A Methodology for obtaining the probability density function of the present worth of probabilistic cash flow profiles

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Abstract
A new approach is presented for analyzing probabilistic cash flow profiles. Integral transform theory is used to obtain a complete analytic characterization of the probability density function of the net present worth of such cash flow profiles. This represents an extension of the current techniques of risk analysis. The methodology includes the usual evaluation and use of the expected value and the second, third and fourth central moments of the density of present worth. However, these descriptive measures do not always provide sufficient information for a complete managerial analysis. The method presented here enables management to fully differentiate between competing investment alternatives using existing methods, such as stochastic dominance, which are based on a knowledge of the form of the associated probability density functions. Simple formulae for evaluating moments of any or all orders are given. Illustrative examples are included to accompany the analytic development for several representative cases of varying complexity. Further research needs are noted in the concluding remarks.