45,000 units

4.

Let X = volume level at which annual total costs are equal $16.00X + $985,600 = $12.80X + $1,113,600 $3.20X = $128,000 X = 40,000 units

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PROBLEM 7-37 (35 MINUTES) 1.

Current income: Sales revenue………………………... Less: Variable costs………………… $ 924,000 Fixed costs……………………. 2,280,000 Operating income….……………….

$3,360,000 3,204,000 $ 156,000

Advanced Electronics has a contribution margin of $58 [($3,360,000 - $924,000) ÷ 42,000 sets] and desires to increase income to $312,000 ($156,000 x 2). In addition, the current selling price is $80 ($3,360,000 ÷ 42,000 sets). Thus: Required sales = (fixed costs + target net profit) ÷ unit contribution margin = ($2,280,000 + $312,000) ÷ $58 = 44,690 sets (rounded), or $3,575,200 (44,690 sets x $80) 2.

If operations are shifted to Slovakia, the new unit contribution margin will be $64 ($80 - $16). Thus: Break-even point = fixed costs ÷ unit contribution margin = $1,984,000 ÷ $64 = 31,000 units

3.

(a) Advanced Electronics desires to have a 31,000-unit break-even point with a $58 unit contribution margin. Fixed cost must therefore drop by $482,000 ($2,280,000 - $1,798,000), as follows: Let X = fixed costs X ÷ $58 = 31,000 units X = $1,798,000 (b)

As the following calculations show, Advanced Electronics will have to generate a contribution margin of $73.55 to produce a 31,000-unit break-even point. Based on an $80.00 selling price, this means that the company can incur variable costs of only $6.45 per unit. Given the current variable cost of $22.00 ($80.00 - $58.00), a decrease of $15.55 per unit ($22.00 - $6.45) is needed. Let X = unit contribution margin $2,280,000 ÷ X = 31,000 units X = $73.55 (rounded)

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PROBLEM 7-37 (CONTINUED 4.

(a)

Increase

(b)

No effect

(c)

Increase

(d)

No effect

PROBLEM 7-38 (40 MINUTES) 1.

Sales mix refers to the relative proportion of each product sold when a company sells more than one product.

2.

(a)

Yes. Plan A sales are expected to total 65,000 units (45,500 + 19,500), which compares favorably against current sales of 60,000 units.

(b)

Yes. Sales personnel earn a commission based on gross dollar sales. As the following figures show, Deluxe sales will comprise a greater proportion of total sales under Plan A. This is not surprising in light of the fact that Deluxe has a higher selling price than Basic ($86 vs. $74). Current Units

Sales Mix

Deluxe……... 39,000 65% Basic………. 21,000 35% Total 60,000 100% (c)

Plan A Units

Sales Mix

45,500 70% 19,500 30% 65,000 100%

Yes. Commissions will total $535,600 ($5,356,000 x 10%), which compares favorably against the current flat salaries of $400,000. Deluxe sales: 45,500 units x $86… $3,913,000 Basic sales: 19,500 units x $74….. 1,443,000 Total………………………………. $5,356,000

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PROBLEM 7-38 (CONTINUED) (d)

No. The company would be less profitable under the new plan. Sales revenue: Deluxe: 39,000 units x $86; 45,500 units x $86… Basic: 21,000 units x $74; 19,500 units x $74….. Total revenue……………………………………. Less variable cost: Deluxe: 39,000 units x $65; 45,500 units x $65… Basic: 21,000 units x $41; 19,500 units x $41….. Sales commissions (10% of sales revenue)……. Total variable cost……………………………… Contribution margin…………………………………….. Less fixed cost (salaries)………………………………. Operating income….…………………………………...

3.

(a)

Current

Plan A

$3,354,000 1,554,000 $4,908,000

$3,913,000 1,443,000 $5,356,000

$2,535,000 861,000

$2,957,500 799,500 535,600 $4,292,600 $1,063,400 ---$1,063,400

$3,396,000 $1,512,000 400,000 $1,112,000

The total units sold under both plans are the same; however, the sales mix has shifted under Plan B in favor of the more profitable product as judged by the contribution margin. Deluxe has a contribution margin of $21 ($86 - $65), and Basic has a contribution margin of $33 ($74 - $41). Plan A Units

Sales Mix

Deluxe……... 45,500 70% Basic………. 19,500 30% Total…… 65,000 100%

McGraw-Hill/Irwin Managerial Accounting, 9/e Global Edition

Plan B Units

Sales Mix

26,000 40% 39,000 60% 65,000 100%

 2011 The McGraw-Hill Companies, Inc. 7-23

PROBLEM 7-38 (CONTINUED) (b)

