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 component that is variable with respect to the units sold.
When represented graphically, the behavior 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 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.
3-13 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 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 Contribution
Income
Margin
$1,200
$1,500
200
500
0
300
300
600
Contribution
Margin %
75.0%
25.0%
30.0%
40.0%
(10–15 min.) CVP computations.
1a.
Sales ($60 per unit × 400,000 units)
Variable costs ($50 per unit × 400,000 units)
Contribution margin
$24,000,000
20,000,000
$ 4,000,000
1b.
Contribution margin (from above)
Fixed costs
Operating income
$ 4,000,000
1,600,000
$ 2,400,000
2a.
Sales (from above)
Variable costs ($32 per unit × 400,000 units)
Contribution margin
$24,000,000
12,800,000
$11,200,000
2b.
Contribution margin
Fixed costs
Operating income
$11,200,000
4,800,000
$ 6,400,000
3.
Operating income is expected to increase by $6,400,000 if Mr. Davidson 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. Wilsar’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
= 8% × $1,000 = $80 per ticket
= $35 per ticket
= $80 – $35 = $45 per ticket
= $22,000 a month
Q
=
FC
$22,000
=
CMU
$45 per ticket
= 489 tickets (rounded up)
1b.
Q
=
FC + TOI
$22,000 + $10,000
=
CMU
$45 per ticket
=
$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
=
FC
$22,000
=
CMU
$51 per ticket
= 432 tickets (rounded up)
2b.
Q
=
FC + TOI
$22,000 + $10,000
=
CMU
$51 per ticket
$32,000
$51 per ticket
= 628 tickets (rounded up)
=
3a.
SP
VCU
CMU
FC
Q
= $48 per ticket
= $29 per ticket
= $48 – $29 = $19 per ticket
= $22,000 a month
FC
$22,000
=
=
CMU
$19 per ticket
= 1,158 tickets (rounded up)
3-4
3b.
Q
=
FC + TOI
$22,000 + $10,000
=
CMU
$19 per ticket
=
$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
=
FC
$22,000
=
CMU
$24 per ticket
= 917 tickets (rounded up)
4b.
Q
=
FC + TOI
$22,000 + $10,000
=
CMU
$24 per ticket
=
$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.
3-5
3-19
(20 min.) CVP exercises.
Revenues
$12,500,000G
12,500,000
12,500,000
12,500,000
12,500,000
13,750,000e
11,250,000g
14,375,000i
12,500,000
Orig.
1.
2.
3.
4.
5.
6.
7.
8.
Gstands
Variable
Costs
$10,000,000G
9,625,000
10,375,000
10,000,000
10,000,000
11,000,000f
9,000,000h
11,500,000j
9,200,000l
Contribution
Margin
$2,500,000
2,875,000a
2,125,000b
2,500,000
2,500,000
2,750,000
2,250,000
2,875,000
3,300,000
Fixed
Costs
$2,250,000G
2,250,000
2,250,000
2,430,000c
2,070,000d
2,250,000
2,250,000
2,587,500k
2,430,000m
Budgeted
Operating
Income
$250,000
625,000
–125,000
70,000
180,000
500,000
0
287,500
870,000
for given.
a$2,500,000 × 1.15; b$2,500,000 × 0.85; c$2,250,000 × 1.08; d$2,250,000 × 0.92; e$12,500,000 × 1.10;
f$10,000,000 × 1.10; g$12,500,000 × 0.90; h$10,000,000 × 0.90; i$12,500,000 × 1.15; j$10,000,000 × 1.15;
k$2,250,000 × 1.15; l$10,000,000 × 0.92; m$2,250,000 × 1.08
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 = $65,000 + $75,000 + $12,000 =
Contribution margin per unit = $29,000 – $25,000 – $600 =
$152,000
Monthly fixed costs
=
Breakeven units per month =
=
$3,400 per car
Contribution margin per unit
2. Tax rate
Target net income
$152,000
$ 3,400
45 cars
25%
$69,000
Target net income $69, 000 $69, 000
=
=
=
$92,000
1 - tax rate
(1 − 0.25)
0.75
Quantity of output units Fixed costs + Target operating income $152, 000 + $92, 000
=
=
= 72 cars
required to be sold
Contribution margin per unit
$3, 400
Target operating income =
3-7
3-22 (20–25 min.) CVP analysis, income taxes.
1. 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.
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
b.
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
= $450,000 ÷ $4.80 per customer
= 93,750 customers
3.
Using the shortcut approach:
Unit
⎛
⎞
Change in
⎛
⎞ ⎜contribution⎟
Change in net income = ⎜number of customers⎟ × ⎜
⎟ × (1 – Tax rate)
⎝
⎠
⎝ margin ⎠
= (150,000 – 125,000) × $4.80 × (1 – 0.30)
= $120,000 × 0.7 = $84,000
New net income
= $84,000 + $105,000 = $189,000
The alternative approach is:
Revenues, 150,000 × $8.00
$1,200,000
Variable costs at 40%
480,000
Contribution margin
720,000
Fixed costs
450,000
Operating income
270,000
Income tax at 30%
81,000
Net income
$ 189,000
3-8
3-23
(30 min.) CVP analysis, sensitivity analysis.
1.
SP = $25.00 × (1 – 0.20 margin to bookstore)
= $25.00 × 0.80 = $20.00
VCU = $ 5.00 variable production and marketing cost
2.00 variable author royalty cost (0.10 × $20.00)
$ 7.00
CMU = $20.00 – $7.00 = $13.00 per copy
FC = $ 630,000 fixed production and marketing cost
4,000,000 up-front payment to Washington
$4,630,000
Solution Exhibit 3-23A shows the PV graph.
SOLUTION EXHIBIT 3-23A
3-9
2a.
