CHAPTER 20
COST-VOLUME-PROFIT ANALYSIS
OVERVIEW OF EXERCISES, PROBLEMS, CASES,
AND INTERNET ASSIGNMENT
Exercises
Topic
20–1
20–2
20–3
20–4
20–5
20–6
20–7
20–8
20–9
Terminology
Cost behavior patterns
Cost classifications
High-low method
Using a cost formula
Using a cost formula
Computing required sales volume
Computing required sales volume
Contribution margin ratio and margin
of safety
Contribution margin and sales volume
Relating contribution margin ratio to
prices
Computing break-even
Cost-volume-profit relationships
Evaluating a marketing strategy
Selecting an activity base
Ethical and behavioral implications of
CVP
20–10
20–11
20–12
20–13
20–14
20–15
20–16
Problems
20–1
20–2
20–3
20–4
20–5
20–6
20–7
20–8
20–9
20–10
20–11
Using cost-volume-profit formulas
Using cost-volume-profit formulas
Setting sales prices
Estimating costs and profits
Preparing a break-even graph
Preparing a break-even graph
Understanding break-even
relationships
Preparing and using a break-even
graph
Changes in costs
Changes in costs and volume
CVP with multiple products
Learning
Objectives
1, 2, 4
1
1
1
1
4, 5
4, 5
4, 5, 6
4, 5
4, 5, 6
1, 4, 5, 6
Characteristics
Conceptual
Conceptual
Conceptual
Mechanical
Conceptual
Conceptual, mechanical
Mechanical
Mechanical
Mechanical
Mechanical
Mechanical
4, 5, 6
1, 4
7
1
5, 6, 7
Mechanical
Mechanical, conceptual
Mechanical, analytical
Conceptual
Conceptual
4, 5, 6
4, 5, 6
4–7
1, 4, 5
3–6
3, 4, 6
1, 2, 4, 5, 6
Mechanical
Mechanical
Mechanical, analytical
Mechanical, analytical
Mechanical, analytical
Mechanical, analytical
Analytical
3–7
Mechanical, analytical
4, 5, 6
4, 6
4, 5, 6
Analytical
Mechanical, analytical
Mechanical, analytical
Solutions Manual Vol. II, Financial and Managerial Accounting 13/e, Williams et al
131
Cases
20–1
20–2
Topic
CVP from multiple perspectives
Evaluating marketing strategies
Learning
Objectives
1
1, 4–7
Characteristics
Conceptual
Conceptual, analytical
Business Week
Assignment
20–3
Business Week assignment: CostVolume-Profit Relationships
1, 4, 6, 7
Conceptual, real, writing
4
Mechanical, conceptual
Internet
Assignment
20–1
Gross margin and contribution margin
DESCRIPTIONS OF PROBLEMS, CASES,
AND INTERNET ASSIGNMENT
Below are brief descriptions of each problem, case, and the Internet assignment. These descriptions are
accompanied by the estimated time (in minutes) required for completion and by a difficulty rating. The time
estimates assume use of the partially filled-in working papers.
Problems
20–1
Murder to Go!
Student is asked to compute contribution margin ratio, break-even sales volume, and several other cost-volume-profit measurements. Math is kept simple
to emphasize underlying relationships. Well-suited to a classroom quiz.
20 Easy
20–2
Arrow Products
Student is asked to analyze the impact of two alternative investments on
operating income. Contribution margin ratio must be used to calculate the
percentage increase in sales revenue needed to make both investments equally
attractive.
20 Easy
20–3
Thermal Tent, Inc.
Use of cost-volume-profit relationships in a pricing decision. Student is to
compute the unit sales prices necessary to achieve a target operating income.
Also determine whether the company can break even if sales price is reduced
to achieve market penetration.
25 Medium
20–4
Blaster Corporation
Illustrates a pricing decision: compute the unit sales price necessary to
achieve a target income at a given unit sales volume. Also compute the
number of units that must be sold annually to break even at an alternative unit
sales price.
25 Medium
132
© The McGraw-Hill Companies, Inc., 2005
20–5
Stop-n-Shop
Profit-volume analysis for a parking lot. Draw a profit-volume graph on an
annual basis. Compute the contribution margin and break-even point.
