Select Solutions to Chapter 7
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 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.
7-15
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.
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.
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.
EXERCISE 7-24 (25 MINUTES)
1
Sales
Revenue
$360,000
Variable
Expenses
$120,000
Total
Contribution
Margin
$240,000
Fixed
Expenses
$90,000
Net
Income
$150,000
Break-Even
Sales
Revenue
$135,000 a
2
3
4
55,000
320,000 c
160,000
11,000
80,000
130,000
44,000
240,000
30,000
25,000
60,000
30,000d
19,000
180,000
-0-
31,250b
80,000
160,000
Explanatory notes for selected items:
a$135,000
b$31,250
= $90,000  (2/3), where 2/3 is the contribution-margin ratio.
= $25,000/.80, where .80 is the contribution-margin ratio.
cBreak-even
sales revenue ..............................................................................
Fixed expenses ...............................................................................................
Variable expenses ...........................................................................................
$80,000
60,000
$20,000
Therefore, variable expenses are 25 percent of sales revenue.
When variable expenses amount to $80,000, sales revenue is $320,000.
d$160,000
is the break-even sales revenue, so fixed expenses must be equal to the
contribution margin of $30,000 and profit must be zero.
EXERCISE 7-26 (25 MINUTES)
1.
Profit-volume graph:
Dollars per year
$300,000
$200,000
$100,000
Break-even point:
20,000 tickets
0
$(100,000)
5,000
10,000
15,000
Loss
area
$(200,000)
Annual fixed
expenses
$(300,000)
$(360,000)
Profit
area

20,000
25,000
Tickets sold
per year
EXERCISE 7-26 (CONTINUED)
2.
Safety margin:
Budgeted sales revenue
(10 games  6,000 seats  .45 full  $20)...............................................
Break-even sales revenue
(20,000 tickets  $20) ...............................................................................
Safety margin .................................................................................................
3.
$540,000
400,000
$140,000
Let P denote the break-even ticket price, assuming a 10-game season and 40 percent
attendance:
(10)(6,000)(.40)P – (10)(6,000)(.40)($2) – $360,000 = 0
24,000P = $408,000
P = $17 per ticket
EXERCISE 7-28 (25 MINUTES)
1.
(a) Traditional income statement:
PACIFIC RIM 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 ...................................................................
$1,000,000
750,000
$ 250,000
$75,000
75,000
150,000
$ 100,000
(b) Contribution income statement:
PACIFIC RIM 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 ......................................
Net income ...................................................................
2.
$1,000,000
$500,000
50,000
15,000
$ 250,000
25,000
60,000
contribution margin
net income
$435,000

 4.35
$100,000
Operatingleverage factor (at $1,000,000 sales level) 
565,000
$ 435,000
335,000
$ 100,000
EXERCISE 7-28 (CONTINUED)
3.
 percentage increase  operating 
  

Percentage increase in net income  
in
sales
revenue
leverage
factor

 

= 12%  4.35
= 52.2%
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.
PROBLEM 7-34 (30 MINUTES)
1.
Break-even point in sales dollars, using the contribution-margin ratio:
fixed expenses
contribution - margin ratio
$540,000  $216,000 $756,000


$30  $12  $6
.4
$30
 $1,890,000
Break - even point 
2.
Target net income, using contribution-margin approach:
fixed expenses  target net income
unit contribution margin
$756,000  $540,000 $1,296,000


$30  $12  $6
$12
 108,000 units
Sales units required to earn income of $540,000 
3.
New unit variable manufacturing cost
= $12  110%
= $13.20
Break-even point in sales dollars:
$756,000
$756,000

$30.00  $13.20  $6.00
.36
$30
 $2,100,000
Break - even point 
PROBLEM 7-34 (CONTINUED)
4.
Let P denote the selling price that will yield the same contribution-margin ratio:
$30.00  $12.00  $6.00
P  $13.20  $6.00

$30.00
P
P  $19.20
.4 
P
.4P  P  $19.20
$19.20  .6P
P  $19.20/.6
P  $32.00
Check: New contribution-margin ratio is:
$32.00  $13.20  $6.00
 .4
$32.00
PROBLEM 7-36 (30 MINUTES)
1.
Break-even point in units, using the equation approach:
$24X – ($15 + $3)X – $1,800,000 = 0
$6X = $1,800,000
X =
$1,800,000
$6
= 300,000 units
2.
New projected sales volume = 400,000  110%
= 440,000 units
Net income = (440,000)($24 – $18) – $1,800,000
= (440,000)($6) – $1,800,000
= $2,640,000 – $1,800,000 = $840,000
3.
Target net income = $600,000 (from original problem data)
New disk purchase price = $15  130% = $19.50
Volume of sales dollars required:
fixed expenses  target net profit
contributi on - margin ratio
$1,800,000  $600,000
$2,400,000


