METHODOLOGY

To determine the volumetric growth of pinus radiata have been used two methods:

We have determined a Logistic Function of the Pine Volumetric growth in according to the record given by the INFOR. In this relationship are considered: volume and age.

b) Function linear : 25 m³/ha/year

This yield corresponds to the Annual Medium Increase used by the INFOR to determine the volume by hectare and by age.

It has been used the Annual Medium Increase applied by the INFOR and corresponds to 22 m³/ha/year. It has not been possible to estimate a function growth logistics by lack of information.

To determine the rotation period the following criteria have been used.

The equilibrium condition is: f’(t) = f(t)/t

Result: 24 years old

The equilibrium condition is:

V = 800 US$/ha (estimated figure by the INFOR for forest land exclusively)

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Result: 18 years old

According to the record given by the INFOR the rotation age of major frequency registered in Chile is of 20 years. This period was used to determine the appreciation not only in the logistic function of the pine volumetric growth, but also in the linear function.

According to the record given by the INFOR the rotation age of major frequency registered in Chile for the eucalyptus is of 12 years. This period was used to determine the appreciation as a linear growth function (264 m³/ha).

The calculus formuli to determine the appreciation of the forestry asset have been suggested by Michael Linddal.¹

The appendix shows assess the asset value and appreciation of a perpetual forest rotation with regeneration costs (Co), rotation age (T), interest rate (r), volume harvested (q(T)), and flat rate current resource rents of timber price (p) less extraction costs (c).

Continuous discounting is assumed: (1+r)^{-rt »} e^-rt.

Every rotation has prior to the establishment (planting) a net present value of R (equation 1). For perpetual forest rotation the net present value is an annuity of a payment R every T year. This is equal to the land value for forest S(T) (equation 2). After planting the establishment costs are sunk cost. The asset value of a forest of age t is equal to the value of the harvest in (T-t) years and the value of forest land thereafter. The asset value is known as the soil expectation value SEV(t) (equation 3). The appreciation from year t to year t+1 (D(t)) is the difference in the asset value (equation 4).

For land coming into forest either as replanted or afforestation the asset value in t=0 is SEV(0)=[S(T) + H(T)] * e^-rT because the regeneration costs are sunk. The asset value for t=T is SEV(T) = S(T) + H(T) just before harvest (sum of stumpage and land value) and S(T) just after harvest (land value only) but before replanting. For forest stands not harvested in year T or with a stand age above T it is assumed that the asset value is H(T) + S(T), i.e. there is neither an appreciation due to growth or a depreciation due to over maturity of the timber.

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