Solution manual cost accounting 12e by horngren ch 03

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CHAPTER 3
COST-VOLUME-PROFIT ANALYSIS
NOTATION USED IN CHAPTER 3 SOLUTIONS
SP:
VCU:
CMU:
FC:
TOI:

Selling price
Variable cost per unit
Contribution margin per unit
Fixed costs
Target operating income

3-1
Cost-volume-profit (CVP) analysis examines the behavior of total revenues, total costs,
and operating income as changes occur in the output level, selling price, variable cost per unit, or
fixed costs of a product.
3-2

The assumptions underlying the CVP analysis outlined in Chapter 3 are

1.

Changes in the level of revenues and costs arise only because of changes in the number
of product (or service) units produced and sold.
Total costs can be separated into a fixed component that does not vary with the output
level and a component that is variable with respect to the output level.

When represented graphically, the behavior of total revenues and total costs are linear
(represented as a straight line) in relation to output level within a relevant range and time
period.
The selling price, variable cost per unit, and fixed costs are known and constant.
The analysis either covers a single product or assumes that the sales mix, when multiple
products are sold, will remain constant as the level of total units sold changes.
All revenues and costs can be added and compared without taking into account the time
value of money.

2.
3.

4.
5.
6.

3-3
Operating income is total revenues from operations for the accounting period minus cost
of goods sold and operating costs (excluding income taxes):
Operating
income
=
Total
revenues
Costs of goods sold and operating, costs (excluding income taxes)

from

operations

–

Net income is operating income plus nonoperating revenues (such as interest revenue)
minus nonoperating costs (such as interest cost) minus income taxes. Chapter 3 assumes
nonoperating revenues and nonoperating costs are zero. Thus, Chapter 3 computes net income
as:
Net income = Operating income – Income taxes
3-4
Contribution margin is the difference between total revenues and total variable costs.
Contribution margin per unit is the difference between selling price and variable cost per unit.
Contribution-margin percentage is the contribution margin per unit divided by selling price.

3-1


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3-5
Three methods to express CVP relationships are the equation method, the contribution
margin method, and the graph method. The first two methods are most useful for analyzing
operating income at a few specific levels of sales. The graph method is useful for visualizing the
effect of sales on operating income over a wide range of quantities sold.
3-6
Breakeven analysis denotes the study of the breakeven point, which is often only an
incidental part of the relationship between cost, volume, and profit. Cost-volume-profit
relationship is a more comprehensive term than breakeven analysis.
3-7
CVP certainly is simple, with its assumption of output as the only revenue and cost
driver, and linear revenue and cost relationships. Whether these assumptions make it simplistic
depends on the decision context. In some cases, these assumptions may be sufficiently accurate

for CVP to provide useful insights. The examples in Chapter 3 (the software package context in
the text and the travel agency example in the Problem for Self-Study) illustrate how CVP can
provide such insights. In more complex cases, the basic ideas of simple CVP analysis can be
expanded.
3-8
An increase in the income tax rate does not affect the breakeven point. Operating income
at the breakeven point is zero, and no income taxes are paid at this point.
3-9
Sensitivity analysis is a ―what-if‖ technique that managers use to examine how a result
will change if the original predicted data are not achieved or if an underlying assumption
changes. The advent of the electronic spreadsheet has greatly increased the ability to explore the
effect of alternative assumptions at minimal cost. CVP is one of the most widely used software
applications in the management accounting area.
3-10

Examples include:
Manufacturing––substituting a robotic machine for hourly wage workers.
Marketing––changing a sales force compensation plan from a percent of sales dollars to
a fixed salary.
Customer service––hiring a subcontractor to do customer repair visits on an annual
retainer basis rather than a per-visit basis.

3-11

Examples include:
Manufacturing––subcontracting a component to a supplier on a per-unit basis to avoid
purchasing a machine with a high fixed depreciation cost.
Marketing––changing a sales compensation plan from a fixed salary to percent of sales
dollars basis.
Customer service––hiring a subcontractor to do customer service on a per-visit basis

rather than an annual retainer basis.

3-12 Operating leverage describes the effects that fixed costs have on changes in operating
income as changes occur in units sold, and hence, in contribution margin. Knowing the degree of
operating leverage at a given level of sales helps managers calculate the effect of fluctuations in
sales on operating incomes.

