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Chapter 10
Differential Analysis: The Key to Decision
Making
Solutions to Questions
10-1 A relevant cost is a cost that differs in
10-2 An incremental cost (or benefit) is the
change in cost (or benefit) that will result from
10-3 No. Variable costs are relevant costs
10-4 No. Not all fixed costs are sunk—only
those for which the cost has already been
10-5 No. A variable cost is a cost that varies
in total amount in direct proportion to changes
10-7 Only those costs that would be avoided
as a result of dropping the product line are
10-8 Not necessarily. An apparent loss may
be the result of allocated common costs or of
as a result of dropping the product is less than
promotes the sale of other products.
10-10 If a company decides to make a part
internally rather than to buy it from an outside
benefits that could be derived from the best
alternative use of the facilities.
customers could be a constraint. Some examples
are machine time, direct labor time, floor space,
contribution margin is maximized. A company
can maximize its total contribution margin by
10-13 Joint products are two or more products
© The McGraw-Hill Companies, Inc., 2016. All rights reserved.
2 Introduction to Managerial Accounting, 7th Edition
the manufacturing process where joint products
can be recognized as individual products.
10-14 Joint costs should not be allocated
among joint products for decision-making
purposes. If joint costs are allocated among the
joint products, then managers may think they
10-15 If the incremental revenue from further
processing exceeds the incremental costs of
further processing, the product should be
processed further.
10-16 Most costs of a flight are either sunk
costs, or costs that do not depend on the
The Foundational 15
1. The total traceable fixed manufacturing overhead for Alpha and Beta is
computed as follows:
Alpha
Beta
Traceable fixed overhead per unit (a) ........
$16
$18
Level of activity in units (b) .......................
100,000
100,000
Total traceable fixed overhead (a) × (b) ....
$1,600,000
$1,800,000
2. The total common fixed expenses is computed as follows:
Alpha
Beta
Common fixed expenses per unit (a) .........
$15
$10
Level of activity in units (b) .......................
100,000
100,000
Total common fixed expenses (a) × (b) .....
$1,500,000
$1,000,000
The company’s total common fixed expenses would be $2,500,000.
3. The profit impact is computed as follows:
Per
Total
Unit
10,000 units
Incremental revenue ............................
$80
$800,000
Incremental costs:
Variable costs:
Direct materials ...............................
30
300,000
Direct labor .....................................
20
200,000
Variable manufacturing overhead .....
7
70,000
Variable selling expenses .................
12
120,000
Total variable cost .............................
$69
690,000
Incremental net operating income .........
$110,000
The Foundational 15 (continued)
4. The profit impact is computed as follows:
Per
Total
Unit
5,000 units
Incremental revenue ............................
$39
$195,000
Incremental costs:
Variable costs:
Direct materials ...............................
12
60,000
Direct labor .....................................
15
75,000
Variable manufacturing overhead .....
5
25,000
Variable selling expenses .................
8
40,000
Total variable cost .............................
$40
200,000
Incremental net operating income .........
$ (5,000)
5. The profit impact is computed as follows:
Incremental revenue
(10,000 units × $80) (a) ................................
$800,000
Incremental variable costs:
Direct materials (5,000 units × $30) ......................
$150,000
Direct labor (5,000 units × $20) ............................
100,000
Variable manufacturing overhead
(5,000 units × $7) ................................
35,000
Variable selling expenses
(5,000 units × $12) ................................
60,000
Total incremental variable cost (b) ...........................
345,000
Foregone sales to regular customers
(5,000 units × $120) (c) ................................
600,000
Incremental net operating income
(a) − (b) – (c) ........................................................
$(145,000)
Note to instructors: Emphasize to students that the variable costs
related to 5,000 units of production are irrelevant to the decision
because they will be incurred whether the special order is accepted or
rejected.
The Foundational 15 (continued)
6. The profit impact of dropping the Beta product line is computed as
follows:
Contribution margin lost if the Beta product line is
dropped* .................................................................
$(3,600,000)
Traceable fixed manufacturing overhead .......................