Consider the effect of a change in employee compensation and determine
sales necessary to produce a given income.
30 Medium
20–6
Rainbow Paints
Draw a cost-volume-profit graph for a paint store. Compute the break-even sales
volume and the operating income likely to result at the highest and lowest
expected sales volume.
30 Medium
20–7
EasyWriter
Calculate changes in profit resulting from additional units begin sold.
Forecast the margin of safety and operating loss. This is an excellent problem
to challenge students’ understanding of contribution margin concepts.
25 Easy
20–8
Simon Teguh
Draw a monthly cost-volume-profit graph for a vending machine business.
Determine the break-even point and the sales volume needed to provide the
owner with a given return on investment. Also consider the effect of a change
in costs upon the break-even point.
40 Strong
20–9
Precision Systems
Compute the increase in selling price necessary to maintain contribution
margin ratio after increase in direct labor cost. Compute sales volume after
wage increase in order to earn a given net income. Consider the effect of
expansion on maximum income that can be earned.
30 Strong
20–10
Percula Farms
Students must analyze two alternative production strategies and determine
which factors or costs have the greatest influence on operating income. Given
two investment options, students must first intuitively decide which should
result in the greatest increase to operating income, and then perform
calculations to confirm their answer.
35 Strong
20–11
Lifefit Products
Calculate break-even in dollars and in units for a multiple product company.
Determine operating income required for a desired margin of safety. Determine sales level required for a desired level of income if fixed costs are
reduced.
35 Strong
Solutions Manual Vol. II, Financial and Managerial Accounting 13/e, Williams et al
133
Cases
20–1
Multiple Perspectives—Attend Our Seminar
Students play the role of a cost-volume-profit seminar leader. They are asked
to motivate individuals to attend their seminar by showing them how the
information can be of benefit. This is a good group problem that encourages
students to think beyond the mechanics of cost-volume-profit analysis.
20 Medium
20–2
Don’t Mess with the Purple Cow
Students are asked to evaluate two alternative marketing proposals and make a
recommendation to management. The problem contains an interesting twist:
neither proposal is as profitable as the status quo—but students’ attention is
not specifically directed toward this vital issue. A lesson in the fact that reallife problems do not come with “instructions” that make the answers clear.
40 Strong
Business Week Assignment
20–3
Business Week Assignment: Cost-Volume-Profit at Puma AG
Students evaluate information provided in a Business Week article about the
product mix strategy of Puma. That mix strategy is related to cost-volumeprofit relationships.
20 Medium
Internet Assignment
20–1
134
Ford Motor Company
Using information contained in the annual report, the student is asked to
calculate the average manufacturing cost and sales revenue per vehicle. The
student is also asked the conceptual difference between contribution margin
and gross margin and whether contribution margin can be calculated from
annual report data.
30 Medium
© The McGraw-Hill Companies, Inc., 2005
SUGGESTED ANSWERS TO DISCUSSION QUESTIONS
1. It is important for management to understand cost-volume-profit relationships in order to do a better
job of planning business operations. Cost-volume-profit analysis is a useful tool for forecasting the
impact of various strategies upon operating income.
2. An activity base is a measure of a type of business activity that “drives” variable costs. The activity
base allows us to quantify the expected relationships between variable costs and the underlying type of
business activity, such as units of production, total sales, or quantities of materials used in production.
These relationships, in turn, assist us in evaluating the reasonableness of the costs incurred in prior
periods and also in forecasting future costs at various levels of business activity.
3. a. Total variable costs increase in approximate proportion to an increase in activity.
b. As total variable costs rise in approximate proportion to an increase in activity, variable costs per
unit of activity remain relatively constant.
4. a. Total fixed costs tend to remain constant despite increases in the level of business activity—so
long as the level of activity remains within the relevant range.
b. Because total fixed costs remain constant, fixed costs per unit of activity decline as the volume of
activity increases. In short, the fixed costs are spread over a greater number of units of activity—
therefore, lower fixed costs per unit.
5. Two factors make the simplifying assumption of straight-line cost-volume relationships useful. First,
unusual patterns of cost behavior (stair-step or curvilinear) tend to offset one another when individual
cost elements are combined into total cost figures. Second, most managerial decisions are based on
projected volume variations within a fairly narrow range. Within this relevant range, straight-line
cost-volume relationships are often good approximations of actual operating conditions.