3-2


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3-13 CVP analysis is always conducted for a specified time horizon. One extreme is a very
short-time horizon. For example, some vacation cruises offer deep price discounts for people
who offer to take any cruise on a day’s notice. One day prior to a cruise, most costs are fixed.
The other extreme is several years. Here, a much higher percentage of total costs typically is
variable.
CVP itself is not made any less relevant when the time horizon lengthens. What happens
is that many items classified as fixed in the short run may become variable costs with a longer
time horizon.
3-14 A company with multiple products can compute a breakeven point by assuming there is a
constant sales mix of products at different levels of total revenue.
3-15 Yes, gross margin calculations emphasize the distinction between manufacturing and
nonmanufacturing costs (gross margins are calculated after subtracting fixed manufacturing
costs). Contribution margin calculations emphasize the distinction between fixed and variable
costs. Hence, contribution margin is a more useful concept than gross margin in CVP analysis.
3-16

a.
b.

c.
d.

(10 min.) CVP computations.
Revenues
$2,000
2,000
1,000
1,500

Variable
Costs
$ 500
1,500
700
900

Fixed
Costs
$300
300
300
300

Total
Operating Contribution
Costs
Income
Margin
$ 800

$1,200
$1,500
200
500
1,800
1,000
0
300
1,200
300
600

3-3

Contribution
Margin %
75.0%
25.0%
30.0%
40.0%


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3-17

(10–15 min.) CVP computations.
1a.

Sales ($25 per unit × 180,000 units)

Variable costs ($20 per unit × 180,000 units)
Contribution margin

$4,500,000
3,600,000
$ 900,000

1b.

Contribution margin (from above)
Fixed costs
Operating income

$ 900,000
800,000
$ 100,000

2a.

Sales (from above)
Variable costs ($10 per unit × 180,000 units)
Contribution margin

$4,500,000
1,800,000
$2,700,000

2b.

Contribution margin

Fixed costs
Operating income

$2,700,000
2,500,000
$ 200,000

3.
Operating income is expected to increase by $100,000 if Ms. Schoenen’s proposal is
accepted.
The management would consider other factors before making the final decision. It is
likely that product quality would improve as a result of using state of the art equipment. Due to
increased automation, probably many workers will have to be laid off. Patel’s management will
have to consider the impact of such an action on employee morale. In addition, the proposal
increases the company’s fixed costs dramatically. This will increase the company’s operating
leverage and risk.

3-4


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3-18

(35–40 min.) CVP analysis, changing revenues and costs.

1a.

SP
VCU

CMU
FC

= 8% × $1,000 = $80 per ticket
= $35 per ticket
= $80 – $35 = $45 per ticket
= $22,000 a month

Q

=

$22,000
FC
=
$45 per ticket
CMU

= 489 tickets (rounded up)
1b.

Q

=

$22,000 $10,000
FC TOI
=
$45 per ticket
CMU

=

$32,000
$45 per ticket

= 712 tickets (rounded up)
2a.

SP
VCU
CMU
FC

= $80 per ticket
= $29 per ticket
= $80 – $29 = $51 per ticket
= $22,000 a month

Q

=

$22,000
FC
=
$51 per ticket
CMU

= 432 tickets (rounded up)

2b.

Q

=

$22,000 $10,000
FC TOI
=
$51 per ticket
CMU

$32,000
$51 per ticket
= 628 tickets (rounded up)

=

3a.

SP
VCU
CMU
FC

= $48 per ticket
= $29 per ticket
= $48 – $29 = $19 per ticket
= $22,000 a month

Q

=

$22,000
FC
=
$19 per ticket
CMU
= 1,158 tickets (rounded up)

3-5


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3b.

Q

=

$22,000 $10,000
FC TOI
=
$19 per ticket
CMU

=

$32,000
$19 per ticket

= 1,685 tickets (rounded up)
The reduced commission sizably increases the breakeven point and the number of tickets
required to yield a target operating income of $10,000:

Breakeven point
Attain OI of $10,000

8%
Commission
(Requirement 2)
432
628

Fixed
Commission of $48
1,158
1,685

4a.
The $5 delivery fee can be treated as either an extra source of revenue (as done below) or
as a cost offset. Either approach increases CMU $5:
SP
VCU
CMU
FC

= $53 ($48 + $5) per ticket

= $29 per ticket
= $53 – $29 = $24 per ticket
= $22,000 a month

Q

=

$22,000
FC
=
$24 per ticket
CMU

= 917 tickets (rounded up)
4b.

