Chapter 13
Relevant Costs for Decision Making
Solutions to Questions
13-1
A relevant cost is a cost that differs in total between the alternatives in a decision.
13-4 No. Not all fixed costs are sunk only those for which the cost has already been irrevocably
incurred. A variable cost can be a sunk cost, if it has already been incurred.
13-7 Only those costs that can be avoided as a result of dropping the product line are relevant in the
decision. Costs that will not differ regardless of whether the line is retained or discontinued are irrelevant.
13-8 Not necessarily. An apparent loss may be the result of allocated common costs or of sunk costs
that cannot be avoided if the product line is dropped. A product line should be discontinued only if the
contribution margin that will be lost as a result of dropping the line is less than the fixed costs that can
be avoided. Even in that situation there may be arguments in favor of retaining the product line if its
presence promotes the sale of other products.
13-9 Allocations of common fixed costs can make a product line (or other segment) appear to be
unprofitable, whereas in fact it may be profitable.
13-11 Any resource that is required to make products and get them into the hands of customers could
be a constraint. Some examples are machine time, direct labor time, floor space, raw materials,
investment capital, supervisory time, and storage space. While not covered in the text, constraints can
also be intangible and often take the form of a formal or informal policy that prevents the organization
from furthering its goals.
13-12 Assuming that fixed costs are not affected, profits are maximized when the total contribution
margin is maximized. A company can maximize its contribution margin by focusing on the products with
the greatest amount of contribution margin per unit of the constrained resource.
13-16 Most costs of a flight are either sunk costs, or costs that do not depend on the number of
passengers on the flight. Depreciation of the aircraft, salaries of personnel on the ground and in the air,
and fuel costs, for example, are the same whether the flight is full or almost empty. Therefore, adding
more passengers at reduced fares at certain times of the week when seats would otherwise be empty
does little to increase the total costs of making the flight, but can do much to increase the total
contribution and total profit.
1
Exercise 13- 1
a.
b.
c.
d.
e.
f.
g.
h.
i.
j.
k.
l.
Case 1
Not
Item
Relevant Relevant
Sales revenue................................
X
Direct materials ................................
X
Direct labor ................................
X
Variable manufacturing
overhead ................................
X
Depreciation Model
B100 machine ................................ X
Book value Model
B100 machine ................................ X
Disposal value Model
B100 machine ................................ X
Market value Model
B300 machine (cost) ................................
X
Fixed manufacturing
overhead ................................
X
Variable selling expense ................................
X
Fixed selling expense ................................
X
General administrative
overhead ................................
X
Case 2
Relevant
Not
Relevant
X
X
X
X
X
X
X
X
X
X
X
X
2
Exercise 13- 2
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.
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:
Dirt
Mountain Racing
Total
Bikes
Bikes
Bikes
Sales................................................................
$300,000 $90,000 $150,000 $60,000
Less variable manufacturing
and selling expenses................................
120,000 27,000
60,000
33,000
Contribution margin ................................
180,000 63,000
90,000
27,000
Less traceable f ixed 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 f ixed
expenses ................................ 88,000 28,000
36,000
24,000
Product line segment margin................................
92,000 $35,000 $ 54,000 $ 3,000
Less common f ixed expenses................................
60,000
Net operating income ................................
$ 32,000
3
Exercise 13-3
1.
Cost of purchasing ......................
Direct materials...........................
Direct labor.................................
Variable manufacturing overhead..
Fixed manufacturing overhead,
traceable1 ................................
Fixed manufacturing overhead,
common ..................................
Total costs ..................................
Difference in favor of continuing
to make the carburetors ............
1
2.
Per Unit
Differential
Costs
Make Buy
$35
$14
10
3
2
$29 $35
$6
15,000 units
Make
Buy
$525,000
$210,000
150,000
45,000
30,000
$435,000 $525,000
$90,000
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.
Make
Buy
$525,000
Cost of purchasing (part 1) ............................
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
$60,000
outside supplier ..........................................................
Thus, the company should accept the offer and purchase the
carburetors from the outside supplier.
4
Exercise 13- 4
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.
Total
for 20
Per Unit 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.
