Question

The Brisbane Manufacturing Company produces a single model of a CD player. Each player is sold for $190 with a resulting contribution margin of $70. Brisbane's management is considering a change in its quality control system. Currently, Brisbane spends $41,500 a year to inspect the CD players. An average of 1,900 units turn out to be defective - 1,330 of them are detected in the inspection process and are repaired for $85. 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. The proposed quality control system involves the purchase of an x-ray machine for $180,000. The machine would last for four years and would have salvage value at that time of $22,000. Brisbane would also spend $430,000 immediately to train workers to better detect and repair defective units. Annual inspection costs would increase by $21,000. This new control system would reduce the number of defective units to 370 per year. 300 of these defective units would be detected and repaired at a cost of $43 per unit. Customers who still received defective players would be given a refund equal to 120% of the purchase price.

3. assuming a discount rate of 8%, what is the net present value if Brisbane keeps using its current system?

4. Assuming a discount rate of 8%, what is the net present value if Brisbane replaces its current system?

Answer 1

Solution: 3) If Brisbane keeps using its current system

Net present value of4 years cost

Annual Inspection cost = 41500

Defective units sent to customers = Total defective units - Detective defective units

   = 1900-1330 = 570

Annual loss on defective units sent to customers = Loss of margin + Extra 20%

= 70*570 + 190*20%*570 = 61560

Annual cost on repair of defective units identified = Identified unit*Repair cost per unit

= 1330*85 = 113050

Total Annual Cost = 41500+61560+113050 = 216110

NPV = 216110 + 216110/(1.08) + 216110/(1.08)² + 216110/(1.08)³ = 773046

4) Under New Mechanism

One time training cost = 43000

Annual Inspection cost = 41500 +21000 = 62500

Defective units sent to customers = Total defective units - Detective defective units

   = 370-300 = 70

Annual loss on defective units sent to customers = Loss of margin + Extra 20%

= 70*70 + 190*20%*70 = 7560

Annual cost on repair of defective units identified = Identified unit*Repair cost per unit

= 300*43 = 12900

Purchase Cost = 180000

Salvage Value (sale value in 4th year) = 22000

1st year cost = One time training cost + Purchase cost + Annual maintenance + Loss on defective units sent to customers+ repair cost of identified units

= 43000+180000+62500+7560+12900 = 305960

2nd & 3rd year = Annual maintenance + Loss on defective units sent to customers+ repair cost of identified units

= 62500+7560+12900= 82960

4th year =  Annual maintenance + Loss on defective units sent to customers+ repair cost of identified units - salvage value

= 62500+7560+12900-22000=60960

NPV = 305960 + 82960/(1.08) + 82960/(1.08)² + 60960/(1.08)³ = 502292

Therefore, NPV under new mechanism is $ 502292, which is less than NPV under current mechanism

Hence, company shall switch to new mechanism instead of the current one.