Question

Consider a highway project with the following costs and benefits. This representation of costs and benefits assumes the costs occur immediately and the benefits occur at the end of year 1, end of year 2 and the end of year 3.

Year	0	1	2	3
Costs	$470,000
Benefits		$275,000	$295,000	$315,000

(a) Calculate the net present value of the project. Assume a discount rate of 4%.

(b) Now suppose all the benefits occur at the start of each period. What happens to your net present value calculation?

Answer 1

a) Net present value of the project = P0 + P1(1 + r)^-1 + P2(1 + r)^-2 + P3(1 + r)^-3

= -470,000 + 275,000(1 + 4%)^-1 + 295,000(1 + 4%)^-2 + 315,000(1 + 4%)^-3

= $347,201

b) When all benefits occur in the beginning of each period we have

Net present value of the project = P0 + P1 + P2(1 + r)^-1 + P3(1 + r)^-2

= -470,000 + 275,000 + 295,000(1 + 4%)^-1 + 315,000(1 + 4%)^-2

= $379,889

Net present value rises when benefits are received in the beginning of the year.