A dam will cost $1,000,000 to build immediately and will yield benefits of $400,
ID: 1155265 • Letter: A
Question
A dam will cost $1,000,000 to build immediately and will yield benefits of $400,000 a year for the next three years. At a discount rate of 10%, which is true?
The benefits are $1,200,000, exceeding the cost, so the project should proceed.
The benefits are $1,200,000, short of the cost, so the project should be rejected.
The benefits are $994,700, short of the cost, so the project should be rejected
The benefits are $994,700, exceeding the cost, so the project should proceed.
The benefits are $1,200,000, exceeding the cost, so the project should proceed.
The benefits are $1,200,000, short of the cost, so the project should be rejected.
The benefits are $994,700, short of the cost, so the project should be rejected
The benefits are $994,700, exceeding the cost, so the project should proceed.
Explanation / Answer
The present value (PV) of benefit should be calculated first.
PV of benefit
Year
Benefit ($), B
10% factors (F) = 1 / (1 + 0.10) ^n [where n = years]
B × F
1
400,000
0.9091
363,640
2
400,000
0.8264
330,560
3
400,000
0.7513
300,520
PV
994,720
Therefore, the PV of benefits is $994,700 (rounded). This should be deducted from the initial cost top get NPV.
NPV = PV of benefits – Initial cost
= 994,700 – 1,000,000
= -5,300
Since the NPV is negative, the PV of benefits becomes short. Therefore, there should be a rejection.
Answer: 3rd option
Year
Benefit ($), B
10% factors (F) = 1 / (1 + 0.10) ^n [where n = years]
B × F
1
400,000
0.9091
363,640
2
400,000
0.8264
330,560
3
400,000
0.7513
300,520
PV
994,720