Plan B is more attractive both to the sales force and to the company. Salespeople earn more money under this arrangement ($549,900 vs. $400,000) and the company is more profitable ($1,283,100 vs. $1,112,000). Sales revenue: Deluxe: 39,000 units x $86; 26,000 units x $86… Basic: 21,000 units x $74; 39,000 units x $74….. Total revenue……………………………………. Less variable cost: Deluxe: 39,000 units x $65; 26,000 units x $65… Basic: 21,000 units x $41; 39,000 units x $41….. Total variable cost……………………………… Contribution margin…………………………………….. Less: Sales force compensation: Flat salaries…………………………………………... Commissions ($1,833,000 x 30%)………………… Operating Income ……………………………….……..

Current

Plan B

$3,354,000 1,554,000 $4,908,000

$2,236,000 2,886,000 $5,122,000

$2,535,000 861,000 $3,396,000 $1,512,000

$1,690,000 1,599,000 $3,289,000 $1,833,000

400,000 $1,112,000

549,900 $1,283,100

PROBLEM 7-39 (35 MINUTES) 1.

Plan A break-even point = fixed costs ÷ unit contribution margin = $34,100 ÷ $31* = 1,100 units Plan B break-even point = fixed costs ÷ unit contribution margin = $72,000 ÷ $40** = 1,800 units * $90 - [($90 x 10%) + $50] ** $90 - $50

2.

Operating leverage refers to the use of fixed costs in an organization’s overall cost structure. An organization that has a relatively high proportion of fixed costs and low proportion of variable costs has a high degree of operating leverage.

McGraw-Hill/Irwin 7-24

 2011 The McGraw-Hill Companies, Inc. Solutions Manual

PROBLEM 7-39 (CONTINUED) 3.

Calculation of contribution margin and profit at 6,000 units of sales:

Sales revenue: 6,000 units x $90………………. Less variable costs: Cost of purchasing product: 6,000 units x $50…………………….…… Sales commissions: $540,000 x 10%……... Total variable cost……………………….. Contribution margin……………………………… Fixed costs…………………………………………. Net income………………………………………….

Plan A

Plan B

$540,000

$540,000

$300,000 54,000 $354,000 $186,000 34,100 $151,900

$300,000 ---$300,000 $240,000 72,000 $168,000

Operating leverage factor = contribution margin ÷ net income Plan A: $186,000 ÷ $151,900 = 1.22 (rounded) Plan B: $240,000 ÷ $168,000 = 1.43 (rounded) Plan B has the higher operating leverage factor. 4 & 5. Calculation of profit at 5,000 units: Sales revenue: 5,000 units x $90………………. Less variable costs: Cost of purchasing product: 5,000 units x $50………………………….. Sales commissions: $450,000 x 10%……... Total variable cost……………………….. Contribution margin……………………………… Fixed costs………………………………………… Net income………………………………………….

Plan A

Plan B

$450,000

$450,000

$250,000 45,000 $295,000 $155,000 34,100 $120,900

$250,000 ---$250,000 $200,000 72,000 $128,000

Plan A profitability decrease: $151,900 - $120,900 = $31,000; $31,000 ÷ $151,900 = 20.4% (rounded) Plan B profitability decrease: $168,000 - $128,000 = $40,000; $40,000 ÷ $168,000 = 23.8% (rounded)

McGraw-Hill/Irwin Managerial Accounting, 9/e Global Edition

 2011 The McGraw-Hill Companies, Inc. 7-25

PROBLEM 7-39 (CONTINUED) Consolidated would experience a larger percentage decrease in income if it adopts Plan B. This situation arises because Plan B has a higher degree of operating leverage. Stated differently, Plan B’s cost structure produces a greater percentage decline in profitability from the drop-off in sales revenue. Note: The percentage decreases in profitability can be computed by multiplying the percentage decrease in sales revenue by the operating leverage factor. Sales dropped from 6,000 units to 5,000 units, or 16.67%. Thus: Plan A: 16.67% x 1.22 = 20.3% (difference due to rounding) Plan B: 16.67% x 1.43 = 23.8% (rounded) 6.

Heavily automated manufacturers have sizable investments in plant and equipment, along with a high percentage of fixed costs in their cost structures. As a result, there is a high degree of operating leverage. In a severe economic downturn, these firms typically suffer a significant decrease in profitability. Such firms would be a more risky investment when compared with firms that have a low degree of operating leverage. Of course, when times are good, increases in sales would tend to have a very favorable effect on earnings in a company with high operating leverage.

McGraw-Hill/Irwin 7-26

 2011 The McGraw-Hill Companies, Inc. Solutions Manual

PROBLEM 7-40 (30 MINUTES) fixed costs unit contribution margin $468,000   90,000 units $25.00  $19.80

1.

