The volume of standing timber in a 35 year old Douglasfir st

The volume of standing timber in a 35 year old Douglas-fir stand under your management is estimated to be 28 mbf per acre. At age 40, the volume is expected to be 34 mbf per acre. Real stumpage price for the 35 year old timber is $280 per mbf. Real stumpage price for the 40 year old timber is expected to be $310 per mbf.

A) What is the average annual volume growth rate for this stand?

B) What is the average annual expected real price growth rate for this timber?

C) What is the average annual expected value growth rate for this stand? (hint: price growth plus volume growth=value)

D) If the real rate of return on equivantely risky alternative investments is 4%, would a profit maximizing timber company harvest this timber now or wait 5 years?

Solution

Requirement a:

Average Annual Volume Growth Rate:

Volume Growth for 5 years = 34-28 = 6mbf

Volume Growth rate for 5 years = 6/28 * 100 = 21.428%

Average Annual Volume Growth Rate = 21.428 / 5 = 4.2856%

Requirement B:

Average Annual Expected real price growth rate:

Real Price Growth for five years = 310-280 = $30

Real Price Growth rate for 5 years = 30/280 * 100 = 10.71428%

Average Annual Real Price Growth Rate = 10.71428 / 5 = 2.142856%

Requirement C:

Average Annual expected value growth rate

= Average Annual Volume Growth rate + Average Annual expected real price growth rate

= 4.2856 + 2.142856

= 6.428456%

Requirement D:

Value of standing timber at the age 35 = 28mbf * 280 = $7840

Value of Standing timber at the age 40 = 34 mbf * 310 = $10540

Present Value of standing timber as existing at age 40 = $10540 / (1+0.04)⁵

= $10540 * 0.8219

= $8662.826

It would be better to wait for 5 years to maximise timber company harvest as the present value of standing timber ($8662.826) is high when compared to the value existing at age 35 ($7840).