Question

The Brisbane Manufacturing Company produces a single model of a CD player. Each player is sold for $182 with a resulting contribution margin of $71. Brisbane's management is considering a change in its quality control system. Currently, Brisbane spends $42,000 a year to inspect the CD players. An average of 1,900 units turn out to be defective: 1,520 of them are detected in the inspection process and are repaired for $75. 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 $210,000. The machine would last for five years and would have salvage value at that time of $18,000. Brisbane would also spend $470,000 immediately to train workers to better detect and repair defective units. Annual inspection costs would increase by $25,000. Brisbane expects this new control system to reduce the number of defective units to 400 per year. 350 of these defective units would be detected and repaired at a cost of only $41 per unit. Customers who still receive defective players will be given a refund equal to 120% of the purchase price.

Required:
a. What is the Year 3 cash flow if Brisbane keeps using its current system?
b. What is the Year 3 cash flow if Brisbane replaces its current system?
c. Assuming a discount rate of 8%, what is the net present value if Brisbane keeps using its current system?
d. Assuming a discount rate of 8%, what is the net present value if Brisbane replaces its current system?

Answer 1

Year 3 cashflow:

current system: 243,360

alternative system: 102,240

Present cost:

current system PV -$971,665.9146

alternative system PV -$1,075,964.17

Step-by-step explanation:

Current Scenario:

42,000 inspection cost

Repairs:

1,520 identified x $75 = 114,000

Refunds:

480 units x $182 = 87,360

Total yearly cost: 243,360

PV of an annuity of $243,360 during 5 years:

Present Value of Annuity

`C * \displaystyle (1-(1+r)^(-time) )/(rate) = PV\\`

C 243,360

time 5

rate 0.08

`243360 * \displaystyle (1-(1+0.08)^(-5) )/(0.08) = PV\\`

PV $971,665.9146

New Scenario:

Inspection cost: $42,000 + $25,000 = $77,000

Repair cost: 350 units x $41 = $14,320

Refunds: 50 units x $182 x 120% = $10,920

Total yearly cost: $102,240

F0 cost:

470,000 workers trainings

210,000 purchase cost

Total F0 cost: 680,000

Present Value of Annuity

`C * \displaystyle (1-(1+r)^(-time) )/(rate) = PV\\`

C 102,240

time 5

rate 0.08

`102240 * \displaystyle (1-(1+0.08)^(-5) )/(0.08) = PV\\`

PV $408,214.6742

PV of residual value:

PRESENT VALUE OF LUMP SUM

`(Maturity)/((1 + rate)^(time) ) = PV`

Maturity 18,000.00

time 5.00

rate 0.08

`(18000)/((1 + 0.08)^(5) ) = PV`

PV 12,250.50

Net present value:

- 680,000 -408,214.67 + 12,250.50 = 1,075,964.17