Break - even point (in units) 

2.

Break - even point (in sales dollars) 

3.

Number of sales units required to earn target operating income

4.

Margin of safety = budgeted sales revenue – break-even sales revenue

fixed cost contribution - margin ratio $468,000   $2,250,000 $25.00  $19.80 $25.00 fixed costs  target operating income unit contribution margin $468,000  $260,000   140,000 units $25.00  $19.80 

= (120,000)($25) – $2,250,000 = $750,000 5.

Break-even point if direct-labor costs increase by 8 percent: New unit contribution margin

= $25.00 – $6.00 – ($5.00)(1.08) – $4.50 – $3.00 – $1.30 = $4.80

fixed costs new unit contribution margin $468,000   97,500 units $4.80

Break-even point 

McGraw-Hill/Irwin Managerial Accounting, 9/e Global Edition

 2011 The McGraw-Hill Companies, Inc. 7-27

PROBLEM 7-40 (CONTINUED) 6.

Contribution margin ratio 

unit contribution margin sales price

$25.00  $19.80 $25.00  .208

Old contribution-margin ratio 

Let P denote sales price required to maintain a contribution-margin ratio of .208. Then P is determined as follows: P  $6.00  ($5.00)(1.08)  $4.50  $3.00  $1.30  .208 P P  $20.20  .208P .792P  $20.20 P  $25.51 (rounded)

Check:

McGraw-Hill/Irwin 7-28

New contributionmargin ratio

$25.51  $6.00  ($5.00)(1.08)  $4.50  $3.00  $1.30 $25.51  .208 (rounded) 

 2011 The McGraw-Hill Companies, Inc. Solutions Manual

PROBLEM 7-41 (40 MINUTES) 1. CVP graph:

Total revenue Dollars per year (in millions) 20 18

Profit area

Break-even point: 80,000 units or $8,000,000 of sales

16 14

Total expenses

12 10 8 6 4

Loss area

Fixed expenses

2 50

McGraw-Hill/Irwin Managerial Accounting, 9/e Global Edition

100

150

200

Units sold per year (in thousands)

 2011 The McGraw-Hill Companies, Inc. 7-29

PROBLEM 7-41 (CONTINUED) 2.

Break-even point: contribution margin $12,000,000   .75 sales $16,000,000 fixed expenses $6,000,000 Break - even point   contribution - margin ratio .75  $8,000,000

Contribution - margin ratio 

3.

Margin of safety = budgeted sales revenue – break-even sales revenue = $16,000,000 – $8,000,000 = $8,000,000 contribution margin (at budgeted sales) operating income (at budgeted sales) $12,000,000  2 $6,000,000

4.

Operating leverage factor (at budgeted sales)



5.

Dollar sales required to earn target operating income



fixed expenses  target operating income contribution - margin ratio



$6,000,000  $9,000,000  $20,000,000 .75

6.

Cost structure: Sales revenue ....................................................... Variable expenses ................................................ Contribution margin............................................. Fixed expenses .................................................... Operating income.................................................

McGraw-Hill/Irwin 7-30

Amount $16,000,000 4,000,000 $12,000,000 6,000,000 $6,000,000

Percent 100.0 25.0 75.0 37.5 37.5

 2011 The McGraw-Hill Companies, Inc. Solutions Manual

PROBLEM 7-42 (35 MINUTES) 1.

(a)

Unit contribution margin  

(b)

sales  variable costs units sold $1,000,000  $700,000  $3 per unit 100,000

Break-even point (in units) 

fixed costs unit contribution margin



$210,000  70,000 units $3

Contribution-margin ratio   Break-even point (in sales dollars)  

2.

Number of units of sales required to earn target after-tax net income

contribution margin sales revenue $1,000,000  $700,000  .3 $1,000,000 fixed costs contribution-margin ratio $210,000  $700,000 .3

target after-tax net income (1  t ) unit contribution margin

fixed costs  

$210,000  

$90,000 (1  .4)

$3



$360,000 $3

 120,000 units 3.

If fixed costs increase by $31,500:

Break-even point (in units) 

McGraw-Hill/Irwin Managerial Accounting, 9/e Global Edition

$210,000  $31,500  80,500 units $3

 2011 The McGraw-Hill Companies, Inc. 7-31

PROBLEM 7-42 (CONTINUED) 4. Profit-volume graph:

Dollars per year $750,000

$500,000

$250,000

0

Break-even point: 70,000 units

Loss 25,000 area

50,000

 75,000

Profit area

100,000

Units sold per year

$(250,000)

$(500,000)

$(750,000)

McGraw-Hill/Irwin 7-32

 2011 The McGraw-Hill Companies, Inc. Solutions Manual

PROBLEM 7-42 (CONTINUED) 5.

