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Financial & Managerial Accounting, 5th Edition
1046
Problem 18-7B (50 minutes)
Part 1 BREAK-EVEN ANALYSIS ASSUMING USE OF SAME MATERIALS
Step 1: Compute break-even in composite units—Use equation in Exhibit 18.27
Break-even in composite units = Fixed costs/Contribution margin per composite unit
* To compute the contribution margin per composite unit
Unit Sales Price
Unit Variable Costs
6 units of Product 1
@ $40 per unit..................................................
@ $30 per unit..................................................
$240
$180
4 units of Product 2
@ $30 per unit..................................................
@ $15 per unit..................................................
120
60
2 units of Product 3
@ $20 per unit..................................................
@ $ 8 per unit..................................................
40
____
16
Selling price of a composite unit ......................
Variable cost of a composite unit .....................
$400
$256
Thus:
Contribution margin per composite unit = $400 - $256 = $144
Contribution margin ratio = $144 / $400 = 36%
Step 2: Compute break-even in individual product unit sales
Unit sales of Product 2 at break-even: 1,875 x 4 = 7,500 units
Unit sales of Product 3 at break-even: 1,875 x 2 = 3,750 units
Step 3: Compute break-even in individual product dollar sales
Problem 18-7B (Continued)
Part 2 BREAK-EVEN ANALYSIS ASSUMING USE OF NEW MATERIALS
Step 1: Compute break-even in composite units—Use equation in Exhibit 18.27
Break-even in composite units = Fixed costs/Contribution margin per composite unit
= ($270,000 + $50,000) / $224*
= 1,429 composite units (rounded to the next unit)
*To compute the contribution margin per composite unit
Unit Sales Price
Unit Variable Costs
6 units of Product 1
@ $40 per unit .....................................................
@ ($30 - $10) per unit .........................................
$240
$120
4 units of Product 2
@ $30 per unit .....................................................
@ ($15 - $5) per unit ...........................................
120
40
2 units of Product 3
@ $20 per unit .....................................................
@ ($8 – $0) per unit ............................................
40
____
16
Selling price of a composite unit ..........................
Variable cost of a composite unit .........................
$400
$176
Thus:
Contribution margin per composite unit = $400 - $176 = $224
Contribution margin ratio = $224 / $400 = 56%
Step 2: Compute break-even in individual product unit sales
Step 3: Compute break-even in individual product dollar sales
Dollar sales of Product 1 at break-even: 8,574 units x $40 = $342,960
Part 3
When a business invests in fixed assets, as in this case, there is an increase
in its risk level (more fixed costs must be recovered). However, investments
in fixed assets can lower variable costs (as is the case here), which lowers its
break-even point, making it easier to make a profit with less sales.
Financial & Managerial Accounting, 5th Edition
1048
SERIAL PROBLEM — SP 18
Serial Problem, Success Systems (50 minutes)
1. Selling price per composite unit
3 desk units @ $1,250 per unit .........................................................
$3,750
2 chairs @ $500 per unit ...................................................................
1,000
Selling price per composite unit ......................................................
$4,750
2. Variable costs per composite unit
3 desk units @ $750 per unit ............................................................
$2,250
2 chairs @ $250 per unit ...................................................................
500
Variable costs per composite unit ...................................................
$2,750
3. Break-even point in composite units
Fixed costs
= Contribution margin per composite unit
4. Unit sales of desk units and chairs at break-even point
Desk units: 3 x 60 units (from 3) ....................................................
180 units
Chairs: 2 x 60 units (from 3) ....................................................
120 units
Reporting in Action — BTN 18-1
1. Some of the costs of Polaris’s services department are:
• Variable: Parts used to repair vehicles, direct labor used to perform
2. As revenues grow, the variable costs will increase in total, as will the
mixed costs. Total fixed costs should not change. Since the “product”
3. Since variable costs are not likely to increase with volume increases by
a constant amount, Polaris cannot use a simple contribution margin
Comparative Analysis — BTN 18-2
1.
Polaris
Arctic Cat
Average selling price per unit .......................
$ 10,500
$ 11,200
Average variable cost per unit ......................
4,200
5,100
Average contribution margin per unit ................
$ 6,300
$ 6,100
Total fixed costs ($ thousands) ....................
$146,570
$133,570
Break-even point in units (rounded) ............
23,266
21,897
2. As unit sales decline, Polaris’s operating profits will fall by $6,300 per
Ethics Challenge — BTN 18-3
Instructor note: This question can serve to generate class discussion on
cost analysis and estimation. Discussion can focus on accounting,
business, and other ethical concerns.