6. The relevant range represents the operating levels (for example, between 40% and 80% of full
capacity) over which output is likely to vary and for which the assumptions made about cost behavior
are reasonably realistic. When the level of activity falls outside the relevant range, assumptions as to
the total amount of fixed costs, the amount of variable costs per unit, and the degree of variability of
semivariable costs may have to be changed.
7. a. Under the high-low method, the levels of a semivariable cost and of the related activity base are
observed at the highest and lowest points of activity within the relevant range. The variable
portion of the semivariable cost is then determined by dividing the change in the semivariable cost
by the change in the activity base between these high and low measurement points. (This is the
slope of the line between these two points.)
b. The fixed portion of the semivariable cost is determined by starting with the total semivariable
cost at either the high or low level of activity, and subtracting the variable portion of the cost as
computed at that level of activity. (The fixed portion is the intersection of the line with the y-axis.)
8. a. The contribution margin is the dollar amount by which revenue exceeds variable costs. Thus, it is
the amount of revenue that is available to cover fixed costs and to contribute to operating income.
Unit contribution margin = unit sales prices  variable costs per unit.
b. The contribution margin ratio is the contribution margin stated as a percentage of sales revenue.
Consequently, it represents the percentage of sales revenue available to cover fixed costs and to
contribute to operating income. Contribution margin ratio = unit contribution margin/unit sales
price.
c. The average contribution margin ratio is similar in concept to the contribution margin ratio except
that it is used in multiproduct environments. Consequently, it takes into account each product’s
individual contribution margin ratio as well as the relative sales mix of all products sold.
Solutions Manual Vol. II, Financial and Managerial Accounting 13/e, Williams et al
135
9. The important relationships shown in a cost-volume-profit graph are changes in revenue, costs, and
operating income in relation to changes in the volume of business activity. The point at which a
business moves from a loss to a profit position (the break-even point) is also shown, but this is
relatively less important because the objective of business endeavor is to earn a high rate of return on
investment, not to break even.
10.
Target Sales Volume (in dollars) =
Fixed Costs + Target Operating Income
Contribution Margin Ratio
$145,000 + $30,000
= $500,000 per month
.35
11. At the break-even point, a company earns a total contribution margin exactly equal to its fixed costs.
By dividing the unit contribution margin into this required total contribution margin, we can determine
the number of units that must be sold to enable the company to cover its fixed costs.
=
12. If the contribution margin ratio is 35%, variable costs must account for the other 65% of total revenue.
If 65% of total revenue is equal to $26 per unit, the unit sales price must be $26  .65, or $40.
13. The margin of safety is the dollar amount by which actual sales volume exceeds the break-even point.
14. If sales volume increases by $19,000 in a company with a 40% contribution margin ratio, operating
income should increase by $7,600 ($19,000  .40).
15. A change in product (sales) mix to a higher proportion of export sales may result in a lower level of
net income if the contribution margin ratio on export sales is lower than the average contribution
margin ratio on all sales. This is often the case with export sales made by American companies,
because sales to foreign customers are made at lower prices. Foreign sales must compete with prices
charged by producers of other nations, whose production costs are often much lower than those of
domestic steel companies. In addition, substantial freight charges are incurred on foreign sales; if the
seller pays these charges, the contribution margin is reduced because freight is a variable expense; if
the buying company pays the freight charges, it will generally insist on a lower price for the product it
purchases.
16. Fixed costs do not vary in response to changes in volume. Thus, the more intensively facilities are
utilized, the lower the fixed cost per unit of output. This usually results in an overall lower unit cost.
17. The assumption that fixed costs remain constant within a relevant range has been violated. To
compensate, only in months that anticipated production reaches or exceeds 4,500 units should
management factor into its analysis the additional fixed cost associated with renting a forklift.
136
© The McGraw-Hill Companies, Inc., 2005
SOLUTIONS TO EXERCISES
Ex. 20–1
a.
b.
c.
d.
e.
f.
g.
h.
