Appendix B
Profitability Analysis
Solutions to Questions
B-1 Absolute profitability measures the
customer, without making any other changes.
B-2 Relative profitability involves ranking
they are not necessary.
B-3 Every business that seeks to maximize
profits has a constraint. No business ever has
time or talent, or it might be some internal
policy that prevents the firm from progressing,
art, or some other objective.
B-4 The absolute profitability of a segment
is measured by the difference between the
B-5 The relative profitability of a segment is
from the segment by the amount of the
constrained resource required by the segment.
Consequently, to measure relative profitability,
B-6 A volume trade-off decision involves
trading off units of one product for another. In
such decisions fixed costs are usually irrelevant
and the products can be ranked by dividing their
B-7 The selling price of a new product
should at least cover its variable costs and
selling price should cover any avoidable fixed
costs of the product. Exactly how much of the
avoidable fixed costs should be covered by each
unit is difficult to determine
a priori
because the
Exercise B-1 (30 minutes)
1. This exercise can be solved by first computing the profitability index of
each new ride and then ranking the rides based on that profitability
index:
Net Present
Value
(A)
Safety
Engineer
Time
Required
(B)
Profitability
Index
(A) ÷ (B)
Ride 1…….
$1,268,200
340
$3,730
Ride 2…….
$1,152,000
360
$3,200
Ride 3…….
$649,600
320
$2,030
Ride 4…….
$644,100
190
$3,390
Ride 5…….
$540,000
250
$2,160
Ride 6…….
$539,200
160
$3,370
Ride 7…….
$462,000
110
$4,200
Ride 8…….
$457,200
360
$1,270
Ride 9…….
$403,200
180
$2,240
Ride 10 …..
$387,500
250
$1,550
Profitability
Index
Safety
Engineer
Time
Required
Cumulative
Amount of
Safety
Engineer
Time
Required
Ride 7…….
$4,200
110
110
Ride 1…….
$3,730
340
450
Ride 4…….
$3,390
190
640
Ride 6…….
$3,370
160
800
Ride 2…….
$3,200
360
1,160
Ride 9…….
$2,240
180
1,340
Ride 5…….
$2,160
250
1,590
Ride 3…….
$2,030
320
1,910
Ride 10 …..
$1,550
250
2,160
Ride 8…….
$1,270
360
2,520
Given the 1,590 hours of safety engineer time available, the seven rides
above the line in the above table should be built.
Exercise B-1 (continued)
2. The total net present value for the seven new rides to be built is
computed as follows:
Ride 7 …….
$ 462,000
Ride 1 …….
1,268,200
Ride 4 …….
644,100
Ride 6 …….
539,200
Ride 2 …….
1,152,000
Ride 9 …….
403,200
Ride 5 …….
540,000
$5,008,700
Exercise B-2 (30 minutes)
1. There is not enough capacity in the bottleneck operation to satisfy demand for all four products. The
total amount of time available in the bottleneck operation is 1,800 hours, but 2,700 hours would be
required to satisfy demand as shown below:
Adirondack
Lake Huron
Oysterman
Voyageur
Total
80
120
100
140
5
4
7
8
400
480
700
1,120
2,700
2. The profitability index should be used to rank the products.
Adirondack
Lake Huron
Oysterman
Voyageur
$485
$268
$385
$600
5
4
7
8
$97
$67
$55
$75
The most profitable use of the bottleneck operation (the constraint) is the Adirondack model,
followed by the Voyageur model and then the Lake Huron and Oysterman models. Because no fixed
costs would be affected by this decision, the optimal plan would be:
Exercise B-2 (continued)
Amount of constrained resource available ………………….
1,800 hours
Less: Constrained resource required for production of 80
units of the Adirondack model ……………………………..
400 hours
Remaining constrained resource available ………………….
1,400 hours
Less: Constrained resource required for production of
140 units of the Voyageur model ………………………….
1,120 hours
Remaining constrained resource available ………………….
280 hours
Less: Constrained resource required for production of 70
units of the Lake Huron model …………………………….
