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Stepwise investment and capacity sizing under uncertainty

Author

Listed:
  • Michail Chronopoulos

    (University of Brighton
    Norwegian School of Economics)

  • Verena Hagspiel

    (Norwegian University of Science and Technology)

  • Stein-Erik Fleten

    (Norwegian University of Science and Technology)

Abstract

The relationship between uncertainty and managerial flexibility is particularly crucial in addressing capital projects. We consider a firm that can invest in a project in either a single (lumpy investment) or multiple stages (stepwise investment) under price uncertainty and has discretion over not only the time of investment but also the size of the project. We confirm that if the capacity of a project is fixed and the investment premium associated with stepwise investment is positive, then lumpy investment becomes more valuable than a stepwise investment strategy under high price uncertainty. By contrast, if a firm has discretion over capacity, then we show that the stepwise investment strategy always dominates that of lumpy investment. In addition, we show that the total amount of installed capacity under a stepwise investment strategy is always greater than that under lumpy investment.

Suggested Citation

  • Michail Chronopoulos & Verena Hagspiel & Stein-Erik Fleten, 2017. "Stepwise investment and capacity sizing under uncertainty," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 39(2), pages 447-472, March.
  • Handle: RePEc:spr:orspec:v:39:y:2017:i:2:d:10.1007_s00291-016-0460-0
    DOI: 10.1007/s00291-016-0460-0
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    1. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," The Review of Financial Studies, Society for Financial Studies, vol. 14(1), pages 113-147.
    2. Andrea Gamba & Nicola Fusari, 2009. "Valuing Modularity as a Real Option," Management Science, INFORMS, vol. 55(11), pages 1877-1896, November.
    3. Kuno J.M. Huisman & Peter M. Kort, 2015. "Strategic capacity investment under uncertainty," RAND Journal of Economics, RAND Corporation, vol. 46(2), pages 376-408, June.
    4. Siddiqui, Afzal S. & Maribu, Karl, 2009. "Investment and upgrade in distributed generation under uncertainty," Energy Economics, Elsevier, vol. 31(1), pages 25-37, January.
    5. Pawlina, G. & Kort, P.M., 2001. "Strategic Capital Budgeting : Asset Replacement Under Uncertainty," Other publications TiSEM e79e30d8-bf35-4cde-ae02-f, Tilburg University, School of Economics and Management.
    6. Andrew B. Abel & Janice C. Eberly, 1996. "Optimal Investment with Costly Reversibility," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 63(4), pages 581-593.
    7. Majd, Saman & Pindyck, Robert S., 1987. "Time to build, option value, and investment decisions," Journal of Financial Economics, Elsevier, vol. 18(1), pages 7-27, March.
    8. Ioannis Karatzas & Fridrik M. Baldursson, 1996. "Irreversible investment and industry equilibrium (*)," Finance and Stochastics, Springer, vol. 1(1), pages 69-89.
    9. Fleten, S.-E. & Maribu, K.M. & Wangensteen, I., 2007. "Optimal investment strategies in decentralized renewable power generation under uncertainty," Energy, Elsevier, vol. 32(5), pages 803-815.
    10. 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.
    11. Bøckman, Thor & Fleten, Stein-Erik & Juliussen, Erik & Langhammer, Håvard J. & Revdal, Ingemar, 2008. "Investment timing and optimal capacity choice for small hydropower projects," European Journal of Operational Research, Elsevier, vol. 190(1), pages 255-267, October.
    12. Manu Goyal & Serguei Netessine, 2007. "Strategic Technology Choice and Capacity Investment Under Demand Uncertainty," Management Science, INFORMS, vol. 53(2), pages 192-207, February.
    13. Dixit, Avinash, 1993. "Choosing among alternative discrete investment projects under uncertainty," Economics Letters, Elsevier, vol. 41(3), pages 265-268.
    14. Krishnan S. Anand & Karan Girotra, 2007. "The Strategic Perils of Delayed Differentiation," Management Science, INFORMS, vol. 53(5), pages 697-712, May.
    15. Joachim Gahungu and Yves Smeers, 2012. "A Real Options Model for Electricity Capacity Expansion," RSCAS Working Papers 2012/08, European University Institute.
    16. Carliss Y. Baldwin & Kim B. Clark, 2000. "Design Rules, Volume 1: The Power of Modularity," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262024667, April.
    17. Jiri Chod & Nils Rudi, 2005. "Resource Flexibility with Responsive Pricing," Operations Research, INFORMS, vol. 53(3), pages 532-548, June.
    18. Kenneth J. Arrow & Anthony C. Fisher, 1974. "Environmental Preservation, Uncertainty, and Irreversibility," Palgrave Macmillan Books, in: Chennat Gopalakrishnan (ed.), Classic Papers in Natural Resource Economics, chapter 4, pages 76-84, Palgrave Macmillan.
