On the net present value distribution affected by a random walk process

• In this paper we attempt to derive properties of the distribution of the net present value NPV, when the un-derlying cash flow is affected by stochastic disturbances in the form of a random walk process, the disturbances thus jumping continuously between each of two values. A leverage is introduced, affecting the size of each jump in relation to time.A given time period is split into a number of sub-periods of equal length. During each sub-period, a fraction of altogether one monetary unit is transferred. This cash flow is subject to the random walk, and is discounted by a given constant discount rate. We study consequences on the distribution of the net present value as the number of sub-periods increases beyond all bounds.Two different processes are studied, which turn out to have rather different properties. In the first, Case A, the two levels between each jump, are chosen as each others negative, and in the second, Case B, except for a timing factor, as each others inverse. Among other consequences, it is shown that the probability distribution of the NPV in Case A is close to, but different from, a lognormal distribution, and that in Case B, the NPV indeed has a lognormal distribution, but lies stable at a constant value. Also is shown that in Case A, the leverage must be at least 1/2 for a limiting distribution to exist, and in Case B at least unity. For leverage values above these values, respectively, the random walk will not affect NPV, and the net present value becomes deterministic.

Ämnesord

TEKNIK OCH TEKNOLOGIER  -- Annan teknik -- Övrig annan teknik (hsv//swe)

ENGINEERING AND TECHNOLOGY  -- Other Engineering and Technologies -- Other Engineering and Technologies not elsewhere specified (hsv//eng)

Nyckelord

Net present value; NPV; Random walk; Distribution of NPV

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