Forest Land Expectation Value or Maximum Sustained Yield? Resolving A Long-Standing Paradox

Abstract

The Faustmann formula, equivalent to the land expectation value (LEV), yields the present value, starting with bare land, of an infinite series of future timber rotations for a stand. If this formula is used to find the rotation age that maximizes the present value, a lower annual harvest will result when compared to a maximum sustained yield (MSY) regime for an ownership with many stands. However, the LEV is strongly preferred by economists. This is the LEV vs. rents paradox. Herein, this paper demonstrates that an infinite series of annual harvests for an ownership under an even flow regime, discounted to the present using any interest rate, will provide the same optimal rotation age as the time of the peak MAI for a single stand, though with different estimates for the profitability, depending on the interest rate. Thus, rotations producing the MSY and the maximum financial return are identical when analyzed at the ownership scale but are not the same when based on the analysis at the stand scale using the Faustmann formula (LEV). This is the solution to the paradox. The formulas for internal rate of return (IRR) and the land valuation for transaction purposes are also presented.