1. CVP analysis allows managers to focus on selling prices, volume, costs, profits, and
sales mix. Many different “what-if” questions can be asked to assess the effect of
4. At the break-even point, all fixed costs are covered. Above the break-even point, only
variable costs need to be covered. Thus, contribution margin per unit is profit per unit,
provided that the unit selling price is greater than the unit variable cost (which it must be
for break-even to be achieved).
5. Variable Cost Ratio = Unit Variable Cost/Price
Contribution Margin Ratio = Contribution Margin/Sales
Contribution Margin Ratio = 1 – Variable Cost Ratio
7. Sales mi
x
is the relative combination of products being sold by a firm. For example, a
sales mix of 3:2 means that three units of one product are sold for every two units of
another product.
8. Packages of products, based on the expected sales mix, are defined as a single product.
Selling price and cost information for this package can then be used to carry out CVP
analysis.
9. This statement is wrong; break-even analysis can be easily adjusted to focus on targeted
profit.
7COST-VOLUME-PROFIT ANALYSIS
DISCUSSION QUESTIONS
CHAPTER 7 Cost-Volume-Profit Analysis
12. Margin of safety is the sales activity in excess of that needed to break even. The higher the
margin of safety, the lower the risk.
13. Operating leverage is the use of fixed costs to extract higher percentage changes in profits as
sales activity changes. It is achieved by increasing fixed costs while lowering variable costs.
Therefore, increased leverage implies increased risk, and vice versa.
14. Sensitivity analysis is a “what-if” technique that examines the impact of changes in underlying
assumptions on an answer. A company can input data on selling prices, variable costs, fixed
costs, and sales mix and set up formulas to calculate break-even points and expected profits.
Then, the data can be varied as desired to see what impact changes have on the expected
profit.
7-1. b
7-5. e
7-6. c
7-7. a
7-8. d
7-9. d Break-Even Units = $7,200/($12 – $3) = 800
MULTIPLE-CHOICE QUESTIONS
CHAPTER 7 Cost-Volume-Profit Analysis
BE 7-13
1.
V
ariable Cost per Unit = Direct Materials + Direct Labor + Variable
Factory Overhead + Variable Selling Expense
3.
Total Per Unit
Sales ($75 × 5,000 helmets)………………………… $375,000 $75.00
Total variable cost ($45 × 5,000 helmets)………
…
225,000 45.00
Total contribution margin………………………
…
$150,000 $30.00
BE 7-14
= $49,500/($75 – $45)
= 1,650 helmets
2.
Total
1.
BRIEF EXERCISES: SET
A
Contribution Margin Income Statement
Head-First Company
Contribution Margin Income Statement
At Break-Even Poin
t
Total Fixed Cost
Unit Contribution Margin
For the Coming Year
Head-First Company
=Break-Even Units
CHAPTER 7 Cost-Volume-Profit Analysis
BE 7-15
= $45/$75
= 0.60, or 60%
3.
Percent
of Sales
Sales ($75 × 5,000 helmets)……………………………
…
$375,000 100%
Total variable cost ($45 × 5,000 helmets)……………
…
225,000 60%
Total contribution margin……………………………
…
$150,000 40%
BE 7-16
1. Break-Even Sales
Dollars
= $49,500/0.40
=
2.
Total
Sales…………………………………………………………………………
…
$123,750
Total variable cost ($123,750 × 0.60)……………………….…………… 74,250
At Break-Even Poin
t
For the Coming Year
Head-First Company
Contribution Margin Income Statement
=Contribution Margin Ratio
$123,750
1. = Variable Cost per Unit
Price
Total Fixed Cost
Variable Cost Ratio
Contribution Margin Income Statement
Head-First Company
CHAPTER 7 Cost-Volume-Profit Analysis
2.
Total
Sales ($75 × 4,380 helmets)……………………………………………
…
$328,500
Total variable cost ($45 × 4,380 helmets)……………………………
…
197,100
Total contribution margin……………………………………………
…
$131,400
…
BE 7-18
= ($49,500 + $81,900)/0.40
=
2.
Total
Sales…………………………………………………………………………
…
$328,500
…
Contribution Margin Ratio
$328,500
At 4,380 Helmets Sold
Head-First Company
Contribution Margin Income Statement
=Sales for Target Income1.
