Question

1. Consider a forest with 100,000 tons of standing timber and a growth rate of 4500 tons of additional biomass per year. Assume the price of timber is $120 per ton and an interest rate of 4%.
   1. What is the value of the forest if it is clear cut? Show and explain your work.
   2. What would be the present value of the timber under a sustainable yield management approach? Show and explain your work.
   3. What would be the present value of the sustainable yield harvest if the interest rate was 6%? Show your work.
   4. What approach to forest management would you recommend under each interest rate scenario?
   5. In class we developed a “marginal benefit of harvesting” and “marginal cost of harvesting” equation and diagram to establish a principle for optimal harvest rotation. Use this diagram to explain what is happening to the optimal harvest rotation in this scenario when the interest rate increases from 4% to 6%. (You do not need to use actual numbers—just reflect the change in the diagram and provide an explanation.)
   6. Consider the optimal harvest rotation model. Use the model to show what would happen to the optimal harvest rotation if the stand of timber was found to be habitat for an endangered and protected species. Explain.

Answer 1

Solving first 4 part as per Chegg policy.

A. Price is given at 120 per ton.

At clear cut, the value of the biomass would be

100000*120=12,000,000

B. Sustainable harvest management is where only the yearly growth is utilized. This is given at 4500 tons an year. Using a discount rate of 4%, the value of this perpetuity is

4500/4%=112500 tons. At 120 per ton, its value is

=120*112500

=13,500,000

C. If the interest rate was 6%, the value of perpetuity would be

4500/6%=75000

At 120 per ton, the monetary value is

75000*120

=9,000,000

D. Under 4% scenario, the monetary value is sustainable management is higher (13.5m vs 12m) so that will be recommended.

Under 6% scenario, the monetary value of clean cut is higher (12m vs 9m) and hence clean cut would be recommended.