Break-even point
Fixed costs
Relevant range
Contribution margin
Unit contribution margin
Economies of scale
Semivariable costs
None (This is not a meaningful measurement; variable costs have already been
deducted in arriving at operating income.)
Ex. 20–2
a. Total variable costs increase approximately in proportion to an increase in the volume
of activity.
b. Variable costs per unit remain relatively constant at all levels of activity; this is the
reason that total variable costs vary in proportion to changes in the volume of activity.
c. Total fixed costs remain relatively constant despite increases in the volume of activity.
d. Because total fixed costs tend to remain constant as the volume of activity increases,
fixed costs per unit decline with increases in the volume of activity.
e. Semivariable costs include both fixed and variable cost elements. Because of the
variable cost element, total semivariable costs tend to rise as the volume of activity
increases. Due to the fixed element of the semivariable cost, however, this increase is
less than proportionate to the increase in the volume of activity.
f.
Ex. 20–3
On a per-unit basis, the fixed elements of a semivariable cost decline as the volume of
activity increases, but the variable elements tend to remain constant. Thus, semivariable costs per unit decline as the volume of activity rises, but not as rapidly as if
the entire cost were fixed.
a. Variable. The cost of goods sold normally rises and falls in almost direct proportion to
changes in net sales. Although fixed manufacturing overhead is a component of cost of
goods sold, it is applied on a per unit basis and, therefore, acts like a variable cost.
b. As described in this exercise, the salaries to salespeople are semivariable with respect
to net sales. The monthly minimum amount represents a fixed cost that does not vary
with fluctuations in net sales. However, the commissions on sales transactions represent a variable element of sales salaries that does fluctuate in approximate proportion
to fluctuations in net sales.
Solutions Manual Vol. II, Financial and Managerial Accounting 13/e, Williams et al
137
c. Income taxes are not a fixed, variable, or semivariable cost with respect to net sales.
Income taxes may be viewed as a variable cost, but the relevant activity base is taxable
income, not net sales. (Different tax brackets complicate the analysis of income taxes
expense, even given taxable income as the activity base. Therefore, cost-volume-profit
analysis usually focuses upon operating income—that is, income before income taxes
expense and other items that resist classification as costs that are fixed, variable, or
semivariable with respect to net sales.)
d. Fixed. Property taxes expense is known for each period and is not affected by fluctuations in sales volume.
e. Fixed. Depreciation expense on a sales showroom is independent of the level of net
sales. Fluctuations in net sales have no effect upon the amount of depreciation applicable during the period to the sales showroom. (Depreciation can become a variable
cost only when it is treated as a product cost, or when depreciation is computed using
the units-of-output method. Neither of these situations applies to the depreciation on a
sales showroom, which is a period cost.)
f.
Ex. 20–4
Fixed. Use of an accelerated method causes depreciation expense to change from one
period to the next, but the expense for each period still remains “fixed” with respect to
fluctuations in net sales. The key idea is that fluctuations in net sales have no effect
upon the amount of depreciation expense applicable to the period.
a. (1)
High point ........................................................
Low point .........................................................
Changes ............................................................
Machine Hours
5,500
2,800
2,700
Manufacturing
Overhead
$311,500
184,600
$126,900
Thus, the estimated variable element of Bursa Mfg. Co.’s manufacturing overhead is
$47 per machine hour. [$126,900 change in cost divided by 2,700 unit change in the
activity base (machine hours)].
(2) Total manufacturing overhead at 5,500 machine-hour level ....................
Variable element of manufacturing overhead at 5,500
machine-hour level (5,500 machine hours  $47 per
machine hour) ..........................................................................................
Fixed element of manufacturing overhead .............................................
$311,500
258,500
$ 53,000
b. Estimated manufacturing overhead at activity level of 5,300 machine hours:
Fixed element [a (2)] ........................................................................................ $ 53,000
Variable cost element ($47 per machine hour  5,300
249,100
machine hours) ...............................................................................................
Total estimated manufacturing overhead ..................................................... $302,100
138
© The McGraw-Hill Companies, Inc., 2005
February
March
Estimated manufacturing overhead:
[February: $53,000 + ($47 per m.h.  3,200 m.h.)