Q

=

$22,000 $10,000
FC TOI
=
$24 per ticket
CMU

=

$32,000

$24 per ticket

= 1,334 tickets (rounded up)
The $5 delivery fee results in a higher contribution margin which reduces both the breakeven
point and the tickets sold to attain operating income of $10,000.

3-6


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3-19

(20 min.) CVP exercises.

Revenues
$10,000,000G
10,000,000
10,000,000
10,000,000
10,000,000
10,800,000e
9,200,000g
11,000,000i
10,000,000

Orig.
1.
2.
3.

4.
5.
6.
7.
8.
Gstands

Variable
Costs

Contribution
Margin

$8,200,000G
8,020,000
8,380,000
8,200,000
8,200,000
8,856,000f
7,544,000h
9,020,000j
7,790,000l

$1,800,000
1,980,000a
1,620,000b
1,800,000
1,800,000
1,944,000
1,656,000

1,980,000
2,210,000

Budgeted
Operating
Income

Fixed
Costs
$1,700,000G
1,700,000
1,700,000
1,785,000c
1,615,000d
1,700,000
1,700,000
1,870,000k
1,785,000m

$100,000
280,000
(80,000)
15,000
185,000
244,000
(44,000)
110,000
425,000

for given.

a$1,800,000 × 1.10; b$1,800,000 × 0.90; c$1,700,000 × 1.05; d$1,700,000 × 0.95; e$10,000,000 × 1.08;
f$8,200,000 × 1.08; g$10,000,000 × 0.92; h$8,200,000 × 0.92; i$10,000,000 × 1.10; j$8,200,000 × 1.10;
k$1,700,000 × 1.10; l$8,200,000 × 0.95; m$1,700,000 × 1.05

3-20

(20 min.) CVP exercises.

1a.

[Units sold (Selling price – Variable costs)] – Fixed costs = Operating income
[5,000,000 ($0.50 – $0.30)] – $900,000 = $100,000

1b.

Fixed costs ÷ Contribution margin per unit = Breakeven units
$900,000 ÷ [($0.50 – $0.30)] = 4,500,000 units
Breakeven units × Selling price = Breakeven revenues
4,500,000 units × $0.50 per unit = $2,250,000
or,
Selling price -Variable costs
Contribution margin ratio =
Selling price
$0.50 - $0.30
=
= 0.40
$0.50
Fixed costs ÷ Contribution margin ratio = Breakeven revenues
$900,000 ÷ 0.40 = $2,250,000

2.

5,000,000 ($0.50 – $0.34) – $900,000

=

$ (100,000)

3.

[5,000,000 (1.1) ($0.50 – $0.30)] – [$900,000 (1.1)]

=

$ 110,000

4.

[5,000,000 (1.4) ($0.40 – $0.27)] – [$900,000 (0.8)]

=

$ 190,000

5.

$900,000 (1.1) ÷ ($0.50 – $0.30)

=

4,950,000 units

6.

($900,000 + $20,000) ÷ ($0.55 – $0.30)

=

3,680,000 units

3-7


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3-21

(10 min.) CVP analysis, income taxes.

1. Monthly fixed costs = $50,000 + $60,000 + $10,000 =
Contribution margin per unit = $25,000 – $22,000 – $500 =
Monthly fixed costs
$120,000
Breakeven units per month =
=
=
Contribution margin per unit
$2,500 per car
2. Tax rate

Target net income

$120,000
$ 2,500
48 cars
40%
$54,000

Target net income $54, 000 $54, 000
$90,000
1 - tax rate
(1 0.40)
0.60
Quantity of output units Fixed costs + Target operating income $12 0, 000 $90, 000
84 cars
required to be sold =
Contribution margin per unit
$2,500

Target operating income =

3-22
1.

(20–25 min.) CVP analysis, income taxes.
Variable cost percentage is $3.20

$8.00 = 40%

Let R = Revenues needed to obtain target net income

$105,000
R – 0.40R – $450,000 =
1 0.30
0.60R = $450,000 + $150,000
R = $600,000 0.60
R = $1,000,000
or,
Target net income
$105,000
$450,000 +
1 Tax rate
1 0.30 = $1,000,000
Breakeven revenues =
=
Contribution margin percentage
0.60
Proof:

2.a.

b.

