Variable cost per unit C 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 units sold, selling price, variable cost per unit, or
fixed costs of a product.
3-2
1.
2.
3.
4.
The assumptions underlying the CVP analysis outlined in Chapter 3 are
Changes in the level of revenues and costs arise only because of changes in the number
of product (or service) units sold.
Total costs can be separated into a fixed component that does not vary with the units sold
and a variable component that changes with respect to the units sold.
When represented graphically, the behaviors of total revenues and total costs are linear
(represented as a straight line) in relation to units sold within a relevant range and time
period.
The selling price, variable cost per unit, and fixed costs are known and constant.
3-3
Operating income is total revenues from operations for the accounting period minus cost
of goods sold and operating costs (excluding income taxes):
Costs of goods sold and operating
Operating income = Total revenues from operations – costs (excluding income taxes)
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.
3-5
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.
3-1
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 an
outcome 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.
3-13 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.
3-2
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 variable and 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.
3-17
(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
Costs
\$ 800
1,800
1,000
1,200
Operating
Income
\$1,200
200
0
300
Contribution
Margin
\$1,500
500
300
600
Contribution
Margin %
75.0%
25.0%
30.0%
40.0%
(10–15 min.) CVP computations.
1a.
Sales (\$68 per unit × 410,000 units)
Variable costs (\$60 per unit × 410,000 units)
Contribution margin
1b.
Contribution margin (from above)
Fixed costs
Operating income
2a.
Sales (from above)
Variable costs (\$54 per unit × 410,000 units)
Contribution margin
2b.
Contribution margin
Fixed costs
Operating income
\$27,880,000
24,600,000
\$ 3,280,000
\$3,280,000
1,640,000
\$1,640,000
\$27,880,000
22,140,000
\$ 5,740,000
\$5,740,000
5,330,000
\$ 410,000
3.
Operating income is expected to decrease by \$1,230,000 (\$1,640,000 − \$410,000) 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. Garrett’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.
3-3
3-18
(35–40 min.) CVP analysis, changing revenues and costs.
1a.
SP
VCU
CMU
FC
= 6% × \$1,500 = \$90 per ticket
= \$43 per ticket
= \$90 – \$43 = \$47 per ticket
= \$23,500 a month
Q
=
FC
\$23,500
=
\$47 per ticket
CMU
= 500 tickets
1b.
Q
=
FC + TOI
\$23,500 + \$17,000
=
\$47 per ticket
CMU
=
\$40,500
\$47 per ticket
= 862 tickets (rounded up)
2a.
SP
VCU
CMU
FC
= \$90 per ticket
= \$40 per ticket
= \$90 – \$40 = \$50 per ticket
= \$23,500 a month
Q
=
FC
\$23,500
=
\$50 per ticket
CMU
= 470 tickets
2b.
Q
=
FC + TOI
\$23,500 + \$17,000
=
\$50 per ticket
CMU
=
\$40,500
\$50 per ticket
= 810 tickets
3a.
SP
VCU
CMU
FC
Q
= \$60 per ticket
= \$40 per ticket
= \$60 – \$40 = \$20 per ticket
= \$23,500 a month
FC
\$23,500
=
\$20 per ticket
CMU
= 1,175 tickets
=
3-4
3b.
Q
=
FC + TOI
\$23,500 + \$17,000
=
\$20 per ticket
CMU
=
\$40,500
\$20 per ticket
= 2,025 tickets
The reduced commission sizably increases the breakeven point and the number of tickets
required to yield a target operating income of \$17,000:
Breakeven point
Attain OI of \$10,000
6%
Commission
(Requirement 2)
470
810
Fixed
Commission of \$60
1,175
2,025
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
= \$65 (\$60 + \$5) per ticket
= \$40 per ticket
= \$65 – \$40 = \$25 per ticket
= \$23,500 a month
Q
=
FC
\$23,500
=
\$25 per ticket
CMU
= 940 tickets
4b.
Q
=
FC + TOI
\$23,500 + \$17,000
=
\$25 per ticket
CMU
=
\$40,500
\$25 per ticket
= 1,620 tickets
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 \$17,000.
3-5
3-19
(20 min.) CVP exercises.
Orig.
1.
2.
3.
4.
5.
6.
7.
8.
Gstands
Revenues
Variable
Costs
Contribution
Margin
\$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
\$8,000,000G
7,800,000
8,200,000
8,000,000
8,000,000
8,640,000f
7,360,000h
8,800,000j
7,600,000l
\$2,000,000
2,200,000a
1,800,000b
2,000,000
2,000,000
2,160,000
1,840,000
2,200,000
2,400,000
Fixed
Costs
\$1,800,000G
1,800,000
1,800,000
1,890,000c
1,710,000d
1,800,000
1,800,000
1,980,000k
1,890,000m
Budgeted
Operating
Income
\$200,000
400,000
0
110,000
290,000
360,000
40,000
220,000
510,000
for given.
a\$2,000,000 × 1.10; b\$2,000,000 × 0.90; c\$1,800,000 × 1.05; d\$1,800,000 × 0.95; e\$10,000,000 × 1.08;
f\$8,000,000 × 1.08; g\$10,000,000 × 0.92; h\$8,000,000 × 0.92; i\$10,000,000 × 1.10; j\$8,000,000 × 1.10;
k\$1,800,000 × 1.10; l\$8,000,000 × 0.95; m\$1,800,000 × 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
3-6
3-21
(10 min.) CVP analysis, income taxes.
1. Monthly fixed costs = \$48,200 + \$68,000 + \$13,000 =
Contribution margin per unit = \$27,000 – \$23,000 – \$600 =
Monthly fixed costs
\$129,200
=
=
Breakeven units per month =
Contribution margin per unit
\$3,400 per car
2. Tax rate
Target net income
\$129,200
\$ 3,400
38 cars
40%
\$51,000
Target net income \$51,000 \$51,000
=
=
=
\$85,000
1 - tax rate
(1 − 0.40)
0.60
Quantity of output units Fixed costs + Target operating income \$129, 200 + \$85,000
=
= 63 cars
required to be sold =
Contribution margin per unit
\$3, 400
Target operating income =
3-22
(20–25 min.) CVP analysis, income taxes.
1. Variable cost percentage is \$3.40 ÷ \$8.50 = 40%
Let R = Revenues needed to obtain target net income
R – 0.40R – \$459,000 =
\$107,100
1 − 0.30
0.60R = \$459,000 + \$153,000
R = \$612,000 ÷ 0.60
R = \$1,020,000
Fixed costs + Target operating income
Contribution margin percentage
Target net income
\$107,100
Fixed costs +
\$459, 000 +
1 − Tax rate
1 − 0.30 = \$1, 020, 000
=
Target revenues =
Contribution margin percentage
0.60
or, Target revenues =
Proof:
2.a.
Revenues
Variable costs (at 40%)
Contribution margin
Fixed costs
Operating income
Income taxes (at 30%)
Net income
\$1,020,000
408,000
612,000
459,000
153,000
45,900
\$ 107,100
Customers needed to break even:
Contribution margin per customer = \$8.50 – \$3.40 = \$5.10
Breakeven number of customers = Fixed costs ÷ Contribution margin per customer
= \$459,000 ÷ \$5.10 per customer
= 90,000 customers
3-7
2.b.
Customers needed to earn net income of \$107,100:
Total revenues ÷ Sales check per customer
\$1,020,000 ÷ \$8.50 = 120,000 customers
3.
Using the shortcut approach:
Change in net income
New net income
Unit
⎛ Change in ⎞
⎛
⎞
= ⎜ number of ⎟ × ⎜ contribution ⎟ × (1 − Tax rate )
⎜ customers ⎟
⎜ margin ⎟
⎝
⎠
⎝
⎠
= (170,000 – 120,000) × \$5.10 × (1 – 0.30)
= \$255,000 × 0.7 = \$178,500
= \$178,500 + \$107,100 = \$285,600
Alternatively, with 170,000 customers,
Operating income = Number of customers × Selling price per customer
– Number of customers × Variable cost per customer – Fixed costs
= 170,000 × \$8.50 – 170,000 × \$3.40 – \$459,000 = \$408,000
Net income
= Operating income × (1 – Tax rate) = \$408,000 × 0.70 = \$285,600
The alternative approach is:
Revenues, 170,000 × \$8.50
Variable costs at 40%
Contribution margin
Fixed costs
Operating income
Income tax at 30%
Net income
\$1,445,000
578,000
867,000
459,000
408,000
122,400
\$ 285,600
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
3-8
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
Units sold
0
100,000
200,000
-1,000
300,000
400,000
252,708 units
-2,000
-3,000
\$3.5 million
-4,000
2a.
Breakeven
FC
number of units = CMU
\$3,500,000
=
\$13.85
= 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)
=
3-9
500,000
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
FC
number of units = 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.
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
Breakeven
\$3,500,000
=
number of units
\$19.80
= 176,768 copies sold (rounded up)
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.
3-10
(10 min.) CVP analysis, margin of safety.
Fixed costs
1.