    19. Gollier, Christian & Proult, David & Thais, Francoise & Walgenwitz, Gilles, 2005. "Choice of nuclear power investments under price uncertainty: Valuing modularity," Energy Economics, Elsevier, vol. 27(4), pages 667-685, July.
    20. Clemens Löffler & Thomas Pfeiffer & Georg Schneider, 2013. "The irreversibility effect and agency conflicts," Theory and Decision, Springer, vol. 74(2), pages 219-239, February.
    21. He, Hua & Pindyck, Robert S., 1992. "Investments in flexible production capacity," Journal of Economic Dynamics and Control, Elsevier, vol. 16(3-4), pages 575-599.
    22. Claude Henry, 1974. "Investment decisions under uncertainty: The "irreversibility effect"," ULB Institutional Repository 2013/327343, ULB -- Universite Libre de Bruxelles.
    23. Lund, Diderik, 2005. "How to analyze the investment-uncertainty relationship in real option models?," Review of Financial Economics, Elsevier, vol. 14(3-4), pages 311-322.
    24. Jorgensen, Steffen & Kort, Peter M., 1993. "Optimal dynamic investment policies under concave-convex adjustment costs," Journal of Economic Dynamics and Control, Elsevier, vol. 17(1-2), pages 153-180.
    25. Pindyck, Robert S, 1988. "Irreversible Investment, Capacity Choice, and the Value of the Firm," American Economic Review, American Economic Association, vol. 78(5), pages 969-985, December.
    26. Kort, Peter M. & Murto, Pauli & Pawlina, Grzegorz, 2010. "Uncertainty and stepwise investment," European Journal of Operational Research, Elsevier, vol. 202(1), pages 196-203, April.
    27. Henry, Claude, 1974. "Investment Decisions Under Uncertainty: The "Irreversibility Effect."," American Economic Review, American Economic Association, vol. 64(6), pages 1006-1012, December.
    28. Dangl, Thomas, 1999. "Investment and capacity choice under uncertain demand," European Journal of Operational Research, Elsevier, vol. 117(3), pages 415-428, September.
    29. Avinash K. Dixit & Robert S. Pindyck, 1994. "Investment under Uncertainty," Economics Books, Princeton University Press, edition 1, number 5474.
    30. Rodrigues, Artur & Armada, Manuel J. Rocha, 2007. "The valuation of modular projects: A real options approach to the value of splitting," Global Finance Journal, Elsevier, vol. 18(2), pages 205-227.
    31. Siddiqui, Afzal & Takashima, Ryuta, 2012. "Capacity switching options under rivalry and uncertainty," European Journal of Operational Research, Elsevier, vol. 222(3), pages 583-595.
    32. Bertola, Giuseppe, 1998. "Irreversible investment," Research in Economics, Elsevier, vol. 52(1), pages 3-37, March.
    33. Luis Alvarez & Rune Stenbacka, 2003. "Optimal risk adoption: a real options approach," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 23(1), pages 123-147, December.
    34. Boomsma, Trine Krogh & Meade, Nigel & Fleten, Stein-Erik, 2012. "Renewable energy investments under different support schemes: A real options approach," European Journal of Operational Research, Elsevier, vol. 220(1), pages 225-237.
    35. 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.
    36. Hagspiel, Verena & Huisman, Kuno J.M. & Kort, Peter M., 2016. "Volume flexibility and capacity investment under demand uncertainty," International Journal of Production Economics, Elsevier, vol. 178(C), pages 95-108.
    37. John V. Leahy, 1993. "Investment in Competitive Equilibrium: The Optimality of Myopic Behavior," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 108(4), pages 1105-1133.
    38. Longstaff, Francis A & Schwartz, Eduardo S, 2001. "Valuing American Options by Simulation: A Simple Least-Squares Approach," University of California at Los Angeles, Anderson Graduate School of Management qt43n1k4jb, Anderson Graduate School of Management, UCLA.
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    7. Zixuan Zhang & Michail Chronopoulos & Dimitrina S. Dimitrova & Ioannis Kyriakou, 2024. "Risk assessment and optimal scheduling of serial projects," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 46(3), pages 709-736, September.
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    9. Ma, Jinrun & Niu, Yingjie, 2019. "The timing and intensity of investment under ambiguity," The North American Journal of Economics and Finance, Elsevier, vol. 49(C), pages 318-330.
    10. Koussis, Nicos & Silaghi, Florina, 2023. "Revenue-sharing and volume flexibility in the supply chain," International Journal of Production Economics, Elsevier, vol. 261(C).
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    More about this item

    Keywords

    Investment analysis; Capacity sizing; Flexibility; Real options;
    All these keywords.

    JEL classification:

    • G00 - Financial Economics - - General - - - General
    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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