Contribution Margin Income Statement
At 4,380 Helmets Sold
Head-First Company
Total Fixed Cost + Target Income
CHAPTER 7 Cost-Volume-Profit Analysis
BE 7-19
1. Any package with 5 bicycle helmets for every 2 motorcycle helmets is fine. For
example, 5:2, or 10:4, or 30:12. Throughout the rest of this exercise, we will use
5:2.
Package
Unit Unit Unit
Variable Contribution Sales Contribution
Produc
t
Price
–
Cost = Margin × Mix = Margin
Total Fixed Cost
= $58,900/$310
= 190 packages
Break-Even Bicycle Helmets = Number of Packages × Sales Mix Amount
= 190 × 5
= 950
3.
Total
Sales [($75 × 950) + ($220 × 380)]…………………………………………
…
$154,850
Total variable cost [($45 × 950) + ($140 × 380)]…………………………
…
95,950
2.
Contribution Margin Income Statement
At Break-Even Poin
t
Head-First Company
Package Contribution Margin
Break-Even Packages =
CHAPTER 7 Cost-Volume-Profit Analysis
BE 7-20
= ($570,000 – $388,000)/$570,000
=
2.
Total
Sales…………………………………………………………………………
…
$184,466
Total variable cost ($184,466 × 0.6807)………………………………
…
125,566
Total contribution margin……………………………….…………… $ 58,900
Total fixed cost…………………………………………………….………
.
58,900
Operating income………………………………………..……………
…
$0
BE 7-21
Head-First Company
Contribution Margin Income Statement
At Break-Even Sales Dollars
1. Contribution Margin Ratio
Sales – Total Variable Cost
Sales
0.3193*
=
CHAPTER 7 Cost-Volume-Profit Analysis
BE 7-23
1. Percent Change in Operating Income = DOL × Percent Change in Sales
= 1.5 × 10%
= 15%
CHAPTER 7 Cost-Volume-Profit Analysis
BE 7-24
1.
V
ariable Cost per Unit = Direct Materials + Direct Labor + Variable
Factory Overhead + Variable Selling Expense
= $12 + $4 + $2 + $3
= $21
3.
Total Per Unit
BE 7-25
= $78,000/($60 – $21)
= 2,000 pairs
2.
Total
Sales ($60 × 2,000 pairs)……………….…….………….…….……………
…
$120,000
Chillmax Company
Contribution Margin Income Statement
At Break-Even Poin
t
BRIEF EXERCISES: SET B
Chillmax Company
Contribution Margin Income Statement
For the Coming Year
1. =Break-Even Units Total Fixed Cost
Unit Contribution Margin
CHAPTER 7 Cost-Volume-Profit Analysis
BE 7-26
= $21/$60
= 0.35, or 35%
3.
Percent
of Sales
Sales ($60 × 3,500 pairs)………………………………………
…
$210,000 100%
BE 7-27
1. Break-Even Sales
Dollars
= $78,000/0.65
=
2.
Total
Sales……………………………………………………………………………….
.
$120,000
At Break-Even Poin
t
$120,000
=Total Fixed Cost
Contribution Margin Ratio
Chillmax Company
Contribution Margin Income Statement
1. Variable Cost Ratio =
V
ariable Cost per Unit
Price
For the Coming Year
Chillmax Company
Contribution Margin Income Statement
CHAPTER 7 Cost-Volume-Profit Analysis
BE 7-28
2.
Total
Sales ($60 × 4,100 pairs)…………………………………………………………
…
$246,000
Total variable cost ($21 × 4,100 pairs)………………………………………… 86,100
Total contribution margin……………………………………………………
…
$159,900
Total fixed cost……….……………………………………………………………
…
78,000
Operating income……………………………………………………………… $ 81,900
2.