Number of units of sales required to earn target after-tax net income

target after- tax net income (1  t ) unit contribution margin

fixed costs  

$210,000  

$90,000 (1  .5)

$3



$390,000 $3

 130,000 units 6.

In the electronic version of the solutions manual, press the CTRL key and click on the following link: Build a Spreadsheet 07-42.xls

PROBLEM 7-43 (40 MINUTES) 1.

In order to break even, during the first year of operations, 10,220 clients must visit the law office being considered by Martin Wong and his colleagues, as the following calculations show. Fixed expenses: Advertising ............................................................................... $ 350,000 Rent (600  $480) ..................................................................... 288,000 Property insurance .................................................................. 27,000 Utilities ..................................................................................... 37,000 Malpractice insurance ............................................................. 160,000 Depreciation ($120,000/4) ........................................................ 30,000 Wages and fringe benefits: Regular wages ($25 + $20 + $15 + $10)  16 hours  360 days .......... $403,200 Overtime wages (200  $15  1.5) + (200  $10  1.5) ........................... 7,500 Total wages ............................................................ $410,700 Fringe benefits at 40% ....................................................... 164,280 574,980 Total fixed expenses...................................................................... $1,466,980

McGraw-Hill/Irwin Managerial Accounting, 9/e Global Edition

 2011 The McGraw-Hill Companies, Inc. 7-33

PROBLEM 7-43 (CONTINUED) Break-even point: 0 = revenue – variable cost – fixed cost 0 = $30X + ($2,000  .2X  .3)* – $4X – $1,466,980 0 = $30X + $120X – $4X – $1,466,980 $146X = $1,466,980 X = 10,048 clients (rounded) *Revenue calculation: $30X represents the $30 consultation fee per client. ($2,000  .2X  .30) represents the predicted average settlement of $2,000, multiplied by the 20% of the clients whose judgments are expected to be favorable, multiplied by the 30% of the judgment that goes to the firm. 2.

Safety margin: Safety margin = budgeted sales revenue  break-even sales revenue Budgeted (expected) number of clients = 50  360 = 18,000 Break-even number of clients = 10,048 (rounded) Safety margin = [($30  18,000) + ($2,000  18,000  .20  .30)] – [($30  10,048) + ($2,000  10,048  .20  .30)] = [$30 + ($2,000  .20  .30)]  (18,000 – 10,048) = $150  7,852 = $1,192,800

McGraw-Hill/Irwin 7-34

 2011 The McGraw-Hill Companies, Inc. Solutions Manual

PROBLEM 7-44 (45 MINUTES) 1.

Break-even point in units:

Break-even point 

fixed costs unit contribution margin

Calculation of contribution margins:

Selling price...................................... Variable costs: Direct material.............................. Direct labor .................................. Variable overhead ........................ Variable selling cost .................... Contribution margin per unit (a)

Computer-Assisted Manufacturing System $30.00 $5.00 6.00 3.00 2.00

16.00 $14.00

Labor-Intensive Production System $30.00 $5.60 7.20 4.80 2.00

19.60 $10.40

Computer-assisted manufacturing system:

$2,440,000  $500,000 $14 $2,940,000  $14  210,000 units

Break-even point in units 

(b)

Labor-intensive production system:

$1,320,000  $500,000 $10.40 $1,820,000  $10.40  175,000 units

Break-even point in units 

McGraw-Hill/Irwin Managerial Accounting, 9/e Global Edition

 2011 The McGraw-Hill Companies, Inc. 7-35

PROBLEM 7-44 (CONTINUED) 2.

Celestial Products, Inc. would be indifferent between the two manufacturing methods at the volume (X) where total costs are equal. $16X + $2,940,000 = $19.60X + $1,820,000 $3.60X = $1,120,000 X = 311,111 units (rounded)

3.

Operating leverage is the extent to which a firm's operations employ fixed operating costs. The greater the proportion of fixed costs used to produce a product, the greater the degree of operating leverage. Thus, the computer-assisted manufacturing method utilizes a greater degree of operating leverage. The greater the degree of operating leverage, the greater the change in operating income (loss) relative to a small fluctuation in sales volume. Thus, there is a higher degree of variability in operating income if operating leverage is high.

4.

Management should employ the computer-assisted manufacturing method if annual sales are expected to exceed 311,111 units and the labor-intensive manufacturing method if annual sales are not expected to exceed 311,111 units.

5.

