Optimal Harvesting Age

Let there be a per unit regeneration cost C. The timber growth  is measured  by volume V(T) which is a function of the age of the timber T. Attaching a price P,  the maximum present value of the stand represented by λ is,

Equation 1

The first order condition gives us

Equation 2

PV' (T) = iPV (T) + i λ

Where V’ is the first order derivative of V.

The results indicate that, the Faustmann harvest age T_F, is the one at which the marginal increase in value from delaying the harvest equals opportunity cost of delaying the harvest. The opportunity cost includes the potential interest income foregone on the delayed receipt of current harvest revenues plus the interest cost of delaying receipts from future harvest cycles. The second component reflects an implicit rental cost of land. The optimum T is popularly known as 'Faustmann Rotation Age'. Let us denote it by T_F.

The first order condition equation 2 can be rewritten to give us the Faustmann condition

Equation 3

Equation 3 can be interpreted as, 'hold timber stocks uncut until the rate of growth in the combined asset value of timber and land just equals market rate of interest'.