1,800,000
Decrease in net operating income if Beta is dropped ......
$(1,800,000)
* Beta’s contribution margin per unit is $40 ($80 − $40). Therefore, the
decrease in contribution margin if Beta is dropped would be $3,600,000
(90,000 units × $40).
Note to instructors: Emphasize that the traceable fixed manufacturing
overhead is avoidable and the common fixed expenses are not.
7. The profit impact of dropping the Beta product line is computed as
follows:
Contribution margin lost if the Beta product line is
dropped* ...................................................................
$(1,600,000)
Traceable fixed manufacturing overhead .........................
1,800,000
Increase in net operating income if Beta is dropped ........
$ 200,000
* Beta’s contribution margin per unit is $40 ($80 − $40). Therefore, the
decrease in contribution margin if Beta is dropped would be $1,600,000
(40,000 units × $40).
8. The profit impact of dropping the Beta product line is computed as
follows:
Contribution margin lost if the Beta product line is
dropped .....................................................................
$(2,400,000)
Traceable fixed manufacturing overhead .........................
1,800,000
Contribution margin on additional Alpha sales* ............
765,000
Increase in net operating income if Beta is dropped ........
$ 165,000
* Alpha’s contribution margin per unit is $51 ($120 − $69). Therefore,
the increase in Alpha’s contribution margin if Beta is dropped would be
$765,000 (15,000 units × $51).
The Foundational 15 (continued)
9. The profit impact of buying 80,000 Alphas from a supplier rather than
making them is computed as follows:
Make
Buy
Cost of purchasing (80,000 units × $80) ........
$6,400,000
Direct materials (80,000 units × $30) ............
$2,400,000
Direct labor (80,000 units × $20) ..................
1,600,000
Variable manufacturing overhead
(80,000 units × $7) ...................................
560,000
Traceable fixed manufacturing overhead ........
1,600,000
Total costs ...................................................
$6,160,000
$6,400,000
Difference in favor of continuing
to make the Alphas ...................
$240,000
Note to instructors: Emphasize that the variable selling expenses are
irrelevant to this decision because they will be incurred regardless of
whether the company makes or buys its Alphas.
10. The profit impact of buying 50,000 Alphas from a supplier rather than
making them is computed as follows:
Make
Buy
Cost of purchasing (50,000 units × $80) ........
$4,000,000
Direct materials (50,000 units × $30) ............
$1,500,000
Direct labor (50,000 units × $20) ..................
1,000,000
Variable manufacturing overhead
(50,000 units × $7) ...................................
350,000
Traceable fixed manufacturing overhead ........
1,600,000
Total costs ...................................................
$4,450,000
$4,000,000
Difference in favor of buying
Alphas from the supplier ...........
$450,000
Note to instructors: Emphasize that the variable selling expenses are
irrelevant to this decision because they will be incurred regardless of
whether the company makes or buys its Alphas.
The Foundational 15 (continued)
11. The pounds of raw material per unit are computed as follows:
Alpha
Beta
Direct material cost per unit (a) ............................
$30
$12
Cost per pound of direct materials (b) ...................
$6
$6
Pounds of direct materials per unit (a) ÷ (b) ..........
5
2
12. The contribution margins per pound of raw materials are computed as
follows:
Alpha
Beta
Selling price per unit...............................
$120
$80
Variable cost per unit .............................
69
40
Contribution margin per unit (a) ..............
$ 51
$40
Pounds of direct material required to
produce one unit (b) ............................
5 pounds
2 pounds
Contribution margin per pound (a) ÷ (b) .
$10.20
$20.00
13. The optimal number of units to produce would be computed as
follows:
Product
Pounds
Per Unit
Units
Produced
Total
Pounds
Beta ...................................
2
60,000
120,000
Alpha ..................................
5
8,000
40,000
Total pounds available .........
160,000
The Foundational 15 (continued)
14. The total contribution margin would be computed as follows:
Alpha
Beta
Number of units produced (a) ...............................
8,000
60,000
Contribution margin per unit (b) ............................
$51
$40
Total contribution margin (a) × (b) ........................
