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Moments and distribution of the net present value of a serial project

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  • Creemers, Stefan

Abstract

We study the Net Present Value (NPV) of a project with multiple stages that are executed in sequence. A cash flow (positive or negative) may be incurred at the start of each stage, and a payoff is obtained at the end of the project. The duration of a stage is a random variable with a general distribution function. For such projects, we obtain exact, closed-form expressions for the moments of the NPV, and develop a highly accurate closed-form approximation of the NPV distribution itself. In addition, we show that the optimal sequence of stages (that maximizes the expected NPV) can be obtained efficiently, and demonstrate that the problem of finding this optimal sequence is equivalent to the least cost fault detection problem. We also illustrate how our results can be applied to a general project scheduling problem where stages are not necessarily executed in series. Lastly, we prove two limit theorems that allow to approximate the NPV distribution. Our work has direct applications in the fields of project selection, project portfolio management, and project valuation.

Suggested Citation

  • Creemers, Stefan, 2018. "Moments and distribution of the net present value of a serial project," European Journal of Operational Research, Elsevier, vol. 267(3), pages 835-848.
    • Handle: RePEc:eee:ejores:v:267:y:2018:i:3:p:835-848
    DOI: 10.1016/j.ejor.2017.12.039
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    Cited by:

    1. Rostami, Salim & Creemers, Stefan & Leus, Roel, 2024. "Maximizing the net present value of a project under uncertainty: Activity delays and dynamic policies," European Journal of Operational Research, Elsevier, vol. 317(1), pages 16-24.
    2. Hazır, Öncü & Ulusoy, Gündüz, 2020. "A classification and review of approaches and methods for modeling uncertainty in projects," International Journal of Production Economics, Elsevier, vol. 223(C).
    3. Dan Cudjoe, 2023. "Energy-economics and environmental prospects of integrated waste-to-energy projects in the Beijing-Tianjin-Hebei region," Environment, Development and Sustainability: A Multidisciplinary Approach to the Theory and Practice of Sustainable Development, Springer, vol. 25(11), pages 12597-12628, November.
    4. Fatemeh Rezaei & Amir Abbas Najafi & Erik Demeulemeester & Reza Ramezanian, 2024. "A stochastic bi-objective project scheduling model under failure of activities," Annals of Operations Research, Springer, vol. 338(1), pages 453-476, July.
    5. Öncü Hazir & Gündüz Ulusoy, 2020. "A classification and review of approaches and methods for modeling uncertainty in projects," Post-Print hal-02898162, HAL.
    6. Szmerekovsky, Joseph G. & Venkateshan, Prahalad & Simonson, Peter D., 2023. "Project scheduling under the threat of catastrophic disruption," European Journal of Operational Research, Elsevier, vol. 309(2), pages 784-794.
    7. Grubbström, Robert W., 2022. "On the net present value distribution affected by a random walk process," International Journal of Production Economics, Elsevier, vol. 250(C).
    8. Hermans, Ben & Leus, Roel & Looy, Bart Van, 2023. "Deciding on scheduling, secrecy, and patenting during the new product development process: The relevance of project planning models," Omega, Elsevier, vol. 116(C).

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