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.
