Question

Alternative 1 has a first cost of $50,000, will produce an $18,000 net annual benefit over its 10 year life and be salvaged for $5,000. Alternative 2 costs $150,000 and has a salvage value of $50,000 after its 10 year useful life. If interest is 15%, what is the minimum amount of annual benefit that Alternative 2 must produce to make it the preffered choice?

a. This value cannot be determined from the data given

b. $23,500

c. $31,450

d. $35,708

Answer 1

Alternative 1

First cost of $50,000

Net Annual benefits = $18,000

Life = 10 years

Salvage value = $5,000

Interest = 15%

NPW = -50,000 + 18,000 (P/A, 15%, 10) + 5,000 (P/F, 15%, 10)

NPW = -50,000 + 18,000 (5.01877) + 5,000 (.24718) = 41,574

Alternative 2

First cost of $150,000

Life = 10 years

Salvage value = $50,000

Interest = 15%

Minimum amount of annual benefit that Alternative 2 must produce to make it the preferred choice and to do the NPW of Alternative 1 must be equal to the NPW of Alternative 2.

Let A is the Annual benefits of Alternative 2

NPW of Alternative 1 = NPW of Alternative 2

41,574 = -150,000 + A (P/A, 15%, 10) + 50,000 (P/F, 15%, 10)

41,574 = -150,000 + A (5.01877) + 50,000 (.24718)

41,574 = -150,000 + A (5.01877) + 12,359

41,574 = -137,641 + 5.01877A

179,215 = 5.01877A

A = 35,708

Answer – d. $35,708