Respuesta :
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.
Based on the various costs of the heating system, the savings it will bring, and the present worth method, the system should be purchased.
Why should the system be purchased?
It should be purchased if the Net Present Worth is above $0.
Net Present Worth = Present worth of inflows - Present of outflows
Inflows = Savings + Residual value
Savings are:
= 500,000 kilo-wat hours x 0.10 kilo-watt per hour
= $50,000
Net present worth:
= ( (50,000 x (P/A,12%,8 years)) + (20,0000 x (P/F, 12%, 8 years))) - 200,000
= $56,458
In conclusion, the NPW is more than $0 so this system should be picked.
Find out more on the Present Worth/ Value Method at https://brainly.com/question/13228231.