Breakeven point revenues =
Contribution margin percentage
\$660,000
= 0.60 or 60%
Contribution margin percentage =
\$1,100,000
Selling price − Variable cost per unit
2.
Contribution margin percentage =
Selling price
SP − \$16
0.60 =
SP
0.60 SP = SP – \$16
0.40 SP = \$16
SP = \$40
3. Breakeven sales in units = Revenues ÷ Selling price = \$1,100,000 ÷ \$40 = 27,500 units
Margin of safety in units = Sales in units – Breakeven sales in units
= 95,000 – 27,500 = 67,500 units
3-24
Revenues, 95,000 units × \$40
Breakeven revenues
Margin of safety
\$3,800,000
1,100,000
\$2,700,000
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 ÷ \$150 = 34 carpets (rounded up)
1b.
2.
Breakeven point under Option 2
\$500Q − \$350Q − (0.10 × \$500Q)
100Q
Q
=
=
=
0
0
0
Operating income under Option 1 = \$150Q − \$5,000
Operating income under Option 2 = \$100Q
Find Q such that \$150Q − \$5,000 = \$100Q
\$50Q = \$5,000
Q = \$5,000 ÷ \$50 = 100 carpets
Revenues = \$500 × 100 carpets = \$50,000
For Q = 100 carpets, operating income under both Option 1 (\$150 × 100 – \$5,000) and
Option 2 (\$100 × 100) = \$10,000
3-11
For Q > 100, say, 101 carpets,
Option 1 gives operating income
= (\$150 × 101) − \$5,000 = \$10,150
Option 2 gives operating income
= \$100 × 101
= \$10,100
So Color Rugs will prefer Option 1.
For Q < 100, say, 99 carpets,
Option 1 gives operating income
= (\$150 × 99) − \$5,000 = \$9,850
Option 2 gives operating income
= \$100 × 99
= \$9,900
So Color Rugs will prefer Option 2.
3.
Contribution margin
Operating income
Contribution margin per unit × Quantity of carpets sold
=
Operating income
Under Option 1, contribution margin per unit = \$500 – \$350, so
\$150 × 100
Degree of operating leverage =
= 1.5
\$10,000
Under Option 2, contribution margin per unit = \$500 – \$350 – 0.10 × \$500, so
\$100 × 100
Degree of operating leverage =
= 1.0
\$10,000
Degree of operating leverage =
4. The calculations in requirement 3 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.
3-12
3-26
(15 min.) CVP analysis, international cost structure differences.
Variable
Variable
Sales Price Annual
Manufacturing Marketing and Contribution
to Retail
Fixed
Cost per
Distribution Cost
Margin
Breakeven
Breakeven
Country
Outlets
Costs
Rug
per Rug
Per Rug
Units
Revenues
(6) × (1)
(1)
(2)
(3)
(4)
(5)=(1)–(3)–(4) (6)=(2) ÷ (5)
Singapore
\$250.00 \$ 9,000,000
\$75.00
\$25.00
\$150.00
60,000
\$15,000,000
Brazil
\$250.00
8,400,000
60.00
15.00
175.00
48,000
12,000,000
United States \$250.00
12,400,000
82.50
12.50
155.00
80,000
20,000,000
Requirement 1
Operating Income
for Budgeted Sales
of 75,000 Rugs
(7)=[75,000 × (5)]–(2)
\$2,250,000
4,725,000
(775,000)
Requirement 2
Brazil has the lowest breakeven point since it has both the lowest fixed costs (\$8,400,000) and the lowest variable cost per unit (\$75.00).
Hence, for a given selling price, Brazil will always have a higher operating income (or a lower operating loss) than Singapore or the U.S.
The U.S. breakeven point is 80,000 units. Hence, with sales of only 75,000 units, it has an operating loss of \$775,000.
3-13
3-27
(30 min.) Sales mix, new and upgrade customers.
1.
SP
VCU
CMU
New
Customers
\$275
100
175
Customers
\$100
50
50
The 60%/40% sales mix implies that, in each bundle, 3 units are sold to new customers and 2
units are sold to upgrade customers.
Contribution margin of the bundle = 3 × \$175 + 2 × \$50 = \$525 + \$100 = \$625
\$15, 000, 000
Breakeven point in bundles =
= 24,000 bundles
\$625
Breakeven point in units is:
72,000 units
Sales to new customers:
24,000 bundles × 3 units per bundle
48,000 units
Sales to upgrade customers: 24,000 bundles × 2 units per bundle
Total number of units to breakeven (rounded)
120,000 units
Alternatively,
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
[\$275 (1.5S) + \$100S] – [\$100 (1.5S) + \$50S] – \$15,000,000 = OI
\$512.5S – \$200S – \$15,000,000 = OI
Breakeven point is 120,000 units when OI = \$0 because
\$312.5S
S
1.5S
BEP
= \$15,000,000
= 48,000 units sold to upgrade customers
= 72,000 units sold to new customers
= 120,000 units
Check
Revenues (\$275 × 72,000) + (\$100 × 48,000)
Variable costs (\$100 × 72,000) + (\$50 × 48,000)
Contribution margin
Fixed costs
Operating income
3-14
\$24,600,000
9,600,000
15,000,000
15,000,000
\$
0
2.
When 220,000 units are sold, mix is:
Units sold to new customers (60% × 220,000)
Units sold to upgrade customers (40% × 220,000)
Revenues (\$275 × 132,000) + (\$100 × 88,000)
Variable costs (\$100 × 132,000) + (\$50 × 88,000)
Contribution margin
Fixed costs
Operating income
3a.
132,000
88,000
\$45,100,000
17,600,000
27,500,000
15,000,000
\$12,500,000
At New 40%/Upgrade 60% mix, each bundle contains 2 units sold to new customers and 3
units sold to upgrade customers.
Contribution margin of the bundle = 2 × \$175 + 3 × \$50 = \$350 + \$150 = \$500
\$15, 000, 000
Breakeven point in bundles =
= 30,000 bundles
\$500
Breakeven point in units is:
Sales to new customers:
30,000 bundles × 2 unit per bundle
60,000 units
Sales to upgrade customers:
30,000 bundles × 3 unit per bundle
90,000 units
Total number of units to breakeven
150,000 units
Alternatively,
= Number of units sold to new customers
Let S
then 1.5S = Number of units sold to upgrade customers
[\$275S + \$100 (1.5S)] – [\$100S + \$50 (1.5S)] – \$15,000,000 = OI
425S – 175S = \$15,000,000
250S = \$15,000,000
S =
60,000 units sold to new customers
90,000 units sold to upgrade customers
1.5S =
BEP =
150,000 units
Check
Revenues (\$275 × 60,000) + (\$100 × 90,000)
\$25,500,000
Variable costs (\$100 × 60,000) + (\$50 × 90,000)
10,500,000
Contribution margin
15,000,000
Fixed costs
15,000,000
Operating income
\$
0
3b. At New 80%/ Upgrade 20% mix, each bundle contains 4 units sold to new customers and 1
unit sold to upgrade customers.
Contribution margin of the bundle = 4 × \$175 + 1 × \$50 = \$700 + \$50 = \$750
\$15, 000, 000
Breakeven point in bundles =
= 20,000 bundles
\$750
Breakeven point in units is:
Sales to new customers:
20,000 bundles × 4 units per bundle
80,000 units
Sales to upgrade customers:
20,000 bundles × 1 unit per bundle
20,000 units
Total number of units to breakeven
100,000 units
3-15
Alternatively,
Let S = Number of units sold to upgrade customers
then 4S= Number of units sold to new customers
[\$275 (4S) + \$100S] – [\$100 (4S) + \$50S] – \$15,000,000 = OI
1,200S – 450S = \$15,000,000
750S = \$15,000,000
S =
20,000 units sold to upgrade customers
80,000 units sold to new customers
4S =
100,000 units
Check
Revenues (\$275 × 80,000) + (\$100 × 20,000)
Variable costs (\$100 × 80,000) + (\$50 × 20,000)
Contribution margin
Fixed costs
Operating income
\$24,000,000
9,000,000
15,000,000
15,000,000
\$
0
3c. As Data 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
40%
60
80
3-16
Customers
60%
40
20
Breakeven
Point
150,000
120,000
100,000
3-28
(30 min.) Sales mix, three products.
1.
SP
VCU
CMU
Coffee
\$2.50
1.25
\$1.25
Bagels
\$3.75
1.75
\$2.00
The sales mix implies that each bundle consists of 4 cups of coffee and 1 bagel.
