Question

3. Suppose a project under consideration has the following stream of benefits and costs. Year O Costs $10,000 Benefits 4 S5,000 $2,000S4,000 S6,000 $8,000 S10,000 $2,000 (a) Find the net present value of the project assuming a discount rate of 5%. Is the project worthwhile? (b) 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.
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Answer #1

Answer:

Given that,

Q(B) Ans:

Let us assume that, 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

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.

Q(a) Ans:

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.

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

Hence 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.

Hence Proved.

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