Faustmann's formula

Faustmann's formula gives the present value of the income stream for forest rotation. It was derived by the German forester "Martin Faustman" in 1849.

The "rotation problem", deciding when to cut down the forest, means solving the problem of maximising Faustmann's formula and this was solved by Bertil Ohlin in 1921 to become the "Faustman-Ohlin theorem", although other German foresters were aware of the correct solution in 1860 [cite book | author=John Cunningham Wood | title=Bertil Ohlin: Critical Assessments | publisher=Routledge | year=1995 | id=ISBN 978-0415074926] .

: "pf"("T") = value of forest at time "T"

: ƒ("T") = stock of timber at time "T"

: "p" = price of timber

: "r" = discount rate

The formula says

: $PV\; =\; pf(T)\; exp(-rT)\; cdot\; \{(1\; +\; exp(-rT)\; +\; exp(-2rT)\; +\; cdots)\; \}\; =\; frac\{pf(T)\}\{exp(rT)\; -\; 1\}$

A theorem ensues:

: Cut the forest when the time rate of change of its value is equal to interest on the value of the forest plus the interest on the value of the land.

Reference

* [http://nzjf.org/free_issues/NZJF13_2_1968/38AE524B-7AC1-4AA8-865C-50B870B42404.pdf PROBLEMS AFFECTING THE USE OF FAUSTMANN'S FORMULA AS A VALUATION TOOL]