Contribution margin of the bundle = 4 × \$1.25 + 1 × \$2 = \$5.00 + \$2.00 = \$7.00
Breakeven point in bundles =
Fixed costs
\$7, 000
=
= 1, 000 bundles
Contribution margin per bundle
\$7.00
Breakeven point is:
Coffee: 1,000 bundlex × 4 cups per bundle = 4,000 cups
Bagels: 1,000 bundles × 1 bagel per bundle = 1,000 bagels
Alternatively,
Let S = Number of bagels sold
4S = Number of cups of coffee sold
Revenues – Variable costs – Fixed costs = Operating income
[\$2.50(4S) + \$3.75S] – [\$1.25(4S) + \$1.75S] – \$7,000 = OI
\$13.75S – \$6.75S – \$7,000 = OI
\$7.00 S=\$7,000
S = 1,000 units of the sales mix
or
S =1,000 bagels sold
4S=4,000 cups of coffee sold
Breakeven point, therefore, is 1,000 bagels and 4,000 cups of coffee when OI = 0
Check
Revenues (\$2.50 × 4,000) + (\$3.75 × 1,000)
Variable costs (\$1.25 × 4,000) + (\$1.75 × 1,000)
Contribution margin
Fixed costs
Operating income
2.
SP
VCU
CMU
Coffee
\$2.50
1.25
\$1.25
\$13,750
6,750
7,000
7,000
\$
0
Bagels
\$3.75
1.75
\$2.00
The sales mix implies that each bundle consists of 4 cups of coffee and 1 bagel.
Contribution margin of the bundle = 4 × \$1.25 + 1 × \$2 = \$5.00 + \$2.00 = \$7.00
Breakeven point in bundles
3-17
=
Fixed costs + Target operating income \$7, 000 + \$28, 000
=
= 5, 000 bundles
Contribution margin per bundle
\$7.00
Breakeven point is:
Coffee: 5,000 bundles × 4 cups per bundle = 20,000 cups
Bagels: 5,000 bundles × 1 bagel per bundle = 5,000 bagels
Alternatively,
Let S = Number of bagels sold
4S = Number of cups of coffee sold
Revenues – Variable costs – Fixed costs = Operating income
[\$2.50(4S) + \$3.75S] – [\$1.25(4S) + \$1.75S] – \$7,000 = OI
[\$2.50(4S) + \$3.75S] – [\$1.25(4S) + \$1.75S] – \$7,000 = 28,000
\$13.75S – \$6.75S = 35,000
\$7.00 S=\$35,000
S = 5,000 units of the sales mix
or
S =5,000 bagels sold
4S=20,000 cups of coffee sold
The target number of units to reach an operating income before tax of \$28,000 is 5,000 bagels
and 20,000 cups of coffee.
Check
Revenues (\$2.50 × 20,000) + (\$3.75 × 5,000)
Variable costs (\$1.25 × 20,000) + (\$1.75 × 5,000)
Contribution margin
Fixed costs
Operating income
3.
SP
VCU
CMU
Coffee
\$2.50
1.25
\$1.25
Bagels
\$3.75
1.75
\$2.00
\$68,750
33,750
35,000
7,000
\$28,000
Muffins
\$3.00
0.75
\$2.25
The sales mix implies that each bundle consists of 3 cups of coffee, 2 bagels and 1 muffin
Contribution margin of the bundle = 3 × \$1.25 + 2 × \$2 + 1 × \$2.25
= \$3.75 + \$4.00 + \$2.25 = \$10.00
Breakeven point in bundles =
Fixed costs
\$7, 000
=
= 700 bundles
Contribution margin per bundle \$10.00
Breakeven point is:
Coffee: 700 bundles × 3 cups per bundle = 2,100 cups
Bagels: 700 bundles × 2 bagels per bundle = 1,400 bagels
Muffins: 700 bundles × 1 muffin per bundle = 700 muffins
3-18
Alternatively,
Let S = Number of muffins sold
2S = Number of bagels sold
3S = Number of cups of coffee sold
Revenues – Variable costs – Fixed costs = Operating income
[\$2.50(3S) + \$3.75(2S) +3.00S] – [\$1.25(3S) + \$1.75(2S) + \$0.75S] – \$7,000 = OI
\$18.00S – \$8S – \$7,000 = OI
\$10.00 S=\$7,000
S = 700 units of the sales mix
or
S =700 muffins
2S=1,400 bagels
3S=2,100 cups of coffee
Breakeven point, therefore, is 2,100 cups of coffee 1,400 bagels, and 700 muffins when OI = 0
Check
Revenues (\$2.50 × 2,100) + (\$3.75 × 1,400) +(\$3.00 × 700)
Variable costs (\$1.25 × 2,100) + (\$1.75 × 1,400) +(\$0.75 × 700)
Contribution margin
Fixed costs
Operating income
\$12,600
5,600
7,000
7,000
\$
0
Bobbie should definitely add muffins to her product mix because muffins have the highest
contribution margin (\$2.25) of all three products. This lowers Bobbie’s overall breakeven point.
If the sales mix ratio above can be attained, the result is a lower breakeven revenue (\$12,600) of
the options presented in the problem.
3-19
3-29
CVP, Not for profit
1.
Ticket sales per concert
Variable costs per concert:
Guest performers
Total variable costs per concert
Contribution margin per concert
Fixed costs
Salaries
Mortgage payments (\$2,000 × 12)
Total fixed costs
Less donations
Net fixed costs
Breakeven point in units =
\$ 2,500
\$ 1,000
500
1,500
\$ 1,000
\$50,000
24,000
\$74,000
40,000
\$34,000
Net fixed costs
\$34,000
=
= 34 concerts
Contribution margin per concert
\$1,000
Check
Donations
Revenue (\$2,500 × 34)
Total revenue
\$ 40,000
85,000
125,000
Less variable costs
Guest performers (\$1,000 × 34)
Marketing and advertising (\$500 × 34)
Total variable costs
Less fixed costs
Salaries
Mortgage payments
Total fixed costs
Operating income
2.
\$34,000
17,000
51,000
\$50,000
24,000
\$
Ticket sales per concert
Variable costs per concert:
Guest performers
Total variable costs per concert
Contribution margin per concert
Fixed costs
Salaries (\$50,000 + \$40,000)
Mortgage payments (\$2,000 × 12)
Total fixed costs
Less donations
Net fixed costs
3-20
74,000
0
\$ 2,500
\$1,000
500
1,500
\$ 1,000
\$90,000
24,000
\$114,000
40,000
\$ 74,000
Breakeven point in units =
Net fixed costs
\$74,000
=
= 74 concerts
Contribution margin per concert
\$1,000
Check
Donations
Revenue (\$2,500 × 74)
Total revenue
\$ 40,000
185,000
225,000
Less variable costs
Guest performers (\$1,000 × 74)
Marketing and advertising (\$500 × 74)
Total variable costs
Less fixed costs
Salaries
Mortgage payments
Total fixed costs
Operating income
\$74,000
37,000
111,000
\$90,000
24,000
114,000
\$
0
Operating Income if 60 concerts are held
Donations
Revenue (\$2,500 × 60)
Total revenue
\$ 40,000
150,000
190,000
Less variable costs
Guest performers (\$1,000 × 60)
Marketing and advertising (\$500 × 60)
Total variable costs
Less fixed costs
Salaries
Mortgage payments
Total fixed costs
Operating income (loss)
\$60,000
30,000
90,000
\$90,000
24,000
114,000
\$ (14,000)
The Music Society would not be able to afford the new marketing director if the number of
concerts were to increase to only 60 events. The addition of the new marketing director would
require the Music Society to hold at least 74 concerts in order to breakeven. If only 60 concerts
were held, the organization would lose \$14,000 annually. The Music Society could look for
other contributions to support the new marketing director’s salary or perhaps increase the
number of attendees per concert if the number of concerts could not be increased beyond 60.
3.
Ticket sales per concert
Variable costs per concert:
Guest performers
Total variable costs per concert
Contribution margin per concert
3-21
\$ 2,500
\$ 1,000
500
1,500
\$ 1,000
Fixed costs
Salaries (\$50,000 + \$40,000)
Mortgage payments (\$2,000 × 12)
Total fixed costs
Deduct donations
Net fixed costs
Breakeven point in units =
\$90,000
24,000
\$114,000
60,000
\$ 54,000
Net fixed costs
\$54,000
=
= 54 concerts
Contribution margin per concert
\$1,000
Check
Donations
Revenue (\$2,500 × 54)
Total revenue
\$ 60,000
135,000
195,000
Less variable costs
Guest performers (\$1,000 × 54)
Marketing and advertising (\$500 × 54)
Total variable costs
Less fixed costs
Salaries
Mortgage payments
Total fixed costs
Operating income
\$54,000
27,000
81,000
\$90,000
24,000
114,000
\$
0
3-22
3-30
(15 min.) Contribution margin, decision making.
1.
Revenues
Deduct variable costs:
Cost of goods sold
Sales commissions
Other operating costs
Contribution margin
\$600,000
\$300,000
60,000
30,000
390,000
\$210,000
\$210,000
= 35%
\$600,000
2.
Contribution margin percentage =
3.
Incremental revenue (15% × \$600,000) = \$90,000
Incremental contribution margin
(35% × \$90,000)
Incremental fixed costs (advertising)
Incremental operating income
\$31,500
13,000
\$18,500
If Mr. Lurvey spends \$13,000 more on advertising, the operating income will increase by
\$18,500, decreasing the operating loss from \$49,000 to an operating loss of \$30,500.