Revenues
Variable costs (at 40%)
Contribution margin
Fixed costs
Operating income
Income taxes (at 30%)
Net income

$1,000,000
400,000
600,000
450,000
150,000
45,000
$ 105,000

Customers needed to earn net income of $105,000:
Total revenues Sales check per customer
$1,000,000 $8 = 125,000 customers
Customers needed to break even:
Contribution margin per customer = $8.00 – $3.20 = $4.80
Breakeven number of customers = Fixed costs Contribution margin per customer

3-8


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= $450,000 $4.80 per customer
= 93,750 customers
3.

Using the shortcut approach:
Change in net income
= (Change in,number of customers,)
(Unit,contribution,margin) (1 – Tax rate)

New net income

= (150,000 – 125,000) $4.80 (1 – 0.30)
= $120,000 0.7 = $84,000
= $84,000 + $105,000 = $189,000

The alternative approach is:
Revenues, 150,000 $8.00
Variable costs at 40%
Contribution margin
Fixed costs
Operating income
Income tax at 30%
Net income

$1,200,000
480,000
720,000
450,000
270,000
81,000
$ 189,000

3-9


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3-23

(30 min.) CVP analysis, sensitivity analysis.

1.

SP = $30.00 (1 – 0.30 margin to bookstore)
= $30.00 0.70 = $21.00
VCU = $ 4.00 variable production and marketing cost
3.15 variable author royalty cost (0.15 $21.00)
$ 7.15
CMU = $21.00 – $7.15 = $13.85 per copy
FC = $ 500,000 fixed production and marketing cost
3,000,000 up-front payment to Washington
$3,500,000

Solution Exhibit 3-23A shows the PV graph.
SOLUTION EXHIBIT 3-23A
PV Graph for Media Publishers

$4,000

FC = $3,500,000
CMU = $13.85 per book sold

3,000

Operating income (000’s)

2,000

1,000

0

U n its so ld
10 0,0 00

20 0,0 00

-1,000

30 0,0 00

40 0,0 00

252,708 units

-2,000

-3,000

$3.5 million
-4,000

3-10

50 0,0 00


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2a.

FC
CMU
$3,500,000
=
$13.85

Breakeven,number of units

=

= 252,708 copies sold (rounded up)
2b.

Target OI =

FC OI
CMU

$3,500,000 $2,000,000
$13.85
$5,500,000
=
$13.85
= 397,112 copies sold (rounded up)
=

3a. Decreasing the normal bookstore margin to 20% of the listed bookstore price of $30 has the
following effects:
=$30.00 (1 – 0.20)
=$30.00 0.80 = $24.00

VCU = $ 4.00 variable production and marketing cost
+ 3.60 variable author royalty cost (0.15 $24.00)
$ 7.60
SP

CMU = $24.00 – $7.60 = $16.40 per copy
Breakeven,number of units =

FC
CMU

$3,500,000
$16.40
= 213,415 copies sold (rounded up)
=

The breakeven point decreases from 252,708 copies in requirement 2 to 213,415 copies.

3-11


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3b.
Increasing the listed bookstore price to $40 while keeping the bookstore margin at 30%
has the following effects:
=$40.00 (1 – 0.30)
=$40.00 0.70 = $28.00
VCU =$ 4.00
variable production and marketing cost

+ 4.20
variable author royalty cost (0.15 $28.00)
$ 8.20
SP

CMU= $28.00 – $8.20 = $19.80 per copy

$3,500,000
$19.80
= 176,768 copies sold (rounded up)

Breakeven,number of units =

The breakeven point decreases from 252,708 copies in requirement 2 to 176,768 copies.
3c. The answers to requirements 3a and 3b decrease the breakeven point relative to that in
requirement 2 because in each case fixed costs remain the same at $3,500,000 while the
contribution margin per unit increases.

3-24
1.

2.

3.

(10 min.) CVP analysis, margin of safety.
Fixed costs
Contributi on margin percentage
$400,000
Contribution margin percentage =

= 0.40 or 40%
$1,000,000
Selling price Variable cost per unit
Contribution margin percentage =
Selling price
SP $12
0.40 =
SP
0.40 SP = SP – $12
0.60 SP = $12
SP = $20

Breakeven point revenues =

Revenues, 80,000 units
Breakeven revenues
Margin of safety

$20

$1,600,000
1,000,000
$ 600,000

3-12


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3-25

(25 min.) Operating leverage.

1a.

