CHAPTER 8
Cost-Volume-Profit Analysis
ANSWERS TO REVIEW QUESTIONS
8-1
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.
8-2
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.
8-3
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.
8-4
The safety margin is the amount by which budgeted sales revenue exceeds breakeven sales revenue.
8-5
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.
8-6
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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8-1
8-7
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).
8-8
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.
8-9
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.
8-10
A profit-volume graph shows the profit to be earned at each level of sales volume.
8-11
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.
8-12
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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8-13
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.
8-14
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 net 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.
8-15
When sales volume increases, Company X will have a higher percentage increase in
profit 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 profit can
be found by multiplying the percentage increase in sales volume by the firm's
operating leverage factor.
8-16
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.
8-17
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.
8-18
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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8-3
8-19
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.
8-20
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 ....................................................
Profit .....................................................................
Company B
$3,500
$2,000
2,100
$1,400
1,000
$ 400
600
$1,400
1,000
$ 400
8-21
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.
8-22
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 8-23 (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
Expenses
$30,000
15,000b
30,000
50,000
Net
Income
$90,000
-050,000
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 8-24 (20 MINUTES)
1.
2.
Break-even point (in units) =
Contribution-margin ratio
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fixed expenses
unit contribution margin
=
$40,000
= 8,000 pizzas
$10  $5
=
unit contribution margin
unit sales price
=
$10  $5
= .5
$10
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8-5
EXERCISE 8-24 (CONTINUED)
3.
4.
Break-even point (in sales dollars)
=
fixed expenses
contribution-margin ratio
=
$40,000
= $80,000
.5
Let X denote the sales volume of pizzas required to earn a target net profit of
$65,000.
$10X – $5X – $40,000 = $65,000
$5X = $105,000
X = 21,000 pizzas
EXERCISE 8-25 (25 MINUTES)
1.
Break-even point (in units)
=
=
fixed costs
unit contribution margin
4,000,000p
3,000p  2,000p
= 4,000 components
p denotes Argentina’s peso, worth 1.004 U.S. dollars on the day this exercise was
written.
2.
3.
New break-even point (in units)
=
(4,000,000p ) (1.10)
3,000p  2,000p
=
4,400,000 p
= 4,400 components
1,000p
Sales revenue (5,000  3,000p)
................................................. 15,000,000p
Variable costs (5,000  2,000p) ........................................................ 10,000,000p
Contribution margin ......................................................................... 5,000,000p
Fixed costs ........................................................................................ 4,000,000p
Net income ........................................................................................ 1,000,000p
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EXERCISE 8-25 (CONTINUED)
4.
New break-even point (in units) =
4,000,000p
2,500p  2,000p
= 8,000 components
5.
Analysis of price change decision:
Price
3,000p
15,000,000p
Sales revenue: (5,000  3,000p) ................................
(6,200  2,500p) ................................
10,000,000p
Variable costs: (5,000  2,000p) ................................
(6,200  2,000p) ................................
5,000,000p
Contribution margin....................................................
4,000,000p
Fixed expenses ...........................................................
1,000,000p
Net income (loss) ........................................................
2,500p
15,500,000p
12,400,000p
3,100,000p
4,000,000p
(900,000p)
The price cut should not be made, since projected net income will decline.
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8-7
EXERCISE 8-26 (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 8-26 (CONTINUED)
2.
Stadium capacity ................................................
Attendance rate ...................................................
Attendance per game .........................................
10,000
 50%
5,000
Break-even point (tickets) 20,000

4
Attendance per game
5,000
The team must play 4 games to break even.
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8-9
EXERCISE 8-27 (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 8-27 (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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8-11
EXERCISE 8-28 (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 ...............................
Net income ...................................................................
$2,000,000
1,500,000
$ 500,000
$150,000
150,000
300,000
$ 200,000
(b) Contribution income statement:
EUROPA PUBLICATIONS, INC.
INCOME STATEMENT
FOR THE YEAR ENDED DECEMBER 31, 20SXX
Sales .........................................................................
Less: Variable expenses:
Variable manufacturing..................................
Variable selling ...............................................
Variable administrative ..................................
Contribution margin ....................................................
Less: Fixed expenses:
Fixed manufacturing ......................................
Fixed selling ...................................................
Fixed administrative .......................................
Net income ...................................................................
2.
Operatingleverage factor (at $2,000,000 sales level) 

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$2,000,000
$1,000,000
100,000
30,000
$ 500,000
50,000
120,000
1,130,000
$ 870,000
670,000
$ 200,000
contribution margin
net income
$870,000
 4.35
$200,000
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EXERCISE 8-28 (CONTINUED)
3.
 percentage increase  operating 
  