Breakeven
number of units
FC
CMU
$4,630,000
=
$13.00
=
= 356,154 copies sold (rounded up)
2b.
Target OI =
FC + OI
CMU
$4,630,000 + $3,000,000
$13.00
$7,630,000
=
$13.00
= 586,923 copies sold (rounded up)
=
3a. Decreasing the normal bookstore margin to 10% of the listed bookstore price of $25 has the
following effects:
= $25.00 × (1 – 0.10)
= $25.00 × 0.90 = $22.50
VCU = $ 5.00 variable production and marketing cost
+ 2.25 variable author royalty cost (0.10 × $22.50)
$ 7.25
SP
CMU = $22.50 – $7.25 = $15.25 per copy
Breakeven
FC
=
number of units
CMU
$4,630,000
=
$15.25
= 303,607 copies sold (rounded up)
The breakeven point decreases from 356,154 copies in requirement 2 to 303,607 copies.
3b.
Increasing the listed bookstore price to $32.50 while keeping the bookstore margin at
20% has the following effects:
= $32.50 × (1 – 0.20)
= $32.50 × 0.80 = $26.00
VCU = $ 5.00
variable production and marketing cost
variable author royalty cost (0.10 × $26.00)
+ 2.60
$ 7.60
CMU= $26.00 – $7.60 = $18.40 per copy
SP
3-10
Breakeven
$4,630,000
=
number of units
$18.40
= 251,630 copies sold (rounded up)
The breakeven point decreases from 356,154 copies in requirement 2 to 251,630 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 $4,630,000 while the
contribution margin per unit increases.
3-24
(10 min.) CVP analysis, margin of safety.
Fixed costs
1.
Breakeven point revenues =
Contribution margin percentage
$600,000
Contribution margin percentage =
= 0.40 or 40%
$1,500,000
Selling price − Variable cost per unit
2.
Contribution margin percentage =
Selling price
SP − $15
0.40 =
SP
0.40 SP = SP – $15
0.60 SP = $15
SP = $25
3. Breakeven sales in units = Revenues ÷ Selling price = $1,500,000 ÷ $25 = 60,000 units
Margin of safety in units = sales in units – Breakeven sales in units
= 80,000 – 60,000 = 20,000 units
Revenues, 80,000 units × $25
Breakeven revenues
Margin of safety
$2,000,000
1,500,000
$ 500,000
3-11
3-25
(25 min.) Operating leverage.
1a.
Let Q denote the quantity of cars sold
Breakeven point under Option 1
$3,500Q − $2,800Q = $5,250
$700Q = $5,250
Q = $5,250 ÷ $700 = 8 cars (rounded up)
1b.
2.
Breakeven point under Option 2
$3,500Q − $2,800Q − (0.15 × $3,500Q)
175Q
Q
= 0
= 0
= 0
Operating income under Option 1 = $700Q − $5,250
Operating income under Option 2 = $175Q
Find Q such that $700Q − $5,250 = $175Q
$525Q = $5,250
Q = $5,250 ÷ $525 = 10 cars
Revenues = $3,500 × 10 cars = $35,000
For Q = 10 cars, operating income under both Option 1 and Option 2 = $1,750
3.
For Q > 10, say, 11 cars,
Option 1 gives operating income
Option 2 gives operating income
So Harry’s will prefer Option 1.
= ($700 × 11) − $5,250 = $2,450
= $175 × 11
= $1,925
For Q < 10, say, 9 cars,
Option 1 gives operating income
Option 2 gives operating income
So Harry’s will prefer Option 2.
= ($700 × 9) − $5,250
= $175 × 9
= $1,050
= $1,575
Contribution margin
Operating income
$700 × 10
Under Option 1, degree of operating leverage =
= 4.0
$1,750
$175 × 10
Under Option 2, degree of operating leverage =
= 1.0
$1,750
Degree of operating leverage =
4. The calculations in requirement 3 indicate that when sales are 10 units, a percentage
change in sales and contribution margin will result in 4 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
Sales price
to retail
outlets
(1)
$32.00
32.00
32.00
Variable
Annual
Manufacturing
Fixed
Cost
per Sweater
Costs
(2)
(3)
$ 6,500,000
$ 8.00
4,500,000
5.50
12,000,000
13.00
Variable
Marketing &
Distribution Cost
per Sweater
(4)
$11.00
11.50
9.00
Contribution
Margin
Per Unit
(5)=(1)-(3)-(4)
$13.00
15.00
10.00
(15 min.) CVP analysis, international cost structure differences.
Country
Singapore
Thailand
United States
Breakeven
Breakeven
Units
Revenues
(6)=(2) ÷ (5)
(6) × (1)
500,000 $16,000,000
300,000
9,600,000
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.
3-13
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
3-27
(30 min.) Sales mix, new and upgrade customers.
1.
SP
VCU
CMU
New
Customers
$230
130
100
Upgrade
Customers
$140
80
60
The 70%/30% sales mix implies that, in each bundle, 7 units are sold to new customers and 3
units are sold to upgrade customers.
Contribution margin of the bundle = 7 × $100 + 3 × $60 = $700 + $180 = $880
$15, 000, 000
Breakeven point in bundles =
= 17,045 bundles
$88
Breakeven point in units is:
Sales to new customers:
17,045 bundles × 7 units per bundle 119,315 units
Sales to upgrade customers: 17,045 bundles × 3 units per bundle
51,135 units
Total number of units to breakeven (rounded)
170,450 units
Alternatively,
Let S = Number of units sold to upgrade customers
2.33S = Number of units sold to new customers
Revenues – Variable costs – Fixed costs = Operating income
[$230 (2.33S) + $140S] – [$130 (2.33S) + $80S] – $15,000,000 = OI
$675.9S – $382.9S – $15,000,000 = OI
Breakeven point is 170,479 units when OI = 0 because
$293S
S
2.33S
BEP
=
=
=
=
$15,000,000
51,195 units sold to upgrade customers (rounded)
119,284 units sold to new customers (rounded)
170,479 units
Check
Revenues ($230 × 119,284) + ($140 × 51,195)
Variable costs ($130 × 119,284) + ($80 × 51,195)
Contribution margin
Fixed costs
Operating income (caused by rounding)
2.