$24  $19.50  $3
.0625
$24
 $38,400,00 0
Volume of sales dollars required 
PROBLEM 7-36 (CONTINUED)
4.
Let P denote the selling price that will yield the same contribution-margin ratio:
P  $19.50  $3
$24  $15  $3

P
$24
P  $22.50
.25 
P
.25 P  P  $22.50
$22.50  .75 P
P  $22.50/.75
P  $30
Check: New contribution-margin ratio is:
$30  $22.50
 .25
$30
5.
The electronic version of the Solutions Manual “BUILD A SPREADSHEET
SOLUTIONS” is available on your Instructors CD and on the Hilton, 8e website:
www.mhhe.com/hilton8e.
PROBLEM 7-37 (30 MINUTES)
1.
Unit contribution margin:
Sales
price…………………………………
Less variable costs:
Sales commissions ($32 x 5%)……
System variable costs………………
Unit contribution
margin………………..
$32.00
$ 1.60
8.00
9.60
$22.40
Break-even point = fixed costs ÷ unit contribution margin
= $1,971,200 ÷ $22.40
= 88,000 units
2.
Model A is more profitable when sales and production average 184,000 units.
Sales revenue (184,000 units x $32.00)……...
Less variable costs:
Sales commissions ($5,888,000 x 5%)…
System variable costs:……………………
184,000 units x $8.00………………….
184,000 units x $6.40………………….
Total variable costs………………………..
Model A
Model B
$5,888,000
$5,888,000
$ 294,400
$ 294,400
1,472,000
$1,766,400
1,177,600
$1,472,000
Contribution margin…………………………... $4,121,600
Less: Annual fixed costs……………………..
1,971,200
Net
$2,150,400
income………………………………………
3.
$4,416,000
2,227,200
$2,188,800
Annual fixed costs will increase by $180,000 ($900,000 ÷ 5 years) because of straightline depreciation associated with the new equipment, to $2,407,200 ($2,227,200 +
$180,000). The unit contribution margin is $24 ($4,416,000 ÷ 184,000 units). Thus:
Required sales = (fixed costs + target net profit) ÷ unit contribution margin
= ($2,407,200 + $1,912,800) ÷ $24
= 180,000 units
4.
Let X = volume level at which annual total costs are equal
$8.00X + $1,971,200 = $6.40X + $2,227,200
$1.60X = $256,000
X = 160,000 units
PROBLEM 7-38 (25 MINUTES)
1.
Closing of mall store:
Loss of contribution margin at Mall Store ..................................................... $(108,000)
Savings of fixed cost at Mall Store (75%) ......................................................
90,000
Loss of contribution margin at Downtown Store (10%) ...............................
(14,400)
Total decrease in operating income .............................................................. $ (32,400)
2.
Promotional campaign:
Increase in contribution margin (10%) ..........................................................
Increase in monthly promotional expenses ($180,000/12) ...........................
Decrease in operating income .......................................................................
3.
$10,800
(15,000)
$(4,200)
Elimination of items sold at their variable cost:
We can restate the November 20x4 data for the Mall Store as follows:
Sales ...................................................................................
Less: variable expenses ...................................................
Contribution margin ..........................................................
Mall Store
Items Sold at
Their
Variable Cost Other Items
$180,000*
$180,000*
180,000
72,000
$
-0$108,000
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......................................................................
$(21,600)
18,000
$ (3,600)
*$180,000 is one half of the Mall Store's dollar sales for November 20x4.
4.
The electronic version of the Solutions Manual “BUILD A SPREADSHEET
SOLUTIONS” is available on your Instructors CD and on the Hilton, 8e website:
www.mhhe.com/hilton8e.
PROBLEM 7-39 (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 (19,500 + 45,500), 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, Cold King sales will comprise a greater proportion of
total sales under Plan A. This is not surprising in light of the fact that Cold
King has a higher selling price than Mister Ice Cream ($43 vs. $37).
Current
Mister Ice Cream ..........