Percentage increase in net income  
 in sales revenue   leverage factor 
= 10%  4.35
= 43.5%
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 8-29 (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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8-13
EXERCISE 8-29 (CONTINUED)
5.
Target net income:
$65,000  $48,750
$162.50
 700 bicycles
Sales volume required to earn target net 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 net income:
High-quality ...........................................................................
Medium-quality .....................................................................
175 (700  .25)
525 (700  .75)
EXERCISE 8-30 (30 MINUTES)
Answers will vary on this question, depending on the airline selected as well as the year of
the inquiry. In a typical year, most airlines report a breakeven load factor of around 65
percent.
EXERCISE 8-31 (25 MINUTES)
1.
The following income statement, often called a common-size income statement,
provides a convenient way to show the cost structure.
Revenue ..............................................................
Variable expenses ..............................................
Contribution margin...........................................
Fixed expenses ..................................................
Net income..........................................................
Amount
$500,000
300,000
$200,000
150,000
$ 50,000
Percent
100
60
40
30
10
2.
Decrease in
Revenue
$75,000*

Contribution Margin
Percentage
40%†
=
Decrease in
Net Income
$30,000
*$75,000 = $500,000  15%
†40%
= $200,000/$500,000
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EXERCISE 8-31 (CONTINUED)
3.
Operatingleverage factor (at revenue of $500,000) 

4.
contribution margin
net income
$200,000
4
$50,000
 percentageincrease  operatingleverage


Percentage change in net income  




in revenue
factor

 

20% 4
 80%
EXERCISE 8-32 (10 MINUTES)
Requirement (1)
$600,000
360,000
$240,000
210,000
$ 30,000
Revenue .......................................................
Less: Variable expenses...........................
Contribution margin ...................................
Less: Fixed expenses ...............................
Net Income (loss) ........................................
Requirement (2)
$ 500,000
600,000
$ (100,000)
125,000
$ (225,000)
EXERCISE 8-33 (20 MINUTES)
fixed expenses
contribution margin ratio
$120,000

 $600,000
.20
1.
Break-even volume of service revenue 
2.
Target before-tax income 

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target after-tax net income
1  tax rate
$48,000
 $80,000
1  .40
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8-15
EXERCISE 8-33 (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 8-34 (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
Net income = (220,000)($16 – $12) – $600,000
= (220,000)($4) – $600,000
= $880,000 – $600,000 = $280,000
3.
Target net income = $200,000 (from original problem data)
New disk purchase price = $10  130% = $13
Volume of sales dollars required:
Volume of sales dollars required


fixed expenses  target net profit
contribution-margin ratio
$600,000  $200,000 $800,000

$16  $13  $2
.0625
$16
 $12,800,000
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8-17
PROBLEM 8-34 (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
PROBLEM 8-35 (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  $4
.4
$20
 $630,000
Break-even point 
2.
Target net income, using contribution-margin approach:
fixed expenses  target net income
unit contribution margin
$252,000  $180,000 $432,000


$20  $8  $4
$8
 54,000 units
Sales units required to earn income of $180,000 
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PROBLEM 8-35 (CONTINUED)
3.
New unit variable manufacturing cost
= $8  110%
= $8.80
Break-even point in sales dollars:
$252,000
$252,000

$20.00  $8.80  $4.00
.36
$20
 $700,000
Break - even point 
4.
Let P denote the selling price that will yield the same contribution-margin ratio:
$20.00  $8.00  $4.00 P  $8.80  $4.00