Celestial Products’ management should consider many other business factors other than operating leverage before selecting a manufacturing method. Among these are:

 Variability or uncertainty with respect to demand quantity and selling price.  The ability to produce and market the new product quickly.  The ability to discontinue production and marketing of the new product while incurring the least amount of loss.

McGraw-Hill/Irwin 7-36

 2011 The McGraw-Hill Companies, Inc. Solutions Manual

PROBLEM 7-45 (45 MINUTES) 1.

Break-even sales volume for each model:

(a)

(b)

(c)

Break-even volume 

annualrental cost unit contribution margin

Break - even volume 

$8,000  25,000 liters $1.75  $1.43

Break - even volume 

$11,000  27,500 liters $1.75  $1.35

Break - even volume 

$20,000  40,816 liters (rounded) $1.75  $1.26

Economy model:

Regular model:

Super model:

McGraw-Hill/Irwin Managerial Accounting, 9/e Global Edition

 2011 The McGraw-Hill Companies, Inc. 7-37

PROBLEM 7-45 (CONTINUED) 2. Profit-volume graph:

Dollars per year (in thousands)

Profit

$20

$10

0

Break-even point: 40,816 liters 10

20

30



40

Profit area

50

Liters sold per year (in thousands)

Loss

Loss area ($10)

($20)

McGraw-Hill/Irwin 7-38

Fixed rental cost: $20,000 per year

 2011 The McGraw-Hill Companies, Inc. Solutions Manual

PROBLEM 7-45 (CONTINUED) 3.

The sales price per liter is the same regardless of the type of machine selected. Therefore, the same profit (or loss) will be achieved with the Economy and Regular models at the sales volume, X, where the total costs are the same. Model Economy .................................................... Regular ......................................................

Variable Cost per Liter $1.43 1.35

Total Fixed Cost $ 8,000 11,000

This reasoning leads to the following equation:

8,000 + 1.43X = 11,000 + 1.35X

Rearranging terms yields the following:

(1.43 – 1.35)X = 11,000 – 8,000 .08X = 3,000 X = 3,000/.08 X = 37,500

Or, stated slightly differently: Volume at which both machines produce the same profit

fixed cost differential variable cost differential $3,000  $.08  37,500 liters 

Check: the total cost is the same with either model if 37,500 liters are sold. Economy Variable cost: Economy, 37,500  $1.43 .......................... Regular, 37,500  $1.35 ............................. Fixed cost: Economy, $8,000 ....................................... Regular, $11,000 ........................................ Total cost .........................................................

Regular

$53,625 $50,625 8,000 $61,625

11,000 $61,625

Since the sales price for popcorn does not depend on the popper model, the sales revenue will be the same under either alternative.

McGraw-Hill/Irwin Managerial Accounting, 9/e Global Edition

 2011 The McGraw-Hill Companies, Inc. 7-39

PROBLEM 7-46 (35 MINUTES) 1.

Unit contribution margin 

$625,000  $375,000 25,000 units

 $10 per unit

2.

3.

Break-even point (in units) 

fixed costs unit contribution margin



$150,000  15,000 units $10

Number of sales units required to earn target operating income

New break - even point (in units)  



fixed costs  target operating income unit contribution margin



$150,000  $140,000  29,000 units $10

new fixed costs new unit contribution margin $150,000  ($24,000/6) *  19,250 units $10  $2 †

*Annual straight-line depreciation on new machine †$2.00

4.

= $4.50 – $2.50 increase in the unit cost of the new part

Number of sales units required to earn target operating income, given manufacturing changes



new fixed costs  target net profit new unit contribution margin



$154,000  $100,000 * $8

 31,750 units

*Last year's profit: ($25)(25,000) – $525,000 = $100,000

McGraw-Hill/Irwin 7-40

 2011 The McGraw-Hill Companies, Inc. Solutions Manual

PROBLEM 7-46 (CONTINUED)

unit contribution margin sales price $10 Old contribution-margin ratio   .40 $25* Contribution-margin ratio 

5.

*Given in problem. Let P denote the price required to cover increased direct-material cost and maintain the same contribution margin ratio:

P  $15*  $2 †  .40 P P  $17  .40P .60P  $17 P  $28.33 (rounded) *Old unit variable cost = $15 = $375,000  25,000 units †Increase

in direct-material cost = $2

Check:

$28.33  $15  $2 $28.33  .40 (rounded)

New contribution-margin ratio 

McGraw-Hill/Irwin Managerial Accounting, 9/e Global Edition

 2011 The McGraw-Hill Companies, Inc. 7-41

PROBLEM 7-47 (40 MINUTES) 1.

