The Brisbane Manufacturing Company produces a single model of a CD player. Each
ID: 2757917 • Letter: T
Question
The Brisbane Manufacturing Company produces a single model of a CD player. Each player is sold for $181 with a resulting contribution margin of $79. Brisbane's management is considering a change in its quality control system. Currently, Brisbane spends $38,000 a year to inspect the CD players. An average of 2,200 units turn out to be defective - 1,760 of them are detected in the inspection process and are repaired for $80. If a defective CD player is not identified in the inspection process, the customer who receives it is given a full refund of the purchase price. Competitors are expected to improve their quality control systems in the future, so if Brisbane does not improve its system, sales volume is expected to fall by 530 CD players a year for the next four years. In other words, it will fall by 530 units in the first year, 1,060 units in the second year, etc.. The proposed quality control system involves the purchase of an x-ray machine for $290,000. The machine would last for four years and would have salvage value at that time of $22,000. Brisbane would also spend $790,000 immediately to train workers to better detect and repair defective units. Annual inspection costs would increase by $25,000. This new control system would reduce the number of defective units to 360 per year. 305 of these defective units would be detected and repaired at a cost of $46 per unit. Customers who still received defective players would be given a refund equal to one-and-a-half times the purchase price. 1. Assuming a discount rate of 8%, what is the net present value if Brisbane keeps using its current system? 2. Assuming a discount rate of 8%, what is the net present value if Brisbane replaces its current system?
Explanation / Answer
1..
current system :
Selling Price
181
contribution Margin
79
Variable cost
102
current inspection cost
38000
defective production(units)
2200
detected and repaired (units)
1760
Undetected defective units (1800-1440)
440
Repair charges per unit
80
calculation of NPV
Years
1
2
3
4
fall in sales units
530
1060
1590
2120
income lost (fall in sales x contribution margin)
41870
83740
125610
167480
current inspection cost
38000
38000
38000
38000
defective units detected and repaired
(1760 units*80)
140800
140800
140800
140800
Refund for defective units (440units*$181)
79640
79640
79640
79640
total
300310
342180
384050
425920
Discont factor @8%
0.925925926
0.85733882
0.793832241
0.735029853
278064.8148
293364.1975
304871.2722
313063.9149
NPV
- 1,189,364
2..
NEW SYSTEM DATA
MACHINE
290000
SALVAGE
22000
TRAINING COST
790000
INSPECTION COST (38000+25000)
63000
DEFECTIVE
360
REPAIRED
305
REPAIR CHG
46
REFUND (181*1.5)
271.5
calculation of NPV
0
1
2
3
4
INSPECTION COST (38000+25000)
63000
63000
63000
63000
REPAIR (305*46)
14030
14030
14030
14030
REFUND (46*181*1.5)
12489
12489
12489
12489
TRAINING COST
790000
MACHINE
290000
SALVAGE
-22000
1080000
89519
89519
89519
67519
Discont factor @8%
1
0.925925926
0.85733882
0.793832241
0.735029853
1080000
82887.96296
76748.11385
71063.06838
49628.48063
NPV
- 1,360,327.63
current system :
Selling Price
181
contribution Margin
79
Variable cost
102
current inspection cost
38000
defective production(units)
2200
detected and repaired (units)
1760
Undetected defective units (1800-1440)
440
Repair charges per unit
80
calculation of NPV
Years
1
2
3
4
fall in sales units
530
1060
1590
2120
income lost (fall in sales x contribution margin)
41870
83740
125610
167480
current inspection cost
38000
38000
38000
38000
defective units detected and repaired
(1760 units*80)
140800
140800
140800
140800
Refund for defective units (440units*$181)
79640
79640
79640
79640
total
300310
342180
384050
425920
Discont factor @8%
0.925925926
0.85733882
0.793832241
0.735029853
278064.8148
293364.1975
304871.2722
313063.9149
NPV
- 1,189,364
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