Wealth accumulation in rotation forestry – Failure of the net present value optimization?

Autoři: Petri P. Kärenlampi aff001
Působiště autorů: Lehtoi Research, Lehtoi, Finland aff001
Vyšlo v časopise: PLoS ONE 14(10)
Kategorie: Research Article
doi: 10.1371/journal.pone.0222918


The rate of wealth accumulation is discussed, and an expression for a momentary rate of capital return is presented. An expected value of the wealth accumulation rate is produced. The return rates depend on any yield function. Three different yield functions are applied, two of them published in the literature, and a third one parametrized using a comprehensive growth model. A common economic objective function, as well as a third known objective function, are applied and compared with the clarified wealth accumulation rate. While direct optimization of wealth appreciation rate always yields best results, procedures gained by maximizing the internal rate of return are only slightly inferior. With external discounting interest rate, the maximization of net present value yields arbitrary results, the financial consequences being at worst devastating.

Klíčová slova:

Finance – Forests – Optimization – Pines – Trees – Forestry – Spruces – Maximum sustainable yield


1. Faustmann M. Berechnung des Wertes welchen Waldboden sowie noch nicht haubare Holzbestande fur die Waldwirtschaftbesitzen. Allg Forst- und Jagdz 1849; Dec, 440–455. (On the determination of the value which forestland and immature stands pose for forestry. Reprinted in Journal of Forest Economics 1995;1: 7–44.)

2. Pearse PH. The optimum forest rotation. Forestry Chronicle 1967;43(2): 178–195.

3. Samuelson PA. Economics of forestry in an evolving society. Economic Inquiry 1976;14: 466–492.

4. Viitala E-J. Faustmann formula before Faustmann in German territorial states. Forest Policy and Economics 2016;65: 47–58.

5. Yin R, Newman DH. Optimal timber rotations with evolving prices and costs revisited. Forest Science 1995;41(3): 477–490.

6. Deegen P, Hostettler M, Navarro GA. The Faustmann model as a model for a forestry of prices. Eur. J. Forest Res. 2011;130: 353–368.

7. Campbell H. Economics of the Forest—UQ eSpace 1999. https://espace.library.uq.edu.au/view/UQ:11074/DP265Oct99.pdf

8. Nyyssönen A. Kiertoaikamalli Suomen metsätaloudessa. Metsätieteen aikakauskirja 1999(3): 540–543.

9. Tahvonen O. Economics of rotation and thinning revisited: the optimality of clearcuts versus continuous cover forestry. Forest Policy and Economics 2016;62: 88–94.

10. Gong P, Löfgren K-G. Could the Faustmann model have an interior minimum solution? Journal of Forest Economics 2016;24; 123–129.

11. Abdallah SB, Lasserre P. Forest land value and rotation with an alternative land use. Journal of Forest Economics 2017;29: 118–127.

12. Price C. Optimal rotation with declining discount rate. J. Forest Economics 2011;17: 307–318.

13. Buongiorno J, Zhou M. Further generalization of Faustmann’s formula for stochastic interest rates. J. Forest Economics 2011;17: 284–257.

14. Brazee RJ. Impacts of declining discount rates on optimal harvest age and land expectation values. J. Forest Economics, 2017;31: 27–38.

15. Price C. Optimal rotation with negative discount rates: completing the picture. J. For. Econ. 2017;29: 87–93.

16. Groom P, Hepburn C, Koundouri P, Pearce D. Discounting the future: the long and the short of it. Environmental and Resource Economics 2005;32: 445–493.

17. Hepburn CJ, Koundouri P. Recent advances in discounting: implications for forest economics. J For Econ 2007;13(2–3): 169–189.

18. Price C. Declining discount rate and the social cost of carbon: forestry consequences, J. For. Econ. 2018;31: 39–45.

19. Loisel P. Faustmann rotation and population dynamics in the presence of a risk of destructive events. J. Forest Economics 2011;17: 235–247,

20. Hyytiäinen K, Haight RG. Evaluation of forest management systems under risk of wildfire. Eur. J. Forest Res. 2010;129: 909–919.

21. Yin R, Newman D. When to cut a stand of trees?. Natural Resource Modeling 1997;10: 251–261.

22. Koskela E, Alvarez LHR. Taxation and rotation age under stochastic forest stand value. Journal of Environmental Economics and Management 2007;54(1): 113–127.

23. Tahvonen O, Salo S. Optimal forest rotation with in-situ preferences. J. Environmental Economics and Management 1999;37: 106–128.

