Question

The initial cost of constructing a permanent dam (i.e., a dam that is expected to last forever) is $425 million. The annual net benefits will depend on the amount of rainfall: $18 million in a “dry” year, $29 million in a “wet” year and $52 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?

Answer 1

The expected value of benefits from the dam is calculated as follows

Expected value = 0.86 x $ 18,000,000 + 0.12 x $ 29,000,000 + 0.02 x $ 52,000,000

Expected value of benefits = $ 20 million

The present value of the expected value of benefits over a period of 100 years is calculalted

Present value = - $425 million + $ 20 million / ( 1+0.05)¹ +  $ 20 million / ( 1+0.05)² +  $ 20 million / ( 1+0.05)³ + ---------+  $ 20 million / ( 1+0.05)¹⁰⁰

Net benefits of the dam if the real discount rate is 5 percent = -$ 28,041,796.00