2. Net present value and cost-benefit. (20 points each for a-c, 10 points for d, total 70 points) Inkster County is considering what to do with this year's excess in tax revenues of S400,000 over projections. The county has benefited from the extraction of natural gas deposits). The inflation rate is forecast to be 2.5 percent per year and the county applies a future discounting rate of an additional 3.0 percent. a. Option 1: Inkster County can invest in a savings account that yields 7 percent annual interest and requires that the funds be invested for 5 years and then released. (The investment option is only available this year.) Calculate the inflation-adjusted value of investing the $400,000 in this account. Hint: one approach is to calculate what the savings account is worth at the end of five years when the accumulated funds are released. This amount can then be compared to the amount expended this year in order to open the savings account. b. Option 2: Inkster County can spend the $400,000 temporarily repairing the many potholes on County Routes 111, 113, and 119, by filling them in with asphalt. These are "shovel-ready" projects and can be finished more or less immediately, but the quick repairs will only last for 3 full years. The city will save $160,000 per year for 3 years in reduced repair costs to its emergency vehicles and motorist lawsuits avoided. Calculate the net present value of spending the S400,000 to repair the potholes. Hint: this is like part (a) except that the benefit occurs at the end of each year instead of only at the end of the time period. c. Option 3: Instead of filling the potholes using asphalt, Inkster County can invest in repairing in the potholes with cement. This method would cost substantially more than asphalt, but would not take any longer to complete and would ensure that the roads remain in good shape for eight years rather than just three. The cost of the repaving would be $1,000,000. (Inkster County can afford this amount by allocating some anticipated tax revenues along with the unexpected excess.) Calculate the net present value of spending to repave the roads. d. Which is the best of the three options for Inkster County judged in terms of net benefit