Question

Two investment opportunities are as follows:________. Alt A Alt B First Cost 200 100 Uniform annual benefit 32 27 End of useful life salvage value 20 0 Useful life, in years 10 5 At the end of 5 years, Alt B is not replaced. Thus, the comparison is 10 years of A versus 5 years of B. If MARR is 10%, which alternative should be selected based on NPV (or NPW) analysis?

Answer 1

Answer:

Since the 4.34 NPV of Alt A is greater than the 2.35 NPV of Alt B, it therefore implies that Alt A should be selected.

Explanation:

Note: The data in the question are merged together. They are therefore sorted before answering the question as follows:

                                                          Alt A              Alt B

First Cost                                           200                 100

Uniform annual benefit                       32                   27

End of useful life salvage value         20                    0

Useful life, in years                              10                     5

The explanation to the answer is now given as follows:

a. Calculation of NPV of Alt A

First Cost = 200

PV of uniform annual benefit = P * ((1 - (1 / (1 + r))^n) / r) ……………………. (2)

Where;

P = uniform annual benefit = 32

r = MACC = 10%, or 0.10

n = number of useful years = 10

Note: The formula for calculating the present value of ordinary annuity is being used here to calculate the Present Value (PV) of uniform annual benefit.

Substitute the values into equation (1) to have:

PV of uniform annual benefit = 32 * ((1 - (1 / (1 + 0.10))^10) / 0.10) = 32 * 6.14456710570468 = 196.63

PV of Salvage value = FV / (1 + r)^n ..................... (2)

Where;

FV = End of useful life salvage value = 20

r = MACC = 10%, or 0.10

n = number of useful years = 10

Note: The normal formula for calculating the present value (PV) is being used here to calculate the PV of Salvage value

Substitute the values into equation (2) to have:

PV of Salvage value = 20 / (1 + 0.10)^10 = 20 / 2.5937424601 = 7.71

Net present value (NPV) of Alt .A = PV of uniform annual benefit + PV of Salvage value - First cost = 196.63 + 7.71 - 200 = 4.34

b. Calculation of NPV of Alt B

First Cost = 100

PV of uniform annual benefit = P * ((1 - (1 / (1 + r))^n) / r) ……………………. (3)

Where;

P = uniform annual benefit = 27

r = MACC = 10%, or 0.10

n = number of useful years = 5

Note: The formula for calculating the present value of ordinary annuity is also being used here to calculate the Present Value (PV) of uniform annual benefit.

Substitute the values into equation (3) to have:

PV of uniform annual benefit = 27 * ((1 - (1 / (1 + 0.10))^5) / 0.10) = 27 * 3.79078676940845 = 102.35

NPV of Alt B = PV of uniform annual benefit - First cost = 102.35 – 100 = 2.35

c. Decision

Since the 4.34 NPV of Alt A is greater than the 2.35 NPV of Alt B, it therefore implies that Alt A should be selected.