A dam is proposed on a stretch of wild river, a river that is currently used for recreation. The dam will generate electricity. The dam will have a useful life of 50 years, after which its reservoir will be full of sediment and the dam will need to be removed. The following are characteristics of the dam:

Initial Cost: \(\$ 100,000,000\)

Electricity produced: 100,000 MWh per year, @ \$100/Mwh.

Cost of decommissioning dam: \(\$ 10,000,000\).

Value of recreation lost: \(\$ 5,000,000\) per year

a. If the social discount rate is \(3 \%\) per year, is the dam a good idea?

b. If the social discount rate is \(10 \%\) per year, is the dam a good idea?

c. Calculate the "cutoff" discount rate, \(c\), such that the dam is a good idea for discount rates \(c\).