Question

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

(1) What is the net present value (NPV) of this investment?

(2) What is the benefit-cost ratio (BCR) of this investment?

(3) What is the 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?

Based on the above questions, please investigate and comment that how the "annual fuel saving" and its variation will affect the results of the above question. For example, the "annual fuel saving" varies +/- 0~300 HK$ based on the original 2000 HK$/year. (* two-page report is required)

Answer 1

Part 1)

Part 2)

Part 3)

IRR of the investment is 10.83%

Part 4)

since present worth of investment is positive at interest rate of 10% , benefit-cost ratio is greater than 1 and IRR is greater than 10%, investment is attractive as per all 3 evaluation criteria

Based on the above questions, please investigate and comment that how the "annual fuel saving" and its variation will affect the results of the above question. For example, the "annual fuel saving" varies +/- 0~300 HK$ based on the original 2000 HK$/year.

Suppose annual savings are HK$ "x" from this investment

annual savings (x)	NPV	Benefit-cost ratio
1700	-1857.5	0.8652
1750	-1431.8	0.8961
1800	-1006.1	0.9270
1850	-580.4	0.9579
1900	-154.7	0.9888
1950	271	1.0197
2000	696.7	1.0506
2050	1122.4	1.0815
2100	1548.1	1.1124
2150	1973.8	1.1433
2200	2399.5	1.1742
2250	2825.2	1.2051
2300	3250.9	1.2360

therefore, annual fuel savings must be atleast 1950 to have a positive NPV at interest rate of 10% and benefit cost ratio of greater than1