$34,602,620
19,602,520
15,000,100
15,000,000
$
100
When 400,000 units are sold, mix is:
Units sold to new customers (70% × 400,000)
280,000
Units sold to upgrade customers (30% × 400,000) 120,000
3-14
Revenues ($230 × 280,000) + ($140 × 120,000)
Variable costs ($130 × 280,000) + ($80 × 120,000)
Contribution margin
Fixed costs
Operating income
3a.
$81,200,000
46,000,000
35,200,000
15,000,000
$20,200,000
At New 60%/Upgrade 40% mix, each bundle contains 3 units sold to new customer and 2
units sold to upgrade customer.
Contribution margin of the bundle = 3 × $100 + 2 × $60 = $300 + $120 = $420
$15, 000, 000
Breakeven point in bundles =
= 35,714 bundles
$42
Breakeven point in units is:
Sales to new customers:
35,714 bundles × 3 units per bundle
107,142 units
Sales to upgrade customers:
35,714 bundles × 2 units per bundle
71,428 units
Total number of units to breakeven
178,570 units
Alternatively,
Let S
= Number of units sold to upgrade customers
Then 1.5S = Number of units sold to new customers
[$230 (1.5S) + $140S] – [$130 (1.5S) + $80S] – $15,000,000 = OI
485S – 275S
= $15,000,000
210S
= $15,000,000
S
=
71,429 units sold to upgrade customers
1.5S
=
107,144 units sold to new customers
BEP
=
178,573 units
Check
Revenues ($230 × 107,144) + ($140 × 71,429)
$34,643,180
Variable costs ($130 × 107,144) + ($80 × 71,429)
19,643,040
Contribution margin
15,000,140
Fixed costs
15,000,000
Operating income (caused by rounding)
$
140
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 × $100 + 1 × $60 = $400 + $60 = $460
$15, 000, 000
= 32,609 bundles (rounded)
Breakeven point in bundles =
$460
Breakeven point in units is:
Sales to new customers:
32,609 bundles × 4 units per bundle
130,436 units
Sales to upgrade customers:
32,609 bundles × 1 unit per bundle
32,609 units
Total number of units to breakeven
163,405 units
3-15
Alternatively,
Let S = Number of units sold to upgrade customers
then 4S = Number of units sold to new customers
[$230 (4S) + $140S] – [$130 (4S) + $80S] – $15,000,000 = OI
1,060S – 600S
= $15,000,000
460S
= $15,000,000
S
=
32,609 units sold to upgrade customers (rounded up)
4S
=
130,436 units sold to new customers (rounded up)
163,045 units
Check
Revenues ($230 × 130,436) + ($140 × 32,609)
Variable costs ($130 × 130,436) + ($80 × 32,609)
Contribution margin
Fixed costs
Operating income (caused by rounding)
$34,565,540
19,565,400
15,000,140
15,000,000
$
140
3c. As MediaPro 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)
3-28
New
Customers
60%
70
80
Upgrade
Customers
40%
30
20
Breakeven
Point
178,570
170,450
163,045
(20 min.) CVP analysis, multiple cost drivers.
1a.
Operating
income
Cost of picture Quantity of ⎞ ⎛ Cost of
Number of ⎞ Fixed
= Revenues − ⎛⎜
×
−⎜
×
⎟−
picture frames ⎟⎠ ⎝ shipment shipments ⎠ costs
⎝ frames
= ($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 × 800) − $240,000 = $312,000
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) − $240,000 = 0
15Q = $300,000
Q = 20,000 picture frames
3-16
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.
3-29 (25 mins) CVP, Not for profit.
1.
Contributions
Fixed costs
Cash available to purchase land
Divided by cost per acre to purchase land
Acres of land PG can purchase
$20,000,000
2,000,000
$18,000,000
÷4,000
4,500 acres
2.
Contributions ($20,000,000 – $6,000,000)
Fixed costs
Cash available to purchase land
Divided by cost per acre to purchase land ($4,000 – $2,000)
Acres of land PG can purchase
$14,000,000
2,000,000
$12,000,000
÷2,000
6,000 acres
On financial considerations alone, SG should take the subsidy because it can purchase
1,500 more acres (6,000 acres – 4,500 acres).
3.
Let the decrease in contributions be $x .
Cash available to purchase land = $20,000,000 – $x – $2,000,000
Cost to purchase land = $4,000 – $2,000 = $2,000
To purchase 4,500 acres, we solve the following equation for x .
PG will be indifferent between taking the government subsidy or not if contributions
decrease by $9,000,000.
3-17
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
3-18
$150,000
60,000
12,000
48,000
10,000
48,000
10,000
338,000
$ 22,000
3-31
(20 min.) Contribution margin, gross margin and margin of safety.
1.
