SOLUTION
(30–40 min.) CVP analysis, income taxes.
1. Revenues – Variable costs – Fixed costs =
rateTax 1
incomenet Target
Alternatively,
Operating income = Revenues – Variable costs – Fixed costs
Net income = Operating income – Income taxes
2. Let Q = Number of units to break even
3. Let X = Net income for 2018
25,000($35.00) – 25,000($18.50) – ($214,500 + $16,500) =
X
1 0.40–
$875,000 – $462,500 – $231,000 =
X
0.60
$181,500 =
X
0.60
X = $108,900
4. Let Q = Number of units to break even with new fixed costs of $146,250
5. Let S = Required sales units to equal 2017 net income
X
X
6. Let A = Amount spent for advertising in 2018
3-42 CVP, sensitivity analysis. The Derby Shoe Company produces its famous shoe, the
Divine Loafer, that sells for $70 per pair. Operating income for 2017 is as follows:
Derby Shoe Company would like to increase its profitability over the next year by at least 25%.
To do so, the company is considering the following options:
Required:
1. Replace a portion of its variable labor with an automated machining process. This would
result in a 20% decrease in variable cost per unit but a 15% increase in fixed costs. Sales
would remain the same.
2. Spend $25,000 on a new advertising campaign, which would increase sales by 10%.
3. Increase both selling price by $10 per unit and variable costs by $8 per unit by using a
higher-quality leather material in the production of its shoes. The higher-priced shoe would
cause demand to drop by approximately 20%.
4. Add a second manufacturing facility that would double Derby’s fixed costs but would
increase sales by 60%.
Evaluate each of the alternatives considered by Derby Shoes. Do any of the options meet or
exceed Derby’s targeted increase in income of 25%? What should Derby do?
SOLUTION
(25 min.) CVP, sensitivity analysis.
Contribution margin per pair of shoes = $70 – $30 = $40
1. Variable costs decrease by 20%; Fixed costs increase by 15%
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2. Increase advertising (fixed costs) by $25,000; Increase sales 20%
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3. Increase selling price by $10.00; Sales decrease 20%; Variable costs increase by $8
Sales revenues 5,000
´
0.80
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($70 + $10) $320,000
4. Double fixed costs; Increase sales by 60%
Sales revenues 5,000
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1.60
´
$70 $560,000
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Alternative 4 yields the highest operating income. Choosing alternative 4 will give Derby
a 20% increase in operating income [($120,000 – $100,000)/$100,000 = 20%], which is less than
For example, Derby can combine actions 1 and 4, automate the machining process and decrease
variable costs by 20% while increasing fixed costs by 15%. This will result in a 38% increase in
operating income as follows:
The point of this problem is that managers always need to consider broader rather than
narrower alternatives to meet ambitious or stretch goals.
3-43 CVP analysis, shoe stores. The HighStep Shoe Company operates a chain of shoe stores
that sell 10 different styles of inexpensive men’s shoes with identical unit costs and selling
prices. A unit is defined as a pair of shoes. Each store has a store manager who is paid a fixed
salary. Individual salespeople receive a fixed salary and a sales commission. HighStep is
considering opening another store that is expected to have the revenue and cost relationships
shown here.
Consider each question independently.
Required:
1. What is the annual breakeven point in (a) units sold and (b) revenues?
2. If 8,000 units are sold, what will be the store’s operating income (loss)?
3. If sales commissions are discontinued and fixed salaries are raised by a total of $15,500,
what would be the annual breakeven point in (a) units sold and (b) revenues?
4. Refer to the original data. If, in addition to his fixed salary, the store manager is paid a
commission of $2.00 per unit sold, what would be the annual breakeven point in (a) units
sold and (b) revenues?
5. Refer to the original data. If, in addition to his fixed salary, the store manager is paid a
commission of $2.00 per unit in excess of the breakeven point, what would be the store’s
operating income if 12,000 units were sold?
SOLUTION
(20–30 min.) CVP analysis, shoe stores.
1. CMU (SP – VCU = $60 – $40) $ 20.00
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2. Pairs sold 8,000
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Total cost of shoes, 8,000
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$37 296,000
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3. Unit variable data (per pair of shoes)
Selling price $ 60.00
Cost of shoes 37.00
Sales commissions 0
CMU, $60 – $37 $ 23
a. Breakeven units, $195,500
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$23 per unit 8,500
b. Breakeven revenues, 8,500 units
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$60 per unit $510,000
4. Unit variable data (per pair of shoes)
Selling price $ 60.00
Cost of shoes 37.00
CMU, $60 – $42 $ 18.00
a. Break even units = $180,000
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$18 per unit 10,000
b. Break even revenues = 10,000 units
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$60 per unit $600,000
5. Pairs sold 12,000
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Contribution margin 234,000
Alternative approach:
Breakeven point in units = 9,000 pairs
Store manager receives commission of $2 on 3,000 (12,000 – 9,000) pairs.
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3-44 CVP analysis, shoe stores (continuation of 3-43). Refer to requirement 3 of Problem
3-43. In this problem, assume the role of the owner of HighStep.
Required:
1. As owner, which sales compensation plan would you choose if forecasted annual sales of the
new store were at least 10,000 units? What do you think of the motivational aspect of your
chosen compensation plan?
