Question

In an environmental project, a ground source heat pump system will be installed, which will result in an annual fuel savings of $2000/year. The initial investment of the heat pump system is $14 000. The life-time of the heat pump system is 20 years. The annual maintenance cost is $300/year. At the end of the 20 years' life time, the salvage value is $1500. The interest rate is 10%.

Please investigate and comment that how the "annual fuel saving" and its variation will affect the results of

(1) The net present value (NPV) of this investment

(2) The benefit-cost ratio (BCR) of this investment

(3) Internal rate of return (IRR) of this investment

(4) Based on the above NPV, BCR and IRR values, please determine whether this investment is attractive or not?

For example, the "annual fuel saving" varies +/- $0~300 based on the original $2000 /year.

Answer 1

(1) Initial investment = $14,000

Benefit : Annual fuel savings     = $2,000 per annum

Less: Cost : Maintenance cost = $300 per annum

Net benefit                              = $1,700 per annum

Life of heat pump = 20 years

Salvage value at end of life = $1,500

Discount rate = 10%

Present value of net benefit = Net benefit x PVAF (10%, 20 years)

Present value of net benefit = 1,700 x 8.514 = $14,473.80

Present value of Salvage value = Salvage value at end of life x PVF(10%, 20years)

Present value of Salvage value = 1,500 x 0.1486 =$222.96

Present value of inflows = Present value of net benefit + Present value of Salvage value

Present value of inflows = $14,473.80 + $222.96 = $14,696.76

NPV = Present value of inflows - Initial investment

NPV = $14,696.76 - $14,000 = $696.76

(2) Benefit-cost ratio (BCR) = PV of benefit / PV of cost

where,

PV of benefit = $2,000 x 8.514 + $1,500 x 0.1486 = $17,250.9

PV of cost = $14,000 + $300 x 8.514 = $16,554.2

Benefit-cost ratio (BCR) = $17,250.9 / $16,554.2 = 1.042

(3) IRR calculated using financial calculator :

CF0 = -14,000

C01 = 1,700

F01 = 19

C20 = 1,700 + 1,500 = 3,200

Compute IRR -

IRR = 10.704%

(4) NPV is positive = $696.76

BCR is greater than 1 = 1.042

IRR is greater than cost of capital i.e. 10% = 10.704%

All the three parameters are favorable. Hence, based on above investment is attractive.