$20.00
P
.4 
P  $12.80
P
.4P  P  $12.80
$12.80  .6P
P  $12.80/.6
P  $21.33 (rounded)
Check: New contribution-margin ratio is:
$21.33  $8.80  $4.00
 .4 (rounded)
$21.33
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PROBLEM 8-36 (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……………………..
Net 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 8-37 (35 MINUTES)
1.
Current income:
Sales revenue………………………...
Less: Variable costs………………… $ 840,000
Fixed costs……………………. 2,280,000
Net income…………………………….
$3,360,000
3,120,000
$ 240,000
Advanced Electronics has a contribution margin of $60 [($3,360,000 - $840,000) ÷
42,000 sets] and desires to increase income to $480,000 ($240,000 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 + $480,000) ÷ $60
= 46,000 sets, or $3,680,000 (46,000 sets x $80)
2.
If operations are shifted to Mexico, the new unit contribution margin will be $62 ($80 $18). Thus:
Break-even point = fixed costs ÷ unit contribution margin
= $1,984,000 ÷ $62
= 32,000 units
3.
(a)
Advanced Electronics desires to have a 32,000-unit break-even point with a
$60 unit contribution margin. Fixed cost must therefore drop by $360,000
($2,280,000 - $1,920,000), as follows:
Let X = fixed costs
X ÷ $60 = 32,000 units
X = $1,920,000
(b)
As the following calculations show, Advanced Electronics will have to
generate a contribution margin of $71.25 to produce a 32,000-unit break-even
point. Based on an $80.00 selling price, this means that the company can
incur variable costs of only $8.75 per unit. Given the current variable cost of
$20.00 ($80.00 - $60.00), a decrease of $11.25 per unit ($20.00 - $8.75) is
needed.
Let X = unit contribution margin
$2,280,000 ÷ X = 32,000 units
X = $71.25
McGraw-Hill/Irwin
Managerial Accounting, 5/e
 2002 The McGraw-Hill Companies, Inc.
8-21
PROBLEM 8-37 (CONTINUED
4.
(a)
Increase
(b)
No effect
(c)
Increase
(d)
No effect
PROBLEM 8-38 (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
McGraw-Hill/Irwin
8-22
 2002 The McGraw-Hill Companies, Inc.
Solutions Manual
PROBLEM 8-38 (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)……………………………….
Net 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, 5/e
Plan B
Units
Sales
Mix
26,000 40%
39,000 60%
65,000 100%
 2002 The McGraw-Hill Companies, Inc.
8-23
PROBLEM 8-38 (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%)…………………
Net 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 8-39 (35 MINUTES)
1.
Plan A break-even point = fixed costs ÷ unit contribution margin
= $22,000 ÷ $22*
= 1,000 units
Plan B break-even point = fixed costs ÷ unit contribution margin
= $66,000 ÷ $30**
= 2,200 units
* $80 - [($80 x 10%) + $50]
** $80 - $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
8-24
 2002 The McGraw-Hill Companies, Inc.
Solutions Manual
PROBLEM 8-39 (CONTINUED)
3.
Calculation of contribution margin and profit at 6,000 units of sales:
Sales revenue: 6,000 units x $80……………….
Less variable costs:
Cost of purchasing product:
6,000 units x $50…………………….……
Sales commissions: $480,000 x 10%……...
Total variable cost………………………..
Contribution margin………………………………
Fixed costs………………………………………….
Net income………………………………………….
Plan A
Plan B
$480,000
$480,000
$300,000
48,000
$348,000
$132,000
22,000
$110,000
$300,000
---$300,000
$180,000
66,000
$114,000
Operating leverage factor = contribution margin ÷ net income
Plan A: $132,000 ÷ $110,000 = 1.2
Plan B: $180,000 ÷ $114,000 = 1.58 (rounded)
Plan B has the higher degree of operating leverage.
4 & 5. Calculation of profit at 5,000 units:
Sales revenue: 5,000 units x $80……………….
Less variable costs:
Cost of purchasing product:
5,000 units x $50…………………………..
Sales commissions: $400,000 x 10%……...
Total variable cost………………………..
Contribution margin………………………………
Fixed costs…………………………………………
Net income………………………………………….
Plan A
Plan B
$400,000
$400,000
$250,000
40,000
$290,000
$110,000
22,000
$ 88,000
$250,000
---$250,000
$150,000
66,000
$ 84,000
Plan A profitability decrease:
$110,000 - $88,000 = $22,000; $22,000 ÷ $110,000 = 20%
Plan B profitability decrease:
$114,000 - $84,000 = $30,000; $30,000 ÷ $114,000 = 26.3% (rounded)
McGraw-Hill/Irwin
Managerial Accounting, 5/e
 2002 The McGraw-Hill Companies, Inc.
8-25
PROBLEM 8-39 (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 1.2 = 20.0%
Plan B: 16.67% x 1.58 = 26.3% (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
8-26
 2002 The McGraw-Hill Companies, Inc.
Solutions Manual
PROBLEM 8-40 (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.
4.
Number of sales units required to
earn target net profit
fixed cost
contribution-margin ratio
$468,000
 $2,250,000
$25.00  $19.80
$25.00

fixed costs  target net profit
unit contribution margin

$468,000  $260,000
 140,000 units
$25.00  $19.80
Margin of safety = budgeted sales revenue – break-even sales revenue
= (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 – $10.50 – ($5.00)(1.08) – $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, 5/e
 2002 The McGraw-Hill Companies, Inc.
8-27
PROBLEM 8-40 (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  $10.50  ($5.00)(1.08)  $3.00  $1.30
 .208
P
P  $20.20  .208P
.792P  $20.20
P  $25.51(rounded)
Check:
McGraw-Hill/Irwin
8-28
New contributionmargin ratio
$25.51  $10.50  ($5.00)(1.08)  $3.00  $1.30
$25.51
 .208 (rounded)

 2002 The McGraw-Hill Companies, Inc.
Solutions Manual
PROBLEM 8-41 (40 MINUTES)
1. CVP graph:
Total revenue
Dollars per year
(in millions)
10
9
Profit
area
Break-even point:
80,000 units or
$4,000,000 of sales
8
7
Total expenses
6
5
4
3
2
Loss
area
Fixed expenses
1
50
McGraw-Hill/Irwin
Managerial Accounting, 5/e
100
150
200
Units sold per year
(in thousands)
 2002 The McGraw-Hill Companies, Inc.
8-29
PROBLEM 8-41 (CONTINUED)
2.
Break-even point:
contribution margin $6,000,000

