Homework Answers
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)
Add Answer to:
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