Mining is proposed for a wilderness area that provides two benefits: recreation (due to backpacking opportunities) and biodiversity (there are endangered wildlife and plants). The mining is expected to reduce backpacking visits from the current 10,000 recreation visitor-days (RVDs) per year to 4,000 RVDs per year for the next 10 years; after that time, recreation use would partially rebound to 7,000 RVDs per year into perpetuity. If the mine is not opened, recreational use is expected to continue at current levels into perpetuity. Mining is expected to bring profits of $1 million per year for the 10 years of mining operations.

a. What is the present value of mining in the area (excluding effects on recreation) if the interest rate is 6%? If it is 3%?

b. If one RVD of backpacking is worth $P, what is the present value of recreation in the area if it is mined? If it is not mined? Do this calculation using both a 6% and a 3% discount rate.

c. How much would an RVD of backpacking have to be worth (i.e., what is P) to make the benefits of mining worth less than the benefits of not mining, considering only the benefits and costs of mining and recreation? Do the calculation for both 6% and 3% discount rates.

d. Suppose that travel cost studies determined that an RVD of backpacking in the wilderness is worth $80 per RVD. Would preservation be the efficient solution, considering only the benefits and costs of recreation and mining, at 6% discount rate? At 3% discount rate?

e. Which discount rate makes the best case for mining?

f. One option for the area is to delay mining for 10 years. If an RVD of backpacking is worth $80, what is the present value of this alternative? How does it compare with the present value of mining the area in the present?