March: $53,000 + ($47 per m.h.  4,900 m.h.)] ............... $ 203,400
Actual manufacturing overhead ......................................... 224,000
Amount over (under) estimated ......................................... $ (20,600)
$ 283,300
263,800
$ 19,500
c.
Ex. 20–5
a. (1) Estimated cost of responding to 125 emergency calls in one month:
Fixed element of monthly emergency response cost ..............................
Variable cost of responding to 125 calls (125 calls  $110 per call) .....
Estimated total cost of responding to emergency calls ..........................
$19,500
13,750
$33,250
(2) Average cost per call (125 calls per month):
Estimated total cost of responding to 125 emergency calls per month
[part a (1)] ................................................................................................
Number of calls ..........................................................................................
Average cost per call ($33,250  125 calls) ..............................................
$ 33,250
125
$ 266
b. The overall cost of responding to emergency calls is semivariable—that is, it includes
both fixed and variable elements. Therefore, when the volume of emergency calls is
unusually low, the average cost of responding to each call will rise, because the fixed
cost elements must be spread over fewer calls.
Ex. 20–6
a. Contribution margin ratio = 70% (100%, minus variable costs of 30%)
b.
Break-Even Sales Volume =
Fixed Costs + Target Profit
Contribution Margin Ratio
= $5,950 + $0
.70
= $8,500
c. Fixed element of room service costs ...................................................................
Variable element of room service costs ($15,000  30%).................................
Estimated total room service costs in a month generating $15,000
room service revenue .........................................................................................
Ex. 20–7
$ 5,950
4,500
$10,450
a. Unit contribution margin, $70  $43 = $27
b. Sales required to break even, $405,000  $27 = 15,000 units
c. ($405,000 + $270,000)  $27 = 25,000 units
Solutions Manual Vol. II, Financial and Managerial Accounting 13/e, Williams et al
139
Ex. 20–8
a. If contribution margin ratio is 40%, variable costs must be 60% of sales price.
Unit sales price = $24 variable costs  .60 = $40
Unit Contribution Margin = Unit Sales Price  Variable Cost per Unit
= $40 (above)  $24 = $16
b. Sales Volume (in units) =
Fixed Costs + Target Operating Income
Unit Contribution Margin
= $660,000 + $300,000
$16
= 60,000 units
c. Sales Volume (in dollars) =
=
Fixed Costs + Target Operating Income
Contribution Margin Ratio
$660,000 + $300,000
.40
= $2,400,000
[or 60,000 units (part b)  $40 unit sales price (part a) = $2,400,000]
Ex. 20–9
a. Contribution Margin Ratio =
Sales Price  Variable Costs
Sales Price
= $24  $18 = 25%
$24
Fixed Costs
Break-Even Sales Volume = Contribution Margin Ratio
=
$240,000
= $960,000
.25
b. Sales volume at 75,000 units (75,000  $24) ..................................................
Less: Break-even sales volume (part a) .........................................................
Margin of safety sales volume.........................................................................
140
$ 1,800,000
960,000
$ 840,000
© The McGraw-Hill Companies, Inc., 2005
Ex. 20–10 a. If variable costs are 70% of sales revenue, the contribution margin ratio must be (1  .7) =
30%.
b. Break-Even Sales Volume =
$15,000 = Fixed Costs ;
.3
c. Sales Volume =
Fixed Costs
CM ratio
Fixed Costs = $4,500.
Fixed Costs + Target Operating Income
Contribution Margin Ratio
= $4,500 + $9,000
.3
= $45,000
Ex. 20–11 a. Break-even sales volume ($80  25,000 units) ...............................................
Contribution margin ratio ..............................................................................
Fixed costs ($2,000,000  .45) ..........................................................................
$ 2,000,000
45%
$ 900,000
b. Break-even sales volume ($80  25,000 units) ...............................................
Less: Fixed costs (part a) .................................................................................
Variable cost of 25,000 units ...........................................................................
Variable cost per unit ($1,100,000  25,000 units) ........................................
$ 2,000,000
900,000
$ 1,100,000
$44
Alternatively, if the contribution margin ratio is 45%, variable costs must amount to 55%
of the unit sales price. Thus, $80 sales price  55% = $44.
Ex. 20–12 a.
Product 1
Product 2
Contribution margin ratio ....................................