 .75
sales
$8,000,000
fixed expenses
$3,000,000
Break-even point 

contribution-margin ratio
.75
 $4,000,000
Contribution-margin ratio 
3.
Margin of safety = budgeted sales revenue – break-even sales revenue
= $8,000,000 – $4,000,000 = $4,000,000
contribution margin (at budgeted sales)
net income (at budgeted sales)
$6,000,000

2
$3,000,000
4.
Operating leverage factor
(at budgeted sales)

5.
Dollar sales required to
earn target net profit

6.
fixed expenses  target net profit
contribution-margin ratio
$3,000,000  $4,500,000

 $10,000,000
.75
Cost structure:
Sales revenue .......................................................
Variable expenses ................................................
Contribution margin.............................................
Fixed expenses ....................................................
Net income............................................................
McGraw-Hill/Irwin
8-30
Amount
$8,000,000
2,000,000
$6,000,000
3,000,000
$3,000,000
Percent
100.0
25.0
75.0
37.5
37.5
 2002 The McGraw-Hill Companies, Inc.
Solutions Manual
PROBLEM 8-42 (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, 5/e
$210,000  $31,500
 80,500 units
$3
 2002 The McGraw-Hill Companies, Inc.
8-31
PROBLEM 8-42 (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
8-32
 2002 The McGraw-Hill Companies, Inc.
Solutions Manual
PROBLEM 8-42 (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
PROBLEM 8-43 (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 Terry Smith and his colleagues, as the following
calculations show.
Fixed expenses:
Advertising ...............................................................................
$ 490,000
Rent (6,000  $28) ....................................................................
168,000
Property insurance ..................................................................
27,000
Utilities .....................................................................................
37,000
Malpractice insurance .............................................................
180,000
Depreciation ($60,000/4) ..........................................................
15,000
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......................................................................
$1,491,980
McGraw-Hill/Irwin
Managerial Accounting, 5/e
 2002 The McGraw-Hill Companies, Inc.
8-33
PROBLEM 8-43 (CONTINUED)
Break-even point:
0 = revenue – variable cost – fixed cost
0 = $30X + ($2,000  .2X  .3)* – $4X – $1,491,980
0 = $30X + $120X – $4X – $1,491,980
$146X = $1,491,980
X = 10,220 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 = 10,220 (rounded)
Safety margin = [($30  18,000) + ($2,000  18,000  .20  .30)]
– [($30  10,220) + ($2,000  10,220  .20  .30)]
= [$30 + ($2,000  .20  .30)]  (18,000 – 10,220)
= $150  7,780
= $1,167,000
McGraw-Hill/Irwin
8-34
 2002 The McGraw-Hill Companies, Inc.
Solutions Manual
PROBLEM 8-44 (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, 5/e
 2002 The McGraw-Hill Companies, Inc.
8-35
PROBLEM 8-44 (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
8-36
 2002 The McGraw-Hill Companies, Inc.
Solutions Manual
PROBLEM 8-45 (45 MINUTES)
1.
Break-even sales volume for each model:
(a)
(b)
(c)
Break-even volume 
annual rental cost
unit contribution margin
Break-even volume 
$8,000
 25,000 tubs
$1.75  $1.43
Break-even volume 
$11,000
 27,500 tubs
$1.75  $1.35
Break-even volume 
$20,000
 40,816 tubs (rounded)
$1.75  $1.26
Economy model:
Regular model:
Super model:
McGraw-Hill/Irwin
Managerial Accounting, 5/e
 2002 The McGraw-Hill Companies, Inc.
8-37
PROBLEM 8-45 (CONTINUED)
2. Profit-volume graph:
Dollars per year (in
thousands)
Profit
$20
$10
0
Break-even point:
40,816 tubs
10
20
30

40
Profit
area
50
Units sold
per year
(in thousands)
Loss
Loss
area
($10)
($20)
McGraw-Hill/Irwin
8-38
Fixed rental cost: $20,000 per year
 2002 The McGraw-Hill Companies, Inc.
Solutions Manual
PROBLEM 8-45 (CONTINUED)
3.
The sales price per tub 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 Tub
$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 tubs

Check: the total cost is the same with either model if 37,500 tubs 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, 5/e
 2002 The McGraw-Hill Companies, Inc.
8-39
PROBLEM 8-46 (35 MINUTES)
1.
Unit contribution margin 
$625,000  $375,000
25,000 units
 $10 per unit
Break-even point (in units) 