Proof (Optional):
Revenues (115% × \$600,000)
Cost of goods sold (50% of sales)
Gross margin
\$690,000
345,000
345,000
Operating costs:
Salaries and wages
Sales commissions (10% of sales)
Depreciation of equipment and fixtures
Store rent
Other operating costs:
⎛ \$30,000
⎞
× \$690, 000 ⎟
Variable ⎜
⎝ \$600,000
⎠
Fixed
Operating income
3-23
\$170,000
69,000
20,000
54,000
13,000
34,500
15,000
375,500
\$ (30,500)
3-31
(20 min.) Contribution margin, gross margin and margin of safety.
1.
Mirabella Cosmetics
Operating Income Statement, June 2011
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
=
= 7,500 units
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 =
Alternatively,
Contribution margin percentage =
Breakeven revenues =
Contribution margin \$40, 000
=
= 40%
Revenues
\$100, 000
Fixed costs
\$30, 000
=
= \$75, 000
Contribution margin percentage
0.40
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 × 40%)
Fixed costs
Operating income
Taxes (30% × \$2,000)
Net income
3-24
8,000
\$80,000
\$32,000
30,000
2,000
600
\$ 1,400
3-32 (30 min.) Uncertainty and expected costs.
1. Monthly Number of Orders
350,000
450,000
550,000
650,000
750,000
Cost of Current System
\$2,500,000 + \$50(350,000) = \$20,000,000
\$2,500,000 + \$50(450,000) = \$25,000,000
\$2,500,000 + \$50(550,000) = \$30,000,000
\$2,500,000 + \$50(650,000) = \$35,000,000
\$2,500,000 + \$50(750,000) = \$40,000,000
Monthly Number of Orders
350,000
450,000
550,000
650,000
750,000
Cost of Partially Automated System
\$10,000,000 + \$40(350,000) = \$24,000,000
\$10,000,000 + \$40(450,000) = \$28,000,000
\$10,000,000 + \$40(550,000) = \$32,000,000
\$10,000,000 + \$40(650,000) = \$36,000,000
\$10,000,000 + \$40(750,000) = \$40,000,000
Monthly Number of Orders
350,000
450,000
550,000
650,000
750,000
Cost of Fully Automated System
\$20,000,000 + \$25(350,000) = \$28,750,000
\$20,000,000 + \$25(450,000) = \$31,250,000
\$20,000,000 + \$25(550,000) = \$33,750,000
\$20,000,000 + \$25(650,000) = \$36,250,000
\$20,000,000 + \$25(750,000) = \$38,750,000
2. Current System Expected Cost:
\$20,000,000 × 0.15 = \$ 3,000,000
25,000,000 × 0.20 =
5,000,000
30,000,000 × 0.35 =
10,500,000
35,000,000 × 0.20 =
7,000,000
40,000,000 × 0.10 =
4,000,000
\$29,500,000
Partially Automated System Expected Cost:
\$24,000,000 × 0.15 = \$ 3,600,000
28,000,000 × 0.20 =
5,600,000
32,000,000 × 0.35 =
11,200,000
36,000,000 × 0.20 =
7,200,000
40,000,000 × 0.10 =
4,000,000
\$31,600,000
Fully Automated System Expected Cost:
\$28,750,000 × 0.15 = \$ 4,312,500
31,250,000 × 0.20 =
6,250,000
33,750,000 × 0.35 =
11,812,500
36,250,000 × 0.20 =
7,250,000
38,750,000 × 0.10 =
3,875,000
\$33,500,000
3-25
3. Foodmart should consider the impact of the different systems on its relationship with
suppliers. The interface with Foodmart’s system may require that suppliers also update their
systems. This could cause some suppliers to raise the cost of their merchandise. It could force
other suppliers to drop out of Foodmart’s supply chain because the cost of the system change
would be prohibitive. Foodmart may also want to consider other factors such as the reliability of
different systems and the effect on employee morale if employees have to be laid off as it
automates its systems.
3-33
(15–20 min.) CVP analysis, service firm.
1.
Revenue per package
Variable cost per package
Contribution margin per package
\$5,000
3,700
\$1,300
Breakeven (packages) = Fixed costs ÷ Contribution margin per package
\$520,000
=
= 400 tour packages
\$1,300 per package
2.
Contribution margin ratio =
\$1,300
Contribution margin per package
= 26%
=
\$5,000
Selling price
Revenue to achieve target income = (Fixed costs + target OI) ÷ Contribution margin ratio
=
Number of tour packages to earn
\$91,000 operating income
\$520,000 + \$91,000
= \$2,350,000, or
0.26
=
\$520, 000 + \$91, 000
= 470 tour packages
\$1,300
Revenues to earn \$91,000 OI = 470 tour packages × \$5,000 = \$2,350,000.
3.
Fixed costs = \$520,000 + \$32,000 = \$552,000
Breakeven (packages) =
Fixed costs
Contribution margin per package
Contribution margin per package =
=
Fixed costs
Breakeven (packages)
\$552,000
= \$1,380 per tour package
400 tour packages
Desired variable cost per tour package = \$5,000 – \$1,380 = \$3,620
Because the current variable cost per unit is \$3,700, the unit variable cost will need to be reduced
by \$80 to achieve the breakeven point calculated in requirement 1.
Alternate Method: If fixed cost increases by \$32,000, then total variable costs must be reduced
by \$32,000 to keep the breakeven point of 400 tour packages.
Therefore, the variable cost per unit reduction = \$32,000 ÷ 400 = \$80 per tour package.
3-26
3-34
(30 min.) CVP, target operating income, service firm.
1.
Revenue per child
Variable costs per child
Contribution margin per child
Breakeven quantity =
=
2.
Target quantity =
=
3.
\$580
230
\$350
Fixed costs
Contribution margin per child
\$5,600
= 16 children
\$350
Fixed costs + Target operating income
Contribution margin per child
\$5,600 + \$10,500
= 46 children
\$350
Increase in rent (\$3,150 – \$2,150)
Field trips
Total increase in fixed costs
Divide by the number of children enrolled
Increase in fee per child
\$1,000
1,300
\$2,300
÷ 46
\$ 50
Therefore, the fee per child will increase from \$580 to \$630.
Alternatively,
New contribution margin per child =
\$5,600 + \$2,300 + \$10,500
= \$400
46
New fee per child = Variable costs per child + New contribution margin per child
= \$230 + \$400 = \$630
3-27
3-35
(20–25 min.)
1.
Selling price
Variable costs per unit:
Production costs
Shipping and handling
Contribution margin per unit (CMU)
CVP analysis.
\$300
\$120
5
125
\$175
Fixed costs
\$1,260,000
= 7,200 units
=
Contribution margin per unit
\$175
Margin of safety (units) = 10,000 – 7,200 = 2,800 units
Breakeven point in units =
2.
Since fixed costs remain the same, any incremental increase in sales will increase
contribution margin and operating income dollar for dollar.
Increase in units sales = 10% × 10,000 = 1,000
Incremental contribution margin = \$175 × 1,000 = \$175,000
Therefore, the increase in operating income will be equal to \$175,000.
Technology Solutions’s operating income in 2011 would be \$490,000 + \$175,000 =
\$665,000.
3.
Selling price
Variable costs:
Production costs \$120 × 130%
Shipping and handling (\$5 – (\$5 × 0.20))
Contribution margin per unit
Target sales in units =
\$300
\$156
4
160
\$140
\$1,260,000 + \$490,000
FC + TOI
=
= 12,500 units
\$140
CMU
Target sales in dollars = \$300 × 12,500 = \$3,750,000
3-28
3-36
(30–40 min.) CVP analysis, income taxes.
1.
Revenues – Variable costs – Fixed costs =
Let X = Net income for 2011
Target net income
1 − Tax rate
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.
4.
Let X = Net income for 2012
22,000(\$25.00) – 22,000(\$13.75) – (\$135,000 + \$11,250)
=
\$550,000 – \$302,500 – \$146,250
=
\$101,250
=
0.60
X
0.60
X = \$60,750
= 0
= 13,000 units
= \$325,000
Let S = Required sales units to equal 2011 net income
\$25.00S – \$13.75S – \$146,250 =
\$54,000
0.60
\$11.25S = \$236,250
S = 21,000 units
Revenues = 21,000 units × \$25 = \$525,000
6.
1 − 0.40
X
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.
X
Let A = Amount spent for advertising in 2012
\$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
3-29
3-37 (25 min.) CVP, sensitivity analysis.
