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Asset Retirement with Infinitely Repeated Alternative Replacements: Harvest Age and Species Choice in Forestry

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  • Skander Ben Abdallah
  • Pierre Lasserre

Abstract

At what age should productive assets be retired? How should replacements be chosen when they differ in their uncertain ability to generate future incomes? As a particular version of that problem, we study the tree harvesting decision with two possible replacement species whose values as timber are stochastic and whose growth functions are deterministic. In the single-rotation (Wicksell) problem starting with a bare piece of land (an empty shop), it is optimal to choose and plant one species immediately if its current value is sufficiently high relative to that of the other species (the alternative equipment). However, if the species are insufficiently price-differentiated, it is preferable to leave the land vacant (the shop empty) despite the opportunity cost of doing so. In the repeated version of the problem, it is never optimal to leave the land bare provided the cost of replacement is null. Furthermore, the optimal harvest (tree retirement) age not only depends on the price and current productivity of the trees in place but also on the price and productivity of the other species, because it may replace the current one. The harvest age reaches a peak at some critical threshold of the relative price that signals the necessity to switch to the alternative species; indeed this is when the opportunity cost of choosing one alternative replacement over the other is the highest. The land value (and also the value of the firm) is similar to an American option with free boundary, infinite expiry period, and endogenous payoff. The paper highlights the opportunity cost of alternative replacement options, and the central role of their volatility in both asset-retirement and replacement-choice decisions. All results are derived analytically; a numerical treatment by the penalty method completes the resolution.

Suggested Citation

  • Skander Ben Abdallah & Pierre Lasserre, 2016. "Asset Retirement with Infinitely Repeated Alternative Replacements: Harvest Age and Species Choice in Forestry," CIRANO Working Papers 2016s-37, CIRANO.
  • Handle: RePEc:cir:cirwor:2016s-37
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    References listed on IDEAS

