Question

Use Present Worth Analysis to determine whether Alternative A or B should be chosen. Items are identically replaced at the end of their useful lives. Assume an interest rate of 6% per year, compounded annually.

Alternative A Alternative B
Initial Cost 350 985
Annual Benefit 80 226
Salvage Value 160 186
Useful Life (yrs) 2 3
A. Alternative B, because it only incurs the initial cost once every three years instead of every two years
B. Alternative B, because it costs $250.00 more than Alternative A, in terms of present worth
C. Alternative A, because its present worth is positive
D. Alternative A, because it costs $250.00 less than Alternative B, in terms of present worth

Answer 1

To determine whether Alternative A or B should be chosen using Present Worth Analysis, calculate the present worth for each alternative. Present Worth of A = -154.48, Present Worth of B = 807.62. Alternative B should be chosen.

Step-by-step explanation:

To determine whether Alternative A or B should be chosen using Present Worth Analysis, we need to calculate the present worth for each alternative. The present worth of a stream of cash flows is determined by discounting each cash flow to its present value using the given interest rate.

For Alternative A, the initial cost of $350 is incurred every 2 years, and the annual benefit of $80 is received for 2 years. The salvage value is $160.

For Alternative B, the initial cost of $985 is incurred every 3 years, and the annual benefit of $226 is received for 3 years. The salvage value is $186.

To calculate the present worth of the cash flows for each alternative, we use the formula:

Present Worth = Initial Cost + (Annual Benefit - Salvage Value) / (1 + Interest Rate)^n

Plugging in the values for Alternative A, we get:

Present Worth of A = 350 + (80 - 160) / (1 + 0.06)^2 = -154.48

For Alternative B, we have:

Present Worth of B = 985 + (226 - 186) / (1 + 0.06)^3 = 807.62

Since the present worth of Alternative B is positive and higher than the present worth of Alternative A, we can conclude that Alternative B should be chosen.

Answer 2

D. Alternative A, because it costs $250.00 less than Alternative B, in terms of present worth.

Step-by-step explanation:

Net Present Worth of Alternative A:

-350 + 80 * (P/A, 6%, 6) - (350 - 160) * (P/F, 6%, 2) - (350 - 160) * (P/F, 6% , 4) + 160 * (P/F, 6% , 6)

= -350 + 80 * 5.41791 - (340 - 160) * 0.942596 - (350 - 160) * 0.888487 + 160 * 0.837484

NPW = $ -429.39

Net Present Worth of Alternative B:

-985 + 226 * (P/A, 6%, 6) - (985 - 226) * (P/F, 6%, 3) - (985 - 186) * (P/F, 6% , 4) + 186 * (P/F, 6% , 6)

= -985 + 226 * 5.41791 - (985 - 186) * 0.942596 - (985 - 186) * 0.888487 + 186 * 0.837484

NPW = $ -657.24