2.
3.
fixed costs
unit contribution margin
$150,000
 15,000 units
$10
Number of sales units required
to earn target net profit
New break-even point (in units) 


fixed costs  target net profit
unit contribution margin

$150,000  $140,000
 29,000 units
$10
new fixed costs
new unit contribution margin
$150,000  ($18,000/6)*
 19,125 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 net profit, given
manufacturing changes

new fixed costs  target net profit
new unit contribution margin

$153,000  $100,000*
$8
 31,625 units
*Last year's profit: ($25)(25,000) – $525,000 = $100,000
McGraw-Hill/Irwin
8-40
 2002 The McGraw-Hill Companies, Inc.
Solutions Manual
PROBLEM 8-46 (CONTINUED)
unit contribution margin
sales price
$10
Old contribution-margin ratio 
 .40
$25*
Contribution-margin ratio 
5.
*Sales price = $25 = $625,000  25,000 units.
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, 5/e
 2002 The McGraw-Hill Companies, Inc.
8-41
PROBLEM 8-47 (40 MINUTES)
1.
Memorandum
Date:
Today
To:
Vice President for Manufacturing, Jupiter Game Company
From:
I.M. Student, 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 activitybased 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 $50 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
$ 15,000
22,400
4,500
166,100
$208,000
30,000
$238,000
fixed costs
unit contribution margin
$238,000
$14
 17,000 units
McGraw-Hill/Irwin
8-42
 2002 The McGraw-Hill Companies, Inc.
Solutions Manual
PROBLEM 8-47 (CONTINUED)
3.
Sales (in units) required to show a profit of $140,000:
Number of sales units required
to earn target net profit
4.
fixed cost  target net profit
unit contribution margin
$238,000  $140,000

$14
 27,000 units

If management adopts the new manufacturing technology:
(a)
Its break-even point will be higher (17,000 units instead of 15,000 units).
(b)
The number of sales units required to show a profit of $140,000 will be lower
(27,000 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, 5/e
 2002 The McGraw-Hill Companies, Inc.
8-43
PROBLEM 8-47 (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: Prepare complete and clear reports and recommendations after
appropriate analysis of relevant and reliable information.
(b)
Integrity: Communicate unfavorable as well as favorable information and
professional judgments or opinions.
(c)
Objectivity: Communicate information fairly and objectively. Disclose fully all
relevant information that could reasonably be expected to influence an intended
user's understanding of the reports, comments, and recommendations presented.
McGraw-Hill/Irwin
8-44
 2002 The McGraw-Hill Companies, Inc.
Solutions Manual
PROBLEM 8-48 (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.
McGraw-Hill/Irwin
Managerial Accounting, 5/e
 2002 The McGraw-Hill Companies, Inc.
8-45
PROBLEM 8-49 (45 MINUTES)
1.
CINCINNATI 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 .......................
$2,000,000
600,000
$2,600,000
$600,000
240,000
$ 360,000
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
$2,600,000

 162,500 units
$16
Total unit sales to break even 
McGraw-Hill/Irwin
8-46
 2002 The McGraw-Hill Companies, Inc.
Solutions Manual
PROBLEM 8-49 (CONTINUED)
Sales proportions:
Weeders ........................................................
Hedge Clippers .............................................
Leaf Blowers .................................................
Total ...............................................................
Sales
Proportion
.25
.25
.50
Total Unit Product Line
Sales
Sales
162,500
40,625
162,500
40,625
162,500
81,250
162,500
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
$2,600,000

 200,000 units
$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, 5/e
Total Unit
Sales
200,000
200,000
200,000
Product Line
Sales
40,000
40,000
120,000
200,000
 2002 The McGraw-Hill Companies, Inc.
8-47
PROBLEM 8-50 (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 net income for sales of 2,100 tons:
Projected contribution margin (2,100  $225) .......................................
Projected fixed costs ..............................................................................
Projected net income ..............................................................................
3.
$472,500
247,500
$225,000
Projected net income including foreign 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:
Foreign order ($450 – $275) .......................................
Regular sales ($500 – $275) .......................................
Total contribution margin ................................................
Foreign
Order
1,500

$175
$262,500
Contribution margin on foreign order .......................................................
Contribution margin on regular sales .......................................................
Total contribution margin ..........................................................................
Fixed costs ..................................................................................................
Net income ..................................................................................................
McGraw-Hill/Irwin
8-48
Regular
Sales
1,500
 $225
$337,500
$262,500
337,500
$600,000
247,500
$352,500
 2002 The McGraw-Hill Companies, Inc.
Solutions Manual
PROBLEM 8-50 (CONTINUED)
4.
New sales territory:
To maintain its current net income, Ohio Limestone Company just needs to break
even on sales in the new territory.
Break-even point in tons 

5.
fixed costs in 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 net profit
contribution margin ratio
$247,500  $94,500

.30
 $1,140,000
Dollar sales required to earn target net profit
McGraw-Hill/Irwin
Managerial Accounting, 5/e
 2002 The McGraw-Hill Companies, Inc.
8-49
PROBLEM 8-51 (35 MINUTES)
$80.00  $52.80
 .34
$80.00
1.
Contribution margin ratio 
2.
Number of units of sales required
to earn target after-tax income
target after-tax net income
(1  t)
unit contribution margin
fixed expenses 

$22,080
(1  .40) $353,600

$80.00  $52.80
$27.20
$316,800 
X
X  13,000 units
3.
Break-even point (in units) for the
mountaineering model

