You want to know if it is economically optimal to harvest your forest stand right now!
You know that prices rapidly change and are impossible to predict perfectly!
The program can be used
directly from
your NETSCAPE of EXPLORER if you have the versions
Netscape 4.5 (or later) or Explorer
4.0 (or later). If you have earlier versions, it is probably not possible
to use the java-program found below.
The program is found at the bottom
of this web page!
You know the following:
(The important parameters
and variables are marked with red
color!)
You know that prices are hard to predict (they may be regarded as stochastic) and that you have several harvest options in the future. This is one of the main concerns which motivates this analysis. In Sweden, the (average) real (inflation adjusted) net price has varied in the interval 100 - 300 SEK/m3 during the period 1953 - 1992 according to Lohmander (1995). See the reference list below. "Net price" is defined as price - harvest and transport costs per volume unit. In the model, pd denotes the maximum deviation from the expected price. In the example just mentioned, the expected price is 200 (SEK/m3) and pd is 100 SEK. In the model, it is assumed that net price has a uniform probability density function. The assumption of a uniform probability density function fits the net prices studied by Lohmander (1995) very well. Other assumptions concerning the stochastic properties of net prices have been made in some of the other references. Please, read more in the references!
You know the real rate of interest, r, in the capital market.
You know the present volume (m3) per hectare, v0, and the yearly growth (m3/(hectare*year)), v1.
You know the net price per m3 right now, p0 (based on the price list of an average year with respect to roundwood net prices). You know the yearly growth of the real net price per m3, p1 (based on the price list of average year with respect to roundwood net prices).
You know the maximum number of years which you accept to wait for the harvest to take place, tmax.
You know the value of the land per hectare, L, which is released after harvest.
You instantly (within 0.1 seconds) obtain the following information:
The optimal reservation price right now, q, which is the lowest net price per cubic metre which is sufficiently high to make it optimal to harvest right now. If the net price right now is lower than q, then you should wait longer!
The expected present value per hectare, w, if you take optimal market adapted harvest decisions right now and at all future points in time.
The probability that it is optimal to harvest right now, pharv, before you get information concerning the net price right now.
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Some typical observations:
The initial values of the parameters found in the program below are typical in many places in Northern Sweden. You may change them in any direction (by pressing the buttons) and investigate the results.
Some of the general results which you will find are:
The expected present value, w, increases if the the net price risk increases (if pd increases). Of course, a high price variation is good if you adapt your harvesting to the prices!
The optimal reservation price, q, increases if the the net price risk increases (if pd increases). Of course, if net prices sometimes are very high, you should not accept to harvest if the net price is rather low. You are willing to wait for a high net price. Your reservation price increases if the net price risk increases!
The expected present value, w, and the optimal
reservation price, q, increase if tmax increases. Of course, it is valuable
to have many alternative harvest years available when you decide if you
should harvest or wait longer.
If tmax is large, you have many options
(and high flexibility). Hence, the expected present value increases and
your satisfaction based on a low price decreases. (Your optimal reservation
price increases.)
The probability that it is optimal to harvest
right now, pharv, is usually affected by the net price risk. It is not
possible to give a short explanation here. Please read the references,
in particular Lohmander (1987), for more details.
References
(Many other references to related issues can be found from http://www.sekon.SLU.se/~plo.)
The program is a simple illustration and application of some principles found in these references:
Lohmander, P., The economics of forest management under risk, Swedish University
of
Agricultural Sciences, Dept. of Forest Economics,Report 79, 1987 (Doctoral
dissertation) (Doktorsavhandling)
Lohmander, P., Pulse extraction under risk and a numerical forestry application,
SYSTEMS ANALYSIS -MODELLING - SIMULATION,
Vol. 5, No. 4, 1988
Lohmander, P., Adaptive decision making in forestry, in: Paredes G. (editor),
Forest
management and planning in a competitive and environmentally concious world,
proceedings from: International Symposium on Systems Analysis and Management
Decisions in Forestry, March 9-12, 1993, Valdivia, Chile, 1994
Lohmander, P., Reservation price models in forest management: Errors in
the
estimation of probability density function parameters and optimal adjustment
of the bias
free point estimates, Management Systems for a Global Forest Economy with
Global
Resource Concerns, Society of American Foresters, Asilomar, California,
September
1994, Brodie, D. & Sessions, J., (Editors),
College of Forestry, Oregon State University, Corvallis, Oregon, USA, 1995
A popular description in swedish of some of the general ideas is found here:
Lohmander, P., Flexibilitet - en ledstjarna for all ekonomisk skoglig planering,
SKOGSFAKTA, Inventering och Ekonomi, No. 23, 1990
One reference which is based on an application of the general ideas is found here:
Lohmander, P., The economically optimal number of plants, the damage probability
and the stochastic roundwood market, in Paredes, G. (editor), Forest management
in a
competitive and environmentally concious world, proceedings from: International
Symposium on Systems Analysis and Management Decisions in Forestry, March
9-12,
Valdivia, 1993, Chile, 1994
A course which treats the methods and applications is:
Management
and Operations Research I and II (Kostnads- Intaktsanalys med
Optimering
I och II) (Press here for information!)
Some numerical results for swedish conditions are found here:
Harvest
year (and present value) optimizations in swedish forestry 1998
The program D2:
Please, press the buttons and see what happens!
As soon as you press some button,
some parameter changes and you get new optimal
results! The initial values of the
parameters are typical in many places in Northern
Sweden.