5
Exercise 13-7
1. Fixed cost per mile ($5,000* ÷ 50,000 miles) ..... $0.10
Variable cost per mile ....................................... 0.07
Average cost per mile ....................................... $0.17
* Insurance .......................... $1,600
Licenses ............................
250
Taxes ................................
150
Garage rent ....................... 1,200
Depreciation ...................... 1,800
Total ................................. $5,000
This answer assumes the resale value of the truck does not decline
because of the wear and tear that comes with use.
2. The insurance, the licenses, and the variable costs (gasoline, oil, tires,
and repairs) would all be relevant to the decision, since these costs are
avoidable by not using the truck. (However, the owner of the garage
might insist that the truck be insured and licensed if it is left in the
garage. In that case, the insurance and licensing costs would not be
relevant since they would be incurred regardless of the decision.) The
taxes would not be relevant, since they must be paid regardless of use;
the garage rent would not be relevant, since it must be paid to park the
truck; and the depreciation would not be relevant, since it is a sunk
cost. However, any decrease in the resale value of the truck due to its
use would be relevant.
3. Only the variable costs of $0.07 would be relevant, since they are the
only costs that can be avoided by having the delivery done
commercially.
4. In this case, only the fixed costs associated with the second truck would
be relevant. The variable costs would not be relevant, since they would
not differ between having one or two trucks. (Students are inclined to
think that variable costs are always relevant in decision-making, and to
think that fixed costs are always irrelevant. This requirement helps to
dispel that notion.)
6
Exercise 13-11
The company should accept orders first for C, second for A, and third for B.
The computations are:
(1)
(2)
(3)
(4)
(5)
A
$24
$3
8
$32
B
$15
$3
5
$14
Direct materials required per unit ........
Cost per pound ..................................
Pounds required per unit (1) ÷ (2) ......
Contribution margin per unit ...............
Contribution margin per pound of
materials used (4) ÷ (3)................... $4.00 $2.80
C
$9
$3
3
$21
$7.00
Since C uses the least amount of material per unit of the three products,
and since it is the most profitable of the three in terms of its use of
materials, some students will immediately assume that this is an infallible
relationship. That is, they will assume that the way to spot the most
profitable product is to find the one using the least amount of the
constrained resource. The way to dispel this notion is to point out that
product A uses more material (the constrained resource) than does product
B, but yet it is preferred over product B. The key factor is not how much of
a constrained resource a product uses, but rather how much contribution
margin the product generates per unit of the constrained resource.
7
Problem 13-16
1. Contribution margin lost if the flight is
discontinued......................................................
$(12,950)
Flight costs that can be avoided if the flight is
discontinued:
Flight promotion ................................................ $ 750
Fuel for aircraft.................................................. 5,800
Liability insurance (1/3 × $4,200) ....................... 1,400
Salaries, flight assistants .................................... 1,500
Overnight costs for flight crew and assistants.......
300
9,750
Net decrease in prof its if the flight is discontinued ..
$ (3,200)
The following costs are not relevant to the decision:
Cost
Reason
Salaries, flight crew
Fixed annual salaries, which will
not change.
Depreciation of aircraft
Sunk cost.
Liability insurance (two-thirds)
Two-thirds of the liability insurance
is unaffected by this decision.
Baggage loading and flight
preparation
This is an allocated cost that will
continue even if the flight is
discontinued.
8
Problem 13-16 (continued)
Alternative Solution:
Keep the Drop the
Flight
Flight
Ticket revenue ...................................... $14,000
$
0
Less variable expenses...........................
1,050
0
Contribution margin............................... 12,950
0
Less flight expenses:
Salaries, flight crew.............................
1,800
1,800
Flight promotion .................................
750
0
Depreciation of aircraft........................
1,550
1,550
Fuel for aircraft...................................
5,800
0
Liability insurance ...............................
4,200
2,800
Salaries, flight assistants .....................
1,500
0
Baggage loading and flight preparation.
1,700
1,700
Overnight costs for flight crew and
assistants at destination....................
300
0
Total flight expenses..............................