Let Q denote the quantity of carpets sold
Breakeven point under Option 1
$500Q $350Q = $5,000
$150Q = $5,000
Q = $5,000

1b.

2.

Breakeven point under Option 2
$500Q $350Q (0.10 $500Q)
100Q
Q

=
=
=

$150 = 34 carpets (rounded up)

0
0
0

Operating income under Option 1 = $150Q
Operating income under Option 2 = $100Q

$5,000

Find Q such that $150Q

$5,000 = $100Q
$50Q = $5,000
Q = $5,000 $50 = 100 carpets

For Q = 100 carpets, operating income under both Option 1 and Option 2 = $10,000
3a.

3b.

4.

For Q > 100, say, 101 carpets,
Option 1 gives operating income
= ($150 101)
Option 2 gives operating income
= $100 101
So Color Rugs will prefer Option 1.
For Q < 100, say, 99 carpets,
Option 1 gives operating income
= ($150 99)
Option 2 gives operating income
= $100 99
So Color Rugs will prefer Option 2.

$5,000 = $10,150
= $10,100

$5,000 = $9,850
= $9,900

Contributi on margin
Operating income
$150 100
Under Option 1, degree of operating leverage =
= 1.5
$10,000
$100 100
Under Option 2, degree of operating leverage =
= 1.0
$10,000

Degree of operating leverage =

5. The calculations in requirement 4 indicate that when sales are 100 units, a percentage
change in sales and contribution margin will result in 1.5 times that percentage change in
operating income for Option 1, but the same percentage change in operating income for Option
2. The degree of operating leverage at a given level of sales helps managers calculate the effect
of fluctuations in sales on operating incomes.

3-13


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3-26

(15 min.) CVP analysis, international cost structure differences.

Variable
Variable
Sales price Annual Manufacturing
Marketing &
Contribution
Country
to retail
Fixed
Cost
Distribution Cost
Margin
Breakeven
Breakeven
outlets
Costs
per Sweater
per Sweater
Per Unit
Units
Revenues
(1)
(2)
(3)
(4)
(5)=(1)-(3)-(4) (6)=(2) (5)

(6) (1)
Singapore
$32.00 $ 6,500,000
$ 8.00
$11.00
$13.00
500,000 $16,000,000
Thailand
32.00
4,500,000
5.50
11.50
15.00
300,000
9,600,000
United States
32.00
12,000,000
13.00
9.00
10.00
1,200,000
38,400,000

Requirement 1

Thailand has the lowest breakeven point since it has both the lowest fixed costs ($4,500,000) and the
lowest variable cost per unit ($17.00). Hence, for a given selling price, Thailand will always have a
higher operating income (or a lower operating loss) than Singapore or the U.S.
The U.S. breakeven point is 1,200,000 units. Hence, with sales of only 800,000 units, it has an

operating loss of $4,000,000.

3-14

Operating Income for
Budgeted Sales of
800,000
Sweaters
(7)=[800,000 (5)] – (2)
$3,900,000
7,500,000
(4,000,000)

Requirement 2


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3-27

(30 min.) Sales mix, new and upgrade customers.

1.

SP
VCU
CMU

New
Customers

$210
90
120

Upgrade
Customers
$120
40
80

Let S = Number of units sold to upgrade customers
1.5S = Number of units sold to new customers
Revenues – Variable costs – Fixed costs = Operating income
[$210 (1.5S) + $120S] – [$90 (1.5S) + $40S] – $14,000,000 = OI
$435S – $175S – $14,000,000 = OI
Breakeven point is 134,616 units when OI = 0 because
$260S
S
1.5S
BEP

=
=
=
=

$14,000,000
53,846 units sold to upgrade customers (rounded)
80,770 units sold to new customers (rounded)
134,616 units

Check
Revenues ($210 80,770) + ($120 53,846)
Variable costs ($90 80,770) + ($40 53,846)
Contribution margin
Fixed costs
Operating income (caused by rounding)
2.

$

$23,423,220
9,423,140
14,000,080
14,000,000
80

When 200,000 units are sold, mix is:
Units sold to new customers (60% 200,000)
Units sold to upgrade customers (40% 200,000)
Revenues ($210 120,000) + ($120 80,000)
Variable costs ($90 120,000) + ($40 80,000)
Contribution margin
Fixed costs
Operating income

3-15

120,000
80,000

$34,800,000
14,000,000
20,800,000
14,000,000
$ 6,800,000


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3a.

