Question

Part 1: Suppose a project under consideration has the following stream of benefits and costs.

Year	0	1	2	3	4	5
Costs	$10,000			$6,000		$2,000
Benefits		$2,000	$4,000	$6,000	$8,000	$10,000

(a)Find the net present value of the project assuming a discount rate of 5%. Is the project worthwhile?

(b)Redo (a) assuming the discount rate is 10%. Would you recommend the project go forward?

(c)Suppose you have discovered that the benefits of the project have been overestimated and a more accurate assessment suggests that the benefit in each year is half of the original estimate. Assuming a discount rate of 5%, would you recommend the project go forward in this case? Briefly explain your answer.

Part 2: The government is contemplating a project that protects a wilderness area. The project is expected to produce annual net benefits of $100,000 into perpetuity. Assuming a discount rate of 8%, what is the net present value associated with this project?

Answer 1

Net present value (NPV) is the difference of present value of net benefits and the initial (year 0) cost.

Net benefit (NB) = Benefit – Cost

A project could be accepted, if it has positive NPV.

a.

NPV at 5% discount rate

Year	NB	5% discount factor = 1/(1 + 0.05)^n	NB × factor
0	0 – 10,000 = -10,000	1	-10,000
1	2,000	0.9524	1,904.80
2	4,000	0.9070	3,628.00
3	6,000 – 6,000 = 0	0.8638	0
4	8,000	0.8227	6,581.60
5	10,000 – 2,000 = 8,000	0.7835	6,268.00
NPV			8,382.40

Answer: NPV is $8,382.40.

Answer: The project is worthwhile, since it has positive NPV.

b.

NPV at 10% discount rate

Year	NB	5% discount factor = 1/(1 + 0.05)^n	NB × factor
0	0 – 10,000 = -10,000	1	-10,000
1	2,000	0.9091	1,818.20
2	4,000	0.8264	3,305.60
3	6,000 – 6,000 = 0	0.7513	0
4	8,000	0.6830	5,464.00
5	10,000 – 2,000 = 8,000	0.6209	4,967.20
NPV			5,555

Answer: NPV is $5,555.

Answer: The project is recommended, since it has positive NPV.

c.

If the benefit becomes ½, net benefits in each year would be as below:

Year	Benefits, B	Costs, C	Net benefits [B – C]
0	0	10,000	-10,000
1	1,000	0	1,000
2	2,000	0	2,000
3	3,000	6,000	-3,000
4	4,000	0	4,000
5	5,000	2,000	3,000

NPV at 5% discount rate

Year	NB	5% discount factor = 1/(1 + 0.05)^n	NB × factor
0	-10,000	1	-10,000
1	1,000	0.9524	952.40
2	2,000	0.9070	1,814.00
3	-3,000	0.8638	-2,591.40
4	4,000	0.8227	3,290.80
5	3,000	0.7835	2,350.50
NPV			-4,183.70

Answer: NPV is -$4,183.70.

Answer: The project is not recommended, since it has negative NPV.

Explanation: Once benefits in each year go down, NB becomes low. This is the reason why NPV becomes negative.

Part 2: NPV at perpetuity would be as below:

NPV = Net benefits / Discount rate

         = $100,000 / 0.08

         = $1,250,000 (Answer)