Simulating land expectation values with consideration of the risk of natural stand damage

Dieter, Matthias (Germany)

Abstract

The Faustmann formula supports decisions about stand establishment and, connected with this, about the choice of tree species and rotation periods. The application of the Faustmann formula makes the assumption necessary that all future payments in regard to their height and time are certain. The criticism concerning this assumption of certainty might be as old as the formula of Faustmann itself.

There are especially two problems when considering the risk of stand damage in the calculation of land expectation values.  First there is a mathematical problem. In the Faustmann formula the length of all rotation periods is constant. Including risk in the calculations of land expectation value the age of enduse differs in dependence of the point in time, damage occur. Hence discounting periods vary also. Analytical solution of this problem seems to be quite difficult. Computer assisted simulations can provide a good approximation to the exact solution.  Second for consideration of risk it is necessary that the probability distribution exist which describes the actual damage risk of the stands. The lack of calculations of land expectation values with consideration of the risk of stand damages in Germany might be especially due to missing information about the natural risk of forest stands.

The presented investigation is based on empirical founded probabilities of survival for different tree species in Southern Germany. Land expectation values with consideration of the risk of natural stand damage are computed in a simulation model on basis of these probabilities. The calculations are done for different lengths of rotation periods.

Payments in the future effect the land expectation value only little due to the long rotation period. Hence simulations over sufficient long periods provide nearly the same results as computations of land expectation values for eternal periods. The presented investigation is done by simulation.

Random variables decide whether a stand is damaged and must be replanted or whether the stand survives in the simulation model. The random variables are set according to the probabilities of survival. Extensive repetitions are necessary when random variables are used.

The results of the simulations are assessed by the expected value of land expectation value and by its dispersions. The results will give an answer to the question whether especially the broad-leaved tress with low revenue get more profitable in comparison with the conifers when considering calamities. In particular for spruce, which is highly endangered by windthrow and -break in middle Europe risk inclusion in calculations is expected to have a noticeable influence on profitability.

Presented as paper 4A-3 in Session 4A by Matthias Dieter
Lehrstuhl für Forstliche Wirtshaftslehre (Department of Forest Economics)
Ludwig-Maximilians-Universität München
Am Hochanger 13
D - 85354 Freising
Tel. +49 / (0)8161 / 71 46 38
Fax. +49 / (0)8161 / 71 46 31
e-mail: md@bwgp.forst.uni-muenchen.de