60%
30%
Relative sales mix ...................................................  40%
 60%
24% +
18% = 42%
Break-Even in Sales =
Fixed Costs
Contribution Margin Ratio
Break-Even in Sales =
$63,000  42% = $150,000
Solutions Manual Vol. II, Financial and Managerial Accounting 13/e, Williams et al
141
b.
Product 1
Product 2
Contribution margin ratio ....................................
60%
30.0%
Relative sales mix ...................................................  25%
 75.0%
15% +
22.5% = 37.5%
Break-Even in Sales =
Fixed Costs + Target Operating Income
Contribution Margin Ratio
Break-Even in Sales = ($63,000 + $12,000)  37.5% = $200,000
Sales
$200,000
180,000
600,000
Variable
Costs
$120,000
105,000
360,000
Contribution
Margin
per Unit
$20
15
30
Sales
$900,000
600,000
500,000
Variable
Costs
$720,000
360,000
350,000
Contribution
Margin Ratio (%)
20%
40%
30%
Ex. 20–13 a.
(1)
(2)
(3)
b.
(1)
(2)
(3)
Ex. 20–14 a. $4,000
b. $6,222
Fixed
Costs
$ 55,000
45,000
150,000
Operating
Income
$25,000
30,000
90,000
Fixed
Costs
$ 85,000
165,000
90,000
Units
Sold
4,000
5,000
8,000
Operating
Income
$95,000
75,000
60,000
($1,800 additional monthly fixed cost, divided by 45% contribution margin)
[($1,800 additional cost + $1,000 target operating income)  45%]
Ex. 20–15 The following activity bases could be suggested to each of your clients:
Client
Freeman’s Retail Floral Shop
Susquehanna Trails Bus Service
Wilson Pump Manufacturers
McCauley & Pratt, Attorneys at Law
Possible Activity Bases
Sales dollars
Passenger miles driven
Number of pumps produced
Sales dollars
Machine hours
Direct labor hours
Billable client hours
Number of cases
Ex. 20–16 It is never ethical to lie to one’s employees. This type of behavior will only serve to
promote an atmosphere of distrust throughout the company. Rather than attempting to
motivate the sales force by lying about sales quotas, the company should consider
rewarding regional sales managers using commissions and bonuses.
142
© The McGraw-Hill Companies, Inc., 2005
SOLUTIONS TO PROBLEMS
20 Minutes, Easy
PROBLEM 20–1
MURDER TO GO!
a. Contribution Margin Ratio = Unit Sales Price  Variable Costs per Unit
Unit Sales Price
=
$28  $7
= 75%
$28
Fixed Costs + $0
b. Break-Even Sales Volume = Contribution Margin Ratio
= $240,000 = $320,000
.75
c. Sales Volume =
=
Fixed Costs + Target Operating Income
Contribution Margin Ratio
$240,000 + $450,000
.75
= $920,000
d.
Sales volume (40,000 units  $28)
Less: Break-even sales volume (per part b )
Margin of safety at 40,000 units
$11 2 0 0 0 0
3 2 0 0 0 0
$ 8 0 0 0 0 0
e. Operating Income = Margin of Safety  Contribution Margin Ratio
= $800,000  .75 = $600,000
Solutions Manual Vol. II, Financial and Managerial Accounting 13/e, Williams et al
143
20 Minutes, Easy
PROBLEM 20–2
ARROW PRODUCTS
a.
Projected operating income without either investment:
($1,200,000  .25)  $80,000
$
2 2 0 0 0 0
Ad Campaign
Ordering System
$ 1 2 6 0 0 0 0 (1) $ 1 2 0 0 0 0 0
. 2 5
. 3 0
$ 3 1 5 0 0 0
$ 3 6 0 0 0 0
(1 0 0 0 0 0 )
(1 0 0 0 0 0 )
$ 2 1 5 0 0 0
$ 2 6 0 0 0 0
Projected sales revenue
 CM ratio
Total contribution margin
minus fixed costs
Operating income
Thus, projected operating revenues will decrease by $5,000 if the ad campaign is chosen ($215,000
 $220,000), and increase by $40,000 ($260,000  $220,000) if the ordering system is chosen.
