Question

assume that a dam cost 17 million to build in a year and that beginning in the next year, the dam yields net benefits of 2 million per year for 10 years. If the discount rate is equal to 7 percent, what is the net present value of the dam? should it be built or not? What happens if the chosen discount rate is 2%? should the dam built, now?

Answer 1

Initial Cost = 17 million

Yearly benefit = $2 million

Time period = 10

Present Value = Current Value/(1+discount rate)^{number of year}

When discount rate is 7%

Current value of 2 million at the end of first year = 200000/(1+0.7)¹ = 1869159

Similarly, Current value of 2 million at the end of second year = 200000/(1+0.7)² = 1746877

Calculating present value of all 10 years:

We find that the total present value of all net benefits is less than the initial cost of building the dam. Thus the dam should not be built.

When discount rate is 2%

Here we see that total present value of all net benefits is greater than the initial cost of building the dam. Thus the dam should be built.