iForest - Biogeosciences and Forestry


Dimensionless numbers for the net present value and the perpetual value of sustainable timber harvests from a monospecific uneven-aged forest

Ignacio López Torres (1)   , Carmen Belda Fullana (2)

iForest - Biogeosciences and Forestry, Volume 12, Issue 1, Pages 35-42 (2019)
doi: https://doi.org/10.3832/ifor2715-011
Published: Jan 10, 2019 - Copyright © 2019 SISEF

Research Articles

This paper proposes a simple and direct method to provide reliable approximations of the net present value (NPV) and the perpetual value (PV) of sustainable timber harvests from a monospecific uneven-aged forest based on dimensionless numbers. In addition, two new dimensionless numbers ρNPV and ρPV are introduced. These use the NPV or PV derived from the sale of timber throughout a harvest cycle, plus the final stocking value (as numerator), and the fair value of standing timber under IAS 41 (as denominator). They can be interpreted as economic performance indicators for forest management, inspired by the return on assets accounting concept, showing how profitable the forest is, relative to its total value, with sustainability and stability criteria. Those approximations to the variables NPV, PV, ρNPV and ρPV, were obtained under conditions of stable equilibrium from a matrix model. In order to exemplify and test the results, the model used data from uneven-aged managed Pinus nigra stands, considering three levels of tree diameter growth, six levels of basal area and 33 levels of recruitment, creating a total of 594 planning scenarios. Furthermore, the study revealed the existence of strong linear correlations between those variables and a dimensionless number.


Dimensionless Numbers, NPV/PV, Equilibrium, Sustainable Harvesting, Matrix Model, IAS 41

Authors’ address

Ignacio López Torres
Universidad Politécnica de Madrid (UPM), Escuela Técnica Superior de Ingeniería de Montes, Forestal y del Medio Natural, Ciudad Universitaria, E-28040 Madrid (Spain)
Carmen Belda Fullana
Universidad Pontificia de Comillas, Alberto Aguilera 23, E-28015 Madrid (Spain)

Corresponding author

Ignacio López Torres


López Torres I, Belda Fullana C (2019). Dimensionless numbers for the net present value and the perpetual value of sustainable timber harvests from a monospecific uneven-aged forest. iForest 12: 35-42. - doi: 10.3832/ifor2715-011

Paper history

Received: Dec 21, 2017
Accepted: Oct 19, 2018

First online: Jan 10, 2019
Publication Date: Feb 28, 2019
Publication Time: 2.77 months

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