Alternative and Indefinitely Repeated Investments: Species Choice and Harvest Age in Forestry

Abstract

The tree harvest problem of forest management is an archetypal investment problem; it involves time, uncertainty, and irreversible actions with consequences in the future. The exercise of the option to cut a tree opens the option of planting a new one or of using the land for alternative purposes. We enrich the tree harvest problem by considering the planting decision too with no cost associated with harvesting or planting. Two tree species are available; their growth is deterministic but their timber unit price is stochastic. In the case of a single rotation, known as the Wicksellian tree harvest problem, the forest manager should plant one species immediately if its price is sufficiently high relative to the price of the other species. However, if prices are close to each other, the manager should wait in order to avoid the mistake of planting the wrong species. Waiting should last until the prices are sufficiently far apart to make the probability of a future price reversal acceptably low. In contrast, when the number of rotations is arbitrarily high, as in Faustman’s problem, waiting before planting the new tree, whatever its species, is never optimal once a harvest has taken place. However, the optimal harvest age depends on the relative timber price. We show that the optimum harvest age increases when the relative price approaches a threshold value signalling the necessity to switch to the alternative species. This is because the decision maker would rather wait than plant the wrong species; letting existing trees grow older is a way to postpone the choice. We also show that the land value increases with the uncertainty of timber prices. The stand value is similar to the value of an American option with a free boundary and an indefinite expiry date but with endogenous payoff.