Let S = Number of units sold to upgrade customers
then S = Number of units sold to new customers

[$210S + $120S] – [$90S + $40S] – $14,000,000 = OI
330S – 130S
=
$14,000,000
200S
=
$14,000,000
S
=
70,000 units sold to upgrade customers
S
=
70,000 units sold to new customers
BEP
=
140,000 units

Check
Revenues ($210 70,000) + ($120 70,000)
$23,100,000
Variable costs ($90 70,000) + ($40 70,000)
9,100,000
Contribution margin
14,000,000
Fixed costs
14,000,000
Operating income
$
0
3b.

Let
S = Number of units sold to upgrade customers
then 9S = Number of units sold to new customers
[$210 (9S) + $120S] – [$90 (9S) + $40S] – $14,000,000 = OI
2,010S – 850S
=
$14,000,000
1,160S
=
$14,000,000
S
=
12,069 units sold to upgrade customers (rounded up)
9S
=
108,621 units sold to new customers (rounded up)

120,690 units

Check
Revenues ($210 108,621) + ($120 12,069)
Variable costs ($90 108,621) + ($40 12,069)
Contribution margin
Fixed costs
Operating income (caused by rounding)

$

$24,258,690
10,258,650
14,000,040
14,000,000
40

3c. As Zapo increases its percentage of new customers, which have a higher contribution
margin per unit than upgrade customers, the number of units required to break even decreases:

Requirement 3(a)
Requirement 1
Requirement 3(b)

New
Customers
50%
60
90

3-16

Upgrade
Customers
50%
40
10

Breakeven
Point
140,000
134,616
120,690


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3-28
1a.

(20 min.) CVP analysis, multiple cost drivers.

Operating
income

= Revenues

Cost of picture
frames

Quantity of
picture frames

Cost of
shipment

Number of
shipments

Fixed

costs

= ($45 40,000) ($30 40,000) ($60 1,000) $240,000
= $1,800,000 $1,200,000 $60,000 $240,000 = $300,000
1b.

Operating
income

= ($45

40,000)

($30

40,000)

($60

2.

Denote the number of picture frames sold by Q, then
$45Q $30Q – (500 $60) $240,000 = 0
$15Q = $30,000 + $240,000 = $270,000
Q = $270,000 $15 = 18,000 picture frames

3.

Suppose Susan had 1,000 shipments.
$45Q $30Q (1,000 $60)
15Q = $300,000
Q = 20,000 picture frames

800)

$240,000 = $312,000

$240,000 = 0

The breakeven point is not unique because there are two cost drivers—quantity of picture
frames and number of shipments. Various combinations of the two cost drivers can yield zero
operating income.

3-17


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3-29

1.

(25–30 min.) Athletic scholarships, CVP analysis.
Variable costs per scholarship offer:
Scholarship amount
Operating costs
Total variable costs

$20,000
2,000
$22,000

Let the number of scholarships be denoted by Q
$22,000 Q = $5,000,000 – $600,000
$22,000 Q = $4,400,000
Q = $4,400,000 ÷ $22,000 = 200 scholarships
2.

Total budget for next year = $5,000,000 × (1.00 – 0.22) = $3,900,000
Then $22,000 Q = $3,900,000 – $600,000 = $3,300,000
Q = $3,300,000 ÷ $22,000 = 150 scholarships

3.

Total budget for next year from above = $3,900,000
Fixed costs
600,000
Variable costs for scholarships
$3,300,000
If the total number of scholarships is to remain at 200:

Variable cost per scholarship $3,300,000 ÷ 200
Variable operating cost per scholarship
Amount per scholarship

3-18

$16,500
2,000
$14,500


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3-30

(15 min.) Contribution margin, decision making.

1.

Revenues
Deduct variable costs:
Cost of goods sold
Sales commissions
Other operating costs
Contribution margin

$500,000
$200,000
50,000
40,000

290,000
$210,000

$210,000
= 42%
$500,000

2.

Contribution margin percentage =

3.

