Question

Please answer question 2

1. The initial cost of constructing a permanent dam (i.e., a dam that is expected to last forever) is $830 million. The annual net benefits will depend on the amount of rainfall: $36 million in a “dry” year, $58 million in a “wet” year, and $104 million in a “flood” year. Meteorological records indicate that over the last 100 years there have been 86 “dry” years, 12 “wet” years, and 2 “flood” years. Assume the annual benefits, measured in real dollars, begin to accrue at the end of the first year. Using the meteorological records as a basis for prediction, what are the net benefits of the dam if the real discount rate is 5 percent?

Initially calculate the expected value of annual net benefits as shown below:

Annual net benefits = (0.86*36) + (0.12*58) + (0.02*104)

=30.96 + 6.96 + 2.08 = 40 million

We need to calculate the present value of annual net benefits. Since, the dam is permanent in nature, therefore use the formula required to calculate the present value of perpetuity.

Hence,

Present Value = (40 million) / 0.05 =$ 800 million

Now, obtain the value of the present value of expected net benefits by subtracting the construction cost from the present value of the annual benefit stream.

Present value of expected net benefits = (800 – 830) million

                               = -30 million

****2. Use several alternative discount rate values to investigate the sensitivity of the present value of net benefits of the dam in exercise 1 to the assumed value of the real discount rate.

Answer 1

We will check discount rate increasing with the rate of 3 percent per year

When discount rate "r"=3%

Then net present value of investment =(40/0.03)-830=1333.3-830=503.3

When discount rate "r"=4%

NPV of Investment =(40/0.04)-830=170

When discount rate "r"=5%

NPV of Investment =(40/0.06)-830=666.67-830=-233.33

When r=4.819%

Them Net present value =0

Hence as per the alternative discount rate analysis when r<4.819% then NPV is positive and when r>4.819% then NOV is negative