Contribution margin per pair of shoes = \$60 – \$25 = \$35
Fixed costs = \$100,000
Units sold = Total sales ÷ Selling price = \$300,000 ÷ \$60 per pair= 5,000 pairs of shoes
1. Variable costs decrease by 20%; Fixed costs increase by 15%
\$300,000
Sales revenues 5,000 × \$60
100,000
Variable costs 5,000 × \$25 × (1 – 0.20)
Contribution margin
200,000
Fixed costs \$100,000 x 1.15
115,000
Operating income
\$ 85,000
2. Increase advertising (fixed costs) by \$30,000; Increase sales 20%
\$360,000
Sales revenues 5,000 × 1.20 × \$60.00
×
×
150,000
Variable costs 5,000 1.20 \$25.00
Contribution margin
210,000
Fixed costs (\$100,000 + \$30,000)
130,000
Operating income
\$ 80,000
3. Increase selling price by \$10.00; Sales decrease 10%; Variable costs increase by \$7
\$315,000
Sales revenues 5,000 × 0.90 × (\$60 + \$10)
144,000
Variable costs 5,000 × 0.90 × (\$25 + \$7)
Contribution margin
171,000
Fixed costs
100,000
Operating income
\$ 71,000
4. Double fixed costs; Increase sales by 60%
Sales revenues 5,000 × 1.60 × \$60
Variable costs 5,000 × 1.60 × \$25
Contribution margin
Fixed costs \$100,000 × 2
Operating income
\$480,000
200,000
280,000
200,000
\$ 80,000
Alternative 1 yields the highest operating income. Choosing alternative 1 will give
Brown a 13.33% increase in operating income [(\$85,000 – \$75,000)/\$75,000 = 13.33%], which
is less than the company’s 25% targeted increase. Alternatives 2 and 4 also generate more
operating income for Brown, but they too do not meet Brown’s target of 25% increase in
operating income. Alternative 3 actually results in lower operating income than under Brown’s
current cost structure. There is no reason, however, for Brown to think of these alternatives as
being mutually exclusive. For example, Brown can combine actions 1 and 2, automate the
machining process and advertise. This will result in a 26.67% increase in operating income as
follows:
3-30
Sales revenue 5,000 × 1.20 × \$60
Variable costs 5,000 × 1.20 × \$25 × (1 – 0.20)
Contribution margin
Fixed costs \$100,000 × 1.15 + \$30,000
Operating income
\$360,000
120,000
240,000
145,000
\$ 95,000
The point of this problem is that managers always need to consider broader rather than
narrower alternatives to meet ambitious or stretch goals.
3-38
(20–30 min.) CVP analysis, shoe stores.
1. CMU (SP – VCU = \$30 – \$21)
a. Breakeven units (FC ÷ CMU = \$360,000 ÷ \$9 per unit)
b. Breakeven revenues
(Breakeven units × SP = 40,000 units × \$30 per unit)
\$
2. Pairs sold
Revenues, 35,000 × \$30
Total cost of shoes, 35,000 × \$19.50
Total sales commissions, 35,000 × \$1.50
Total variable costs
Contribution margin
Fixed costs
Operating income (loss)
35,000
\$1,050,000
682,500
52,500
735,000
315,000
360,000
\$ (45,000)
3. Unit variable data (per pair of shoes)
Selling price
Cost of shoes
Sales commissions
Variable cost per unit
Annual fixed costs
Rent
Salaries, \$200,000 + \$81,000
Other fixed costs
Total fixed costs
9.00
40,000
\$1,200,000
\$
\$
30.00
19.50
0
19.50
\$
60,000
281,000
80,000
20,000
\$ 441,000
CMU, \$30 – \$19.50
a. Breakeven units, \$441,000 ÷ \$10.50 per unit
b. Breakeven revenues, 42,000 units × \$30 per unit
3-31
\$
10.50
42,000
\$1,260,000
4. Unit variable data (per pair of shoes)
Selling price
Cost of shoes
Sales commissions
Variable cost per unit
Total fixed costs
\$
30.00
19.50
1.80
\$
21.30
\$ 360,000
CMU, \$30 – \$21.30
a. Break even units = \$360,000 ÷ \$8.70 per unit
b. Break even revenues = 41,380 units × \$30 per unit
5. Pairs sold
Revenues (50,000 pairs × \$30 per pair)
Total cost of shoes (50,000 pairs × \$19.50 per pair)
Sales commissions on first 40,000 pairs (40,000 pairs × \$1.50 per pair)
Sales commissions on additional 10,000 pairs
[10,000 pairs × (\$1.50 + \$0.30 per pair)]
Total variable costs
Contribution margin
Fixed costs
Operating income
\$
8.70
41,380 (rounded up)
\$1,241,400
50,000
\$1,500,000
\$ 975,000
60,000
18,000
\$1,053,000
\$ 447,000
360,000
\$ 87,000
Alternative approach:
Breakeven point in units = 40,000 pairs
Store manager receives commission of \$0.30 on 10,000 (50,000 – 40,000) pairs.
Contribution margin per pair beyond breakeven point of 10,000 pairs =
\$8.70 (\$30 – \$21 – \$0.30) per pair.
Operating income = 10,000 pairs × \$8.70 contribution margin per pair = \$87,000.
3-32
3-39
(30 min.) CVP analysis, shoe stores (continuation of 3-38).
Salaries + Commission Plan
No. of
CM
units sold per Unit
(1)
(2)
40,000
\$9.00
42,000
9.00
44,000
9.00
46,000
9.00
48,000
9.00
50,000
9.00
52,000
9.00
54,000
9.00
56,000
9.00
58,000
9.00
60,000
9.00
62,000
9.00
64,000
9.00
66,000
9.00
CM
(3)=(1) × (2)
\$360,000
378,000
396,000
414,000
432,000
450,000
468,000
486,000
504,000
522,000
540,000
558,000
576,000
594,000
Fixed
Costs
(4)
\$360,000
360,000
360,000
360,000
360,000
360,000
360,000
360,000
360,000
360,000
360,000
360,000
360,000
360,000
Operating
Income
(5)=(3)–(4)
0
18,000
36,000
54,000
72,000
90,000
108,000
126,000
144,000
162,000
180,000
198,000
216,000
234,000
Higher Fixed Salaries Only
CM
per Unit
(6)
\$10.50
10.50
10.50
10.50
10.50
10.50
10.50
10.50
10.50
10.50
10.50
10.50
10.50
10.50
3-33
Operating
CM
Fixed Costs
Income
(7)=(1) × (6)
(8)
(9)=(7)–(8)
\$420,000
\$441,000
\$ (21,000)
441,000
441,000
0
462,000
441,000
21,000
483,000
441,000
42,000
504,000
441,000
63,000
525,000
441,000
84,000
546,000
441,000
105,000
567,000
441,000
126,000
588,000
441,000
147,000
609,000
441,000
168,000
630,000
441,000
189,000
651,000
441,000
210,000
672,000
441,000
231,000
693,000
441,000
252,000
Difference in favor
of higher-fixedsalary-only
(10)=(9)–(5)
\$(21,000)
(18,000)
(15,000)
(12,000)
(9,000)
(6,000)
(3,000)
0
3,000
6,000
9,000
12,000
15,000
18,000
1.
See preceding table. The new store will have the same operating income under either
compensation plan when the volume of sales is 54,000 pairs of shoes. This can also be calculated
as the unit sales level at which both compensation plans result in the same total costs:
Let Q = unit sales level at which total costs are same for both plans
\$19.50Q + \$360,000 + \$81,000 = \$21Q + \$360,000
\$1.50 Q = \$81,000
Q = 54,000 pairs
2.
When sales volume is above 54,000 pairs, the higher-fixed-salaries plan results in lower
costs and higher operating incomes than the salary-plus-commission plan. So, for an expected
volume of 55,000 pairs, the owner would be inclined to choose the higher-fixed-salaries-only
plan. But it is likely that sales volume itself is determined by the nature of the compensation
plan. The salary-plus-commission plan provides a greater motivation to the salespeople, and it
may well be that for the same amount of money paid to salespeople, the salary-plus-commission
plan generates a higher volume of sales than the fixed-salary plan.
3.
Let TQ = Target number of units
For the salary-only plan,
\$30.00TQ – \$19.50TQ – \$441,000
\$10.50TQ
TQ
TQ
For the salary-plus-commission plan,
\$30.00TQ – \$21.00TQ – \$360,000
\$9.00TQ
TQ
TQ
= \$168,000
= \$609,000
= \$609,000 ÷ \$10.50
= 58,000 units
= \$168,000
= \$528,000
= \$528,000 ÷ \$9.00
= 58,667 units (rounded up)
The decision regarding the salary plan depends heavily on predictions of demand. For
instance, the salary plan offers the same operating income at 58,000 units as the commission plan
offers at 58,667 units.
4.
WalkRite Shoe Company
Operating Income Statement, 2011
Revenues (48,000 pairs × \$30) + (2,000 pairs × \$18)
Cost of shoes, 50,000 pairs × \$19.50
Commissions = Revenues × 5% = \$1,476,000 × 0.05
Contribution margin
Fixed costs
Operating income
3-34
\$1,476,000
975,000
73,800
427,200
360,000
\$ 67,200
3-40
(40 min.) Alternative cost structures, uncertainty, and sensitivity analysis.