Incremental revenue (20% × $500,000) = $100,000
Incremental contribution margin
(42% × $100,000)
Incremental fixed costs (advertising)
Incremental operating income

$42,000
10,000
$32,000

If Mr. Schmidt spends $10,000 more on advertising, the operating income will increase
by $32,000, converting an operating loss of $10,000 to an operating income of $22,000.
Proof (Optional):
Revenues (120% × $500,000)
Cost of goods sold (40% of sales)
Gross margin

$600,000
240,000
360,000

Operating costs:
Salaries and wages
Sales commissions (10% of sales)
Depreciation of equipment and fixtures
Store rent
Advertising
Other operating costs:
$40,000
Variable (
× $600,000)
$500,000
Fixed
Operating income

3-19

$150,000
60,000
12,000
48,000
10,000
48,000
10,000

338,000

$ 22,000


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3-31

(20 min.) Contribution margin, gross margin and margin of safety.

1.
Mirabella Cosmetics
Operating Income Statement, June 2005
Units sold
Revenues
Variable costs
Variable manufacturing costs
Variable marketing costs
Total variable costs
Contribution margin
Fixed costs
Fixed manufacturing costs
Fixed marketing & administration costs
Total fixed costs
Operating income
2.

10,000
$100,000
$ 55,000
5,000

60,000
40,000
$ 20,000
10,000
30,000
$ 10,000

$40,000
$4 per unit
10,000 units
Fixed costs
$30, 000
Breakeven quantity =
Contribution margin per unit $4 per unit
Revenues
$100, 000
$10 per unit
Selling price =
Units sold 10,000 units
Breakeven revenues = 7,500 units $10 per unit = $75,000

Contribution margin per unit =

7,500 units

Alternatively,
Contribution margin percentage =

Breakeven Revenues =

Contribution margin
Revenues

Fixed costs
Contribution margin percentage

$40, 000
$100, 000
$30, 000
0.40

40%

$75, 000

3. Margin of safety (in units) = Units sold – Breakeven quantity
= 10,000 units – 7,500 units = 2,500 units
4.

Units sold
Revenues (Units sold Selling price = 8,000 $10)
Contribution margin (Revenues CM percentage = $80,000
Fixed costs
Operating income
Taxes (30% $2,000)
Net income

3-20

40%)

8,000
$80,000
$32,000
30,000
2,000
600
$ 1,400


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3-32 (15–20 min.)

Uncertainty, CVP analysis (chapter appendix).

1.
Pay-per-view Audience
(number of homes
subscribing to the event)
(1)
100,000
200,000
300,000
400,000
500,000
1,000,000
Total

Expected

Expected Payment
Probability Audience
to Foreman
(2)
(3) = (1) (2) (4) = (3) (25% $16)
0.05
5,000
$ 20,000
0.10
20,000
80,000
0.30
90,000
360,000
0.35
140,000
560,000
0.15
75,000
300,000
0.05
50,000
200,000
380,000
1,520,000

Fixed payment
Total expected payment to Foreman

2,000,000

$3,520,000

2.
Selling price
$
16
Variable cost per subscribing home ($4 to Foreman + $2 to cable company)
6
Contribution margin per subscribing home
$
10
Fixed costs (Foreman, $2,000,000 + other costs, $1,000,000)
$3,000,000
FC
$3, 000, 000
Breakeven number of subscribing homes =
300,000 homes
CMU
$10
3.
Brady’s expected audience size of 380,000 homes is more than 25% bigger than the
breakeven audience size of 300,000 homes. So, if she is confident of the assumed probability
distribution, she has a good margin of safety, and should proceed with her plans for the fight. She
will only lose money if the pay-per-view audience is 100,000 or 200,000, which together have a
0.15 probability of occurring.

3-21


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3-33

(15–20 min.) CVP analysis, service firm.

1.

Revenue per package
Variable cost per package
Contribution margin per package

$4,000
3,600
$ 400

Breakeven (units) = Fixed costs ÷ Contribution margin per package
=

2.

$480,000
= 1,200 tour packages
$400 per package

Contribution margin ratio =

Contributi on margin per package
$400
=
= 10%

Selling price
$4,000

Revenue to achieve target income = (Fixed costs + target OI) ÷ Contribution margin ratio
$480,000 $100,000
= $5,800,000, or
0.10
Number of tour packages to earn $100,000 operating income:

=

$480,000 $100,000
= 1,450 tour packages
$400
Revenues to earn $100,000 OI = 1,450 tour packages × $4,000 = $5,800,000.
3.