$369,600
 10,500 units
$88.00  $52.80
Let Y denote the variable cost of the touring model such that the break-even point
for the touring model is 10,500 units.
Then we have:
$316,800
$80.00  Y
(10,500)  ($80.00  Y )  $316,800
10,500 
$840,000  10,500Y  $316,800
10,500Y  $523,200
Y  $49.83 (rounded)
Thus, the variable cost per unit would have to decrease by $2.97 ($52.80 – $49.83).
McGraw-Hill/Irwin
8-50
 2002 The McGraw-Hill Companies, Inc.
Solutions Manual
PROBLEM 8-51 (CONTINUED)
$316,800  110%
$80.00  ($52.80)(90%)
$348,480

$32.48
 10,729 units (rounded)
4.
5.
New break-even point 
Weighted-average unit
contribution margin
Break-even point
 (50%  $35.20)  (50%  $27.20)
 $31.20
fixed costs
weighted-average unit contribution margin
$343,200

 11,000 units (or 5,500 of each type)
$31.20

PROBLEM 8-52 (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, 5/e
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
 2002 The McGraw-Hill Companies, Inc.
8-51
PROBLEM 8-52 (CONTINUED)
total fixed 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.
Required sales dollars 
total fixed costs  target income before income taxes
contribution margin ratio
$10,800
$16,000
 1  .675
Contribution margin ratio  1 
 .325
$4,800,000  $1,600,000
.325
$6,400,000

.325
 $19,692,308
Required sales dollars to break even 
McGraw-Hill/Irwin
8-52
 2002 The McGraw-Hill Companies, Inc.
Solutions Manual
PROBLEM 8-52 (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, 5/e
 2002 The McGraw-Hill Companies, Inc.
8-53
SOLUTIONS TO CASES
CASE 8-53 (50 MINUTES)
1.
The break-even point is 16,900 patient-days calculated as follows:
COMPUTATION OF BREAK-EVEN POINT
IN PATIENT-DAYS: PEDIATRICS
FOR THE YEAR ENDED JUNE 30, 20X2
Total fixed costs:
Medical center charges .........................................................................................
Supervising nurses ($25,000  4) .......................................................................
Nurses
($20,000  10) .....................................................................
Aids
($9,000  20) .......................................................................
Total fixed costs
.............................................................................................
$2,900,000
100,000
200,000
180,000
$3,380,000
Contribution margin per patient-day:
Revenue per patient-day .......................................................................................
$300
Variable cost per patient-day:
($6,000,000 ÷ $300 = 20,000 patient-days)
($2,000,000 ÷ 20,000 patient-days) ..................................................................
Contribution margin per patient-day ....................................................................
100
$200
Break-even point
in patient-days
McGraw-Hill/Irwin
8-54
total fixed costs
$3,380,000

contribution margin per patient-day
$200
 16,900 patient days

 2002 The McGraw-Hill Companies, Inc.
Solutions Manual
CASE 8-53 (CONTINUED)
2. Net earnings would decrease by $606,660, calculated as follows:
COMPUTATION OF LOSS FROM RENTAL
OF ADDITIONAL 20 BEDS: PEDIATRICS
FOR THE YEAR ENDED JUNE 30, 20X2
Increase in revenue
(20 additional beds  90 days  $300 charge per day) ...................................
$ 540,000
Increase in expenses:
Variable charges by medical center
(20 additional beds  90 days  $100 per day) ...........................................
$ 180,000
Fixed charges by medical center
($2,900,000  60 beds = $48,333 per bed, rounded)
($48,333  20 beds) .......................................................................................
966,660
Salaries
(20,000 patient-days before additional 20 beds + 20 additional
beds  90 days = 21,800, which does not exceed 22,000 patient-days;
therefore, no additional personnel are required) ........................................
Total increase in expenses ....................................................................................
Net change in earnings from rental of additional 20 beds...................................
-0$1,146,660
$ (606,660)
McGraw-Hill/Irwin
Managerial Accounting, 5/e
 2002 The McGraw-Hill Companies, Inc.
8-55
CASE 8-54 (45 MINUTES)
1.
a. In order to break even, Oakley must sell 500 units. This amount represents the
point where revenue equals total costs.
Revenue  variable costs  fixed costs
$400X  $200X  $100,000
$200X  $100,000
X  500 units
b. In order to achieve its after-tax profit objective, Oakley must sell 2,500 units. This
amount represents the point where revenue equals total costs plus the before-tax
profit objective.
Revenue  variable costs  fixed costs  before - tax profit
$400X  $200X  $100,000  [$240,000  (1  .4)]
$400X  $200X  $100,000  $400,000
$200X  $500,000
X  2,500 units
2.
To achieve its annual after-tax profit objective, Oakley should select the first
alternative, where the sales price is reduced by $40 and 2,700 units are sold during
the remainder of the year. This alternative results in the highest profit and is the
only alternative that equals or exceeds the company’s profit objective. Calculations
for the three alternatives follow.
McGraw-Hill/Irwin
8-56
 2002 The McGraw-Hill Companies, Inc.
Solutions Manual
CASE 8-54 (CONTINUED)
Alternative (1):
Re venue  ($400)(350)  ($360)(2,700)
 $1,112,000
Variable cost  $200  3,050
 $610,000
Before - tax profit  $1,112,000  $610,000  $100,000
 $402,000
After - tax profit  $402,000  (1  .4)
 $241,200
Alternative (2):
Re venue  ($400)(350)  ($370)(2,200)
 $954,000
Variable cost  ($200)(350) ($175)(2,200)
 $455,000
Before - tax profit  $954,000  $455,000  $100,000
 $399,000
After - tax profit  $399,000  (1  .4)
 $239,400
Alternative (3):
Re venue  ($400)(350)  ($380)(2,000)
 $900,000
Variable cost  $200  2,350
 $470,000
Before - tax profit  $900,000  $470,000  $90,000
 $340,000
After - tax profit  $340,000  (1  .4)
 $204,000
McGraw-Hill/Irwin
Managerial Accounting, 5/e
 2002 The McGraw-Hill Companies, Inc.
8-57
CASE 8-55 (50 MINUTES)
1.
Break-even point for 20x2, based on current budget:
$10,000,000  $6,000,000  $2,000,000
 .20
$10,000,000
fixed expenses
Break-even point 
contribution-margin ratio
$100,000

