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SOLUTION
(15 min.) CVP analysis, international cost structure differences.
Variable Variable
Sales Price Annual Manufacturing Marketing and Contribution Operating Income
to Retail Fixed Cost per Distribution Cost Margin Breakeven Breakeven for Budgeted Sales
Country Outlets Costs Rug per Rug Per Rug Units Revenues of 80,000 Rugs
(1) (2) (3) (4)
(5) = (1) – (3)
– (4)
(6) = (2)
¸
(5) (6)
´
(1) (7) = [80,000
´
(5)]–(2)
Portugal $250.00 $7,500,000 $45.00 $10.00 $195.00 38,462 $ 9,615,500 $ 8,100,000
Even though Italy has the lowest contribution margin per Rug, it has the lowest breakeven point because
Braided Rugs should move its production to Italy because even though it has the lowest
contribution margin per rug, it also has very low (compared to the other countries) fixed costs. At
Requirement
1
Requirement 2
3-32 Sales mix, new and upgrade customers. Chartz 1-2-3 is a top-selling electronic spreadsheet
product. Chartz is about to release version 5.0. It divides its customers into two groups: new
customers and upgrade customers (those who previously purchased Chartz 1-2-3 4.0 or earlier
versions). Although the same physical product is provided to each customer group, sizable
differences exist in selling prices and variable marketing costs:
The fixed costs of Chartz 1-2-3 5.0 are $16,500,000. The planned sales mix in units is 60% new
customers and 40% upgrade customers.
Required:
1. What is the Chartz 1-2-3 5.0 breakeven point in units, assuming that the planned 60%40%
sales mix is attained?
2. If the sales mix is attained, what is the operating income when 170,000 total units are sold?
3. Show how the breakeven point in units changes with the following customer mixes:
a. New 40% and upgrade 60%
b. New 80% and upgrade 20%
c. Comment on the results.
SOLUTION
(30 min.) Sales mix, new and upgrade customers.
1.
New
Customers
Upgrade
Customers
SP
$195
$115
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.
$16,500,000
$550
Breakeven point in units is:
Sales to new customers: 30,000 bundles 3 units per bundle 90,000 units
Sales to upgrade customers: 30,000 bundles 2 units per bundle 60,000 units
Total number of units to breakeven (rounded) 150,000 units
Alternatively,
Let S= Number of units sold to upgrade customers
Check
Revenues ($195 90,000) + ($115 60,000) $24,450,000
Contribution margin 16,500,000
Operating income $ 0
2. When 170,000 units are sold, mix is:
Units sold to new customers (60% 170,000) 102,000
Units sold to upgrade customers (40% 170,000) 68,000
Contribution margin 18,700,000
3a. At New 40%/Upgrade 60% mix, each bundle contains 2 units sold to new customers and 3
units sold to upgrade customers.
$16,500,000
$500
Breakeven point in units is:
Sales to new customers: 33,000 bundles × 2 unit per bundle 66,000 units
Alternatively,
Let S = Number of units sold to new customers
then 1.5S= Number of units sold to upgrade customers
[$195S + $115 (1.5S)] – [$65S + $35 (1.5S)] – $16,500,000 = OI
367.5S – 117.5S= $16,500,000
250S= $16,500,000
Check
3b. At New 80%/ Upgrade 20% mix, each bundle contains 4 units sold to new customers and 1
unit sold to upgrade customers.
$16,500,000
$600
Breakeven point in units is:
Alternatively,
Let S = Number of units sold to upgrade customers
then 4S= Number of units sold to new customers
[$195 (4S) + $115S] – [$65 (4S) + $35S] – $16,500,000 = OI
895S – 295S= $16,500,000
Check
3c. As Chartz 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:
New
Customers
Upgrade
Customers
Breakeven
Point
Requirement 3(a)
Requirement 1
Requirement 3(b)
40%
60
80
60%
40
20
165,000
150,000
137,500
3-33 Sales mix, three products. The Kenosha Company has three product lines of beer mugs—
A, B, and C—with contribution margins of $5, $4, and $3, respectively. The president foresees
sales of 175,000 units in the coming period, consisting of 25,000 units of A, 100,000 units of B,
and 50,000 units of C. The company’s fixed costs for the period are $351,000.
Required:
1. What is the company’s breakeven point in units, assuming that the given sales mix is
maintained?
2. If the sales mix is maintained, what is the total contribution margin when 175,000 units are
sold? What is the operating income?
