SOLUTION
(20 min.) CVP exercises.
Revenues
Variable
Costs
Contribution
Margin
Fixed
Costs
Budgeted
Operating
Income
Orig. $11,000,000G$7,500,000G$3,500,000 $3,000,000G$500,000
1. 11,000,000 7,150,000 3,850,000a3,000,000 850,000
2. 11,000,000 7,850,000 3,150,000b3,000,000 150,000
9. Alternative 1, a 10% increase in contribution margin holding revenues constant, yields the highest budgeted operating income
3-25 CVP exercises. The Doral Company manufactures and sells pens. Currently, 5,000,000 units are sold per year at $0.50 per unit.
Fixed costs are $900,000 per year. Variable costs are $0.30 per unit.
Consider each case separately:
Required:
1. a. What is the current annual operating income?
b. What is the current breakeven point in revenues?
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Compute the new operating income for each of the following changes:
2. A $0.04 per unit increase in variable costs
3. A 10% increase in fixed costs and a 10% increase in units sold
4. A 20% decrease in fixed costs, a 20% decrease in selling price, a 10% decrease in variable cost per unit, and a 40% increase in
units sold
Compute the new breakeven point in units for each of the following changes:
4. A 10% increase in fixed costs
5. A 10% increase in selling price and a $20,000 increase in fixed costs
SOLUTION
(20 min.) CVP exercises.
1a. [Units sold (Selling price – Variable costs)] – Fixed costs = Operating income
1b. Fixed costs ÷ Contribution margin per unit = Breakeven units
or,
Contribution margin ratio =
price Selling
costs Variable price Selling –
=
$0.50
$0.30 – $0.50
= 0.40
Fixed costs ÷ Contribution margin ratio = Breakeven revenues
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3. [5,000,000 (1.1) ($0.50 – $0.30)] – [$900,000 (1.1)] = $ 110,000
3-26 CVP analysis, income taxes. Westover Motors is a small car dealership. On average, it sells a car for $32,000, which it
purchases from the manufacturer for $28,000. Each month, Westover Motors pays $53,700 in rent and utilities and $69,000 for
salespeople’s salaries. In addition to their salaries, salespeople are paid a commission of $400 for each car they sell. Westover Motors
also spends $10,500 each month for local advertisements. Its tax rate is 40%.
Required:
1. How many cars must Westover Motors sell each month to break even?
2. Westover Motors has a target monthly net income of $69,120. What is its target monthly operating income? How many cars
must be sold each month to reach the target monthly net income of $69,120?
SOLUTION
(10 min.) CVP analysis, income taxes.
Target net income $69,120 $69,120
1 tax rate (1 0.40) 0.60
= = =
– –
Fixed costs + Target operating income $133, 200 $115, 200
Contribution margin per unit $3,600
+
= =
3-27 CVP analysis, income taxes. The Home Style Eats has two restaurants that are open 24 hours a day. Fixed costs for the two
restaurants together total $430,500 per year. Service varies from a cup of coffee to full meals. The average sales check per customer is
$8.75. The average cost of food and other variable costs for each customer is $3.50. The income tax rate is 36%. Target net income is
$117,600.
Required:
1. Compute the revenues needed to earn the target net income.
2. How many customers are needed to break even? To earn net income of $117,600?
3. Compute net income if the number of customers is 170,000.
SOLUTION
(20–25 min.) CVP analysis, income taxes.
1. Variable cost percentage is $3.50 $8.75 = 40%
Let R = Revenues needed to obtain target net income
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or,
Fixed costs + Target operating income
Target revenues Contribution margin percentage
=
Target net income $117,600
Fixed costs + $430,000
1 Tax rate 1 0.36
Target revenues $1,023,750
Contribution margin percentage 0.60
+
– –
= = =
Proof: Revenues $1,023,750
Variable costs (at 40%) 409,500
2.a. Customers needed to break even:
Contribution margin per customer = $8.75 – $3.50 = $5.25
2.b. Customers needed to earn net income of $117,600:
3. Using the shortcut approach:
Change in net income =
( )
Change in Unit
number of contribution 1 Tax rate
customers margin
æ ö æ ö
ç ÷ ç ÷
´ ´ –
ç ÷ ç ÷
è ø è ø
Alternatively, with 170,000 customers,
Operating income = Number of customers Selling price per customer
– Number of customers Variable cost per customer – Fixed costs
The alternative approach is:
Revenues, 170,000 $8.75 $1,487,500
Variable costs at 40% 595,000
3-28 CVP analysis, sensitivity analysis. Perfect Fit Jeans Co. sells blue jeans wholesale to major retailers across the country. Each
pair of jeans has a selling price of $50 with $35 in variable costs of goods sold. The company has fixed manufacturing costs of
$2,250,000 and fixed marketing costs of $250,000. Sales commissions are paid to the wholesale sales reps at 10% of revenues. The
company has an income tax rate of 20%.
Required:
1. How many jeans must Perfect Fit sell in order to break even?
2. How many jeans must the company sell in order to reach:
a. a target operating income of $420,000?
b. a net income of $420,000?