Total
Sales…………………………………………………………………………………
…
$246,000
Total variable cost ($246,000 × 0.35)…………………………………………
…
86,100
…
At 4,100 Pairs of Shoes Sold
Contribution Margin Income Statement
At 4,100 Pairs of Shoes Sold
Chillmax Company
Contribution Margin Income Statement
Chillmax Company
1. Break-Even Units = Total Fixed Cost + Target Income
Unit Contribution Margin
CHAPTER 7 Cost-Volume-Profit Analysis
BE 7-30
1. Any package with 4 pairs of shoes for every 1 carryall is fine. For
example, 4:1, or 8:2, or 24:6. Throughout the rest of this exercise, we will use
4:1.
Package
Unit Unit Unit
Variable Contribution Sales Contribution
Product Price – Cost = Margin × Mix = Margin
= $91,500/$183
= 500 packages
Break-Even Pairs of Shoes = Number of Packages × Sales Mix Amount
= 500 × 4
= 2,000
3.
Total
Sales [($60 × 2,000) + ($36 × 500)]………………………………………
…
$138,000
Total variable cost [($21 × 2,000) + ($9 × 500)]…………………………
…
46,500
Chillmax Company
Contribution Margin Income Statement
At Break-Even Poin
t
2. Break-Even Packages = Package Contribution Margin
Total Fixed Cost
CHAPTER 7 Cost-Volume-Profit Analysis
BE 7-31
= ($210,000 – $81,375)/$210,000
=
* Rounded
2.
Total
Sales…………………………………………………………………………
…
$149,388
Total variable cost ($149,388 × 0.3875)…………………………………
…
57,888
Total contribution margin……………………………….……………
…
$ 91,500
Total fixed cost…………………………………………………….……….
…
91,500
Operating income………………………………………..……………
…
$0
BE 7-32
1. Margin of Safety in Units = Budgeted Units – Break-Even Units
= 3,500 – 2,000
= 1,500
At Break-Even Sales Dollars
Chillmax Company
Contribution Margin Income Statement
0.6125
1. Contribution Margin Ratio = Sales – Total Variable Cost
Sales
*
CHAPTER 7 Cost-Volume-Profit Analysis
*Rounded
BE 7-34
1. Percent Change in Operating Income = DOL × Percent Change in Sales
= 2.3 × 10%
= 23%
CHAPTER 7 Cost-Volume-Profit Analysis
E 7-35
1. Direct materials…………………………………….……………….……
…
$ 4.98
Direct labor………………………………………….……………….……
…
2.10
V
ariable factory overhead………………………….……………….…
…
1.00
V
ariable selling and administrative expense………………………
…
2.00
Unit variable cost………………………………………………………….
…
$10.08
Unit Contribution Margin = Price – Unit Variable Cost
= $24.00 – $10.08
= $13.92
4. Sales ($24 × 3,000)……..……………….……………………….………
…
$72,000
V
ariable cost ($10.08 × 3,000)……..…………………….……………
…
30,240
Total contribution margin…………………………………….……… $41,760
Fixed cost ($26,500 + $15,260).………………….……………….……
…
41,760
Operating income…………………….……………….………………
…
$0
E 7-36
1. At break-even:
Total Fixed Cost = Total Contribution Margin = $349,600
2. Operating Income = (Price × Quantity) – (Variable Cost per Unit × Quantity) –
Fixed Cost
$166,000 = ($120 × 15,600) – (Variable Cost per Unit × 15,600) – $458,000
$166,000 = $1,872,000 – (Variable Cost per Unit × 15,600) – $458,000
V
ariable Cost per Unit × 15,600 = $1,248,000
V
ariable Cost per Unit = $1,248,000/15,600 = $80
EXERCISES
V
CHAPTER 7 Cost-Volume-Profit Analysis
4. Break-Even Units = Total Fixed Cost/(Price – Variable Cost per Unit)
23,600 = $103,840/[Price – (0.56 × Price)]
Price – (0.56 × Price) = $103,840/23,600
Price(1.00 – 0.56) = $4.40
Price = $4.40/(1.00 – 0.56)
Price = $4.40/0.44 = $10.00
O
R
$103,840/0.44 = $236,000
$236,600/23,600 = $10.00
CHAPTER 7 Cost-Volume-Profit Analysis
2.
