The owner of one acre of western hemlock Tsuga heterophylla

The owner of one acre of western hemlock (Tsuga heterophylla) needs to plan a harvest rotation length. Assume that the stumpage price is p = $2 per cubic foot and fixed costs of harvest are C = 3, 917.18. The volume (in cubic feet) of the stand at any point in time is given by W(t) = at - bt^2 = 133.33t - .22t^2. The land owner applies a discount rate of r = .05, and the present value of bare land is S = -$1, 109.78 per acre. What is the forest owner\'s efficient rotation length, rounded to the nearest year? Show your work, and plot your solution using a figure.

Solution

As per Given Data

Price of stumpage (p) = 2$ per cubic foot

Cost of Harvest C= 3917.8 $

Volume is Given by Wt= at-bt square= 133.33t-0.22t sqr

Discount rate = 0.5

Present value of Bare land = 1109.78 $ per acres

What is the forest owner’s efficient rotation length, rounded to the next year?

Wt= 133.33t-0.22t sqr

W= 133.33-0.22 t

The value of t is 1 year

Hence W = 133.11 is the volume

P is 3917.8*0.5*1/100= 1958.75

So the Final Value is 1958.75 as discount

3917.8-1958.75 = 1959.05

The forest owner’s efficient rotation length, rounded to the next year is 1959.05$