3. How many jeans would Perfect Fit have to sell to earn the net income in requirement 2b if: (Consider each requirement
independently.)
a. the contribution margin per unit increases by 10%.
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b. the selling price is increased to $51.50.
c. the company outsources manufacturing to an overseas company increasing variable costs per unit by $2.00 and saving 70% of
fixed manufacturing costs.
SOLUTION
CVP analysis, sensitivity analysis.
1. CMU = $50−$35−(0.10 × $50) = $10
Q =
CMU
FC
=
$2,500,000
$10 per pair
= 250,000 pairs
Note: No income taxes are paid at the breakeven point because operating income is $0.
2a. Q =
CMU
TOI FC
=
=
$2,920,000
$10 per pair
Target net income $420,000 $420,000
1 tax rate (1 0.20) 0.80
= = =
– –
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Quantity of output units
required to be sold
=
Fixed costs + Target operating income $2,500,000 $525,000
Contribution margin per unit $10
+
=
= 302,500 pairs
3a. Contribution margin per unit increases by 10%
Contribution margin per unit = $10 × 1.10 = $11
Quantity of output units
required to be sold
=
Fixed costs + Target operating income $2,500,000 $525,000
Contribution margin per unit $11
+
=
= 275,000 pairs
The net income target in units decreases from 302,500 pairs in requirement 2b to 275,000 pairs.
3b. Increasing the selling price to $51.50
Quantity of output units
required to be sold
=
Fixed costs + Target operating income $2,500,000 $525,000
Contribution margin per unit $11.35
+
=
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3c. Increase variable costs by $2 per unit and decrease fixed manufacturing costs by 70%.
Quantity of output units
required to be sold
=
Fixed costs + Target operating income $925, 000 $525,000
Contribution margin per unit $8
+
=
3-29 CVP analysis, margin of safety. Suppose Morrison Corp.’s breakeven point is revenues of $1,100,000. Fixed costs are $660,000.
Required:
1. Compute the contribution margin percentage.
2. Compute the selling price if variable costs are $16 per unit.
3. Suppose 75,000 units are sold. Compute the margin of safety in units and dollars.
4. What does this tell you about the risk of Morrison making a loss? What are the most likely reasons for this risk to increase?
SOLUTION
(10 min.) CVP analysis, margin of safety.
1. Breakeven point revenues =
percentagemargin on Contributi
costs Fixed
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$660,000
$1,100,000
2. Contribution margin percentage =
price Selling
unit per cost Variable price Selling
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
= 75,000 – 27,500 = 47,500 units
3. The risk of making a loss is low. Sales would need to decrease by 47,500 units ÷ 75,000 units = 63.33% before Morrison Corp.
3-30 Operating leverage. Cover Rugs is holding a 2-week carpet sale at Josh’s Club, a local warehouse store. Cover Rugs plans to
sell carpets for $950 each. The company will purchase the carpets from a local distributor for $760 each, with the privilege of
returning any unsold units for a full refund. Josh’s Club has offered Cover Rugs two payment alternatives for the use of space.
Option 1: A fixed payment of $7,410 for the sale period
Option 2: 10% of total revenues earned during the sale period
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Assume Cover Rugs will incur no other costs.
Required:
1. Calculate the breakeven point in units for (a) Option 1 and (b) Option 2.
2. At what level of revenues will Cover Rugs earn the same operating income under either option?
a. For what range of unit sales will Cover Rugs prefer Option 1?
b. For what range of unit sales will Cover Rugs prefer Option 2?
3. Calculate the degree of operating leverage at sales of 65 units for the two rental options.
4. Briefly explain and interpret your answer to requirement 3.
SOLUTION
(25 min.) Operating leverage.
1a. Let Q denote the quantity of carpets sold
Breakeven point under Option 1
1b. Breakeven point under Option 2
2. Operating income under Option 1 = $190Q $7,410
Operating income under Option 2 = $95Q
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For Q = 78 carpets, operating income under both Option 1 ($190 × 78 – $7,410) and Option 2 ($95 × 78) = $7,410
For Q > 78, say, 79 carpets,
So Color Rugs will prefer Option 1.
For Q < 78, say, 77 carpets,
So Color Rugs will prefer Option 2.
3. Degree of operating leverage =
Contribution margin
Operating income
Contribution margin per unit Quantity of carpets sold
Operating income
´
=
4. The calculations in requirement 3 indicate that when sales are 65 units, a percentage change in sales and contribution margin will
result in 2.5 times that percentage change in operating income for Option 1, but the same percentage change in operating income for
3-31 CVP analysis, international cost structure differences. Braided Rugs, Inc., is considering three possible countries for the sole
manufacturing site of its newest area rug: Italy, Portugal, and Thailand. All area rugs are to be sold to retail outlets in the United States
for $250 per unit. These retail outlets add their own markup when selling to final customers. Fixed costs and variable cost per unit
(area rug) differ in the three countries.
Required:
1. Compute the breakeven point for Braided Rugs, Inc., in each country in (a) units sold and (b) revenues.
2. If Braided Rugs, Inc., plans to produce and sell 80,000 rugs in 2017, what is the budgeted operating income for each of the three
manufacturing locations? Comment on the results.
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