3. What would operating income be if the company sold 25,000 units of A, 75,000 units of B,
and 75,000 units of C? What is the new breakeven point in units if these relationships persist
in the next period?
4. Comparing the breakeven points in requirements 1 and 3, is it always better for a company to
choose the sales mix that yields the lower breakeven point? Explain.
SOLUTION
(15–25 min.) Sales mix, three products.
1. Sales of A, B, and C are in ratio 25,000 : 100,000 : 50,000. So for every 1 unit of A, 4
(100,000 ÷ 25,000) units of B are sold, and 2 (50,000 ÷ 25,000) units of C are sold.
2. Contribution margin:
A: 25,000 $5
3. Contribution margin
A: 25,000 $5 $125,000
Contribution margin of the bundle = 1 $5 + 3 $4 + 3 $3 = $5 + $12 + $9 = $26
Breakeven point in bundles =
$351,000
$26
= 13,500 bundles
Breakeven point in units is:
Product A: 13,500 bundles × 1 unit per bundle 13,500 units
Alternatively,
Let Q = Number of units of A to break even
$5Q + $4(3Q) + $3(3Q) – $351,000 = 0
$26Q = $351,000
Q = 13,500 ($351,000 ÷ $26) units of A
3Q = 40,500 units of B
3Q = 40 ,500 units of C
Total = 94 ,500 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.
4. No, it is not always better to choose the sales mix with the lowest breakeven point because
3-34 CVP, not-for-profit. Genesee Music Society is a not-for-profit organization that brings
guest artists to the community’s greater metropolitan area. The music society just bought a small
concert hall in the center of town to house its performances. The lease payments on the concert
hall are expected to be $4,000 per month. The organization pays its guest performers $1,800 per
concert and anticipates corresponding ticket sales to be $4,500 per concert. The music society
also incurs costs of approximately $1,000 per concert for marketing and advertising. The
organization pays its artistic director $33,000 per year and expects to receive $30,000 in
donations in addition to its ticket sales.
Required:
1. If the Genesee Music Society just breaks even, how many concerts does it hold?
2. In addition to the organization’s artistic director, the music society would like to hire a
marketing director for $25,500 per year. What is the breakeven point? The music society
anticipates that the addition of a marketing director would allow the organization to increase
the number of concerts to 41 per year. What is the music society’s operating income/(loss) if it
hires the new marketing director?
3. The music society expects to receive a grant that would provide the organization with an
additional $17,000 toward the payment of the marketing director’s salary. What is the
breakeven point if the music society hires the marketing director and receives the grant?
SOLUTION
CVP, Not for profit
1. Ticket sales per concert $ 4,500
Variable costs per concert:
Fixed costs
Salaries $33,000
Lease payments ($4,000 × 12) 48 ,000
Total fixed costs $81,000
Less donations 30 ,000
Net fixed costs $51 ,000
Less fixed costs
Salaries $58,500
Operating income $ 0
Operating Income if 41 concerts are held
Donations $ 30,000
Less variable costs
Guest performers ($1,800 × 41) $73,800
Less fixed costs
Salaries $58,500
The Music Society would not be able to afford the new marketing director if the number of
concerts were to increase to only 41 events. The addition of the new marketing director would
require the Music Society to hold at least 45 concerts in order to breakeven. If only 41 concerts
were held, the organization would lose $6,800 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 41.
3. Ticket sales per concert $ 4,500
Variable costs per concert:
Guest performers $ 1,800
Marketing and advertising 1 ,000
Total variable costs per concert 2 ,800
Contribution margin per concert $ 1 ,700
Fixed costs
Total fixed costs $106,500
Deduct donations 47 ,000
Net fixed costs $ 59 ,500
Breakeven point in units =
Net fixed costs
Contribution margin per concert
=
$59,500
$1,700
= 35 concerts
Check
Less variable costs
Guest performers ($1,800 × 35) $63,000
Less fixed costs
Salaries $58,500
3-35 Contribution margin, decision making. Welch Men’s Clothing’s revenues and cost data
for 2017 are as follows:
Mr. Welch, the owner of the store, is unhappy with the operating results. An analysis of other
operating costs reveals that it includes $30,000 variable costs, which vary with sales volume, and
$15,000 (fixed) costs.
Required:
1. Compute the contribution margin of Welch Men’s Clothing.
2. Compute the contribution margin percentage.
3. Mr. Welch estimates that he can increase units sold, and hence revenues by 25% by incurring
additional advertising costs of $8,000. Calculate the impact of the additional advertising costs
on operating income.
4. What other actions can Mr. Welch take to improve operating income?
