2. Return to the set-up of problem #1. Now assume that the forest owner faces the risk of severe fire that requires replanting of the stand. Such a fire occurs on average once roughly every 38 years. Specifically, assume that the forest owner’s fire risk parameter is λ = .02637. This risk is reflected in the value of bare forest land in the area, which in this scenario is S = $2,917.92 per acre. Assume all other parameters from problem #1 remain the same.

a. Write down a condition the forest owner may use to choose a rotation length that maximizes the (expected) net present value of profits from timber harvest in this scenario. In a few sentences, interpret the condition.

b. What is the forest owner’s efficient rotation length given the risk of fire, rounded to the nearest year?

c. Using a figure, compare your solution from problem #2.b with your solution from problem #1.b. In a few sentences, interpret your results.

Problem 1

The owner of one acre of ponderosa pine (Pinus ponderosa) needs to plan a forest rotation length. Unless the owner chooses to sell the forest land, it will be kept in forestry and the chosen rotation will be maintained indefinitely. Assume that the stumpage price is p = $2.50 per cubic feet and the fixed cost of harvest is C = $4,350.90. The volume (in cubic feet) of the stand at any point in time is given by W(t) = at – bt2 = 141.2t - 0.2824t 2 , where t is measured in years. Assume that the forest owner uses an annual discount rate of r = .01 and that the present value of bare land is S = $17,912.46 per acre.