3. Consider a hydroelectric dam with an initial (year 2021) construction cost of $1.4 billion. Beginning in 2022, the project yields benefits in the form of electricity and irrigation water that start out at $175 million per year. These benefits, however, decline at an annual rate of 2% as the dam depreciates over time. The last year of benefits is in 2122, when the dam is shut down.

a. Ignoring environmental impacts, calculate the projects net present value for discount rates ranging from 0% to 15 % per year in 1% increments. Summarize your calculations in a graph of net present value vs. the discount rate.

b. Now suppose that this project would generate environmental costs in the form of reduced wild river recreation opportunities and the loss of riparian habitat. These costs start out at $15 million per year in 2021 and rise at an annual rate of 3% as the economy grows and willingness-to-pay for conservation increases. To keep things simple, assume that environmental costs are zero after the dam is shut down after 2122 and the river is restored. Taking environmental costs into consideration, how does the net present value of the project change as the discount rate is increased from 0% to 15 % per year? Again, summarize your calculations in a graph.

c. Briefly explain the factors that account for the relationship between the discount rate and the projects net present value i.e., whats the intuition behind your calculations in part (b)?