1. Calculate the land expectation value (LEV) for a tract of forest land under the following assumptions (16 pts):

▪   the owner’s primary objective for owning the land is income generation;

▪   the owner’s nominal alternate rate of return is 7%, and inflation is expected to average 3%;

▪   the best prescription (given the owner’s objective) for managing the stand is to plant 600 loblolly pine trees per acre, thin at age 18, and clearcut at age 28;

▪   the expected yield for the thin at age 18 is 12 cords of pine pulpwood per acre;

▪   the clearcut at age 28 is expected to yield 11 cords of pine pulpwood and 6 thousand board feet (mbf) of pine sawtimber per acre;

▪   the current pine pulpwood stumpage price is $22 per cord and the current pine sawtimber price is $390 per mbf;

▪   it costs $200 per acre to establish the stand;

▪   annual taxes and management costs together are $5 per acre,

▪   all prices, costs, revenues, and the real alternative rate of return are expected to remain constant in real terms.

2. The tract described in problem 1 is currently forested with loblolly pine. After

cruising the property you estimated that there are 6 mbf of pine sawtimber, 16 cords   of pine pulpwood, and 6 cords of hardwood pulpwood per acre. You have entered the stand data into a growth and yield simulator for loblolly pine, and it projects the stand will grow an additional 3.5 mbf of pine sawtimber and 1 cord of pine pulpwood per    acre in the next 5 years. You estimate that the hardwood pulpwood volume will          remain approximately constant. Assume that you will replant the stand after harvest    and that the yield for the new stand will follow the yield data in problem 1. Use the    economic data from problem 1, and assume that hardwood pulpwood sells for $12 per cord (16 pts).

a. Calculate the forest value of this tract assuming you will cut it now (6 pts).

b. Calculate the forest value of this tract assuming you will cut it in 5 years (10 pts).

3. In what sense can you have too much inventory volume in a forest (8 pts)?

4. What is the difference between formulating and solving a linear programming problem (8 pts)?

5. Consider the development of a management plan for a 27,400 acre forest. The area    has been classified into two site classes. The predicted yields for each site class for a range of rotation ages are given in Table 5.1. The current age class distribution of the forest by site class is shown in Table 5.2 (65 pts).

Table 5.1. Yield Projections for Site Classes I and II.

Table 5.2. Initial forest acreage by site and age class.

On the next page is a linear programming formulation designed to help develop a   management plan for the 27,400 acre forest described above. The linear program    minimizes the discounted costs over a 30-year planning horizon. The linear             programming formulation was developed using a real interest rate of 4%. Real        stumpage prices are assumed to be $35 per cord. It is assumed that stand                 establishment costs are $150 per acre and timber sale costs are $10 per acre plus $1 per cord sold. (Note: timber sale costs occur at the time of the final harvest.)           Furthermore, all prices and costs will be assumed to remain constant in real dollars.

Note that the variable XABCD represents the number of acres from site class A, initial   age class B, that are assigned to be cut first in period C and cut again in period D. If D is 0, the stand will only be cut once during the planning horizon, and if both C and D  are zero, the stand will not be cut at all. The possible decisions are to cut in periods 1, 2, or 3 or cut in both periods 1 and 3, or to not cut at all.

As an example, X2310 is the number of acres from site class 2 (Site II) and initial age class 3 (age 25 initially) that are cut in decade 1 and not again. Pages 5 and 6 list the output from a commercial solver. The questions (questions 5.a through 5.g) on pages 4 through 6 test your ability to interpret the linear programming formulation of the    forest management problem and its solution.

LINEAR PROGRAMMING FORMULATION FOR QUESTION 5

a. Show how the objective function coefficient on the variable X2313 was calculated (8 pts).

b. What is the purpose of the constraint in row 7? State precisely what it requires (8 pts).