V
ariable Cost Ratio = $23,760/$88,000 = 0.27, or 27%
O
R
V
ariable Cost Ratio = 1 – Contribution Margin Ratio
= 1.00 – 0.73 = 0.27
= $43,800/0.73 = $60,000
E 7-38
1. Sales ($18.00 × 19,000)………………..………………………..…… $342,000
V
ariable cost ($14.60 × 19,000)…………………….………………
…
277,400
Total contribution margin……………………………………….. $ 64,600
Fixed cost………………………………………………………………
.
68,000
Operating income (loss)………………………….………………
…
$ (3,400)
2. Break-Even Units = $68,000/($18.00 – $14.60) = 20,000
E 7-39
1. Break-Even Units = ($111,425 + $48,350)/($2.75 – $1.65)
= $159,775/$1.10
=
2. Unit variable cost includes all variable costs on a unit basis:
Direct materials…………………………………………………….…
…
$0.37
V
V
145,250
3.
Contribution Margin Ratio
Total Fixed Cost
=Break-Even Sales Revenue
CHAPTER 7 Cost-Volume-Profit Analysis
E 7-39 (Concluded)
Unit variable manufacturing cost includes the variable costs of production
on a unit basis:
Direct materials………………………………………………………
…
$0.37
Direct labor…………………..…………………………………………
…
0.63
V
ariable factory overhead…………………………………………… 0.53
Unit variable manufacturing cost…………………………………
…
$1.53
4. Sales revenue to earn $13,530 = 157,550 × $2.75 = $433,263
E 7-40
1. Break-Even Units = ($245,650 + $297,606)/($8.12 – $4.56) = 152,600
2. Expected sales in units……………………………………………..
…
225,000
Break-even units………………………………………………………. (152,600)
Margin of safety (in units)……………………………………………
.
72,400
…
4. If the price decreases, then the risk facing the company will go up. The
price decrease means that the contribution margin per unit will decrease
and the break-even units will increase. The increase in the break-even units
will lead to a decrease in the margin of safety, as Comer, then, would be
operating closer to the break-even point.
j
CHAPTER 7 Cost-Volume-Profit Analysis
E 7-41
Laertes Ophelia Fortinbras Claudius
Sales $15,000 $15,600 $16,250 $10,600
Total variable cost 5,000 11,700 9,750 5,300
Total contribution margin $10,000 $ 3,900 $ 6,500 $ 5,300
Total fixed cost 9,500 4,000 6,136 4,452
Operating income (loss) $ 500 $ (100) $ 364 $ 848
(Note: Calculated break-even units that include a fractional amount have been
rounded to the nearest whole unit.)
Laertes
Total fixed cost = $10,000 – $500 = $9,500
Units sold = $15,000/$5.00 = 3,000
V
ariable cost per unit = $5,000/3,000 = $1.67 (rounded)
Contribution margin per unit = $5.00 – $1.67 = $3.33
Contribution margin ratio = $10,000/$15,000 = 0.67, or 67% (rounded)
Break-even units = $9,500/$3.33 = 2,853 (rounded)
*
*
*
*
*
*
*
*
V
CHAPTER 7 Cost-Volume-Profit Analysis
E 7-41 (Concluded)
Fortinbras
Sales = 125 × $130.00 = $16,250
Total contribution margin = $16,250 – $9,750 = $6,500
Total fixed cost = $6,500 – $364 = $6,136
V
ariable cost per unit = $9,750/125 = $78.00
Contribution margin ratio = $6,500/125 = $52.00
Break-even units = $6,136/$52.00 = 118
E 7-42
1.
V
ariable Cost Ratio = $302,950/$415,000 = 0.73, or 73%
Contribution Margin Ratio = $112,050/$415,000 = 0.27, or 27%
2. Because all fixed costs are covered at break-even, the contribution margin
portion of any revenue above break-even contributes directly to operating
3. Break-Even Sales Revenue = $64,800/0.27 = $240,000
Sales…………………………………………………………………………… $240,000
V
ariable cost ($240,000 × 0.73)…..……………..….……………………
…
175,200
Contribution margin……………………………………………………
…
$ 64,800
Fixed cost……………..………………………………………………………
…
64,800
Operating income………………………………………………………… $0
…
5. Sales revenue………………..………………………………………………
…
$380,000
Break-even sales……………………………………………………………
…
240,000
Margin of safety………………..…………………………………………
…
$140,000
V