24. Tahvonen O, Salo S, Kuuluvainen J. Optimal forest rotation and land values under a borrowing constraint. J Economic Dynamics and Control 2001;5: 1595–1627.

25. Kuuluvainen J. Virtual price approach to short-term timber supply under credit rationing. Journal of Environmental Economics and Management 1990;19: 109–126.

26. Heaps T. The forestry maximum principle. Journal of Economic Dynamics and Control 1984;7: 131–151.

27. Termansen M. Economies of scale and the optimality of rotational dynamics in forestry. Environ. Resource Econ. 2007; 37: 643.

28. Wallentin C, Nilsson U. Storm and snow damage in a Norway spruce thinning experiment in southern Sweden. Forestry 2014;87: 229–238.

29. Pukkala T, Laiho O, Lähde E. Continuous cover management reduces wind damage. For. Ecol. Manag. 2016;372: 120–127.

30. Seidl R, Thom D, Kautz M, et al., Forest disturbances under climate change. Nature Climate Change volume 2017;7: 395–402.

31. Backéus S, Wikström P, Lämås T. Modeling carbon sequestration and timber production in a regional case study. Silva Fenn. 2006;40: 615–629.

32. Gorte RW. Carbon Sequestration in Forests. Congressional Research Service 7–5700. RL31432. 2009.

33. Boulding KE. Economic Analysis. Harper & Row 1941, 3rd ed. 1955.

34. Newman DH. The Optimal Forest Rotation: A Discussion and Annotated Bibliography. USDA Forest Service, Southeastern Forest Experiment Station, General Technical Report SE-48, 1988.

35. Bollandsås OM, Buongiorno J, Gobakken T. Predicting the growth of stands of trees of mixed species and size: A matrix model for Norway. Scand. J. For. Res. 2008;23: 167–178.

36. Halvorsen E, Buongiorno J, Bollandsås O-M. NorgePro: A Spreadsheet Program for the Management of All-Aged, Mixed-Species Norwegian Forest Stands; Department of Forest and Wildlife Ecology: Madison, WI, USA, 2015. Available online: labs.russell.wisc.edu/buongiorno/files/NorgePro/NorgeProManual_4_24_15.doc (accessed on October 12, 2018).

37. Pressler MR. Zur Verständigung über der Reinertragswaldbau und dessen Betriebsideal. Allgemeine Forst und Jagd Zeitung 1860;36: 173–191.

38. Kärenlampi PP. (2019), "State-space approach to capital return in nonlinear growth processes", Agricultural Finance Review 2019,79(4):508–518. https://doi.org/10.1108

39. Leslie A. A review of the concept of the normal forest. Australian Forestry 1966;30(2): 139–147.

40. Kärenlampi PP. Stationary forestry with human interference. Sustainability 2018; 10(10): 3662.

41. Kärenlampi PP. Spruce forest stands at stationary state. J. For. Res. (2019). https://doi.org/10.1007/s11676-019-00971-4

42. Rämö J, Tahvonen O. Economics of harvesting boreal uneven-aged mixed-species forests. Can. J. For. Res. 2015;45: 1102–1112.

43. Heinonen J. Koealojen puu-ja puustotunnusten laskentaohjelma KPL. In Käyttöohje (Software for Computing Tree and Stand Characteristics for Sample Plots. User’s Manual); Research Reports; Finnish Forest Research Institute: Vantaa, Finland, 1994. (In Finnish)

44. Tahvonen O. Optimal structure and development of uneven-aged Norway spruce forests. Canadian Journal of Forest Research 2011;41(12): 2389–2402.

45. Pukkala T. Plenterwald, Dauerwald, or clearcut? Forest Policy and Economics 2016;62: 125–134.

46. Pyy J, Ahtikoski A, Laitinen E. Introducing a non-stationary matrix model for stand-level optimization, an even-aged pine (Pinus sylvestris L.) stand in Finland. Forests 2017;8: 163.

47. Sinha A, Rämö J, Malo P, Kallio M, Tahvonen O. Optimal management of naturally regenerating uneven-aged forests. European Journal of Operational Research 2017;256(3): 886–900.

48. Pukkala T, Lähde E, Laiho O. Optimizing the structure and management of uneven-sized stands in Finland. Forestry 2010;83(2): 129–142.

49. Kärenlampi PP. Harvesting design by capital return. Forests 2019; 10(3): 283.

Článek vyšel v časopise


2019 Číslo 10