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

Thomas Astebro and Yigal Gerchak
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Yigal Gerchak: Department of Management Sciences - University of Waterloo [Waterloo]

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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.

Keywords: Calculating; Expectation; Variance; Present Value; Random Profit Stream; Uncertain Duration (search for similar items in EconPapers)
Date: 2000
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Published in Engineering Economics, 2000, 45 (4), pp.339-349. ⟨10.1080/00137910008967557⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-00648005

DOI: 10.1080/00137910008967557

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