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.

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.

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