Question

The government of Cristal Clean Village has been concerned by the toxic air pollution risk in the
village and initiated a new policy campaign called “Clean Air Better Lives”. Two green energy
companies in the village, Air Hunter Ltd, and Cristal Air Ltd, proposed projects that can potentially deliver the objective of the campaign. The projects’ benefit and cost streams are computed as follows. The discount rate for the projects is 10%.

	year	0	1	2	3	4	5 and after*
Cristal Air	Benefits	2000	7000	12000	17000	22000	100
	Costs	5000	20000	15000	5000	5000	0
Air Hunter	Benefits	0	5000	10000	20000	10000	1000
	Costs	5000	20000	15000	5000	5000	0

*This means that the payment stream of year 5 will go on forever.
i. What are the net present values (NPVs) (NPV of the net benefits) of each project?
ii. Which project should be selected?

Answer 1

Formula for calculating the net present value is following

Net Present Value (NPV) = CF/(1+i)ⁿ

CF = Cash Flow

i = Discount rate

n = Number of years

We have been given the following information

Cristal Air

Year	Benefits	Costs	Cash Flow	Present Value of the Cash Flow
0	2,000	5,000	-3000	-3000.0
1	7,000	20,000	-13000	-11818.2
2	12,000	15,000	-3000	-2479.3
3	17,000	5,000	12000	9015.8
4	22,000	5,000	17000	11611.2
5	100	-	100	62.1
Net Present Value				3391.6

Air Hunter

Year	Benefits	Costs	Cash Flow	Present Value of the Cash Flow
0	-	5,000	-5000	-5000.0
1	5,000	20,000	-15000	-13636.4
2	10,000	15,000	-5000	-4132.2
3	20,000	5,000	15000	11269.7
4	10,000	5,000	5000	3415.1
5	1,000	-	1000	620.9
Net Present Value				-7462.9

Since, the NPV of Cristal Air is positive while that of Air Hunter is negative so, Cristal Air should be selected.