1. Contribution margin per
page assuming current
fixed leasing agreement
= \$0.15 – \$0.03 – \$0.04 = \$0.08 per page
Fixed costs = \$1,000
Breakeven point =
Fixed costs
\$1, 000
=
= 12,500 pages
Contribution margin per page \$0.08 per page
Contribution margin per page
assuming \$10 per 500 page = \$0.15–\$0.02a – \$0.03 – \$.04 = \$0.06 per page
commission agreement
Fixed costs = \$0
Breakeven point =
Fixed costs
\$0
=
= 0 pages
Contribution margin per page \$0.06 per page
(i.e., Stylewise makes a profit no matter how few pages it sells)
a
\$10/500 pages = \$0.02 per page
2. Let x denote the number of pages Stylewise must sell for it to be indifferent between the
fixed leasing agreement and commission based agreement.
To calculate x we solve the following equation.
\$0.15 x – \$0.03 x – \$0.04 x – \$1,000 = \$0.15 x – \$0.02 x – \$0.03 x – \$.04 x
\$0.08 x – \$1,000 = \$0.06 x
\$0.02 x = \$1,000
x = \$1,000 ÷ \$0.02 = 50,000 pages
For sales between 0 to 50,000 pages, Stylewise prefers the commission based agreement
because in this range, \$0.06 x > \$0.08 x – \$1,000. For sales greater than 50,000 pages,
Stylewise prefers the fixed leasing agreement because in this range, \$0.08 x – \$1,000 >
\$.06 x .
3. Fixed leasing agreement
Pages
Variable
Revenue
Sold
Costs
(1)
(2)
(3)
20,000
20,000 × \$.15=\$ 3,000
20,000 × \$.07=\$1,400
40,000
40,000 × \$.15=\$ 6,000
40,000 × \$.07=\$2,800
60,000
60,000 × \$.15=\$ 9,000
60,000 × \$.07=\$4,200
80,000
80,000 × \$.15=\$12,000
80,000 × \$.07=\$5,600
100,000
100,000 × \$.15=\$15,000 100,000 × \$.07=\$7,000
Expected value of fixed leasing agreement
3-35
Fixed
Costs
(4)
\$1,000
\$1,000
\$1,000
\$1,000
\$1,000
Operating
Income
(Loss)
(5)=(2)–(3)–(4)
\$ 600
\$2,200
\$3,800
\$5,400
\$7,000
Probability
(6)
0.20
0.20
0.20
0.20
0.20
Expected
Operating
Income
(7)=(5) × (6)
\$ 120
440
760
1,080
1,400
\$3,800
Commission-based leasing agreement:
Pages
Variable
Sold
Revenue
Costs
(1)
(3)
(2)
20,000
20,000 × \$.15=\$ 3,000
20,000 × \$.09=\$1,800
40,000
40,000 × \$.15=\$ 6,000
40,000 × \$.09=\$3,600
60,000 × \$.09=\$5,400
60,000
60,000 × \$.15=\$ 9,000
80,000
80,000 × \$.15=\$12,000
80,000 × \$.09=\$7,200
100,000
100,000 × \$.15=\$15,000 100,000 × \$.09=\$9,000
Expected value of commission based agreement
Operating
Income
(4)=(2)–(3)
\$1,200
\$2,400
\$3,600
\$4,800
\$6,000
Probability
(5)
0.20
0.20
0.20
0.20
0.20
Expected
Operating Income
(6)=(4) × (5)
\$ 240
480
720
960
1,200
\$3,600
Stylewise should choose the fixed cost leasing agreement because the expected value is higher
than under the commission-based leasing agreement. The range of sales is high enough to make
the fixed leasing agreement more attractive.
3-36
3-41 (20-30 min.) CVP, alternative cost structures.
1.
Variable cost per computer = \$100 + (\$15 × 10) + \$50 = \$300
Contribution margin per computer = Selling price –Variable cost per computer
= \$500 – \$300 = \$200
Breakeven point = Fixed costs ÷ Contribution margin per computer
= \$4,000 ÷ \$200 = 20 computers (per month)
2.
Target number of computers =
=
Fixed costs + Target operating income
Contribution margin per computer
\$4,000 + \$5,000
= 45 computers
\$200
3.
Contribution margin per computer = Selling price – Variable cost per computer
= \$500 – \$200 – \$50 = \$250
Fixed costs = \$4,000
Fixed costs
\$4, 000
=
= 16 computers
Breakeven point =
Contribution margin per computer
\$250
4.
Let x be the number of computers for which PC Planet is indifferent between paying
a monthly rental fee for the retail space and paying a 20% commission on sales. PC
Planet will be indifferent when the profits under the two alternatives are equal.
\$500 x – \$300 x – \$4,000 = \$500 x – \$300 x – \$500 (0.20) x
\$200 x – \$4,000 = \$100 x
\$100 x = \$4,000
x = 40 computers
For sales between 0 and 40 computers, PC Planet prefers to pay the 20% commission because in
this range, \$100 x > \$200 x – \$4,000. For sales greater than 40 computers, the company prefers
to pay the monthly fixed rent of \$4,000 because \$200 x – \$4,000 > \$100 x
3-37
3-42
(30 min.)
CVP analysis, income taxes, sensitivity.
1a.To breakeven, Agro Engine Company must sell 1,200 units. This amount represents the point
where revenues equal total costs.
Let Q denote the quantity of engines sold.
Revenue
=
Variable costs + Fixed costs
\$3,000Q
=
\$500Q + \$3,000,000
\$2,500Q
=
\$3,000,000
Q
=
1,200 units
Breakeven can also be calculated using contribution margin per unit.
Contribution margin per unit = Selling price – Variable cost per unit = \$3,000 – \$500 = \$2,500
Breakeven
= Fixed Costs ÷ Contribution margin per unit
= \$3,000,000 ÷ \$2,500
= 1,200 units
1b.
To achieve its net income objective, Agro Engine Company must sell 2,000 units. This
amount represents the point where revenues equal total costs plus the corresponding operating
income objective to achieve net income of \$1,500,000.
Revenue = Variable costs + Fixed costs + [Net income ÷ (1 – Tax rate)]
\$3,000Q = \$500Q + \$3,000,000 + [\$1,500,000 ÷ (1 − 0.25)]
\$3,000Q = \$500Q + \$3,000,000 + \$2,000,000
Q = 2,000 units
2. To achieve its net income objective, Agro Engine Company should select alternative c,
where fixed costs are reduced by 20% and selling price is reduced by 10% resulting in 1,700
additional units being sold through the end of the year. This alternative results in the highest net
income and is the only alternative that equals or exceeds the company’s net income objective of
\$1,500,000. Calculations for the three alternatives are shown below.
Alternative a
Revenues
=
Variable costs =
Operating income
Net income =
a
(\$3,000 × 300) + (\$2,400a × 2,000) = \$5,700,000
\$500 × 2,300b = \$1,150,000
=
\$5,700,000 − \$1,150,000 − \$3,000,000 = \$1,550,000
\$1,550,000 × (1 − 0.25) = \$1,162,500
\$3,000 – (\$3,000 × 0.20) = ;
b
300 units + 2,000 units.
3-38
Alternative b
Revenues
=
Variable costs =
Operating income
Net income =
(\$3,000 × 300) + (\$2,750c × 1,800) = \$5,850,000
(\$500 × 300) + (\$450d × 1,800) = \$960,000
=
\$5,850,000 − \$960,000 − \$3,000,000 = \$1,890,000
\$1,890,000 × (1 − 0.25) = \$1,417,500
c
\$3,000 – \$250; d\$450.
Alternative c
Revenues
Variable costs
Operating income
Net income
=
=
=
=
(\$3,000 × 300) + (\$2,700e× 1,700) = \$5,490,000
\$500 × 2000f = \$1,000,000
\$5,490,000 − \$1,000,000 − \$2,400,000g = \$2,090,000
\$2,090,000 × (1 − 0.25) = \$1,567,500
e
\$3,000 – (0.10 × \$3,000) = \$3,000 – \$300; f300units + 1,700 units;
\$3,000,000 – (0.20 × \$3,000,000)
g
3-39
3-43
(30 min.) Choosing between compensation plans, operating leverage.
1. We can recast Marston’s income statement to emphasize contribution margin, and then use it
to compute the required CVP parameters.
Marston Corporation
Income Statement
For the Year Ended December 31, 2011
Using Sales Agents
\$26,000,000
Revenues
Variable Costs
Cost of goods sold—variable
Marketing commissions
Contribution margin
Fixed Costs
Cost of goods sold—fixed
Marketing—fixed
Operating income
\$11,700,000
4,680,000
2,870,000
3,420,000
Contribution margin percentage
(\$9,620,000 ÷ 26,000,000;
\$11,700,000 ÷ \$26,000,000)
Breakeven revenues
(\$6,290,000 ÷ 0.37;
\$8,370,000 ÷ 0.45)
Degree of operating leverage
(\$9,620,000 ÷ \$3,330,000;
\$11,700,000 ÷ \$3,330,000)
16,380,000
9,620,000
6,290,000
\$ 3,330,000
Using Own Sales Force
\$26,000,000
\$11,700,000
2,600,000
2,870,000
5,500,000
14,300,000
11,700,000
8,370,000
\$ 3,330,000
37%
45%
\$17,000,000
\$18,600,000
2.89
3.51
2.
