Question

Consider a heat pump purchase with the following details:

* Initial cost: 20,000 USD

* Annual savings: 3,000 USD for 20 years

* Annual maintenance costs: 250 USD for 20 years

* Estimated salvage value: 500 USD at the end of 20 years

(a) If the interest rate is 10%, what is the net present worth of this heat pump?

(b) Calculate the simple payback period of the heat pump.

(c) Calculate the Benefit/Cost ratio of the heat pump purchase.

(d) Does the heat pump purchase make sense financially? Why?

Answer 1

(a)

Net Annual Benefit (NB) = Annual saving - Annual cost = 3,000 - 250 = 2,750

Net present worth (NPW) (USD) = - 20,000 + NAB x P/A(10%, 20) + 500 x P/F(10%, 20)

= - 20,000 + 2,750 x 8.5136 + 500 x 0.1486

= - 20,000 + 23,412.4 + 74.3

= 3,486.7

(b)

Simple payback period (PBP) is the year by when cumulative cash flow is equal to zero.

PBP = Initial cost / NAB

= 20,000 / 2,750

= 7.27 years

(c)

Benefit/cost (B/C) ratio = Annual saving / (AW of Initial cost + Annual cost - AW of salvage value)

= 3,000 / [20,000 x A/P(10%, 20) + 250 - 500 x A/F(10%, 20)]

= 3,000 / [(20,000 x 0.1175) + 250 - (500 x 0.0175)]

= 3,000 / (2,350 + 250 - 8.75)

= 3,000 / 2,591.25

= 1.16

(d)

The heat pump has Positive NPW and B/C Ratio higher than 1, therefore it is acceptable.