Mirabella Cosmetics
Operating Income Statement, June 2008
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 =
=
= 7,500 units
Contribution margin per unit $4 per unit
Revenues
$100, 000
Selling price =
=
= $10 per unit
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
3-19
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
300,000
400,000
500,000
600,000
700,000
Cost of Current System
$1,000,000 + $40(300,000) = $13,000,000
$1,000,000 + $40(400,000) = $17,000,000
$1,000,000 + $40(500,000) = $21,000,000
$1,000,000 + $40(600,000) = $25,000,000
$1,000,000 + $40(700,000) = $29,000,000
Monthly Number of Orders
300,000
400,000
500,000
600,000
700,000
Cost of Partially Automated System
$5,000,000 + $30(300,000) = $14,000,000
$5,000,000 + $30(400,000) = $17,000,000
$5,000,000 + $30(500,000) = $20,000,000
$5,000,000 + $30(600,000) = $23,000,000
$5,000,000 + $30(700,000) = $26,000,000
Monthly Number of Orders
300,000
400,000
500,000
600,000
700,000
Cost of Fully Automated System
$10,000,000 + $20(300,000) = $16,000,000
$10,000,000 + $20(400,000) = $18,000,000
$10,000,000 + $20(500,000) = $20,000,000
$10,000,000 + $20(600,000) = $22,000,000
$10,000,000 + $20(700,000) = $24,000,000
2. Current System Expected Cost:
$13,000,000 × 0.1 = $ 1,300,000
17,000,000 × 0.25 = 4,250,000
21,000,000 × 0.40 = 8,400,000
25,000,000 × 0.15 = 3,750,000
29,000,000 × 0.10 = 2,900,000
$ 20,600,000
Partially Automated System Expected Cost:
$14,000,000 × 0.1 = $ 1 ,400,000
17,000,000 × 0.25 = 4,250,000
20,000,000 × 0.40 = 8,000,000
23,000,000 × 0.15 = 3,450,000
26,000,000 × 0.1 = 2,600,000
$19,700,000
Fully Automated System Expected Cost:
$16,000,000 × 0.1 = $ 1,600,000
18,000,000 × 0.25 = 4,500,000
20,000,000 × 0.40 = 8,000,000
22,000,000 × 0.15 = 3,300,000
24,000,000 × 0.10 = 2,400,000
$19,800,000
3-20
3. Dawmart should consider the impact of the different systems on its relationship with suppliers.
The interface with Dawmart’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 Dawmart’s supply chain because the cost of the system change would be prohibitive.
Dawmart 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
$4,500
3,600
$ 900
Breakeven (units) = Fixed costs ÷ Contribution margin per package
$540,000
= 600 tour packages
=
$900 per package
2.
Contribution margin ratio =
$900
Contribution margin per package
=
= 20%
$4,500
Selling price
Revenue to achieve target income = (Fixed costs + target OI) ÷ Contribution margin ratio
$540,000 + $90,000
=
= $3,150,000, or
0.20
$540,000 + $90,000
= 700 tour packages
Number of tour packages to earn $90,000 operating income: =
$900
Revenues to earn $90,000 OI = 700 tour packages × $4,500 = $3,150,000.
3.
Fixed costs = $540,000 + $30,000 = $570,000
Breakeven (units) =
Fixed costs
Contribution margin per unit
Fixed costs
Breakeven (units)
$570,000
=
= $950 per tour package
600 tour packages
Contribution margin per unit =
Desired variable cost per tour package = $4,500 – $950 = $3,550
Because the current variable cost per unit is $3,600, the unit variable cost will need to be reduced
by $50 to achieve the breakeven point calculated in requirement 1.
Alternate Method: If fixed cost increases by $30,000, then total variable costs must be
reduced by $30,000 to keep the breakeven point of 600 tour packages.
3-21
Therefore, the variable cost per unit reduction = $30,000 ÷ 600 = $50 per tour package
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
Contribution margin per child
$5,600
= 14 children
$400
Fixed costs + Target operating income
Contribution 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
3-22
3-35
(20–25 min.)
1.
Selling price
Variable costs per unit:
Purchase price
$20.00
Shipping and handling
5.00
Contribution margin per unit (CMU)
CVP analysis.
$34.00
25.00
$ 9.00
$50,000
Fixed costs
=
= 5,556 units
$9.00
Contr. margin per unit
Margin of safety (units) = 10,000 – 5,556 = 4,444 units
Breakeven point in units =
2.
Since Winston is operating above the breakeven point, any incremental contribution
margin will increase operating income dollar for dollar.
Increase in units sales = 15% × 10,000 = 1,500
Incremental contribution margin = $9 × 1,500 = $13,500
Therefore, the increase in operating income will be equal to $13,500.
Winston’s operating income in 2008 would be $40,000 + $13,500 = $53,500.
3.
Selling price
Variable costs:
Purchase price $20 × 125%
Shipping and handling
Contribution margin per unit
Target sales in units =
$34.00
$25.00
5.00
30.00
$ 4.00
$50,000 + $40,000
FC + TOI
=
= 22,500 units
$4
CMU
Target sales in dollars = $34 × 22,500 = $7,650,000
3-23
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 2008
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 2009
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.
= 0
= 13,000 units
= $325,000
Let S = Required sales units to equal 2008 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
3-24
6.
Let A = Amount spent for advertising in 2009
$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
3-37 (25 min.) CVP, sensitivity analysis.
Contribution margin per corkscrew = $250 – 200 = $50
Fixed costs = $50,000
Units sold = Total sales ÷ Selling price = $375,000 ÷ $250 per unit = 1,500 units
1. Sales increase 12%
Sales revenues 1,500 × 1.12 × $250
Variable costs 1,500 × 1.12 × $200
Contribution margin
Fixed costs
Operating income
$420,000
336,000
84,000
50,000
$ 34,000
2. Increase fixed costs $2,000; Increase sales 40%
Sales revenues 1,500 × 1.40 × $250
$525,000
Variable costs 1,500 × 1.40 × $200
420,000
Contribution margin
105,000
Fixed costs ($50,000 + $2,000)
52,000
Operating income
$ 53,000
3. Increase selling price to $300; Sales decrease 25%
Sales revenues 1,500 × 0.75 × $300
$337,500
Variable costs 1,500 × 0.75 × $200
225,000
Contribution margin
112,500
Fixed costs
50,000
Operating income
$ 62,500
4. Increase selling price to $375; Variable costs increase $70 per corkscrew
Sales revenues 1,500 × $375
$562,500
Variable costs 1,500 × $270
405,000
Contribution margin
157,500
Fixed costs
50,000
Operating income
$107,500
Alternative 4 yields the highest operating income. If APP is confident that unit sales will not
decrease despite increasing the selling price, it should choose alternative 4.