$408,000
$2,400,000
The company’s total contribution margin would be $2,808,000
($408,000 + $2,400,000).
15. The maximum price per pound is computed as follows:
Alpha
Regular direct material cost per pound .............................
$ 6.00
Contribution margin per pound of direct materials .............
10.20
Maximum price to be paid per pound................................
$16.20
Because the company has satisfied all demand for Betas, it would use
additional raw materials to produce Alphas.
Exercise 10-1 (15 minutes)
Case 1
Case 2
Item
Relevant
Not
Relevant
Relevant
Not
Relevant
a.
Sales revenue .................
X
X
b.
Direct materials ..............
X
X
c.
Direct labor ....................
X
X
d.
Variable manufacturing
overhead .....................
X
X
e.
Depreciation— Model
B100 machine ..............
X
X
f.
Book value— Model
B100 machine ..............
X
X
g.
Disposal value— Model
B100 machine ..............
X
X
h.
Market value—Model
B300 machine (cost) ....
X
X
i.
Fixed manufacturing
overhead .....................
X
X
j.
Variable selling expense ..
X
X
k.
Fixed selling expense ......
X
X
l.
General administrative
overhead .....................
X
X
Exercise 10-2 (30 minutes)
1. No, production and sale of the racing bikes should not be discontinued.
If the racing bikes were discontinued, then the net operating income for
the company as a whole would decrease by $11,000 each quarter:
Lost contribution margin ................................
$(27,000)
Fixed costs that can be avoided:
Advertising, traceable ..................................
$ 6,000
Salary of the product line manager ..............
10,000
16,000
Decrease in net operating income for the
company as a whole ...................................
$(11,000)
The depreciation of the special equipment is a sunk cost and is not
relevant to the decision. The common costs are allocated and will
continue regardless of whether or not the racing bikes are discontinued;
thus, they are not relevant to the decision.
Alternative Solution:
Current
Total
Total If
Racing
Bikes Are
Dropped
Difference:
Net
Operating
Income
Increase or
(Decrease)
Sales ..........................................
$300,000
$240,000
$(60,000)
Variable expenses .......................
120,000
87,000
33,000
Contribution margin.....................
180,000
153,000
(27,000)
Fixed expenses:
Advertising, traceable ...............
30,000
24,000
6,000
Depreciation on special
equipment* ...........................
23,000
23,000
0
Salaries of product managers ....
35,000
25,000
10,000
Common allocated costs ...........
60,000
60,000
0
Total fixed expenses ....................
148,000
132,000
16,000
Net operating income ..................
$ 32,000
$ 21,000
$ (11,000)
*Includes pro-rated loss on the special equipment if it is disposed of.
Exercise 10-2 (continued)
2. The segmented report can be improved by eliminating the allocation of
the common fixed expenses. Following the format introduced in Chapter
12 for a segmented income statement, a better report would be:
Total
Dirt
Bikes
Mountain
Bikes
Racing
Bikes
Sales ...................................
$300,000
$90,000
$150,000
$60,000
Variable manufacturing and
selling expenses ................
120,000
27,000
60,000
33,000
Contribution margin .............
180,000
63,000
90,000
27,000
Traceable fixed expenses:
Advertising ........................
30,000
10,000
14,000
6,000
Depreciation of special
equipment ......................
23,000
6,000
9,000
8,000
Salaries of the product line
managers .......................
35,000
12,000
13,000
10,000
Total traceable fixed
expenses...........................
88,000
28,000
36,000
24,000
Product line segment margin
92,000
$35,000
$ 54,000
$ 3,000
Common fixed expenses .......
60,000
Net operating income ...........
$ 32,000
Exercise 10-3 (30 minutes)
1.
Per Unit
Differential
Costs
15,000 units
Make
Buy
Make
Buy
Cost of purchasing .......................
$35
$525,000
Direct materials ...........................
$14
$210,000
Direct labor .................................
10
150,000
Variable manufacturing overhead .
3
45,000
Fixed manufacturing overhead,
traceable1 .................................
2
30,000
Fixed manufacturing overhead,
common ...................................
