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Invest or Exit? Optimal Decisions in the Face of a Declining Profit Stream

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  • H. Dharma Kwon

    (Department of Business Administration, University of Illinois at Urbana--Champaign, Champaign, Illinois 61820)

Abstract

Even in the face of deteriorating and highly volatile demand, firms often invest in, rather than discard, aging technologies. To study this phenomenon, we model the firm's profit stream as a Brownian motion with negative drift. At each point in time, the firm can continue operations, or it can stop and exit the project. In addition, there is a one-time option to make an investment that boosts the project's profit rate. Using stochastic analysis, we show that the optimal policy always exists and that it is characterized by three thresholds. There are investment and exit thresholds before investment, and there is a threshold for exit after investment. We also effect a comparative statics analysis of the thresholds with respect to the drift and the volatility of the Brownian motion. When the profit boost upon investment is sufficiently large, we find a novel result: the investment threshold decreases in volatility.

Suggested Citation

  • H. Dharma Kwon, 2010. "Invest or Exit? Optimal Decisions in the Face of a Declining Profit Stream," Operations Research, INFORMS, vol. 58(3), pages 638-649, June.
    • Handle: RePEc:inm:oropre:v:58:y:2010:i:3:p:638-649
    DOI: 10.1287/opre.1090.0740
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    References listed on IDEAS

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    Cited by:

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    2. Hagspiel, Verena & Huisman, Kuno J.M. & Kort, Peter M. & Lavrutich, Maria N. & Nunes, Cláudia & Pimentel, Rita, 2020. "Technology adoption in a declining market," European Journal of Operational Research, Elsevier, vol. 285(1), pages 380-392.
    3. Miyakawa, Daisuke & Oikawa, Koki & Ueda, Kozo, 2021. "Firm Exit during the COVID-19 Pandemic: Evidence from Japan," Journal of the Japanese and International Economies, Elsevier, vol. 59(C).
    4. H. Dharma Kwon & Steven A. Lippman, 2019. "Acquisition of Project-Specific Assets with Bayesian Updating," Papers 1901.04120, arXiv.org.
    5. Alain Bensoussan & Benoit Chevalier-Roignant & Alejandro Rivera, 2022. "A model for wind farm management with option interactions," Post-Print hal-04325553, HAL.
    6. Hagspiel, V. & Huisman, Kuno & Kort, Peter M. & Nunes, Claudia & Pimentel, Rita, 2018. "Product Innovation of an Incumbent Firm : A Dynamic Analysis," Discussion Paper 2018-048, Tilburg University, Center for Economic Research.
    7. Guo, Liquan & Ng, Adolf K.Y. & Jiang, Changmin & Long, Jiancheng, 2021. "Stepwise capacity integration in port cluster under uncertainty and congestion," Transport Policy, Elsevier, vol. 112(C), pages 94-113.
    8. Volker Krätschmer & Marcel Ladkau & Roger J. A. Laeven & John G. M. Schoenmakers & Mitja Stadje, 2018. "Optimal Stopping Under Uncertainty in Drift and Jump Intensity," Mathematics of Operations Research, INFORMS, vol. 43(4), pages 1177-1209, November.
    9. Qiang Li & Junwei Wang & Jian Ni & Lap Keung Chu & Congdong Li, 2019. "The optimal time to make a risky investment under a permanent exit option," Journal of Intelligent Manufacturing, Springer, vol. 30(7), pages 2669-2680, October.
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    12. H. Dharma Kwon & Steven A. Lippman, 2011. "Acquisition of Project-Specific Assets with Bayesian Updating," Operations Research, INFORMS, vol. 59(5), pages 1119-1130, October.
    13. Apurva Jain & Swapnil Rayal, 2023. "Managing medical equipment capacity with early spread of infection in a region," Production and Operations Management, Production and Operations Management Society, vol. 32(5), pages 1415-1432, May.
    14. Niu, Wenju & Shen, Houcai, 2022. "Investment in process innovation in supply chains with knowledge spillovers under innovation uncertainty," European Journal of Operational Research, Elsevier, vol. 302(3), pages 1128-1141.
    15. Jostein Tvedt, 2022. "Optimal Entry and Exit Decisions Under Uncertainty and the Impact of Mean Reversion," SN Operations Research Forum, Springer, vol. 3(4), pages 1-21, December.
    16. Fehmi Tanrısever & S. Sinan Erzurumlu & Nitin Joglekar, 2012. "Production, Process Investment, and the Survival of Debt‐Financed Startup Firms," Production and Operations Management, Production and Operations Management Society, vol. 21(4), pages 637-652, July.
    17. Lavrutich, Maria N., 2017. "Capacity choice under uncertainty in a duopoly with endogenous exit," European Journal of Operational Research, Elsevier, vol. 258(3), pages 1033-1053.
    18. Alain Bensoussan & Benoît Chevalier‐Roignant & Alejandro Rivera, 2022. "A model for wind farm management with option interactions," Production and Operations Management, Production and Operations Management Society, vol. 31(7), pages 2853-2871, July.
    19. Vicky Henderson & David Hobson, 2013. "Risk Aversion, Indivisible Timing Options, and Gambling," Operations Research, INFORMS, vol. 61(1), pages 126-137, February.
    20. Sarkar, Sudipto, 2018. "Optimal DOL (degree of operating leverage) with investment and production flexibility," International Journal of Production Economics, Elsevier, vol. 202(C), pages 172-181.
    21. Yongyi Zhou & Yulin Zhang & Mark Goh, 2021. "Choice of pricing and advertising schemes for a two‐sided platform," Managerial and Decision Economics, John Wiley & Sons, Ltd., vol. 42(7), pages 1865-1885, October.
    22. Hagspiel, Verena & Huisman, Kuno J.M. & Nunes, Clàudia, 2015. "Optimal technology adoption when the arrival rate of new technologies changes," European Journal of Operational Research, Elsevier, vol. 243(3), pages 897-911.

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