3-25
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
Advertising
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
4. Unit variable data (per pair of shoes)
Selling price
Cost of shoes
Sales commissions
Variable cost per unit
Total fixed costs
$
10.50
42,000
$1,260,000
$
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
3-26
$
8.70
41,380 (rounded up)
$1,241,400
5. Pairs sold
50,000
Revenues (50,000 pairs × $30 per pair)
$1,500,000
Total cost of shoes (50,000 pairs × $19.50 per pair)
$ 975,000
Sales commissions on first 40,000 pairs (40,000 pairs × $1.50 per pair) 60,000
Sales commissions on additional 10,000 pairs
[10,000 pairs × ($1.50 + $0.30 per pair)]
18,000
Total variable costs
$1,053,000
Contribution margin
$ 447,000
Fixed costs
360,000
Operating income
$ 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.
3-27
3-39
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
Salaries + Commission Plan
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
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
(30 min.) CVP analysis, shoe stores (continuation of 3-38).
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
3-28
Higher Fixed Salaries Only
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, 2008
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
3-29
$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 assuming fixed rental arrangement = $50 – $30 = $20 per bouquet
Fixed costs = $5,000
Breakeven point = $5,000 ÷ $20 per bouquet = 250 bouquets
Contribution margin assuming $10 per arrangement rental agreement
= $50 – $30 – $10 = $10 per bouquet
Fixed costs = $0
Breakeven point = $0 ÷ $10 per bouquet = 0
(i.e. EB makes a profit no matter how few bouquets it sells)
2. Let x denote the number of bouquets EB must sell for it to be indifferent between the
fixed rent and royalty agreement.
To calculate x we solve the following equation.
$50 x – $30 x – $5,000 = $50 x – $40 x
$20 x – $5,000 = $10 x
$10 x = $5,000
x = $5,000 ÷ $10 = 500 bouquets
For sales between 0 to 500 bouquets, EB prefers the royalty agreement because in this
range, $10 x > $20 x – $5,000. For sales greater than 500 bouquets, EB prefers the fixed
rent agreement because in this range, $20 x – $5,000 > $10 x .
3. If we assume the $5 savings in variable costs applies to both options, we solve the
following equation for x .
$50 x – $25 x – $5,000 = $50 x – $35 x
$25 x – $5,000 = $15 x
$10 x = $5,000
x = $5,000 ÷ $10 per bouquet = 500 bouquets
The answer is the same as in Requirement 2, that is, for sales between 0 to 500
bouquets, EB prefers the royalty agreement because in this range, $15 x > $25 x –
$5,000. For sales greater than 500 bouquets, EB prefers the fixed rent agreement
because in this range, $25 x – $5,000 > $15 x .
4. Fixed rent agreement:
Bouquets
Sold
(1)
Revenue
(2)
200 × $50=$10,000
200
400
400 × $50=$20,000
600
600 × $50=$30,000
800
800 × $50=$40,000
1,000
1,000 × $50=$50,000
Expected value of rent agreement
Fixed
Costs
(3)
$5,000
$5,000
$5,000
$5,000
$5,000
Variable
Costs
(4)
200 × $30=$ 6,000
400 × $30=$12,000
600 × $30=$18,000
800 × $30=$24,000
1,000 × $30=$30,000
3-30
Operating
Income
(Loss)
(5)=(2)–(3)–(4)
Probability
(6)
$ (1,000)
$ 3,000
$ 7,000
$11,000
$15,000
0.20
0.20
0.20
0.20
0.20
Expected
Operating
Income
(7)=(5) × (6)
$ ( 200)
600
1,400
2,200
3,000
$7,000
Royalty agreement:
Bouquets
Sold
(1)
Revenue
(2)
200 × $50=$10,000
200
400
400 × $50=$20,000
600
600 × $50=$30,000
800
800 × $50=$40,000
1,000
1,000 × $50=$50,000
Expected value of royalty agreement
Variable
Costs
(3)
200 × $40=$ 8,000
400 × $40=$16,000
600 × $40=$24,000
800 × $40=$32,000
1,000 × $40=$40,000
Operating
Income
(4)=(2)–(3)
$2,000
$4,000
$6,000
$8,000
$10,000
Probability
(5)
0.20
0.20
0.20
0.20
0.20
Expected
Operating Income
(6)=(4) × (5)
$ 400
800
1,200
1,600
2,000
$6,000
EB should choose the fixed rent agreement because the expected value is higher than the royalty
agreement. EB will lose money under the fixed rent agreement if EB sells only 200 bouquets but
this loss is more than made up for by high operating incomes when sales are high.
3-41 (20-30 min.) CVP, alternative cost structures.
1.
Variable cost per doughnut = $0.20 + $0.10 = $0.30
Contribution margin per doughnut = Selling price –Variable cost per doughnut
= $0.80 – $0.30 = $0.50
Breakeven point = Fixed costs ÷ Contribution margin per doughnut
= $70 ÷ $0.50 = 140 doughnuts (per day)
Fixed costs + Target operating income
Contribution margin per doughnut
$70 + $75
=
= 290 doughnuts
$0.50
3. Contribution margin per doughnut = Selling price – Variable cost per doughnut
= $0.80 – $0.20 = $0.60
Fixed costs = $70 + $20 = $90
Fixed costs
$90
Breakeven point =
=
= 150 doughnuts
Contribution margin per doughnut
$0.60
2.