 $500,000
.20
Contribution-margin ratio 
2.
Break-even point given employment of sales personnel:
New fixed expenses:
Previous fixed expenses ........................................................................
Sales personnel salaries ........................................................................
Sales manager's salary ..........................................................................
Total .........................................................................................................
$
$
100,000
90,000
160,000
350,000
New contribution-margin ratio:
Sales ........................................................................................................
Cost of goods sold .................................................................................
Gross margin ..........................................................................................
Commissions (at 5%) ..............................................................................
Contribution margin ...............................................................................
Contribution-margin ratio 
$10,000,000
6,000,000
$ 4,000,000
500,000
$ 3,500,000
$3,500,000
 .35
$10,000,000
fixed expenses
contribution-margin ratio
$350,000

 $1,000,000
.35
Estimated break-even point 
McGraw-Hill/Irwin
8-58
 2002 The McGraw-Hill Companies, Inc.
Solutions Manual
CASE 8-55 (CONTINUED)
3.
Assuming a 25% sales commission:
New contribution-margin ratio:
Sales ........................................................................................................
Cost of goods sold .................................................................................
Gross margin ..........................................................................................
Commissions (at 25%) ............................................................................
Contribution margin ...............................................................................
Contribution-margin ratio 
Sales volume in dollars
required to earn after-tax
net income
$10,000,000
6,000,000
$ 4,000,000
2,500,000
$ 1,500,000
$1,500,000
 .15
$10,000,000
target after-tax net income
(1  t )
contribution-margin ratio
fixed expenses 

$1,330,000
$2,000,000
(1  .3)