The calculations indicate that at sales of \$26,000,000, a percentage change in sales and
contribution margin will result in 2.89 times that percentage change in operating income if
Marston continues to use sales agents and 3.51 times that percentage change in operating income
if Marston employs its own sales staff. The higher contribution margin per dollar of sales and
higher fixed costs gives Marston more operating leverage, that is, greater benefits (increases in
operating income) if revenues increase but greater risks (decreases in operating income) if
revenues decrease. Marston also needs to consider the skill levels and incentives under the two
alternatives. Sales agents have more incentive compensation and hence may be more motivated
to increase sales. On the other hand, Marston’s own sales force may be more knowledgeable and
skilled in selling the company’s products. That is, the sales volume itself will be affected by who
sells and by the nature of the compensation plan.
3.
Variable costs of marketing
Fixed marketing costs
Operating income = Revenues −
= 15% of Revenues
= \$5,500,000
Variable
Fixed
Fixed
Variable −
− marketing − marketing
manuf. costs manuf. costs
costs
costs
Denote the revenues required to earn \$3,330,000 of operating income by R, then
3-40
R − 0.45R − \$2,870,000 − 0.15R − \$5,500,000 = \$3,330,000
R − 0.45R − 0.15R = \$3,330,000 + \$2,870,000 + \$5,500,000
0.40R = \$11,700,000
R = \$11,700,000 ÷ 0.40 = \$29,250,000
3-44
(15–25 min.) Sales mix, three products.
1. Sales of A, B, and C are in ratio 20,000 : 100,000 : 80,000. So for every 1 unit of A, 5
(100,000 ÷ 20,000) units of B are sold, and 4 (80,000 ÷ 20,000) units of C are sold.
Contribution margin of the bundle = 1 × \$3 + 5 × \$2 + 4 × \$1 = \$3 + \$10 + \$4 = \$17
\$255,000
= 15,000 bundles
Breakeven point in bundles =
\$17
Breakeven point in units is:
Product A:
15,000 bundles × 1 unit per bundle
15,000 units
Product B:
15,000 bundles × 5 units per bundle
75,000 units
Product C:
15,000 bundles × 4 units per bundle
60,000 units
Total number of units to breakeven
150,000 units
Alternatively,
Let Q = Number of units of A to break even
5Q = Number of units of B to break even
4Q = Number of units of C to break even
Contribution margin – Fixed costs = Zero operating income
\$3Q + \$2(5Q) + \$1(4Q) – \$255,000
\$17Q
Q
5Q
4Q
Total
2.
Contribution margin:
A: 20,000 × \$3
B: 100,000 × \$2
C: 80,000 × \$1
Contribution margin
Fixed costs
Operating income
= 0
= \$255,000
=
15,000 (\$255,000 ÷ \$17) units of A
=
75,000 units of B
=
60,000 units of C
= 150,000 units
\$ 60,000
200,000
80,000
\$340,000
255,000
\$ 85,000
3-41
3.
Contribution margin
A: 20,000 × \$3
B: 80,000 × \$2
C: 100,000 × \$1
Contribution margin
Fixed costs
Operating income
\$ 60,000
160,000
100,000
\$320,000
255,000
\$ 65,000
Sales of A, B, and C are in ratio 20,000 : 80,000 : 100,000. So for every 1 unit of A, 4
(80,000 ÷ 20,000) units of B and 5 (100,000 ÷ 20,000) units of C are sold.
Contribution margin of the bundle = 1 × \$3 + 4 × \$2 + 5 × \$1 = \$3 + \$8 + \$5 = \$16
\$255,000
= 15,938 bundles (rounded up)
Breakeven point in bundles =
\$16
Breakeven point in units is:
Product A:
15,938 bundles × 1 unit per bundle
15,938 units
Product B:
15,938 bundles × 4 units per bundle
63,752 units
Product C:
15,938 bundles × 5 units per bundle
79,690 units
Total number of units to breakeven
159,380 units
Alternatively,
Let Q = Number of units of A to break even
4Q = Number of units of B to break even
5Q = Number of units of C to break even
Contribution margin – Fixed costs = Breakeven point
\$3Q + \$2(4Q) + \$1(5Q) – \$255,000
\$16Q
Q
4Q
5Q
Total
= 0
= \$255,000
=
15,938 (\$255,000 ÷ \$16) units of A (rounded up)
=
63,752 units of B
=
79,690 units of C
= 159,380 units
Breakeven point increases because the new mix contains less of the higher contribution
margin per unit, product B, and more of the lower contribution margin per unit, product C.
3-42
3-45 (40 min.) Multi-product CVP and decision making.
1. Faucet filter:
Selling price
Variable cost per unit
Contribution margin per unit
\$80
20
\$60
Pitcher-cum-filter:
Selling price
Variable cost per unit
Contribution margin per unit
\$90
25
\$65
Each bundle contains 2 faucet models and 3 pitcher models.
So contribution margin of a bundle = 2 × \$60 + 3 × \$65 = \$315
Breakeven
Fixed costs
\$945,000
point in
=
=
= 3,000 bundles
Contribution
margin
per
bundle
\$315
bundles
Breakeven point in units of faucet models and pitcher models is:
Faucet models: 3,000 bundles × 2 units per bundle = 6,000 units
Pitcher models: 3,000 bundles × 3 units per bundle = 9,000 units
Total number of units to breakeven
15,000 units
Breakeven point in dollars for faucet models and pitcher models is:
Faucet models: 6,000 units × \$80 per unit = \$ 480,000
Pitcher models: 9,000 units × \$90 per unit =
810,000
Breakeven revenues
\$1,290,000
Alternatively, weighted average contribution margin per unit =
Breakeven point =
\$945,000
= 15,000 units
\$63
2
× 15,000 units = 6,000 units
5
3
Pitcher-cum-filter: × 15,000 units = 9,000 units
5
Breakeven point in dollars
Faucet filter: 6,000 units × \$80 per unit = \$480,000
Pitcher-cum-filter: 9,000 units × \$90 per unit = \$810,000
Faucet filter:
2. Faucet filter:
Selling price
Variable cost per unit
Contribution margin per unit
\$80
15
\$65
3-43
(2 × \$60) + (3 × \$65)
= \$63
5
Pitcher-cum-filter:
Selling price
Variable cost per unit
Contribution margin per unit
\$90
16
\$74
Each bundle contains 2 faucet models and 3 pitcher models.
So contribution margin of a bundle = 2 × \$65 + 3 × \$74 = \$352
Breakeven
Fixed costs
\$945,000 + \$181, 400
point in
=
=
= 3, 200 bundles
Contribution
margin
per
bundle
\$352
bundles
Breakeven point in units of faucet models and pitcher models is:
Faucet models: 3,200 bundles × 2 units per bundle = 6,400 units
Pitcher models: 3,200 bundles × 3 units per bundle = 9,600 units
Total number of units to breakeven
16,000 units
Breakeven point in dollars for faucet models and pitcher models is:
Faucet models: 6,400 bundles × \$80 per unit = \$ 512,000
Pitcher models: 9,600 bundles × \$90 per unit =
864,000
Breakeven revenues
\$1,376,000
Alternatively, weighted average contribution margin per unit =
Breakeven point =
\$945,000 + \$181,400
= 16, 000 units
\$70.40
(2 × \$65) + (3 × \$74)
= \$70.40
5
2
× 16,000 units = 6,400 units
5
3
Pitcher-cum-filter: × 16, 000 units = 9, 600 units
5
Breakeven point in dollars:
Faucet filter: 6,400 units × \$80 per unit = \$512,000
Pitcher-cum-filter: 9,600 units × \$90 per unit = \$864,000
Faucet filter:
3. Let x be the number of bundles for Pure Water Products to be indifferent between
the old and new production equipment.
Operating income using old equipment = \$315 x – \$945,000
Operating income using new equipment = \$352 x – \$945,000 – \$181,400
At point of indifference:
\$315 x – \$945,000 = \$352 x – \$1,126,400
\$352 x – \$315 x = \$1,126,400 – \$945,000
\$37 x = \$181,400
x = \$181,400 ÷ \$37 = 4,902.7 bundles
= 4,903 bundles (rounded)
3-44
Faucet models = 4,903 bundles × 2 units per bundle = 9,806 units
Pitcher models = 4,903 bundles × 3 units per bundle = 14,709 units
Total number of units
24,515 units
Let x be the number of bundles,
When total sales are less than 24,515 units (4,903 bundles), \$315x − \$945,000 >
\$352x − \$1,126,400, so Pure Water Products is better off with the old equipment.
When total sales are greater than 24,515 units (4,903 bundles), \$352x − \$1,126,400 >
\$315x − \$945,000, so Pure Water Products is better off buying the new equipment.
At total sales of 30,000 units (6,000 bundles), Pure Water Products should buy the
new production equipment.