17,600
7,850
Net operating loss ................................. $ (4,650) $ (7,850)
Difference:
Net
Operating
Income
Increase or
(Decrease)
$(14,000)
1,050
(12,950)
0
750
0
5,800
1,400
1,500
0
300
9,750
$ (3,200)
2. The goal of increasing the seat occupancy could be obtained by
eliminating flights with a lower-than-average seat occupancy. By
eliminating these flights and keeping the flights with a higher average
seat occupancy, the overall average seat occupancy for the company as
a whole would be improved. This could reduce profits, however, in at
least two ways. First, the flights that are eliminated could have
contribution margins that exceed their avoidable costs (such as in the
case of flight 482 in part 1). If so, then eliminating these flights would
reduce the company s total contribution margin more than it would
reduce total costs, and profits would decline. Second, these flights
might be acting as feeder flights, bringing passengers to cities where
connections to more profitable flights are made.
9
Problem 13-17
1.
Per 16-Ounce
T-Bone
Revenue from further processing:
Sales price of one filet mignon (6 ounces ×
$4.00 per pound ÷ 16 ounces per pound) .......
Sales price of one New York cut (8 ounces ×
$2.80 per pound ÷ 16 ounces per pound).......
Total revenue from further processing..................
Less sales revenue from one T-bone steak ...........
Incremental revenue from further processing .......
Less cost of further processing ............................
Profit per pound from further processing .............
$1.50
1.40
2.90
2.25
0.65
0.25
$0.40
2. The T-bone steaks should be processed further into the filet mignon and
the New York cut. This will yield $0.40 per pound in added profit for the
company. The $0.45 profit per pound shown in the text is not relevant
to the decision, since it contains allocated joint costs. The company will
incur the joint costs regardless of whether the T-bone steaks are sold
outright or processed further; thus, this cost should be ignored in the
decision.
10
Problem 13-18
1. The simplest approach to the solution is:
Gross margin lost if the store is closed ............
Costs that can be avoided:
Sales salaries.............................................. $70,000
Direct advertising........................................ 51,000
Store rent................................................... 85,000
Delivery salaries.......................................... 4,000
Store management salaries
($21,000 $12,000)................................. 9,000
Salary of new manager ............................... 11,000
General off ice compensation........................ 6,000
Insurance on inventories ($7,500 × 2/3)....... 5,000
Utilities ...................................................... 31,000
Employment taxes ...................................... 15,000 *
Decrease in company prof its if the North
Store is closed ............................................
*Salaries avoided by closing the store:
Sales salaries ............................................
Delivery salaries........................................
Store management salaries........................
Salary of new manager..............................
General off ice compensation ......................
Total avoided...............................................
Employment tax rate....................................
Employment taxes avoided ...........................
$(316,800)
287,000
$ (29,800)
$70,000
4,000
9,000
11,000
6,000
100,000
× 15%
$15,000
11
Problem 13-18 (continued)
2. Based on the data in (1), the North Store should not be closed. If the
store is closed, then the company s overall net operating income will
decrease by $29,800 per quarter. If the store space cannot be subleased
or the lease broken without penalty, a decision to close the store would
cause an even greater decline in the company s overall net income. If
the $85,000 rent cannot be avoided and the North Store is closed, the
company s overall net operating income would be reduced by $114,800
per quarter ($29,800 + $85,000).
3. Under these circumstances, the North Store should be closed. The
computations are as follows:
Gross margin lost if the North Store is closed (part 1) ...... $(316,800)
Gross margin gained from the East Store: $720,000 ×
1/4 = $180,000; $180,000 × 45%* = $81,000 .............
81,000
Net operating loss in gross margin .................................. (235,800)
Less costs that can be avoided if the North Store is
closed (part 1)............................................................
287,000
Net advantage of closing the North Store ........................ $ 51,200
* The East Store s gross margin percentage is:
$486,000 ÷ $1,080,000 = 45%
12
Problem 13- 23
1. Since the fixed costs will not change as a result of the order, they are
not relevant to the decision. The cost of the new machine is relevant,
and this cost will have to be recovered by the current order since there
is no assurance of future business from the retail chain.
Total
Unit 5,000 units
Revenue from the order ($50 × 84%)................... $42
$210,000
Less costs associated with the order:
Direct materials ................................................ 15
75,000
Direct labor ......................................................
