(Expected Value Analysis) The initial cost of constructing a permanent dam (i.e., a dam that is expected to last forever) is $544 million. The annual net benefits will depend on the amount of rainfall: $15 million in a "dry" year, $33 million in a "wet" year, and $50 million in a "flood" year. Meteorological records indicate that over the last 100 years there have been 70 "dry" years, 22 "wet" years, and 8 "flood" years. Assume the annual benefits, measured in real dollars, begin to accrue at the end of the first year.

Use the meteorological record as a basis for assigning probabilities to "dry", "wet" and "flood" years. Assume a real discount rate of 5 percent.

(a) Calculate the expected value of the annual net benefits.

(b) Calculate the present value of the stream of (expected) annual net benefits. (HINT: The formula for the present value of a perpetuity is PV of perpetuity = Annual Payment / Discount Rate

(c) What are the net benefits of the dam?

(d) What is the internal rate of return of the dam? (HINT: Try nearby whole number discount rates).