Memorandum

Date:

Today

To:

Vice President for Manufacturing, Halong Game Company

From:

Controller

Subject:

Activity-Based Costing

The $150,000 cost that has been characterized as fixed is fixed with respect to sales volume. This cost will not increase with increases in sales volume. However, as the activity-based costing analysis demonstrates, these costs are not fixed with respect to other important cost drivers. This is the difference between a traditional costing system and an ABC system. The latter recognizes that costs vary with respect to a variety of cost drivers, not just sales volume. 2.

New break-even point if automated manufacturing equipment is installed: Sales price ..................................................................................................... Costs that are variable (with respect to sales volume): Unit variable cost (.8  $375,000  25,000) ........................................... Unit contribution margin .............................................................................. Costs that are fixed (with respect to sales volume): Setup (300 setups at $40 per setup) ............................................. Engineering (800 hours at $28 per hour) ..................................... Inspection (100 inspections at $45 per inspection) .................... General factory overhead .............................................................. Total .......................................................................................... Fixed selling and administrative costs .............................................. Total costs that are fixed (with respect to sales volume) ........... Break - even point (in units)  

$26 12 $14 $ 12,000 22,400 4,500 176,100 $215,000 30,000 $245,000

fixed costs unit contribution margin $245,000 $14

 17,500 units

McGraw-Hill/Irwin 7-42

 2011 The McGraw-Hill Companies, Inc. Solutions Manual

PROBLEM 7-47 (CONTINUED) 3.

Sales (in units) required to show operating income of $140,000: fixed cost  target operating income Number of sales units required  to earn target operating income unit contribution margin $245,000  $140,000 $14  27,515 units (rounded) 

4.

If management adopts the new manufacturing technology: (a)

Its break-even point will be higher (17,500 units instead of 15,000 units).

(b)

The number of sales units required to show operating income of $140,000 will be lower (27,515 units instead of 29,000 units).

(c)

These results are typical of situations where firms adopt advanced manufacturing equipment and practices. The break-even point increases because of the increased fixed costs due to the large investment in equipment. However, at higher levels of sales after fixed costs have been covered, the larger unit contribution margin ($14 instead of $10) earns a profit at a faster rate. This results in the firm needing to sell fewer units to reach a given target profit level.

McGraw-Hill/Irwin Managerial Accounting, 9/e Global Edition

 2011 The McGraw-Hill Companies, Inc. 7-43

PROBLEM 7-47 (CONTINUED) 5.

The controller should include the break-even analysis in the report. The Board of Directors needs a complete picture of the financial implications of the proposed equipment acquisition. The break-even point is a relevant piece of information. The controller should accompany the break-even analysis with an explanation as to why the break-even point will increase. It would also be appropriate for the controller to point out in the report that the advanced manufacturing equipment would require fewer sales units at higher volumes in order to achieve a given target profit, as in requirement (3) of this problem. To withhold the break-even analysis from the controller's report would be a violation of the following ethical standards: (a)

Competence: Provide decision support information and recommendations that are accurate, clear, concise, and timely.

(b)

Integrity: Refrain from engaging in any conduct that would prejudice carrying out duties ethically.

(c)

Credibility: Communicate information fairly and objectively. Disclose all relevant information that could reasonably be expected to influence an intended user's understanding of the reports, analyses, and recommendations.

McGraw-Hill/Irwin 7-44

 2011 The McGraw-Hill Companies, Inc. Solutions Manual

PROBLEM 7-48 (25 MINUTES) 1.

Closing of downtown store: Loss of contribution margin at Downtown Store .......................................... $(36,000) Savings of fixed cost at Downtown Store (75%) ........................................... 30,000 Loss of contribution margin at Mall Store (10%) ........................................... (4,800) Total decrease in operating income ............................................................... $(10,800)

2.

Promotional campaign: Increase in contribution margin (10%) ........................................................... Increase in monthly promotional expenses ($60,000/12) ............................. Decrease in operating income ........................................................................

3.

$ 3,600 (5,000) $(1,400)

Elimination of items sold at their variable cost: We can restate the November 20x1 data for the Downtown Store as follows:

Sales .................................................................................. Less: variable expenses ................................................... Contribution margin..........................................................

Downtown Store Items Sold at Their Variable Cost Other Items $60,000* $60,000* 60,000 24,000 $ -0$ 36,000

If the items sold at their variable cost are eliminated, we have: Decrease in contribution margin on other items (20%) .............................. Decrease in fixed expenses (15%) ................................................................ Decrease in operating income ......................................................................

