3. The Faustmann Model (Part I)
Forest rent has been a widely used criterion in Central Europe - possibly because the cutting rule favoured a relatively long rotation (and it is implicitly compatible with non-timber benefits). One justification for applying the forest rent was to avoid compounding and rotations that were considered unrealistically short within land rent theory. The forest rent approach includes timber prices and regeneration costs, which correspond to the Faustmann Model with a zero rate of interest. However, this still excludes an alternative investment option and assumes that a forest owner does not have a loan (or that a forest business has control over unlimited capital). Following forest rent may potentially lead to excess investments in forestry that cause large economic losses (Hyytiäinen & Tahvonen 2003).
Since the intent is to have a method that values forestland, the Faustmann Model (land rent theory) has become the best known for providing a benchmark model for determining optimal timber rotation age. Faustmann (1849) showed that the value of a forest can be expressed as a sum of discounted net cash flow over an infinite time period. A forest owner's goal is to choose rotation so that the value of a forest is maximized. So, mathematically, the goal is to maximize:
where r is the discount rate.
The basic logic of this Faustmann formula (or land expectation value, LEV or soil expectation value, SEV) is as follows: for even-aged timber production, the net present value is basically formed by a perpetual periodic series of clear-cutting revenues at the end of every rotation of T years. By compounding each rotation's regeneration and other possible costs (as well as possible revenues from thinnings to the end of rotation), all (compounded) cash flows can be added to the end of rotation and apply a general present value formula for a perpetual periodic series,
where p is the amount of fixed payment occurring every T years in a series. More importantly, the first payment in this formula is at the end of first period.
The cutting rule: marginal change in cutting value at harvest age=discount rate (cutting value at harvest age) + discount rate (soil expectation value at harvest age) or
Faustmann’s Rule I
Interpretation: It is optimal to cut a stand, when the rate of change is aligned with respect to time and is equal to the interest on the value of forest capital invested in timber and land (i.e. when marginal benefits from delaying harvests are equal to marginal costs of delaying harvest (Figure E12). Marginal costs of delaying harvests include not only foregone interest payments, but also the value lost from delaying the next rotations.
The optimum condition can also be rewritten as:
Faustmann’s Rule IIInterpretation: It is optimal to cut a stand, when the relative value growth rate is equal to the interest rate modified by the land rent component (Figure E13). This land rent component is always positive; therefore it increases the ‘effective’ interest rate (opportunity cost of timber) and subsequently shortens the rotation period. The Faustmann rotation is ceteris paribus (other things being equal) shorter, the higher the timber price and interest rate and the lower the planting costs. From Figures E10-13 we saw the general relationship between different cutting rules: TF<TMAI<TFR. Hence, quite intuitively, the varying goals imply varying optimal cutting behaviour.