Target number of doughnuts =
4. Let x be the number of doughnuts for which Dom is indifferent between hiring Jason or
hiring Alan. Dom will be indifferent when the profits under the two alternatives are
equal.
$0.50 x – $70 = $0.60 x – $90
20 = 0.10 x
x = $20 ÷ $0.10 = 200 doughnuts
For sales between 0 and 200 doughnuts, Dom prefers Jason to repackage the
doughnuts because in this range, $0.50 x – $70 > $0.60 x – $50. For sales greater than
200 doughnuts, Dom prefers Alan to repackage the doughnuts because in this range,
$0.60 x – $90 > $0.50 x – $70.
3-31
3-42
(30 min.) CVP analysis, income taxes, sensitivity.
1a.
To break even, Almo Company must sell 500 units. This amount represents the point
where revenues equal total costs.
Let Q denote the quantity of canopies sold.
Revenue
= Variable costs + Fixed costs
$400Q = $200Q + $100,000
$200Q = $100,000
Q = 500 units
Breakeven can also be calculated using contribution margin per unit.
Contribution margin per unit = Selling price – Variable cost per unit = $400 – $200 = $200
Breakeven = Fixed Costs ÷ Contribution margin per unit
= $100,000 ÷ $200
= 500 units
1b.
To achieve its net income objective, Almo Company must sell 2,500 units. This amount
represents the point where revenues equal total costs plus the corresponding operating income
objective to achieve net income of $240,000.
Revenue = Variable costs + Fixed costs + [Net income ÷ (1 – Tax rate)]
$400Q = $200Q + $100,000 + [$240,000 ÷ (1 − 0.4)]
$400 Q = $200Q + $100,000 + $400,000
Q = 2,500 units
2.
To achieve its net income objective, Almo Company should select the first alternative
where the sales price is reduced by $40, and 2,700 units are sold during the remainder of the
year. This alternative results in the highest net income and is the only alternative that equals or
exceeds the company’s net income objective. Calculations for the three alternatives are shown
below.
Alternative 1
Revenues
Variable costs
Operating income
Net income
=
=
=
=
($400 × 350) + ($360a × 2,700) = $1,112,000
$200 × 3,050b = $610,000
$1,112,000 − $610,000 − $100,000 = $402,000
$402,000 × (1 − 0.40) = $241,200
a$400 – $40; b350 units + 2,700 units.
Alternative 2
Revenues
Variable costs
Operating income
Net income
=
=
=
=
($400 × 350) + ($370c × 2,200) = $954,000
($200 × 350) + ($190d × 2,200) = $488,000
$954,000 − $488,000 − $100,000 = $366,000
$366,000 × (1 − 0.40) = $219,600
c$400 – $30; d$200 – $10.
3-32
Alternative 3
Revenues
Variable costs
Operating income
Net income
=
=
=
=
($400 × 350) + ($380e× 2,000) = $900,000
$200 × 2,350f = $470,000
$900,000 − $470,000 − $90,000g = $340,000
$340,000 × (1 − 0.40) = $204,000
e$400 – (0.05 × $400) = $400 – $20; f350 units + 2,000 units; g$100,000 – $10,000
3-43
(30 min.) Choosing between compensation plans, operating leverage.
1. We can recast Secure Seniors’ income statement to emphasize contribution margin, and then
use it to compute the required CVP parameters.
Secure Seniors Corporation
Income Statement
For the Year Ended December 31, 2008
Revenues
Variable Costs
Cost of goods sold—variable
Marketing commissions
Contribution margin
Fixed Costs
Cost of goods sold—fixed
Marketing—fixed
Operating income
Using Sales Agents
$35,000,000
$16,500,000
7,000,000
3,000,000
2,500,000
Contribution margin percentage
($11,500,000 ÷ 35,000,000;
$15,700,000 ÷ $35,000,000)
Breakeven revenues
($5,500,000 ÷ 0.33;
$9,700,000 ÷ 0.45)
Degree of operating leverage
($11,500,000 ÷ $6,000,000;
$15,700,000 ÷ $6,000,000)
Using Own Sales Force
$35,000,000
$16,500,000
23,500,000
2,800,000 19,300,000
$11,500,000
$15,700,000
5,500,000
$6,000,000
3,000,000
6,700,000
9,700,000
$ 6,000,000
33%
45%
$16,666,667
$21,555,556
1.92
2.62
The calculations indicate that at sales of $35,000,000, a percentage change in sales and
contribution margin will result in 1.92 times that percentage change in operating income if Secure
Seniors continues to use sales agents and 2.62 times that percentage change in operating income if
Secure Seniors employs its own sales staff. The higher contribution margin per dollar of sales and
higher fixed costs gives Secure Seniors more operating leverage, that is, greater benefits (increases in
operating income) if revenues increase but greater risks (decreases in operating income) if revenues
decrease. Secure Seniors 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, Secure Seniors’ 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.
2.
3-33
3.
Variable costs of marketing
Fixed marketing costs
Operating income = Revenues −
= 12% of Revenues
= $6,700,000
Variable
Fixed
Variable −
Fixed
− marketing − marketing
manuf. costs manuf. costs
costs
costs
Denote the revenues required to earn $6,000,000 of operating income by R, then
R − 0.45R − $3,000,000 − 0.12R − $6,700,000 = $6,000,000
R − 0.45R − 0.12R = $6,000,000 + $3,000,000 + $6,700,000
0.43R = $15,700,000
R = $15,700,000 ÷ 0.43 = $36,511,628
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
Breakeven point in bundles =
= 15,000 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
= 0
= $255,000
=
15,000 ($255,000 ÷ $17) units of A
=
75,000 units of B
=
60,000 units of C
= 150,000 units
3-34
2.
