A simple, direct space heating system is currently being used in a professional medical office complex. An upgraded "variable air-volume system" retrofit can be purchased and installed for $200,000 (investment cost). Its power savings in the future will be 500,000 kilo-Watt hours per year over its estimated life of 8 years. The cost of electricity is $0.10 per kilo-Watt hour. If the firm’s cost of capital is 12% per year and the residual value of the system in 8 years is $20,000, should the new system be purchased? Use the present worth method.

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30-06-2021
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A simple, direct space heating system is currently being used in a professional medical office complex. An upgraded "variable air-volume system" retrofit can be purchased and installed for $200,000 (investment cost). Its power savings in the future will be 500,000 kilo-Watt hours per year over its estimated life of 8 years. The cost of electricity is $0.10 per kilo-Watt hour. If the firm’s cost of capital is 12% per year and the residual value of the system in 8 years is $20,000, should the new system be purchased? Use the present worth method.

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amcool amcool · Answer 1 · 2021-07-01T00:08:53+02:00

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.

Parrain Parrain · Answer 2 · 2022-03-15T15:30:25+01:00

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.