A Closed-Form Methodology for Computing Present Worth Statistics of Risky Discrete Cash-Flows

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Abstract
A closed-form methodology for obtaining statistical moments of present worth for discrete cash flows is shown and proposed for use in economic risk analysis. Coefficients of alternative cash-flow time-series are viewed as independent random variables with known probability (density) functions. Inputs to this methodology consist of: the time-series form, probability (density) functions with parameter values for each series coefficient, and the discount rate. The methodology converts these informational inputs into the 1st, 2nd,…, rth statistical moment of present worth for that series. This methodology is based on a decomposition of the zeta transform method and theorems on products and sums of moments for independent random variables. Moments are as exact as the computational precision allows. Expected present worths are easily computed but variances entail moderate effort for manual computation Calculations of higher moments of present worth are extensive and computer computations are recommended. This methodology is theoretically developed and numerically illustrated.