2. Suppose the target operating income is $69,000. How many units must be sold to reach the
target operating income under (a) the original salary-plus-commissions plan and (b) the
higher-fixed-salaries-only plan? Which method would you prefer? Explain briefly.
3. You open the new store on January 1, 2017, with the original salary-plus-commission
compensation plan in place. Because you expect the cost of the shoes to rise due to inflation,
you place a firm bulk order for 11,000 shoes and lock in the $37 price per unit. But toward
the end of the year, only 9,500 shoes are sold, and you authorize a markdown of the
remaining inventory to $50 per unit. Finally, all units are sold. Salespeople, as usual, get paid
a commission of 5% of revenues. What is the annual operating income for the store?
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SOLUTION
(30 min.) CVP analysis, shoe stores (continuation of 3-43).
1. For an expected volume of 10,000 pairs, the owner would be inclined to choose the
higher-fixed-salaries-only plan because income would be higher by $14,500 compared to the
salary-plus-commission plan.
2. Let TQ = Target number of units
For the salary-only plan,
$60TQ – $37TQ – $195,500 = $69,000
For the salary-plus-commission plan,
$60TQ – $40TQ – $180,000 = $69,000
The decision regarding the salary plan depends heavily on predictions of demand and the
effect that the different compensation plans have on sales as discussed in requirement 1. For
instance, the salary plan offers the same operating income at 11,500 units as the commission plan
offers at 12,450 units.
3. HighStep Shoe Company
Operating Income Statement, 2017
Revenues (9,500 pairs
´
$60) + (1,500 pairs
´
$50) $645,000
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3-45 Alternate cost structures, uncertainty, and sensitivity analysis. Corporate Printing
Company currently leases its only copy machine for $1,500 a month. The company is considering
replacing this leasing agreement with a new contract that is entirely commission based. Under the
new agreement, Corporate would pay a commission for its printing at a rate of $20 for every 500
pages printed. The company currently charges $0.20 per page to its customers. The paper used in
printing costs the company $0.05 per page and other variable costs, including hourly labor,
amount to $0.10 per page.
Required:
1. What is the company’s breakeven point under the current leasing agreement? What is it under
the new commission-based agreement?
2. For what range of sales levels will Corporate prefer (a) the fixed lease agreement and (b) the
commission agreement?
3. Do this question only if you have covered the chapter appendix in your class. Corporate
estimates that the company is equally likely to sell 20,000, 30,000, 40,000, 50,000, or 60,000
pages of print. Using information from the original problem, prepare a table that shows the
expected profit at each sales level under the fixed leasing agreement and under the
commission-based agreement. What is the expected value of each agreement? Which
agreement should Corporate choose?
SOLUTION
(40 min.) Alternative cost structures, uncertainty, and sensitivity analysis.
1. Contribution margin per
2. Let
x
denote the number of pages Corporate Printing must sell for it to be indifferent
between the fixed leasing agreement and commission based agreement.
To calculate
x
we solve the following equation.
x
For sales between 0 to 37,500 pages, Corporate Printing prefers the commission-based
agreement because in this range, $0.01
x
> $0.05
x
– $1,500. For sales greater than
x
x
3. Fixed leasing agreement
Pages Sold
(1)
Revenue
(2)
Variable
Costs
(3)
Fixed
Costs
(4)
Operating
Income
(Loss)
(5) = (2) – (3) – (4)
Probability
(6)
20,000
20,000 $.20=$ 4,000 20,000 $.15=$3,000 $1,500
$ (500) 0.20
30,000 $.20=$ 6,000 30,000 $.15=$4,500 $1,500
Expected value of fixed leasing agreement
Commission-based leasing agreement:
Pages
Sold
(1)
Revenue
(2)
Variable
Costs
(3)
Operating
Income
(4) = (2) –(3)
Probability
(5)
Expected
Operating
Income
(6)=(4) (5)
20,000
20,000 $.20=$ 4,000 20,000 $.19= $3,800
$200 0.20 $ 40
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´
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x
x
30,000 $.20=$ 6,000 30,000 $.19= $5,700
Corporate Printing should choose the fixed cost leasing agreement because the expected value is
3-46 CVP, alternative cost structures. Classical Glasses operates a kiosk at the local mall,
selling sunglasses for $30 each. Classical Glasses currently pays $1,000 a month to rent the
space and pays two full-time employees to each work 160 hours a month at $10 per hour. The
store shares a manager with a neighboring kiosk and pays 50% of the manager’s annual salary of
$60,000 and benefits of $12,000. The wholesale cost of the sunglasses to the company is $10 a
pair.
Required:
1. How many sunglasses does Classical Glasses need to sell each month to break even?
2. If Classical Glasses wants to earn an operating income of $5,300 per month, how many
sunglasses does the store need to sell?
3. If the store’s hourly employees agreed to a 15% sales-commission-only pay structure,
instead of their hourly pay, how many sunglasses would Classical Glasses need to sell to
earn an operating income of $5,300?
4. Assume Classical Glasses pays its employees hourly under the original pay structure, but is
able to pay the mall 10% of its monthly revenue instead of monthly rent. At what sales levels
would Classical Glasses prefer to pay a fixed amount of monthly rent, and at what sales
levels would it prefer to pay 10% of its monthly revenue as rent?
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