$(7,200) 6,000 $(1,200)

*$60,000 is one half of the Downtown Store's dollar sales for November 20x1. 4. In the electronic version of the solutions manual, press the CTRL key and click on the following link: Build a Spreadsheet 07-48.xls

McGraw-Hill/Irwin Managerial Accounting, 9/e Global Edition

 2011 The McGraw-Hill Companies, Inc. 7-45

PROBLEM 7-49 (45 MINUTES) 1. CHENNAI TOOL COMPANY BUDGETED INCOME STATEMENT FOR THE YEAR ENDED DECEMBER 31, 20X2 Weeders Unit selling price ............................... $28 Variable manufacturing cost ........... $13 Variable selling cost ......................... 5 Total variable cost ............................ $18 Contribution margin per unit ........... $10 Unit sales ..........................................  50,000 Total contribution margin ............ $500,000

Hedge Clippers $36 $12 4 $16 $20  50,000 $1,000,000

Leaf Blowers Total $48 $25 6 $31 $17  100,000 $1,700,000 $3,200,000

Fixed manufacturing overhead........ Fixed selling and administrative costs .................... Total fixed costs ........................... Income before taxes ......................... Income taxes (40%) .......................... Budgeted net income .......................

$2,160,000 600,000 $2,760,000 $440,000 176,000 $ 264,000

2. (a) Unit Contribution Weeders ...................................................... $10 Hedge Clippers ........................................... 20 Leaf Blowers ............................................... 17 Weighted-average unit contribution margin ..............................

(b) Sales Proportion .25 .25 .50

(a)  (b) $ 2.50 5.00 8.50 $16.00

total fixed costs weighted - average unit contribution margin $2,760,000   172,500 units $16

Total unit sales to break even 

McGraw-Hill/Irwin 7-46

 2011 The McGraw-Hill Companies, Inc. Solutions Manual

PROBLEM 7-49 (CONTINUED) Sales proportions:

Weeders ........................................................ Hedge Clippers ............................................. Leaf Blowers ................................................. Total ...............................................................

Sales Proportion .25 .25 .50

Total Unit Product Line Sales Sales 172,500 43,125 172,500 43,125 172,500 86,250 172,500

3. (a) Unit Contribution Weeders ................................................................... $10 Hedge Clippers* ...................................................... 19 Leaf Blowers† .......................................................... 12 Weighted-average unit contribution margin .........

(b) Sales Proportion .20 .20 .60

(a)  (b) $ 2.00 3.80 7.20 $13.00

*Variable selling cost increases. Thus, the unit contribution decreases to $19 [$36 – ($12 + $4 + $1)]. †The

variable manufacturing cost increases 20 percent. Thus, the unit contribution decreases to $12 [$48 – (1.2  $25) – $6].

total fixed costs weighted - average unit contribution margin $2,760,000   212,308 units (rounded) $13

Total unit sales to break even 

Sales proportions: Sales Proportions Weeders .............................................................. .20 Hedge Clippers ................................................... .20 Leaf Blowers ....................................................... .60 Total .....................................................................

McGraw-Hill/Irwin Managerial Accounting, 9/e Global Edition

Total Unit Sales 212,308 212,308 212,308

Product Line Sales 53,077 53,077 106,154 212,308

 2011 The McGraw-Hill Companies, Inc. 7-47

PROBLEM 7-50 (45 MINUTES) 1.

Unit contribution margin 

$405,000  $225 per ton 1,800

Break-even volume in tons 

fixed costs unit contribution margin

 2.

$247,500  1,100 tons $225

Projected operating income for sales of 2,100 tons: Projected contribution margin (2,100  $225) ....................................... Projected fixed costs .............................................................................. Projected operating income ...................................................................

3.

$472,500 247,500 $225,000

Projected operating income including German order: Variable cost per ton = $495,000/1,800 = $275 per ton Sales price per ton for regular orders = $900,000/1,800 = $500 per ton

Sales in tons ..................................................................... Contribution margin per ton: German order ($450 – $275) ...................................... Regular sales ($500 – $275) ....................................... Total contribution margin ................................................

German Order 1,500 

$175

$262,500

Contribution margin on German order...................................................... Contribution margin on regular sales ....................................................... Total contribution margin .......................................................................... Fixed costs .................................................................................................. Operating income .......................................................................................

McGraw-Hill/Irwin 7-48

Regular Sales 1,500  $225 $337,500 $262,500 337,500 $600,000 247,500 $352,500

 2011 The McGraw-Hill Companies, Inc. Solutions Manual

PROBLEM 7-50 (CONTINUED) 4.

New sales territory: To maintain its current operating income, Ohio Limestone Company just needs to break even on sales in the new territory.