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    1. Abildtrup, Jens & Strange, Niels, 2000. "The option value of non-contaminated forest watersheds," Forest Policy and Economics, Elsevier, vol. 1(2), pages 115-125, August.
    2. Jean-Paul Décamps & Thomas Mariotti & Stéphane Villeneuve, 2006. "Irreversible investment in alternative projects," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 28(2), pages 425-448, June.
    3. Clarke, Harry R. & Reed, William J., 1989. "The tree-cutting problem in a stochastic environment : The case of age-dependent growth," Journal of Economic Dynamics and Control, Elsevier, vol. 13(4), pages 569-595, October.
    4. Gregory S. Amacher & Markku Ollikainen & Erkki A. Koskela, 2009. "Economics of Forest Resources," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262012480, March.
    5. Ye, Meng-Hua, 1990. "Optimal replacement policy with stochastic maintenance and operation costs," European Journal of Operational Research, Elsevier, vol. 44(1), pages 84-94, January.
    6. Avinash K. Dixit & Robert S. Pindyck, 1994. "Investment under Uncertainty," Economics Books, Princeton University Press, edition 1, number 5474.
    7. Geltner, David & Riddiough, Timothy & Stojanovic, Srdjan, 1996. "Insights on the Effect of Land Use Choice: The Perpetual Option on the Best of Two Underlying Assets," Journal of Urban Economics, Elsevier, vol. 39(1), pages 20-50, January.
    8. Samuelson, Paul A, 1976. "Economics of Forestry in an Evolving Society," Economic Inquiry, Western Economic Association International, vol. 14(4), pages 466-492, December.
    9. Hultkrantz, Lars & Andersson, Linda & Mantalos, Panagiotis, 2014. "Stumpage prices in Sweden 1909–2012: Testing for non-stationarity," Journal of Forest Economics, Elsevier, vol. 20(1), pages 33-46.
    10. Willassen, Yngve, 1998. "The stochastic rotation problem: A generalization of Faustmann's formula to stochastic forest growth," Journal of Economic Dynamics and Control, Elsevier, vol. 22(4), pages 573-596, April.
    11. Kassar, Ilhem & Lasserre, Pierre, 2004. "Species preservation and biodiversity value: a real options approach," Journal of Environmental Economics and Management, Elsevier, vol. 48(2), pages 857-879, September.
    12. repec:elg:eechap:14605_8 is not listed on IDEAS
    13. Reed, William J., 1993. "The decision to conserve or harvest old-growth forest," Ecological Economics, Elsevier, vol. 8(1), pages 45-69, August.
    14. Insley, Margaret, 2002. "A Real Options Approach to the Valuation of a Forestry Investment," Journal of Environmental Economics and Management, Elsevier, vol. 44(3), pages 471-492, November.
    15. Sohngen, Brent & Mendelsohn, Robert, 1998. "Valuing the Impact of Large-Scale Ecological Change in a Market: The Effect of Climate Change on U.S. Timber," American Economic Review, American Economic Association, vol. 88(4), pages 686-710, September.
    16. Alvarez, Luis H. R. & Koskela, Erkki, 2005. "Wicksellian theory of forest rotation under interest rate variability," Journal of Economic Dynamics and Control, Elsevier, vol. 29(3), pages 529-545, March.
    17. Saphores, Jean-Daniel, 2003. "Harvesting a renewable resource under uncertainty," Journal of Economic Dynamics and Control, Elsevier, vol. 28(3), pages 509-529, December.
    18. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    19. Andersson, Linda & Hultkrantz , Lars & Mantalos , Panagiotis, 2013. "Stumpage Prices in Sweden 1909-2011: Testing for Non-Stationarity," Working Papers 2013:1, Örebro University, School of Business.
    20. Skander BEN ABDALLAH & Pierre LASSERRE, 2015. "Optimum Forest Rotations of Alternative Tree Species," Cahiers de recherche 06-2015, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    21. Alvarez, Luis H.R. & Koskela, Erkki, 2007. "Optimal harvesting under resource stock and price uncertainty," Journal of Economic Dynamics and Control, Elsevier, vol. 31(7), pages 2461-2485, July.
    22. Tommi Ekholm, 2015. "Optimal forest rotation age under efficient climate change mitigation," Papers 1505.05669, arXiv.org, revised Oct 2015.
    23. David H. Newman & Charles B. Gilbert & William F. Hyde, 1985. "The Optimal Forest Rotation with Evolving Prices," Land Economics, University of Wisconsin Press, vol. 64(4), pages 347-353.
    24. Thomas A. Thomson, 1992. "Optimal Forest Rotation When Stumpage Prices Follow a Diffusion Process," Land Economics, University of Wisconsin Press, vol. 68(3), pages 329-342.
    25. Malchow-Moller, Nikolaj & Thorsen, Bo Jellesmark, 2005. "Repeated real options: optimal investment behaviour and a good rule of thumb," Journal of Economic Dynamics and Control, Elsevier, vol. 29(6), pages 1025-1041, June.
    26. Morck, Randall & Schwartz, Eduardo & Stangeland, David, 1989. "The Valuation of Forestry Resources under Stochastic Prices and Inventories," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 24(04), pages 473-487, December.
    27. Conrad, Jon M., 1997. "On the option value of old-growth forest," Ecological Economics, Elsevier, vol. 22(2), pages 97-102, August.
    28. Mauer, David C. & Ott, Steven H., 1995. "Investment under Uncertainty: The Case of Replacement Investment Decisions," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 30(04), pages 581-605, December.
    29. Richardson, Steven & Kefford, Adrian & Hodkiewicz, Melinda, 2013. "Optimised asset replacement strategy in the presence of lead time uncertainty," International Journal of Production Economics, Elsevier, vol. 141(2), pages 659-667.
    30. Sahashi, Yoshinao, 2002. "Optimal forestry control with variable forest area," Journal of Economic Dynamics and Control, Elsevier, vol. 26(5), pages 755-796, May.
    31. Brennan, Michael J. & Schwartz, Eduardo S., 1978. "Finite Difference Methods and Jump Processes Arising in the Pricing of Contingent Claims: A Synthesis," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 13(03), pages 461-474, September.
    32. Reed, William J & Clarke, Harry R, 1990. "Harvest Decisions and Asset Valuation for Biological Resources Exhibiting Size-Dependent Stochastic Growth," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 31(1), pages 147-169, February.
    33. Lyon, Kenneth S., 1981. "Mining of the forest and the time path of the price of timber," Journal of Environmental Economics and Management, Elsevier, vol. 8(4), pages 330-344, December.
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    More about this item

    Keywords

    Real options; stochastic prices; American option; asset retirement; replacement option; penalty method; forestry; Faustmann; alternative species; rotation;

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • Q23 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Renewable Resources and Conservation - - - Forestry

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