Question

The Larkspur Furniture Company needs a new grinder. Compute the present worth for these mutu- ally exclusive alternatives and identify which you would recommend given i = 6% per year. Larkspur uses a 10-year planning horizon. Alternative A B Initial cost Annual costs Salvage value Life $4500 $300 $500 5 years $5500 $400 $0 10 years

Answer 1

Interest Rate = 6%

Planning horizon = 10 years

Therefore, Alternative has to be repeated two times. Alternative A has the life of 5 years and to be equal to planning horizon, it is to be repeated two times.

Alternative A

Initial Cost = 4,500

Annual Cost = 300

Salvage Value = 500

PW = 4,500 + 4,500 (P/F, 6%, 5) + 300 (P/A, 6%, 10) – 500 (P/F, 6%, 5) – 500 (P/F, 6%, 10)

PW = 4,500 + 4,500 (0.74726) + 300 (7.36009) – 500 (0.74726) – 500 (0.55839)

PW = 9,418

Alternative B

Initial Cost = 5,500

Annual Cost = 400

Salvage Value = 0

PW = 5,500 + 400 (P/A, 6%, 10)

PW = 5,500 + 400 (7.36009)

PW = 8,444

On the basis of PW comparison, select the Alternative B because of less PW or less cost.

Both the alternatives are cost dominated. So, the negative sign to cost is ignored and salvage value is deducted.