MEMORANDUM
To: “Mechanics” and “Owners”
From: Your name
RE: Analysis of labor costs for survey
Date: Current date
The memorandum should include many of the following points:
Objectivity: A statement about the need to be objective in the analysis. Both
ethical and professional concerns should motivate the preparer’s desire for
objectivity.
Cost Accounting Estimation: The memorandum should outline how cost
Business Concerns: The memorandum should point out that the repair
business should follow established business practices for setting cost
estimates. There should also be an expressed concern of fairness for the
customer in getting a fair value for the amount paid. Another concern will be a
possible perception that the repair business typically overcharges the
the quality of mechanical work. Is the work being done correctly and is
customer safety in jeopardy by paying the mechanic on a job-by-job basis?
Who is responsible for establishing a fair compensation system? These
issues are likely topics for the memorandum.
Communicating in Practice — BTN 18-4
Instructor note: Reports will vary, but a typical report would likely include
assumptions similar to the following.
1. Revenue (salary) assumptions
• Find job that pays a specified amount.
2. Cost assumptions
• Find living accommodations at a specified amount.
Taking It to the Net — BTN 18-5
The site offers many tools for an entrepreneur in assessing costs, sales,
and profits. Specifically, a spreadsheet file is provided that allows an
entrepreneur to identify the start-up costs of the business. A new business
requires many different types of costs for the different resources to be
Also, many of the tools (such as the worksheet) are in the form of a
spreadsheet. This means an entrepreneur can modify the spreadsheet and
use it to conduct various types of “what-if” analyses by considering
different possible scenarios of business.
Financial & Managerial Accounting, 5th Edition
1052
Teamwork in Action — BTN 18-6
(a) Questions for school administrators (others are possible)
• Number of students that would attend the theater.
(b) Questions for owners (others are possible)
• List of other potential markets for theater showings during school
days.
Entrepreneurial Decision — BTN 18-7
1. Costs that won’t change regardless of how many footballs Paul
Cunningham makes (i.e. fixed costs) likely include rent, depreciation on
sewing equipment, and salaries.
2. Overly optimistic sales estimates could lead the company to expand into
markets or products that are unable to break-even or make profits.
3. Paul Cunningham can use CVP techniques to manage his company.
Focusing on contribution margin per unit enables the company to set
Hitting the Road — BTN 18-8
1. There is no set solution for this problem. Answers will vary because each
student will make different estimates for groups, costs, and volume. The
instructor should make certain the student follows the correct steps in
preparing a multiproduct break-even analysis. This activity is designed to
show the student that several estimates are required in this type of CVP
analysis.
One simple example with crucial facts
Product
Estimated
Selling
Price per
unit
Estimated
CM ratio
Estimated
CM
per unit
Estimated
Sales
Mix
Estimated CM
for each
component in
composite unit
Burgers ................................
$2.00
0.75
$1.50
3.5
$ 5.25
Fries ................................
$1.00
0.70
$0.70
5.0
3.50
Drinks ................................
$1.00
0.90
$0.90
3.5
3.15
Desserts...............................
$0.50
0.40
$0.20
1.2
0.24
Other ................................
$0.80
0.30
$0.24
1.0
0.24
Total contribution margin (CM) per composite unit ................................
$12.38
Estimated fixed costs per year: $500,000
Break-even point in composite unit sales: $500,000/$12.38 = 40,388
Unit sales of individual products per year required to break-even:
Burgers ................................
40,388 x 3.5 =
141,358 units
Fries ................................
40,388 x 5.0 =
201,940 units
Drinks ................................
40,388 x 3.5 =
141,358 units
Desserts...............................
40,388 x 1.2 =
48,466 units
Other ................................
40,388 x 1.0 =
40,388 units
In general, when evaluating a student’s solutions, look for:
• Estimated selling price of products
• Estimated contribution margin per item
• Estimated sales mix
• Estimated composite contribution margin
• Estimated fixed costs per year
Multiproduct Break-Even Point.
2. The report should properly interpret the analysis from part 1. This
question is also designed to show students that a fast food restaurant
must sell high volumes of certain product categories to make a profit.
Global Decision — BTN 18-9
1. Managers at Piaggio likely use multiproduct CVP analysis when
2. If Piaggio adds a new product line to their offerings, they will have to
consider its selling price and any variable costs, such as cost of the
