Journal of Forest Economics > Vol 17 > Issue 3

Further generalization of Faustmann's formula for stochastic interest rates

Joseph Buongiorno, , Mo Zhou
Suggested Citation
Joseph Buongiorno and Mo Zhou (2011), "Further generalization of Faustmann's formula for stochastic interest rates", Journal of Forest Economics: Vol. 17: No. 3, pp 248-257.

Publication Date: 0/8/2011
© 0 2011 Joseph Buongiorno, Mo Zhou
JEL Codes:C61L73Q23M1
EconomicsRiskMarkov chainOptimizationDecision makingDiscount rate


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In this article:
Dynamic programming 
Linear programming 
Dual linear programming 


Markov decision process (MDP) models generalize Faustmann's formula by recognizing that future stand states, prices, and interest rates, are not known exactly. Buongiorno (Forest Science 47(4) 2001) presents a dynamic programming and a linear programming formulation of the MDP model with a fixed interest rate. Both formulations are generalized here to account for a stochastic interest rate. The objective function is the expected present value of returns over an infinite horizon. It gives, like Faustmann's formula, the value of the land and the eventual standing trees. The changes between stand states, prices, and interest rate, are represented by Markov chains. Faustmann's formula is a special case where the change from one state to another has 0 or 1 probability, and the interest rate is constant. The MDP model applies to any stand state, even- or uneven-aged, and the best decisions are tied uniquely to the current system state. An example shows the effects of recognizing variations in interest rate on the land expectation value, and the cost of ignoring them.