(1) ($1,200,000  1.05)
b. For the ad campaign to result in an equal increase in operating income, the total contribution
margin produced must equal that of the ordering system ($360,000).
Sales Revenue  .25 = $360,000
Sales Revenue = $1,440,000
Percentage Increase =
144
$1,440,000  $1,200,000
= 20%
$1,200,000
© The McGraw-Hill Companies, Inc., 2005
25 Minutes, Medium
a.
PROBLEM 20–3
THERMAL TENT, INC.
Required contribution margin per unit:
Budgeted operating income
Fixed costs
Total required contribution margin
Number of units to be produced and sold
Required contribution margin per unit ($800,000  50,000 units)
Required sales price per unit:
Required contribution margin per unit
Variable costs and expenses per unit
Total required unit sales price
$2 6 0 0
5 4 0 0
$8 0 0 0
5 0 0
$
0
0
0
0
1
0
0
0
0
6
$
1 6
8 4
$ 1 0 0
b. Break-Even Sales Volume (in units) =
=
Fixed Costs
Contribution Margin per Unit
$540,000
$16
= 33,750 units
c.
Margin of safety at 50,000 units:
Sales volume at 50,000 units ($100 50,000 units)
Less: Break-even sales volume ($100 33,750 units)
Margin of safety
$50 0 0 0 0 0
33 7 5 0 0 0
$16 2 5 0 0 0
Operating income at 50,000 units:
Margin of safety
Contribution margin ratio ($100  $84)  $100
Operating income ($1,625,000  .16)
$16 2 5 0 0 0
. 1 6
$ 2 6 0 0 0 0
Solutions Manual Vol. II, Financial and Managerial Accounting 13/e, Williams et al
145
PROBLEM 20–3
THERMAL TENT, INC. (concluded)
d. No. With a unit sales price of $94, the break-even sales volume in units is 54,000 units:
Unit contribution margin = $94  $84 variable costs = $10
Break-even sales volume (in units) =
$540,000
$10
= 54,000 units
Unless Thermal Tent has the ability to manufacture 54,000 units (or lower fixed and/or variable
costs), setting the unit sales price at $94 will not enable Thermal Tent to break even.
146
© The McGraw-Hill Companies, Inc., 2005
25 Minutes, Medium
a.
b.
Sales price per unit:
Budgeted costs
Add: Budgeted operating income
Budgeted sales revenue
Sales price per unit ($3,150,000  30,000 units)
(1) Total fixed costs:
Manufacturing overhead ($720,000  75%)
Selling and administrative expenses ($600,000  80%)
Total fixed costs
(2) Variable costs and expenses per unit:
Direct materials
Direct labor
Manufacturing overhead ($24 25%)
Selling and administrative expenses ($20  20%)
Total variable costs per unit
(3) Unit contribution margin:
Sales price per unit
Less: Variable costs per unit [from (2) ]
Unit contribution margin
(4) Number of units required to break even:
Fixed costs [from (1) ]
Contribution margin per unit [from (3) ]
Number of units required to break even ($1,020,000  $80)
Solutions Manual Vol. II, Financial and Managerial Accounting 13/e, Williams et al
PROBLEM 20–4
BLASTER CORP.
$22 5 0 0
9 0 0 0
$31 5 0 0
$ 1
0
0
0
0
0
0
0
5
$
5 4 0 0 0 0
4 8 0 0 0 0
$10 2 0 0 0 0
$ 2 1
1 0
6
4
$ 4 1
$ 1 2 1
4 1
$
8 0
$10 2 0 0 0 0
$ 8 0
1 2 7 5 0
147
30 Minutes, Medium
PROBLEM 20–5
STOP-N-SHOP
a.
STOP_N_SHOP
Cost-Volume-Profit Graph
Annual Basis
Revenues or costs (in thousands)
1000
Revenue
750
Profit area
Break-even
point
500
Total cost
250
Loss
area
Fixed cost
Variable cost
0
0
500
1000
1500
2000
Parking-space hours (in thousands)
148
© The McGraw-Hill Companies, Inc., 2005
PROBLEM 20–5
STOP-N-SHOP (continued)
Operating data:
Revenue per parking-space hour .......................................................................................
Variable costs per parking-space hour..............................................................................