280 hours
Remaining constrained resource available ………………….
0 hours
3. The total contribution margin under the above plan would be $141,560:
Adirondack
Lake Huron
Oysterman
Voyageur
Total
$485
$268
$385
$600
80
70
0
140
$38,800
$18,760
$0
$84,000
$141,560
Exercise B-3 (10 minutes)
The selling price of the new praline cappuccino product should at least
cover its variable cost and its opportunity cost. The variable cost of the
new product is $0.30 and its opportunity cost can be computed by
Problem B-4 (30 minutes)
1. The constraint is customer representatives’ time and the incremental profit is revenues less cost of
drugs sold and customer service costs.
Leafcrest
Pharmacy
Providence
Hospital
Pharmacy
Madison Clinic
Pharmacy
Jenkins
Pharmacy
Total revenues ………………………
$272,650
$2,948,720
$1,454,880
$155,280
Cost of drugs sold ………………….
211,470
2,234,480
1,119,440
115,920
Customer service costs …………..
10,640
74,400
42,000
4,480
Incremental profit (a) …………….
$ 50,540
$ 639,840
$ 293,440
$ 34,880
Customer representative time (b)
190 hours
1,240 hours
560 hours
80 hours
Profitability index (a) ÷ (b)………
$266 per hour
$516 per hour
$524 per hour
$436 per hour
The Madison Clinic Pharmacy is the most profitable of the customers, followed by the Providence
Hospital Pharmacy, the Jenkins Pharmacy, and lastly the Leafcrest Pharmacy.
2. The company could certainly afford to pay its customer representatives more in order to retain them.
The company makes at least $266 in incremental profit per hour of customer representative time
Problem B-5 (60 minutes)
1. There is not enough kiln capacity to satisfy demand for all four products.
The total amount of time available is 2,000 hours, but 2,600 hours
would be required to satisfy demand as shown below:
Traditional
Brick
Textured
Facing
Cinder
Block
Roman
Brick
Total
Annual demand in
pallets (a) ………..
90
110
100
120
Hours required in
the drying kiln
per pallet (b)…….
8
8
4
5
Total hours required
in the drying kiln
(a) × (b) ………….
720
880
400
600
2,600
2. The profitability index should be used to rank the products.
Traditional
Brick
Textured
Facing
Cinder
Block
Roman
Brick
Contribution margin per
pallet (a) ………………
$472
$632
$376
$440
Hours required in drying
kiln per pallet (b) ……
8
8
4
5
Profitability index
(a) ÷ (b) ……………….
$59
$79
$94
$88
The most profitable use of the bottleneck operation (the constraint) is
the Cinder Block product, followed by the Roman Brick product and then
the Textured Facing and Traditional Brick products. Because no fixed
costs would be affected by this decision, the optimal plan would be:
Problem B-5 (continued)
Amount of constrained resource available
2,000 hours
Less: Constrained resource required for
production of 100 pallets of Cinder
Block ………………………………………….
400 hours
Remaining constrained resource available
1,600 hours
Less: Constrained resource required for
production of 120 pallets of Roman
Brick …………………………………………..
600 hours
Remaining constrained resource available
1,000 hours
Less: Constrained resource required for
production of 110 pallets of Textured
Facing ………………………………………..
880 hours
Remaining constrained resource available
120 hours
Less: Constrained resource required for
production of 15 pallets of Traditional
Brick …………………………………………..
120 hours
Remaining constrained resource available
0 hours
3. The total contribution margin under the above plan would be $167,000:
Traditional
Brick
Textured
Facing
Cinder
Block
Roman
Brick
Total
Contribution
margin per
pallet (a) ……
$472
$632
$376
$440
Optimal
production
plan (b) …….
15
110
100
120
Total
contribution
margin
(a) × (b) ……
$7,080
$69,520
$37,600
$52,800
$167,000
4. The company should be willing to pay up to $59 per hour to operate the
kiln until demand is satisfied for traditional bricks.