Fixed costs = $480,000 + $24,000 = $504,000
Breakeven (units) =

Fixed costs
Contributi on margin per unit

Contribution margin per unit =

=

Fixed costs
Breakeven (units)
$504,000

= $420 per tour package
1,200 tour packages

Desired variable cost per tour package = $4,000 – $420 = $3,580
Because the current variable cost per unit is $3,600, the unit variable cost will need to be reduced
by $20 to achieve the breakeven point calculated in requirement 1.
Alternate Method: If fixed cost increases by $24,000, then total variable costs must be reduced
by $24,000 to keep the breakeven point of 1,200 tour packages.
Therefore, the variable cost per unit reduction = $24,000 ÷ 1,200 = $20 per tour package.

3-22


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3-34

(30 min.) CVP, target income, service firm.

1.

Revenue per child
Variable costs per child
Contribution margin per child
Breakeven quantity =

=

2.

Target quantity =

=
3.

$600
200
$400

Fixed costs
Contributi on margin per child

$5,600
= 14 children
$400

Fixed costs Target operating income
Contributi on margin per child

$5,600 $10,400
= 40 children
$400

Increase in rent ($3,000 – $2,000)
Field trips
Total increase in fixed costs
Divide by the number of children enrolled
Increase in fee per child

$1,000

1,000
$2,000
÷ 40
$ 50

Therefore, the fee per child will increase from $600 to $650.
Alternatively,
New contribution margin per child =

$5,600

$2,000 $10,400
= $450
40

New fee per child = Variable costs per child + New contribution margin per child
= $200 + $450 = $650

3-23


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3-35

(20–25 min.) CVP analysis.

1.

Selling price

Variable costs per unit:
Purchase price
$10.00
Shipping and handling
2.00
Contribution margin per unit (CMU)

$16.00

12.00
$ 4.00

Fixed costs
$600,000
=
= 150,000 units
Contr. margin per unit
$4.00
Margin of safety (units) = 200,000 – 150,000 = 50,000 units

Breakeven point in units =

2.
Since Galaxy is operating above the breakeven point, any incremental contribution
margin will increase operating income dollar for dollar.
Increase in units sales = 10% × 200,000 = 20,000
Incremental contribution margin = $4 × 20,000 = $80,000
Therefore, the increase in operating income will be equal to $80,000.
Galaxy’s operating income in 2005 would be $200,000 + $80,000 = $280,000.
3.

Selling price
Variable costs:
Purchase price $10 × 130%
Shipping and handling
Contribution margin per unit
Target sales in units =

$16.00
$13.00
2.00

15.00
$ 1.00

FC TOI
$600,000 $200,000
=
= 800,000 units
CMU
$1

Target sales in dollars = $16 × 800,000 = $12,800,000

3-24


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3-36

(30–40 min.) CVP analysis, income taxes.

1.

Revenues – Variable costs – Fixed costs =

Target net income
1 Tax rate

Let X = Net income for 2005
20,000($25.00) – 20,000($13.75) – $135,000 =
$500,000 – $275,000 – $135,000 =

X
1 0.40
X

0.60
$300,000 – $165,000 – $81,000 = X
X = $54,000

Alternatively,
Operating income = Revenues – Variable costs – Fixed costs
= $500,000 – $275,000 – $135,000 = $90,000
Income taxes = 0.40 × $90,000 = $36,000
Net income = Operating income – Income taxes
= $90,000 – $36,000 = $54,000

2.

Let Q = Number of units to break even
$25.00Q – $13.75Q – $135,000 = 0
Q = $135,000 $11.25 = 12,000 units

3.

Let X = Net income for 2006
22,000($25.00) – 22,000($13.75) – ($135,000 + $11,250)

=

$550,000 – $302,500 – $146,250

=

$101,250

=

X
1 0.40
X

0.60
X

0.60
X = $60,750

4.

Let Q = Number of units to break even with new fixed costs of $146,250
$25.00Q – $13.75Q – $146,250
Q = $146,250 $11.25
Breakeven revenues = 13,000 $25.00

5.

Let S = Required sales units to equal 2005 net income
$25.00S – $13.75S – $146,250 =
$11.25S = $236,250
S = 21,000 units
Revenues = 21,000 units

6.

= 0
= 13,000 units
= $325,000

$54,000
0.60

$25 = $525,000

Let A = Amount spent for advertising in 2006
$550,000 – $302,500 – ($135,000 + A) =

$60,000

0.60
$550,000 – $302,500 – $135,000 – A = $100,000
$550,000 – $537,500 = A
A = $12,500

3-25