by Peter Lohmander (Preliminary Version 2000-08-06)
The quality of the timber changes with time and the size of the trees changes. For these reasons, there is a deterministic trend in the net price dpdt per m3sk and year (in relation to the market average price that year). It is possible that your stand right now has a lower or higher net price than the market average. The net price of your stand - the net price of the market average right now is denoted dp.
You sell to the "stumpage market". The average price in that market during a particular year follows this stochastic process: P(t+1) = pa + pb*P(t) + RND(t). The random numbers RND(t) are independent and identically distributed random numbers.
Each year has a new RND. The
mean value is zero and the standard deviation is sigma.
The real rate of interest (after
tax) in continuous time, is r.
tmax
is the maximum number of years you are prepared to wait for the sales.
The three examples at the bottom
of this web page differ only with respect to tmax.
You find that the expected present value of the stand and the optimal reservation
price increase if you have the option to wait longer.
The theories and optimization
principles used in this software are found and described here: http://www.sekon.SLU.se/~PLO.
The real stumpage price in Sweden
As you notice here, the real stumpage prices vary rapidly and are not possible to predict with high precision. The parameters found in the examples below are derived from the data found in the graph below.
Example 1: tmax = 1
This is a typical example from Jamtland, Northern Sweden.
You are prepared to wait only one year (tmax = 1). The expected present
value of the stand (including the value of the land) is 41552 SEK/hectare.
If you get the price offer 292 SEK/m3sk or higher, you should harvest instantly.
Otherwise, you should wait longer for a better price.
Example 2: tmax = 6
This is almost the same basic example. Now, however,
you are prepared to wait up to six years (tmax = 6). The expected present
value of the stand (including the value of the land) is higher than before,
48121 SEK/hectare. If you get the price offer 334 SEK/m3sk or higher, you
should harvest instantly. Otherwise, you should wait longer for a better
price.
Example 3: tmax = 11
This is almost the same basic example. Now, however,
you are prepared to wait up to eleven years (tmax = 11). The expected present
value of the stand (including the value of the land) is higher than before,
49711 SEK/hectare. If you get the price offer 341 SEK/m3sk or higher, you
should harvest instantly. Otherwise, you should wait longer for a better
price.
Very welcome to my web page for more information!