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Calculating the Expectation and Variance of the Present Value for a Random Profit Stream of Uncertain Duration

Author

Listed:
  • Thomas B. Astebro

    (Department of Management Sciences - University of Waterloo [Waterloo])

  • Yigal Gerchak

    (Department of Management Sciences - University of Waterloo [Waterloo])

Abstract

We derive the mean and variance of the random discounted sum [[[sigma].sup.N].sub.n=1] [[theta].sup.n][X.sub.n], when N is uncertain, as are the [X.sub.n]'s. This quantity arises in applications involving random cash-flows over an uncertain number of years. One such application is R&D projects, where both the magnitude and duration of cash-flows are uncertain at the time of investment decision. Previous models have assumed cash-flow duration to be certain. We relax this assumption. We then specialize these results to geometric, mixed-geometric and Poisson distributions of the cash-flow duration.

Suggested Citation

  • Thomas B. Astebro & Yigal Gerchak, 2000. "Calculating the Expectation and Variance of the Present Value for a Random Profit Stream of Uncertain Duration," Post-Print hal-00648005, HAL.
    • Handle: RePEc:hal:journl:hal-00648005
    DOI: 10.1080/00137910008967557
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    Cited by:

    1. Thomas Åstebro & Samir Elhedhli, 2006. "The Effectiveness of Simple Decision Heuristics: Forecasting Commercial Success for Early-Stage Ventures," Management Science, INFORMS, vol. 52(3), pages 395-409, March.
    2. Astebro, Thomas B. & Dahlin, Kristina B., 2005. "Opportunity knocks," Research Policy, Elsevier, vol. 34(9), pages 1404-1418, November.

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