Cold King .....................
Total .......................
(c)
Plan A
Units
Sales
Mix
Units
Sales
Mix
21,000
39,000
60,000
35%
65%
100%
19,500
45,500
65,000
30%
70%
100%
Yes. Commissions will total $267,800 ($2,678,000 x 10%), which compares
favorably against the current flat salaries of $200,000.
Mister Ice Cream sales: 19,500 units x $37 ..............
Cold King sales: 45,500 units x $43..........................
Total sales ............................................................
$ 721,500
1,956,500
$2,678,000
PROBLEM 7-39 (CONTINUED)
(d)
No. The company would be less profitable under the new plan.
Sales revenue:
Mister Ice Cream: 21,000 units x $37; 19,500 units x $37 ...............
Cold King: 39,000 units x $43; 45,500 units x $43 ..........................
Total revenue ...............................................................................
Less variable cost:
Mister Ice Cream: 21,000 units x $20.50; 19,500 units x $20.50 .....
Cold King: 39,000 units x $32.50; 45,500 units x $32.50 ................
Sales commissions (10% of sales revenue) .......................................
Total variable cost .......................................................................
Contribution margin ................................................................................
Less fixed cost (salaries) .........................................................................
Net income ..............................................................................................
3.
(a)
Current
Plan A
$ 777,000
1,677,000
$2,454,000
$ 721,500
1,956,500
$2,678,000
$ 430,500
1,267,500
$ 399,750
1,478,750
267,800
$2,146,300
$ 531,700
----___
$ 531,700
$1,698,000
$ 756,000
200,000
$ 556,000
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. Cold King has a contribution margin of $10.50 ($43.00 $32.50), and Mister Ice Cream has a contribution margin of $16.50 ($37.00 $20.50).
Plan A
Units
Mister Ice Cream ..............
Cold King .........................
Total ............................
19,500
45,500
65,000
Sales
Mix
30%
70%
100%
Plan B
Units
39,000
26,000
65,000
Sales
Mix
60%
40%
100%
PROBLEM 7-39 (CONTINUED)
(b)
Plan B is more attractive both to the sales force and to the company.
Salespeople earn more money under this arrangement ($274,950 vs. $200,000),
and the company is more profitable ($641,550 vs. $556,000).
Sales revenue:
Mister Ice Cream: 21,000 units x $37; 39,000 units x $37...............
Cold King: 39,000 units x $43; 26,000 units x $43 ..........................
Total revenue ..............................................................................
Less variable cost:
Mister Ice Cream: 21,000 units x $20.50; 39,000 units x $20.50.....
Cold King: 39,000 units x $32.50; 26,000 units x $32.50 ................
Total variable cost .......................................................................
Contribution margin ...............................................................................
Less: Sales force compensation:
Flat salaries .......................................................................................
Commissions ($916,500 x 30%).......................................................
Net income..............................................................................................
Current
Plan B
$ 777,000
1,677,000
$2,454,000
$1,443,000
1,118,000
$2,561,000
$ 430,500
1,267,500
$1,698,000
$ 756,000
$ 799,500
845,000
$1,644,500
$ 916,500
200,000
$ 556,000
274,950
$ 641,550
PROBLEM 7-41 (45 MINUTES)
1.
Break-even sales volume for each model:
Break-even volume 
(a)
(b)
(c)
annual rental cost
unit contribution margin
Standard model:
Break - even volume 
$16,000
 25,000 tubs
$3.50  $2.86
Break - even volume 
$22,000
 27,500 tubs
$3.50  $2.70
Break - even volume 
$40,000
 40,816 tubs (rounded)
$3.50  $2.52
Super model:
Giant model:
PROBLEM 7-41 (CONTINUED)
2. Profit-volume graph:
Dollars per year (in
thousands)
Profit
$40
$20
0
Break-even point:
40,816 tubs
10
20
30