Fixed costs per year:
Supervisor’s salary ..........................................................................................................
Wages ($300  52  5) .....................................................................................................
Rent on lot ($7,250  12) .................................................................................................
Fixed maintenance and other expenses ($3,000  12) ..................................................
$ 24,000
78,000
87,000
36,000
Total fixed costs ...................................................................................................................
$225,000
50 cents
5 cents
Capacity = 800 spaces  2,500 hours per year = 2,000,000 parking-space hours per year
Revenue at full capacity = 2,000,000  $0.50 = $1,000,000 per year
Solutions Manual Vol. II, Financial and Managerial Accounting 13/e, Williams et al
149
PROBLEM 20–5
STOP-N-SHOP (concluded)
b.
Contribution margin ratio:
Parking charge per hour
Less: Variable costs per unit
Contribution margin per unit
Contribution margin ratio ($0.45$0.50)
Break-even sales volume:
Fixed costs:
Rent on lot ($7,250  12)
Supervisor’s salary
Wages ($300  52  5)
Fixed maintenance and other costs ($3,000  12)
Total annual fixed costs
Contribution margin ratio (above)
Break-even sales volume ($225,000  .90)
c.
$
8
2
7
3
$2 2
7
4
8
6
5
0
0
0
0
0
0
0
0
0
0
9
$2 5 0 0 0
(1) New contribution margin ratio per parking-space hour:
Parking charge per hour
Less: Variable costs ($0.05  $0.15)
Contribution margin per unit
New contribution margin ratio ($0.30  $0.50)
New level of fixed costs:
Rent on lot ($7,250  12)
Supervisor’s salary
Vacation pay ($300  2  5)
Fixed maintenance and other costs ($3,000  12)
Total fixed costs under new arrangement
(2) Required sales revenue to produce desired operating income:
Total fixed costs under new arrangement (above)
Add: Target profit
Total contribution margin required
New contribution margin ratio (above)
Sales volume ($450,000  .60)
150
$ 0
0
$ 0
9 0
0
0
0
0
0
0 %
0
$ 0
0
$ 0
6 0
$
8 7 0
2 4 0
3 0
3 6 0
$1 5 0 0
0
0
0
0
0
50
05
45
%
50
20
30
%
0
0
0
0
0
$1 5 0 0 0 0
3 0 0 0 0 0
$4 5 0 0 0 0
6 0 %
$7 5 0 0 0 0
© The McGraw-Hill Companies, Inc., 2005
30 Minutes, Medium
a.
PROBLEM 20–6
RAINBOW PAINTS
Contribution margin ratio:
Unit sales price
Less: Variable costs per unit
Contribution margin per gallon
Contribution margin ratio ($4 $10, the unit sales price)
$ 1 0
6
$ 4
4 0 %
Break-even sales volume in dollars:
Fixed costs ($3,160  $3,640  $1,200)
Contribution margin ratio (above)
Break-even sales volume in dollars ($8,000  .4)
$
8 0 0 0
4 0 %
$ 2 0 0 0 0
Break-even sales volume in gallons:
Break-even sales volume in dollars (above)
Unit sales price
Break-even sales volume in gallons ($20,000  $10 per gallon)
b.
On the following page.
c.
Projected operating income at various levels:
Contribution margin per gallon ($10  $6)
Total contribution margin at indicated volume
Less: Fixed costs
Projected monthly operating income
$ 2 0 0 0 0
$ 1 0
2 0 0 0
2,200 Gallons
$
4
$ 8 8 0 0
8 0 0 0
$ 8 0 0
Solutions Manual Vol. II, Financial and Managerial Accounting 13/e, Williams et al
2,600 Gallons
$
4
$ 1 0 4 0 0
8 0 0 0
$ 2 4 0 0
151
PROBLEM 20–6
RAINBOW PAINTS (concluded)
b.
RAINBOW PAINTS
Cost-Volume-Profit Graph
Monthly Basis
35000
30000
Revenue
line
Profit
Revenues or Costs
25000
Break-even
point
20000
Total cost
line
15000
Variable costs
10000
Loss
area
5000
Fixed costs
0
0
500
1000
1500
2000
2500
3000
Gallons Sold
152
© The McGraw-Hill Companies, Inc., 2005