8
40,000
Variable manufacturing overhead .......................
3
15,000
Variable selling expense ($4 × 25%) ..................
1
5,000
Special machine ($10,000 ÷ 5,000 units)............
2
10,000
Total costs .......................................................... 29
145,000
Net increase in prof its.......................................... $13
$ 65,000
2. Revenue from the order:
Reimbursement for costs of production (variable
production costs of $26, plus fixed manufacturing
overhead cost of $9 = $35 per unit; $35 per unit ×
5,000 units)...........................................................
Fixed fee ($1.80 per unit × 5,000 units) .....................
Total revenue..............................................................
Less incremental costs variable production costs
($26 per unit × 5,000 units) ......................................
Net increase in prof its .................................................
3. Sales revenue:
From the U.S. Army (above) ......................................
From regular channels ($50 per unit × 5,000 units).....
Net decrease in revenue ..............................................
Less variable selling expenses avoided if the Army s
order is accepted ($4 per unit × 5,000 units)..............
Net decrease in prof its if the Army s order is accepted ...
$175,000
9,000
184,000
130,000
$ 54,000
$184,000
250,000
(66,000)
20,000
$(46,000)
13
Problem 13-24
1.
Sewing
Debbie Trish Sarah Mike
Kit
Direct labor cost per unit ................................
$ 3.20 $2.00 $ 5.60 $ 4.00 $ 1.60
Direct labor hours per
unit* (a) ................................
0.40 0.25
0.70
0.50
0.20
Selling price................................
$13.50 $5.50 $21.00 $10.00 $ 8.00
Less variable costs:
Direct materials ................................
4.30 1.10
6.44
2.00
3.20
Direct labor ................................
3.20 2.00
5.60
4.00
1.60
Variable overhead ................................
0.80 0.50
1.40
1.00
0.40
Total variable costs................................
8.30 3.60 13.44
7.00
5.20
Contribution margin (b) ................................
$ 5.20 $1.90 $ 7.56 $ 3.00 $ 2.80
Contribution margin per
DLH (b) ÷ (a)................................
$13.00 $7.60 $10.80 $ 6.00 $14.00
* Direct labor cost per unit ÷ 8 direct labor hour.
2.
Estimated
DLH Per
Total
Sales
Product
Unit
Hours
(units)
Debbie ................................
0.40 hours
50,000
20,000
Trish ................................0.25 hours
42,000
10,500
Sarah ................................
0.70 hours
35,000
24,500
Mike................................0.50 hours
40,000
20,000
Sewing Kit ................................
0.20 hours 325,000
65,000
Total hours required ................................
140,000
3. Since the Mike doll has the lowest contribution margin per labor hour, its
production should be reduced by 20,000 dolls (10,000 excess hours
divided by 0.5 hours production time per doll = 20,000 dolls). Thus,
production and sales of the Mike doll will be reduced to one-half of that
planned, or 20,000 dolls for the year.
14
Problem 13- 24 (continued)
4. Since the additional capacity would be used to produce the Mike doll,
the company should be willing to pay up to $14 per hour ($8 usual rate
plus $6 contribution margin per hour) for added labor time. Thus, the
company could employ workers for overtime at the usual time-and-ahalf rate of $12 per hour ($8 × 1.5 = $12), and still improve overall
profit.
5. Additional output could be obtained in a number of ways including
working overtime, adding another shift, expanding the workforce,
contracting out some work to outside suppliers, and eliminating wasted
labor time in the production process. The first four methods are costly,
but the last method can add capacity at very low cost.
Note: Some would argue that direct labor is a fixed cost in this situation
and should be excluded when computing the contribution margin per
unit. However, when deciding which products to emphasize, no harm is
done by misclassifying a fixed cost as a variable cost providing that the
fixed cost is the constraint. If direct labor were removed from the
variable cost category, the net effect would be to bump up the
contribution margin per direct labor-hour by $8 for each of the products.
The products will be ranked exactly the same in terms of the
contribution margin per unit of the constrained resource whether direct
labor is considered variable or fixed. However, this only works when the
fixed cost is the cost of the constraint itself.
15