3.
Contribution margin:
A: 20,000 × $3
B: 100,000 × $2
C: 80,000 × $1
Contribution margin
Fixed costs
Operating income
Contribution margin
A: 20,000 × $3
B: 80,000 × $2
C: 100,000 × $1
Contribution margin
Fixed costs
Operating income
$ 60,000
200,000
80,000
$340,000
255,000
$ 85,000
$ 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
Breakeven point in bundles =
= 15,938 bundles (rounded up)
$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.
3-35
3-45 (40 min.) Multi-product CVP and decision making.
1. Gas oven:
Selling price
Variable cost per unit
Contribution margin per unit
$1,850
1,100
$ 750
Electric oven:
Selling price
Variable cost per unit
Contribution margin per unit
$1,650
650
$1,000
Each bundle contains 1 gas model and 3 electric models.
So contribution margin of a bundle = 1 × $750 + 3 × $1,000 = $3,750
Breakeven
Fixed costs
$15, 000, 000
point in
=
=
= 4, 000 bundles
Contribution
margin
per
bundle
$3,
750
bundles
Breakeven point in units of gas models and electric models is:
Gas models: 4,000 bundles × 1 unit per bundle
= 4,000 units
Electric models: 4,000 bundles × 3 units per bundle = 12,000 units
Total number of units to breakeven
16,000 units
Breakeven point in dollars for gas models and electric models is:
Gas models: 4,000 units × $1,850 per unit
= $ 7,400,000
Electric models: 12,000 units × $1,650 per unit =
19,800,000
Breakeven revenues
$ 27,200,000
Alternatively, weighted average contribution margin per unit
=
(1×$750) + (3×$1,000)
= $937.50
4
Breakeven point =
$15,000,000
= 16,000 units
$937.50
1
× 16,000 units = 4,000 units
4
3
Electric: × 16, 000 units = 12,000 units
4
Breakeven point in dollars
Gas: 4,000 units × $1,850 per unit = $7,400,000
Electric: 12,000 units × $1,650 per unit = $19,800,000
Gas:
3-36
2. Gas oven:
Selling price
Variable cost per unit
Contribution margin per unit
Electric oven:
Selling price
Variable cost per unit
Contribution margin per unit
$1,850
900
$ 950
$1,650
400
$1,250
Each bundle contains 1 gas model and 3 electric models.
So contribution margin of a bundle = 1 × $950 + 3 × $1,250 = $4,700
Breakeven
Fixed costs
$15, 000, 000 + $3, 500, 000
point in
=
=
Contribution margin per bundle
$4, 700
bundles
= 3, 936 bundles
Breakeven point in units of gas models and electric models is:
= 3,936 units
Gas models: 3,936 bundles × 1 unit per bundle
Electric models: 3,936 bundles × 3 units per bundle = 11,808 units
Total number of units to breakeven
15,744 units
Breakeven point in dollars for gas models and electric models is:
Gas models: 3,936 bundles × $1,850 per unit
= $ 7,281,600
Electric models: 11,808 bundles × $1,650 per unit = 19,483,200
Breakeven revenues
$26,764,800
Alternatively,
(1 × $950) + (3 × $1,250)
= $1,175
4
$15,000,000+3,500,000
Breakeven point =
= 15, 745 units
$1,175
1
Gas oven:
× 15,745 units = 3,936 units
4
3
Electric oven: × 15, 745 units = 11,809 units
4
Breakeven point in dollars:
Gas oven: 3,936 units × $1,850 per unit = $7,281,600
Electric oven: 11,809 units × $1,650 per unit = $19,484,850
weighted average contribution margin per unit =
3. Let x be the number of bundles for Ovens Only Incorporated to be indifferent
between the old and new production equipment.
Operating income using old equipment = $3,750 x – $15,000,000
3-37
Operating income using new equipment = $4,700 x – $15,000,000 + $3,500,000
At point of indifference:
$3,750 x – $15,000,000 = $4,700 x – $18,500,000
$4,700 x – $3,750 x = $18,500,000 – $15,000,000
$950 x = $3,500,000
x = $3,500,000 ÷ $950 = 3,684.2 bundles
= 3,684 bundles (rounded)
Gas models = 3,684 bundles × 1 unit per bundle
= 3,684 units
Electric models = 3,684 bundles × 3 units per bundle = 11,052 units
Total number of units
14,736 units
Let x be the number of bundles,
When total sales are less than 14,736 units (3,684 bundles), $3,750x − $15,000,000 >
$4,700x − $18,500,000, so Ovens Only Incorporated is better off with the old
equipment.
When total sales are greater than 14,736 units (3,684 bundles), $4,700x − $18,500,000 >
$3,750x − $15,000,000, so Ovens Only Incorporated is better off buying the new
equipment.
At total sales of 32,000 units (8,000 bundles), Ovens Only Incorporated should buy
the new production equipment.
Check
$4,700 × 8,000 – $18,500,000 = $19,100,000 is greater than $3,750 × 8,000 –
$15,000,000 = $15,000,000.
3-46
(20–25 min.) Sales mix, two products.
1. Sales of standard and deluxe carriers are in the ratio of 150,000 : 50,000. So for every 1
unit of deluxe, 3 (150,000 ÷ 50,000) units of standard are sold.
