Reference no: EM132374032
Question 1. The relationship between the volume of timber, the value per cubic metre, (price) and the age of the stand is given below. Assume successive crop rotations and the applicable discount rate is 3%. Please round dollar values to two decimal places.
| Stand age (years) |
Timber volume (m3) |
value per m3 |
a) Mean Annual Increment |
Site value b) |
Site value c) |
Site value d) |
Site value e) |
| 65 |
1485 |
20 |
|
|
|
|
|
| 70 |
1705 |
22 |
|
|
|
|
|
| 75 |
1900 |
24 |
|
|
|
|
|
| 80 |
2061 |
26 |
|
|
|
|
|
| 85 |
2180 |
28 |
|
|
|
|
|
To answer to following questions fill in the table with the appropriate values. Describe the formula used for each column for part b) to part e). For each part, you must show your formula used and at least one of the calculations.
a) The biological decision rule chooses the age of harvest where the Mean Annual increment (Average Product) is maximized. The Mean Annual increment is found by dividing Timber Volume by stand age. What is the optimum age of rotation using the biological decision rule? _____
b) The optimal age of rotation from an economic perspective is the age that results in the highest Site Value. What is the optimum age of rotation from the economic perspective?_______
c) What is the optimal economic age of rotation if planting costs of $4500 are introduced at the beginning of each rotation?_______Does the optimal age of harvest increase or decrease? _______Why do you think it increases or decreases?
d) Starting from the original conditions (in part a), what happens to the optimal economic age of rotation if value per cubic metre increases by $15 at each age and why? ______
e) Starting from the original conditions (in part a), what happens to the optimal economic age of rotation if the discount rate is decreased to 2.5%? _______
Question 2. You are considering purchasing land to grow successive even aged crops of merchantable timber lasting forever. The trees are currently 30 years old. Each rotation involves the following costs and benefits:
Planting costs at the beginning of each rotation are $10000
At age 10, the stand undergoes precommercial thinning which costs $4500.
The rotation age is 80 years, and the stumpage value is $250000
The stand also requires an annual management cost of $310 per year.
You require a 2% return on investment.
a) What is the most that you would be willing to pay for this land given the trees are 30 years old? Show your time line and calculation.
b) Suppose that this land is for sale for $72061.48. Find the internal rate of return on this investment assuming that you are going to follow growing successive even aged crops of merchantable timber lasting forever. Use an iterative process to find the internal rate of return to the nearest 3 decimal places. (hint, you are starting with r 0.020 and the internal rate of return is less than r= 0.030) Show the equation that you are marks) trying to solve.