40
Profit
area
50
Loss
Loss
area
($20)
($40)
Fixed rental cost: $40,000 per year
Tubs sold
per year
(in thousands)
PROBLEM 7-41 (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 Standard and Super
models at the sales volume, X, where the total costs are the same.
Model
Standard .....................................................
Super ..........................................................
Variable Cost
per Tub
$2.86
2.70
Total
Fixed Cost
$16,000
22,000
This reasoning leads to the following equation: 16,000 + 2.86X = 22,000 + 2.70X
Rearranging terms yields the following:
(2.86 – 2.70)X = 22,000 – 16,000
.16X = 6,000
X = 6,000/.16
X = 37,500
Or, stated slightly differently:
Volume at which both machines
produce the same profit
fixed cost differential
variable cost differential
$6,000

$.16
 37,500 tubs

Check: the total cost is the same with either model if 37,500 tubs are sold.
Standard
Variable cost:
Standard, 37,500  $2.86 ...........................
Super, 37,500  $2.70 ................................
Fixed cost:
Standard, $16,000 ......................................
Super, $22,000............................................
Total cost .........................................................
Super
$107,250
$101,250
16,000
$123,250
22,000
$123,250
Since the sales price for popcorn does not depend on the popper model, the sales
revenue will be the same under either alternative.
PROBLEM 7-43 (35 MINUTES)
1.
Plan A break-even point = fixed costs ÷ unit contribution margin
= $33,000 ÷ $33*
= 1,000 units
Plan B break-even point = fixed costs ÷ unit contribution margin
= $99,000 ÷ $45**
= 2,200 units
* $120 - [($120 x 10%) + $75]
** $120 - $75
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.
PROBLEM 7-43 (CONTINUED)
3.
Calculation of contribution margin and profit at 6,000 units of sales:
Sales revenue: 6,000 units x $120……………….
Less variable costs:
Cost of purchasing product:
6,000 units x
$75…………………….……
Sales commissions: $720,000 x 10%……...
Total variable cost………………………..
Contribution
margin………………………………
Fixed
costs………………………………………….
Net
income………………………………………….
Plan A
Plan B
$720,000
$720,000
$450,000
$450,000
72,000
$522,000
$198,000
----__
$450,000
$270,000
33,000
99,000
$165,000
$171,000
Plan A has a higher percentage of variable costs to sales (72.5%) compared to Plan
B (62.5%). Plan B’s fixed costs are 13.75% of sales, compared to Plan A’s 4.58%.
Operating leverage factor = contribution margin ÷ net income
Plan A: $198,000 ÷ $165,000 = 1.2
Plan B: $270,000 ÷ $171,000 = 1.58 (rounded)
Plan B has the higher degree of operating leverage.
4 & 5. Calculation of profit at 5,000 units:
Plan A
Plan B
Sales revenue: 5,000 units x
$120……………….
Less variable costs:
Cost of purchasing product:
5,000 units x
$75…………………………..
Sales commissions: $600,000 x 10%……...
$600,000
$600,000
$375,000
$375,000
Total variable
cost………………………..
Contribution
margin………………………………
Fixed
costs…………………………………………
Net
income………………………………………….
$435,000
__
$375,000
$165,000
$225,000
33,000
99,000
$132,000
$126,000
60,000
----
PROBLEM 7-43 (CONTINUED)
Plan A profitability decrease:
$165,000 - $132,000 = $33,000; $33,000 ÷ $165,000 = 20%
Plan B profitability decrease:
$171,000 - $126,000 = $45,000; $45,000 ÷ $171,000 = 26.3% (rounded)
PneumoTech 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.
CASE 7-55 (50 MINUTES)
1.
Break-even point for 20x4, based on current budget:
$15,000,00 0  $9,000,000  $3,000,000
 .20
$15,000,00 0
fixed expenses
Break - even point 
contributi on - margin ratio
$150,000

 $750,000
.20
Contributi on - margin ratio 
2.
Break-even point given employment of sales personnel:
New fixed expenses:
Previous fixed expenses .......................................................................
Sales personnel salaries (3 x $45,000) .................................................
Sales managers’ salaries (2  $120,000) ..............................................
Total ........................................................................................................
$
$
150,000
135,000
240,000
525,000
New contribution-margin ratio:
Sales ........................................................................................................
Cost of goods sold .................................................................................
Gross margin ..........................................................................................
6,000,000
Commissions (at 5%) .............................................................................
Contribution margin ...............................................................................
Contribution - margin ratio 
$5,250,000
 .35
$15,000,000
fixed expenses
contribution - margin ratio
$525,000

 $1,500,000
.35
Estimated break - even point 
$15,000,000
9,000,000
$
750,000
$ 5,250,000
CASE 7-55 (CONTINUED)
1.
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
$15,000,000
9,000,000
$ 6,000,000
3,750,000
$ 2,250,000
$2,250,000
 .15
$15,000,000
target after - tax net income
(1  t )
contributi on - margin ratio
fixed expenses 

$1,995,000
$3,000,000
(1  .3)


.15
.15
 $20,000,00 0
$150,000 
Check:
Sales ....................................................................
20,000,000
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 ..........................................................
$
12,000,000
$ 8,000,000
$ 5,000,000
150,000
5,150,000
$ 2,850,000
855,000
$ 1,995,000
CASE 7-55 (CONTINUED)
2.
Sales dollar volume at which Lake Champlain 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 – $525,000 = .15X – $150,000
.20X = $375,000
X = $375,000/.20
X = $1,875,000
Thus, the company will have the same before-tax income under the two
alternatives if the sales volume is $1,875,000.
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 ...................................................................
*$1,875,000  5% = $93,750
†$1,875,000  25% = $468,750
Alternatives
Employ
Sales
Pay 25%
Personnel
Commission
$1,875,000
$1,875,000
1,125,000
1,125,000
$ 750,000
$ 750,000
93,750*
525,000
$ 131,250
39,375
$ 91,875
468,750†
150,000
$ 131,250
39,375
$ 91,875