Section 1 – Executive Summary
This report analyzes the case “Tree Values” to find an optimal way for Mr. Smith to manage his forestland and harvest the crop trees. The fundamental idea in this report is based on the concept of present value. A number of options are analyzed and the one with highest present value of pay off is considered. Questions 9, 10, and 11 give Mr. Smith 3 options:
* Option 1: Harvest all crop trees now and receive $8,160 * Option 2: Let the forest grow without thinning, then harvest all crop trees 60 years from now and receive $537,962.01 at harvesting, equivalent to $28,800.08 now * Option 3: Thin and manage the forest, then harvest all crop trees 50 years from now and receive $670,033.56 at harvesting, equivalent to $58,429.42 now Based on the present value of the money received at harvesting, it is highly recommended that Mr. Smith should choose option 3. Furthermore, provided Mr. Smith decides to thin and manage his forest, in case he needs money soon to use for other purposes, he can harvest all of his crop trees at the 40th year to receive $410,608.68 at harvesting, equivalent to $58,325.19 at present, instead of waiting for 10 more years. This is because the present value of money received at the 40th year is just a little ($104.23) less than that of money received at the 50th year.
Section 2 – Analysis
In order to choose the best offer, the amount of payment in each offer is discounted to present at the discount rate of 10%. This is just a basic discounting problem, using the formula PV=FV(1+r)t
In this formula, FV is the amount of payment, r is the discount rate of 10%, t is the number of years from now in each offer. Table 1 in the appendix summarizes the present value of payment in each offer. It also shows that offer 8 has the highest payment’s present value of $140.61. Therefore, offer 8, which pays $274 seven years from now, will be chosen. |Offer |Payment($) |Yearsfrom now |PresentValue ($) | |1 |100 |0 |100.00 | |2 |120 |1 |109.09 | |3 |142 |2 |117.36 | |4 |166 |3 |124.72 | |5 |192 |4 |131.14 | |6 |219 |5 |135.98 | |7 |246 |6 |138.86 | |8 |274 |7 |140.61 | |9 |300 |8 |139.95 |
The price of a tree at increments of 10 years between now and 60 years from now will be calculated first. This is done by using the following formula: Price per Tree=$MBF1000×Board Feet per Tree
A tree has certain diameter at breast height (DBH) at certain time (e.g., 10” now, 11” at 10th year, 12” at 20th year, etc.). With different DBH, the tree would yield different board feet of lumber, which are found in Exhibit 1 of the case. Because there is no change in tree grade, the tree will be in grade 4 at any time during the period of 60 years. Therefore, the stumpage price (with no increase) is always equal to $40 per thousand board feet (MBF) as shown in Exhibit 2 of the case. After the prices are calculated, they are discounted at the discount rate of 5% to present. Table 2 shows the price of the tree at 0th, 10th, 20th, 30th, 40th, 50th, and 60th years and the corresponding present value. The optimal time to harvest the tree will be chosen based on...