Break-even point in tons   5.

fixed costsin new territory unit contribution margin on sales in new territory $61,500  307.5 tons $225  $25

Automated production process:

Break-even point in tons  

$247,500  $58,500 $225  $25 $306,000  1,224 tons $250

Break-even point in sales dollars  1,224 tons $500 per ton  $612,000 6.

Changes in selling price and unit variable cost: New unit contribution margin  ($500)(90%)  ($275  $40)  $135 $135 ($500)(90%)  .30

New contribution margin ratio 

fixed costs  target operating income contribution margin ratio $247,500  $94,500  .30  $1,140,000

Dollar sales required to earn targe t operating income 

McGraw-Hill/Irwin Managerial Accounting, 9/e Global Edition

 2011 The McGraw-Hill Companies, Inc. 7-49

PROBLEM 7-51 (35 MINUTES) $162.50  $117.00  .28 $162.50

1.

Contribution margin ratio 

2.

Number of units of sales required to earn target after-tax net income

target after - tax net income (1  t) unit contribution margin

fixed expenses  

$44,160 (1  .40) $614,250 X  $162.50  $117.00 $45.50 $540,650 

X  13,500 units

3.

Break-even point (in units) for the mountaineering model



$693,000  11,000 units $180.00  $117.00

Let Y denote the variable cost of the touring model such that the break-even point for the touring model is 11,000 units. Then we have: $540,650 $162.50  Y (11,000)  ($162.50  Y )  $540,650 $1,787,500  11,000Y  $540,650 11,000Y  $1,246,850 Y  $113.35 11,000 

Thus, the variable cost per unit would have to decrease by $3.65 ($117.00 – $113.35).

McGraw-Hill/Irwin 7-50

 2011 The McGraw-Hill Companies, Inc. Solutions Manual

PROBLEM 7-51 (CONTINUED) 4.

5.

$540,650  110% $162.50  ($117.00)(90%) $594,715  $57.20  10,397 units (rounded)

New break - even point 

Weighted-average unit contribution margin Break-even point

 (50%  $63.00)  (50%  $45.50)  $54.25 fixed costs  weighted - average unit contribution margin $616,825   11,370 units (rounded; or 5,685 of each type) $54.25

PROBLEM 7-52 (45 MINUTES) 1.

SUMMARY OF EXPENSES

Manufacturing .................................................................... Selling and administrative ................................................ Interest ............................................................................... Costs from budgeted income statement ..................... If the company employs its own sales force: Additional sales force costs ......................................... Reduced commissions [(.15 – .10)  $16,000]............. Costs with own sales force ............................................... If the company sells through agents: Deduct cost of sales force ............................................ Increased commissions [(.225 – .10)  $16,000] ......... Costs with agents paid increased commissions ............

McGraw-Hill/Irwin Managerial Accounting, 9/e Global Edition

Expenses per Year (in thousands) Variable Fixed $ 7,200 $2,340 2,400 1,920 540 $ 9,600 $4,800 2,400 (800) $ 8,800

$7,200 (2,400)

2,000 $ 10,800

$4,800

 2011 The McGraw-Hill Companies, Inc. 7-51

PROBLEM 7-52 (CONTINUED)

totalfixed expenses contribution margin ratio total variable expenses Contribution-margin ratio  1  sales revenue

Break-even sales dollars 

(a)

$9,600,000 $16,000,000  1  .60

Contribution margin ratio  1   .40

$4,800,000 .40  $12,000,000

Break-even sales dollars 

(b)

$8,800,000 $16,000,000  1  .55

Contribution margin ratio  1 

 .45 $7,200,000 .45  $16,000,000

Break-even sales dollars 

2.

Requiredsales dollars 

totalfixed costs  target income beforeincome taxes contribution margin ratio

$10,800 $16,000  1  .675  .325

Contribution margin ratio  1 

$4,800,000  $1,600,000 .325 $6,400,000  .325  $19,692,308

Required sales dollars to break even 

McGraw-Hill/Irwin 7-52

 2011 The McGraw-Hill Companies, Inc. Solutions Manual

PROBLEM 7-52 (CONTINUED) 3.

The volume in sales dollars (X) that would result in equal net income is the volume of sales dollars where total expenses are equal. Total expenses with agents paid increased commission

= total expenses with own sales force

$10,800,000 $8,800,000 X  $4,800,000  X  $7,200,000 $16,000,000 $16,000,000 .675 X  $4,800,000  .55 X  $7,200,000 .125 X  $2,400,000 X  $19,200,000 Therefore, at a sales volume of $19,200,000, the company will earn equal before-tax income under either alternative. Since before-tax income is the same, so is after-tax net income.

McGraw-Hill/Irwin Managerial Accounting, 9/e Global Edition

 2011 The McGraw-Hill Companies, Inc. 7-53