Answer:
Since the present worth (PW) is $56,459.65 and positive, the new system should be purchased.
Explanation:
C = Cost of the upgraded "variable air-volume system" retrofit = $200,000
S = Residual value of the system = $20,000
n = Estimated life of the upgraded "variable air-volume system" retrofit = 8
r = cost of capital per year = 12%, or 0.12
P = Amount of power savings per year = Number of kilo-Watt hours per year * Cost of electricity per kilo-Watt hour = 500,000 * $0.10 = $50,000
Using the formula for calculating the present value (PV) or ordinary annuity, the PV of P can be calculated:
PV of P = P * ((1- (1/(1 + r))^n) / r) = $50,000 * ((1- (1/(1 + 0.12))^8) / 0.12) = $248,381.99
The PV of the residual value (PV of S) can be calculated as follows:
PV of S = S / (1 + r)^n = $20,000 / (1 + 0.12)^8 = $8,077.66
The present worth (PW) can now be calculated as follows:
PW = PV of P + PV of S - C = $248,381.99 + $8,077.66 - $200,000 = $56,459.65
Since the present worth (PW) is $56,459.65 and positive, the new system should be purchased.