.15
.15
 $13,333,333 (rounded)
$100,000 
Check (all figures rounded to the nearest dollar):
Sales ....................................................................
Cost of goods sold (60% of sales) .....................
Gross margin ......................................................
Selling and administrative expenses:
Commissions ................................................
All other expenses (fixed) ............................
Income before taxes ...........................................
Income tax expense (30%) .................................
Net income ..........................................................
McGraw-Hill/Irwin
Managerial Accounting, 5/e
$ 13,333,333
8,000,000
$ 5,333,333
$ 3,333,333
100,000
3,433,333
$ 1,900,000
570,000
$ 1,330,000
 2002 The McGraw-Hill Companies, Inc.
8-59
CASE 8-55 (CONTINUED)
4.
Sales dollar volume at which Niagra Falls Sporting Goods Company is indifferent:
Let X denote the desired volume of sales.
Since the tax rate is the same regardless of which approach management chooses,
we can find X so that the company’s before-tax income is the same under the two
alternatives. (In the following equations, the contribution-margin ratios of .35 and
.15, respectively, were computed in the preceding two requirements.)
.
.35X – $350,000 = .15X – $100,000
.20X = $250,000
X = $250,000/.20
X = $1,250,000
Thus, the company will have the same before-tax income under the two alternatives
if the sales volume is $1,250,000.
Check:
Sales ............................................................................
Cost of goods sold (60% of sales) .............................
Gross margin...............................................................
Selling and administrative expenses:
Commissions ..........................................................
All other expenses (fixed) ......................................
Income before taxes ...................................................
Income tax expense (30%) .........................................
Net income...................................................................
Alternatives
Employ
Sales
Pay 25%
Personnel
Commission
$1,250,000
$1,250,000
750,000
750,000
$ 500,000
$ 500,000
62,500*
350,000
$ 87,500
26,250
$ 61,250
312,500†
100,000
$ 87,500
26,250
$ 61,250
*$1,250,000  5% = $62,500
†$1,250,000  25% = $312,500
McGraw-Hill/Irwin
8-60
 2002 The McGraw-Hill Companies, Inc.
Solutions Manual
CURRENT ISSUES IN MANAGERIAL ACCOUNTING
ISSUE 8-56
"RELIANCE GROUP MAY SEE SHIELD FROM CREDITORS," THE WALL STREET JOURNAL,
AUGUST 15, 2000, DEVON SPURGON, GREGORY ZUCKERMAN, AND FRANCINE L. POPE.
1. Managers apply operating leverage to convert small changes in sales into large
changes in a firm’s profitability. Fixed costs are the lever that managers use to take
a small increase in sales and obtain a much larger increase in net income. Having a
cost structure with relatively high fixed costs provides rewards and risks to a firm.
With a high degree of operating leverage, each additional sale decreases the average
cost per unit. Each dollar of revenue becomes pure profit once the fixed costs are
covered. This is beneficial if sales are increasing; however, the reverse is true if
sales are decreasing. With decreasing sales, the fixed costs do not decrease, and
profit declines significantly more than revenue.
2. In the article, high operating leverage was not working to benefit Reliance Group
Holdings, Inc. Consequently, its stock rating was downgraded.
ISSUE 8-57
"E-COMMERCE -- DEBATE -- TALKING TO THE PLAYERS: WILL THE INTERNET TAKE
OVER COMMERCE? WE ASKED THREE PEOPLE WHO ASK THEMSELVES THAT
QUESTION ALL THE TIME," THE WALL STREET JOURNAL, JULY 12, 1999, THOMAS E.
WEBER.
According to Ken Seiff, Amazon is capturing such a huge amount of market share that it
will eventually be able to build the most cost efficient distribution system, not only in the
e-commerce field, but also in the traditional retail world. Once Amazon has developed
this system and cemented its place as the online retailer of choice, price wars will not be
as costly for Amazon as for its competitors.
McGraw-Hill/Irwin
Managerial Accounting, 5/e
 2002 The McGraw-Hill Companies, Inc.
8-61
ISSUE 8-58
"HAPPY SHOPPER," MANAGEMENT ACCOUNTING, JULY/AUGUST 2000, TONY
BRABAZON.
The cost of losing a customer will vary across the customer life cycle. The loss can be
estimated using discounted customer contribution margin, where the discounted
customer contribution margin is calculated as the gross profit per customer less
customer-related costs such as administration, distribution and financing.
ISSUE 8-59
"POSTAL SERVICE COULD FACE LOSS," THE ASSOCIATED PRESS, AUGUST 31, 2000,
RANDOLPH E. SCHMID.
1. It is important for the U.S. Postal Service to forecast the volume and cost variables
discussed in the article so its management can determine the revenue required to
cover costs and determine cost of postage.
2. Unexpected costs will increase the break-even point in cost-volume-profit analysis.
A decline in the volume of first-class mail will decrease the weighted-average
contribution margin and increase the break-even point. An increase in advertising
mail will increase revenue and decrease the breakeven point.
ISSUE 8-60
"START YOUR OWN FIRM," JOURNAL OF ACCOUNTANCY, MAY 2000, ROBERT B. SCOTT,
JR.
1. The contribution margin is defined as sales revenue less all variable costs.
2. For a CPA firm, as described in the article, the contribution margin would be
calculated as a client’s total fees less all direct-service costs, such as staff time.
According to the article, a client who generates total fees that are one and one half
times the cost to service the engagement, especially a large client, may be worth
keeping and developing. If the CPA is unable to recover at least one and one half
times the direct-service cost, the CPA should consider ending the relationship.
McGraw-Hill/Irwin
8-62
 2002 The McGraw-Hill Companies, Inc.
Solutions Manual
ISSUE 8-61
"CHAIN REACTION," CMA MANAGEMENT, MARCH 1999, ANDREA SIGURDSON.
1. Cost-volume-profit analysis is a study of the relationships between sales volume,
expenses, revenue, and profit.
2. CVP analysis can be applied to determine the effectiveness of an investment, for
example, in seasonal price discounting or price specials. In price-sensitive
categories, managers can use detailed studies of consumer price elasticity to better
understand the ongoing relationship between pricing, volume and category profits.
The principles of activity-based management applied to product categories can help
management understand the actual costs of distribution and warehousing at the
individual item level. A true picture of category and subcategory profitability can
then be determined. Real estate and occupancy costs are also charged back to
product categories within the store to develop a comprehensive picture of total profit
or loss for each category. Using this information, retailers can assign strategic roles
to each product category. High profile ones, although not always strong profit
contributors, can help build overall customer traffic. Assigning clear category roles
aids in the decision making process when allocating investment resources or scarce
retail space among competing product categories.
McGraw-Hill/Irwin
Managerial Accounting, 5/e
 2002 The McGraw-Hill Companies, Inc.
8-63