Total costs ..................................
$29
$35
$435,000
$525,000
Difference in favor of continuing to
make the carburetors ................
$6
$90,000
1
Only the supervisory salaries can be avoided if the carburetors are
purchased. The remaining book value of the special equipment is a
sunk cost; hence, the $4 per unit depreciation expense is not
relevant to this decision.
Based on these data, the company should reject the offer and should
continue to produce the carburetors internally.
2.
Make
Buy
Cost of purchasing (part 1) ............................
$525,000
Cost of making (part 1) .................................
$435,000
Opportunity cost—segment margin foregone
on a potential new product line ...................
150,000
Total cost ......................................................
$585,000
$525,000
Difference in favor of purchasing from the
outside supplier ..........................................
$60,000
Thus, the company should accept the offer and purchase the
carburetors from the outside supplier.
Exercise 10-4 (15 minutes)
Only the incremental costs and benefits are relevant. In particular, only the
variable manufacturing overhead and the cost of the special tool are
relevant overhead costs in this situation. The other manufacturing
overhead costs are fixed and are not affected by the decision.
Per Unit
Total
for 20
Bracelets
Incremental revenue .............................
$169.95
$3,399.00
Incremental costs:
Variable costs:
Direct materials ...............................
$ 84.00
1,680.00
Direct labor .....................................
45.00
900.00
Variable manufacturing overhead .....
4.00
80.00
Special filigree .................................
2.00
40.00
Total variable cost ..............................
$135.00
2,700.00
Fixed costs:
Purchase of special tool ....................
250.00
Total incremental cost ...........................
2,950.00
Incremental net operating income .........
$ 449.00
Even though the price for the special order is below the company's regular
price for such an item, the special order would add to the company's net
operating income and should be accepted. This conclusion would not
necessarily follow if the special order affected the regular selling price of
bracelets or if it required the use of a constrained resource.
Exercise 10-5 (20 minutes)
1. The most profitable use of the constrained resource is determined by
the contribution margin per unit of the constrained resource. In part 1,
the constrained resource is time on the plastic injection molding
machine. Therefore, the analysis would proceed as follows:
Ski
Golf
Fishing
Guard
Guard
Guard
Selling price per unit ..................
$200
$300
$255
Variable cost per unit ................
60
140
55
Contribution margin per unit (a) .
$140
$160
$200
Plastic injection molding machine
processing time required to
produce one unit (b) ...............
2 minutes
5 minutes
4 minutes
Contribution margin per unit of
the constrained resource
(a) ÷ (b) ................................
$70 per
minute
$32 per
minute
$50 per
minute
Production of the Ski Guard product would be the most profitable use of
the constrained resource which is, in this case, time on the plastic
injection molding machine. The contribution margin per minute is $70
for this product, which is larger than for the other two products.
2. In this part, the constraint is the available pounds of plastic pellets.
Ski
Golf
Fishing
Guard
Guard
Guard
Selling price per unit ..................
$200
$300
$255
Variable cost per unit ................
60
140
55
Contribution margin per unit (a) .
$140
$160
$200
Pounds of plastic pellets required
to produce one unit (b) ...........
7 pounds
4 pounds
8 pounds
Contribution margin per unit of
the constrained resource
(a) ÷ (b) ................................
$20 per
pound
$40 per
pound
$25 per
pound
In this case, production of the Golf Guard would be the most profitable
use of the constrained resource. The contribution margin per unit of the
constrained resource for this product is $40, which is larger than for the
other two products.
Exercise 10-5 (continued)
3. The Fishing Guard product has the largest unit contribution margin, but
it is not the most profitable use of the constrained resource in either
Exercise 10-6 (20 minutes)
1. The value of relaxing the constraint can be determined by computing
the contribution margin per unit of the constrained resource:
Sofa
Selling price per unit ...................................................
$1,800
Variable cost per unit .................................................
1,200
Contribution margin per unit (a) ..................................
$ 600
Upholstery shop time required to produce one unit (b) .
10 hours
Contribution margin per unit of the constrained
resource (a) ÷ (b) ...................................................
