Forest valuation and forest decision-making under consideration of risks.

In the forestry scientific literature lots of authors tried to quantify survival risks (e.g. MOBBING, 1986; KURTH et al., 1987; DEEGEN, 1994; KONIG, 1996; DIETER, 1997; BRAUNIG und DIETER, 1999; KOUBA, 2002; HOLECY und HANEWINKEL, 2006; BEINHOFER, 2007; MOHRING et al., 2010; STAUPENDAHL, 2011 and PRICE, 2011). Thereby there are still very different suggestions on how to survival risks can be integrated practicable into models of forest valuation and operational decision making. In this paper, based on the classical Faustmann approach, survival risks were to be integrated into economic decision processes. For this purpose the deterministic approach has been extended to the risk of loss of forest stands, using a two-parametric Weibull distribution (formula 1). The result is a stochastic approach in which the harvest age T of each stand is a random variable whose probability is determined by the risk level and the time pattern of risk. Figure 1 shows an example of using a two-parametric Weibull function generated by survival function S(t) with parameters alpha=3.0 and S-100=0.5 and the corresponding age-dependent failure rates or hazard rates h(t) (see STAUPENDAHL, 2011). As a consequence the cash flow of forest production and its present value are also affected by risk. Selected economic aspects were illustrated with sample calculations based on expected annuities of a spruce stand (see figure 2 and 3). The results revealed a clear influence of survival risks on economic valuation criteria of forest stands. It is obvious that increasing risks reduce the annuities as the annual performance measures, but also suggest a shorter rotation period because the particular maxima are shifted to the left (figure 4). The differences between the risk-free variant and the risk variants can be interpreted as the respective average annual risk costs in EUR/ha/year. Therefore they should explicitly be taken into account in forest valuation and business decision models. Particular attention was paid to the criterion for the optimal rotation period (formula 4 and 5). Survival risks have impact on the success of an existing stand as well as all following stands, thus they affect the optimality criterion in opposing directions. The formulas can be interpreted as follows: the realization of the increment value f(u) of the stand ties up capital in the amount of the current value, so that interest costs in the amount of rf(u) arise. Simultaneously, the reforestation is postponed so that an amount equal to the soil rent rB(u) of the following stand is lost annually. The net effect has to be investigated numerically. The sample calculations show that late risks tend to lead to an advancement of the optimal rotation period whereas typical youth risks tend to a postponement of the optimal harvesting time. It is hope the proposed approach lays the methodological foundation for practical applications. Its flexibility and practicability will be particularly useful for this purpose.