Check
\$352× 6,000 – \$1,126,400 = \$985,600 is greater than \$315× 6,000 –\$945,000 =
\$945,000.
3-46
(20–25 min.) Sales mix, two products.
1. Sales of standard and deluxe carriers are in the ratio of 187,500 : 62,500. So for every 1
unit of deluxe, 3 (187,500 ÷ 62,500) units of standard are sold.
Contribution margin of the bundle = 3 × \$10 + 1 × \$20 = \$30 + \$20 = \$50
\$2, 250, 000
= 45,000 bundles
Breakeven point in bundles =
\$50
Breakeven point in units is:
Standard carrier: 45,000 bundles × 3 units per bundle
135,000 units
Deluxe carrier:
45,000 bundles × 1 unit per bundle
45,000 units
Total number of units to breakeven
180,000 units
Alternatively,
Let Q = Number of units of Deluxe carrier to break even
3Q
= Number of units of Standard carrier to break even
Revenues – Variable costs – Fixed costs = Zero operating income
\$28(3Q) + \$50Q – \$18(3Q) – \$30Q – \$2,250,000 =
\$84Q + \$50Q – \$54Q – \$30Q =
\$50Q =
Q =
3Q =
0
\$2,250,000
\$2,250,000
45,000 units of Deluxe
135,000 units of Standard
The breakeven point is 135,000 Standard units plus 45,000 Deluxe units, a total of 180,000
units.
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2a.
2b.
Unit contribution margins are: Standard: \$28 – \$18 = \$10; Deluxe: \$50 – \$30 = \$20
If only Standard carriers were sold, the breakeven point would be:
\$2,250,000 ÷ \$10 = 225,000 units.
If only Deluxe carriers were sold, the breakeven point would be:
\$2,250,000 ÷ \$20 = 112,500 units
3. Operating income = Contribution margin of Standard + Contribution margin of Deluxe - Fixed costs
= 200,000(\$10) + 50,000(\$20) – \$2,250,000
= \$2,000,000 + \$1,000,000 – \$2,250,000
= \$750,000
Sales of standard and deluxe carriers are in the ratio of 200,000 : 50,000. So for every 1
unit of deluxe, 4 (200,000 ÷ 50,000) units of standard are sold.
Contribution margin of the bundle = 4 × \$10 + 1 × \$20 = \$40 + \$20 = \$60
\$2, 250, 000
= 37,500 bundles
Breakeven point in bundles =
\$60
Breakeven point in units is:
Standard carrier: 37,500 bundles × 4 units per bundle
150,000 units
Deluxe carrier:
37,500 bundles × 1 unit per bundle
37,500 units
Total number of units to breakeven
187,500 units
Alternatively,
Let Q = Number of units of Deluxe product to break even
4Q = Number of units of Standard product to break even
\$28(4Q) + \$50Q – \$18(4Q) – \$30Q – \$2,250,000
\$112Q + \$50Q – \$72Q – \$30Q
\$60Q
Q
4Q
=
=
=
=
=
0
\$2,250,000
\$2,250,000
37,500 units of Deluxe
150,000 units of Standard
The breakeven point is 150,000 Standard +37,500 Deluxe, a total of 187,500 units.
The major lesson of this problem is that changes in the sales mix change breakeven points
and operating incomes. In this example, the budgeted and actual total sales in number of units
were identical, but the proportion of the product having the higher contribution margin declined.
Operating income suffered, falling from \$875,000 to \$750,000. Moreover, the breakeven point
rose from 180,000 to 187,500 units.
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3-47
1.
(20 min.) Gross margin and contribution margin.
Ticket sales (\$24 × 525 attendees)
Variable cost of dinner (\$12a × 525 attendees)
Variable invitations and paperwork (\$1b × 525)
Contribution margin
Fixed cost of dinner
Fixed cost of invitations and paperwork
Operating profit (loss)
a
b
2.
Ticket sales (\$24 × 1,050 attendees)
Variable cost of dinner (\$12 × 1,050 attendees)
Variable invitations and paperwork (\$1 × 1,050)
Contribution margin
Fixed cost of dinner
Fixed cost of invitations and paperwork
Operating profit (loss)
(30 min.)
1.
Contribution margin percentage =
10,975
\$ (5,200)
\$25,200
\$12,600
1,050
9,000
1,975
13,650
11,550
10,975
\$ 575
Ethics, CVP analysis.
=
=
Breakeven revenues
=
=
Revenues − Variable costs
Revenues
\$5,000,000 − \$3,000,000
\$5,000,000
\$2,000,000
= 40%
\$5,000,000
Fixed costs
Contribution margin percentage
\$2,160,000
= \$5,400,000
0.40
If variable costs are 52% of revenues, contribution margin percentage equals 48%
(100% − 52%)
Breakeven revenues
=
=
3.
9,000
1,975
6,825
5,775
\$6,300/525 attendees = \$12/attendee
\$525/525 attendees = \$1/attendee
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2.
\$12,600
\$6,300
525
Fixed costs
Contribution margin percentage
\$2,160,000
= \$4,500,000
0.48
Revenues
Variable costs (0.52 × \$5,000,000)
Fixed costs
Operating income
\$5,000,000
2,600,000
2,160,000
\$ 240,000
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4.
Incorrect reporting of environmental costs with the goal of continuing operations is
unethical. In assessing the situation, the specific “Standards of Ethical Conduct for Management
Accountants” (described in Exhibit 1-7) that the management accountant should consider are
listed below.
Competence
Clear reports using relevant and reliable information should be prepared. Preparing reports on
the basis of incorrect environmental costs to make the company’s performance look better than it
is violates competence standards. It is unethical for Bush not to report environmental costs to
make the plant’s performance look good.
Integrity
The management accountant has a responsibility to avoid actual or apparent conflicts of interest
and advise all appropriate parties of any potential conflict. Bush may be tempted to report lower
environmental costs to please Lemond and Woodall and save the jobs of his colleagues. This
action, however, violates the responsibility for integrity. The Standards of Ethical Conduct
require the management accountant to communicate favorable as well as unfavorable
information.
Credibility
The management accountant’s Standards of Ethical Conduct require that information should be
fairly and objectively communicated and that all relevant information should be disclosed. From
a management accountant’s standpoint, underreporting environmental costs to make
performance look good would violate the standard of objectivity.
Bush should indicate to Lemond that estimates of environmental costs and liabilities should
be included in the analysis. If Lemond still insists on modifying the numbers and reporting lower
environmental costs, Bush should raise the matter with one of Lemond’s superiors. If after taking
all these steps, there is continued pressure to understate environmental costs, Bush should
consider resigning from the company and not engage in unethical behavior.
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3-49
(35 min.) Deciding where to produce.
Peoria
Selling price
Variable cost per unit
Manufacturing
Marketing and distribution
Contribution margin per unit (CMU)
Fixed costs per unit
Manufacturing
Marketing and distribution
Operating income per unit
Moline
\$150.00
\$72.00
14.00
30.00
19.00
86.00
64.00
49.00
\$ 15.00
CMU of normal production (as shown above)
CMU of overtime production
(\$64 – \$3; \$48 – \$8)
1.
Annual fixed costs = Fixed cost per unit × Daily
production rate × Normal annual capacity
(\$49 × 400 units × 240 days;
\$29.50 × 320 units × 240 days)
Breakeven volume = FC ÷ CMU of normal
production (\$4,704,000 ÷ \$64; \$2,265,600 ÷ 48)
2.
Units produced and sold
Normal annual volume (units)
(400 × 240; 320 × 240)
Units over normal volume (needing overtime)
CM from normal production units (normal
annual volume × CMU normal production)
(96,000 × \$64; 76,800 × 48)
CM from overtime production units
(0; 19,200 × \$40)
Total contribution margin
Total fixed costs
Operating income
Total operating income
\$150.00
\$88.00
14.00
15.00
14.50
102.00
48.00
29.50
\$ 18.50
\$64
\$48
61
40
\$4,704,000
\$2,265,600
73,500 units
47,200 units
96,000
96,000
96,000
0
76,800
19,200
\$6,144,000
\$3,686,400
0
6,144,000
4,704,000
\$1,440,000
768,000
4,454,400
2,265,600
\$2,188,800
\$3,628,800
3.
The optimal production plan is to produce 120,000 units at the Peoria plant and 72,000
units at the Moline plant. The full capacity of the Peoria plant, 120,000 units (400 units × 300
days), should be used because the contribution from these units is higher at all levels of
production than is the contribution from units produced at the Moline plant.
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Contribution margin per plant:
Peoria, 96,000 × \$64
Peoria 24,000 × (\$64 – \$3)
Moline, 72,000 × \$48
Total contribution margin
Deduct total fixed costs
Operating income
\$ 6,144,000
1,464,000
3,456,000
11,064,000
6,969,600
\$ 4,094,400
The contribution margin is higher when 120,000 units are produced at the Peoria plant and
72,000 units at the Moline plant. As a result, operating income will also be higher in this case
since total fixed costs for the division remain unchanged regardless of the quantity produced at
each plant.
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