$60 per hour
2. To answer this question, it is desirable to compute the contribution
margin per unit of the constrained resource for all three products:
Recliner
Sofa
Loveseat
Selling price per unit ..................
$1,400
$1,800
$1,500
Variable cost per unit ................
800
1,200
1,000
Contribution margin per unit (a) .
$ 600
$ 600
$ 500
Upholstery shop time required to
produce one unit (b) ...............
8 hours
10 hours
5 hours
Contribution margin per unit of
the constrained resource
(a) ÷ (b) ................................
$75 per
hour
$60 per
hour
$100 per
hour
The offer to upholster chairs for $45 per hour should be accepted.
The time would be used to upholster Loveseats. If this increases the
total production and sales of those chairs, the time would be worth
$100 per hour—a net gain of $55 per hour. If Loveseats are already
being produced up to demand, then having these chairs upholstered
in the other company would free up capacity to produce more of the
other two chairs. In both cases, the additional time is worth more
than $45 per hour.
Exercise 10-7 (10 minutes)
A
B
C
Selling price after further processing ....
$20
$13
$32
Selling price at the split-off point .........
16
8
25
Incremental revenue per pound or
gallon ..............................................
$ 4
$ 5
$ 7
Total quarterly output in pounds or
gallons ............................................
×15,000
×20,000
×4,000
Total incremental revenue ...................
$60,000
$100,000
$28,000
Total incremental processing costs .......
63,000
80,000
36,000
Total incremental profit or loss ............
$(3,000)
$ 20,000
$(8,000)
Therefore, only product B should be processed further.
Exercise 10-8 (30 minutes)
1.
A
B
C
(1)
Contribution margin per unit ...........................
$54
$108
$60
(2)
Direct material cost per unit ...........................
$24
$72
$32
(3)
Direct material cost per pound ........................
$8
$8
$8
(4)
Pounds of material required per unit (2) ÷ (3) .
3
9
4
(5)
Contribution margin per pound (1) ÷ (4) .........
$18
$12
$15
2. The company should concentrate its available material on product A:
A
B
C
Contribution margin per pound (above) .
$ 18
$ 12
$ 15
Pounds of material available ..................
× 5,000
× 5,000
× 5,000
Total contribution margin ......................
$90,000
$60,000
$75,000
Although product A has the lowest contribution margin per unit and the
second lowest contribution margin ratio, it is preferred over the other
two products because it has the greatest amount of contribution margin
per pound of material, and material is the company’s constrained
resource.
3. The price Barlow Company would be willing to pay per pound for
additional raw materials depends on how the materials would be used.
If there are unfilled orders for all of the products, Barlow would
presumably use the additional raw materials to make more of product A.
Exercise 10-9 (15 minutes)
1. Annual profits will increase by $39,000:
Per Unit
15,000
Units
Incremental sales ................................
$14.00
$210,000
Incremental costs:
Direct materials ................................
5.10
76,500
Direct labor ......................................
3.80
57,000
Variable manufacturing overhead .......
1.00
15,000
Variable selling and administrative .....
1.50
22,500
Total incremental costs ........................
11.40
171,000
Incremental profits ..............................
$ 2.60
$ 39,000
The fixed costs are not relevant to the decision because they will be
incurred regardless of whether the special order is accepted or rejected.
2. The relevant cost is $1.50 (the variable selling and administrative
Exercise 10-10 (15 minutes)
The target production level is 40,000 starters per period, as shown by the
relations between per-unit and total fixed costs.
“Cost”
Per
Differential
Costs
Unit
Make
Buy
Explanation
Direct materials ......
$3.10
$3.10
Can be avoided by buying
Direct labor ............
2.70
2.70
Can be avoided by buying
Variable
manufacturing
overhead .............
0.60
0.60
Can be avoided by buying
Supervision ............
1.50
1.50
Can be avoided by buying
Depreciation
1.00
—
Sunk Cost
Rent ......................
0.30
—
Allocated Cost
Outside purchase
price ...................
$8.40
Total cost ...............
$9.20
$7.90
$8.40