Contribution margin of the bundle = 3 × $6 + 1 × $12 = $18 + $12 = $30
$1, 200, 000
Breakeven point in bundles =
= 40,000 bundles
$30
Breakeven point in units is:
Standard carrier: 40,000 bundles × 3 units per bundle
120,000 units
Deluxe carrier:
40,000 bundles × 1 unit per bundle
40,000 units
Total number of units to breakeven
160,000 units
Alternatively,
Let Q = Number of units of Deluxe carrier to break even
3Q
= Number of units of Standard carrier to break even
3-38
Revenues – Variable costs – Fixed costs = Zero operating income
$20(3Q) + $30Q – $14(3Q) – $18Q – $1,200,000 =
$60Q + $30Q – $42Q – $18Q =
$30Q =
Q =
3Q =
0
$1,200,000
$1,200,000
40,000 units of Deluxe
120,000 units of Standard
The breakeven point is 120,000 Standard units plus 40,000 Deluxe units, a total of 160,000
units.
2a.
2b.
Unit contribution margins are: Standard: $20 – $14 = $6; Deluxe: $30 – $18 = $12
If only Standard carriers were sold, the breakeven point would be:
$1,200,000 ÷ $6 = 200,000 units.
If only Deluxe carriers were sold, the breakeven point would be:
$1,200,000 ÷ $12 = 100,000 units
3. Operating income = Contribution margin of Standard + Contribution margin of Deluxe - Fixed costs
= 180,000($6) + 20,000($12) – $1,200,000
= $1,080,000 + $240,000 – $1,200,000
= $120,000
Sales of standard and deluxe carriers are in the ratio of 180,000 : 20,000. So for every 1
unit of deluxe, 9 (180,000 ÷ 20,000) units of standard are sold.
Contribution margin of the bundle = 9 × $6 + 1 × $12 = $54 + $12 = $66
$1, 200, 000
= 18,182 bundles (rounded up)
Breakeven point in bundles =
$66
Breakeven point in units is:
Standard carrier: 18,182 bundles × 9 units per bundle
163,638 units
Deluxe carrier:
18,182 bundles × 1 unit per bundle
18,182 units
Total number of units to breakeven
181,820 units
Alternatively,
Let Q = Number of units of Deluxe product to break even
9Q = Number of units of Standard product to break even
$20(9Q) + $30Q – $14(9Q) – $18Q – $1,200,000
$180Q + $30Q – $126Q – $18Q
$66Q
Q
9Q
=
=
=
=
=
0
$1,200,000
$1,200,000
18,182 units of Deluxe (rounded up)
163,638 units of Standard
The breakeven point is 163,638 Standard + 18,182 Deluxe, a total of 181,820 units.
3-39
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 $300,000 to $120,000. Moreover, the
breakeven point rose from 160,000 to 181,820 units.
3-47
1.
(20 min.) Gross margin and contribution margin.
Ticket sales ($25 × 400 attendees)
Variable cost of dinner ($12.50a × 400 attendees)
$5,000
Variable invitations and paperwork ($1.25b × 400)
500
Contribution margin
Fixed cost of dinner
3,000
Fixed cost of invitations and paperwork
2,000
Operating profit (loss)
a
b
2.
$10,000
5,500
4,500
5,000
$ (500)
$5,000/400 attendees = $12.50/attendee
$500/400 attendees = $1.25/attendee
Ticket sales ($25 × 600 attendees)
Variable cost of dinner ($12.50 × 600 attendees)
Variable invitations and paperwork ($1.25 × 600)
Contribution margin
Fixed cost of dinner
Fixed cost of invitations and paperwork
Operating profit (loss)
3-48
(30 min.)
1.
Contribution margin percentage =
$15,000
$ 7,500
750
3,000
2,000
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
3-40
8,250
6,750
5,000
$ 1,750
2.
If variable costs are 52% of revenues, contribution margin percentage equals 48% (100%
− 52%)
Breakeven revenues
=
=
3.
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
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.
3-41
3-49
(35 min.) Deciding where to produce.
Pennsylvania
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
$1,200
200
1,000
250
CMU of normal production (as shown above)
CMU of overtime production
($2,100 – $60; $1,900 – $140)
1.
Annual fixed costs = Fixed cost per unit × Daily
production rate × Normal annual capacity
($1,250 × 245 units × 230 days;
$700 × 200 units × 230 days)
Breakeven volume = FC ÷ CMU of normal
production ($70,437,500 ÷ $2,100;
$32,200,000 ÷ $1,900)
2.
Units produced and sold
Normal annual volume (units)
(245 × 230; 200 × 230)
Units over normal volume (needing overtime)
CM from normal production units (normal
annual volume × CMU normal production)
(56,350 × $2,100; 46,000 × 1,900)
CM from overtime production units
(350 × 2,040; 10,000 × $1,760)
Total contribution margin
Total fixed costs
Operating income
Total operating income
New Jersey
$3,500
1,400
2,100
1,250
$ 850
$3,500
$1,400
200
500
200
1,600
1,900
700
$1,200
$2,100
$1,900
2,040
1,760
$70,437,500
$32,200,000
33,542 units
16,947 Units
56,000
56,000
56,350
350
46,000
10,000
$118,335,000
$87,400,000
714,000
119,049,000
70,437,500
$ 8,611,500
17,600,000
10,500,000
32,200,000
$72,800,000
$24,188,500
3-42
3.
The optimal production plan is to produce 68,600 units at the Pennsylvania plant and
56,000 units at the New Jersey plant. The full capacity of the Pennsylvania plant, 68,600 units
(245 units × 280 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 New Jersey plant.
Contribution margin per plant:
Pennsylvania, 56,000 × $2,100
Pennsylvania 12,600 × ($2,100 – $60)
New Jersey, 56,000 × $1,900
Total contribution margin
Deduct total fixed costs
Operating income
$ 117,600,000
25,704,000
106,400,000
249,704,000
102,637,500
$ 147,066,500
The contribution margin is higher when 68,600 units are produced at the Pennsylvania plant and
56,000 units at the New Jersey 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.
3-43