General historical background:
The name "FAUSIMP1" is constructed
from "Faustmann", "Simple" and "Version 1". Martin Faustmann wrote his
famous forest economics article in 1849. He did not consider risk, uncertainty,
constraints or economies of scale. Still, the model by Faustmann has been
very dominating during 150 years. In the same way, the mathematical principles
discovered by Newton have been very dominating for hundreds of years. It
is well known that Einstein and Heisenberg made new fundamental discoveries
long ago. Still the Newton ideas can be used with good results in many
applications of today. If you consider risk, uncertainty, constraints or
economies of scale, you may find even better solutions in some cases. Please
visit my web page http://www.sekon.SLU.se/~PLO
for more information and software!
General problem description:
Right now, you have a forest
stand. The age of the stand is approaching the age of the final felling.
The only remaining forest management activity in the stand is the final
felling. Now, you can optimize the economic result of your harvest decision
in a very simple way. Here, it is assumed that everything is known with
certainty. (This can of course be questioned! Compare the other models
and information found from http://www.sekon.SLU.se/~PLO.)
This model is based on classical maximization of the present value via
selection of the harvest year. It is assumed that the following information
is known:
The volume per hectare right
now, v0, the
growth of the volume per hectare and year, v1,
the net price (= price - harvest costs) per cubic metre right now, p0,
the growth of the net price per cubic metre per year, p1,
the value per hectare of the bare land released after harvest, L,
and the rate of interest (%) in the capital market, r.
Your questions:
1. How many years from now should I harvest my forest
stand in order to maximize the present value per hectare?
2. How high is the maximum present value per hectare?
3. Which is the present value per hectare if I harvest
at some other point in time, "tev" years from now?
Your data:
In the java program below, you
enter information in a table. The information is v0, v1, p0, p1, L, r and
tev.
The volume per hectare, V(t), is a function of time,
t. V(t) = v0
+ v1*t
(t = 0 right now and increases one step each year)
The net price per cubic metre, P(t), is a function
of time, t. P(t) = p0
+ p1*t
L is the value per hectare
of the bare land released after harvest.
The rate of interest in continuous time, r,
is defined in the unit %.
An arbitrary harvest year, which you suggest, is denoted
by tev.
Your solution:
When the table is full, just press the "SOLVE" button
and your results appear below the table!
If you want to modify some data in the table, just
do that and press "SOLVE" again!
Note: If the "Optimal harvest year" turns out to be
negative, such as -5, this means that you should have cut 5 years ago!
Example solution:
Assume that you enter the following data: v0 = 160,
v1 = 5, p0 = 190, p1 = 1, L = 2000, r = 3, tev = 40.
(We may use the currency in your country, such as
$US, SEK, £, or anything else. You should not enter the currency
in the table. In this section, we just assume that the currency is SEK.)
Then you should get the following results:
The optimal harvest year occurs about 6 years from
now.
The optimal (maximum) present value is 32777 SEK/hectare.
Your suggested harvest year, tev, 40 years from now,
would give the present value 25541 SEK/hectare. That is much worse than
the maximum value 32777 SEK/hectare.
Welcome to my home page http://www.sekon.SLU.se/~PLO for more information and software! There you can find much more about optimal decisions under risk, uncertainty, constraints, economies of scale, continuous cover forestry, plantations and more!
Peter Lohmander