A Statistical Analysis of Risk in Capital Investment Projects

The object of this paper is twofold: first, to present a brief survey of the various techniques used in the measurement of risk in capital investment proposals; second, to show how, under certain assumptions, the probability distributions of the two most commonly used profitability criterion functions, viz. Net Present Value and Internal Rate of Return, can be obtained. This approach was first presented by Hillier in a paper published in Management Science for the single investment case. It was further generalized by him to the case of interrelated investments in an outstanding paper published in July 1964 as Technical Report No. 73 under contract with the office of Naval Research. These papers are theoretically oriented. The present paper discusses Hillier's approach and considers some numerical examples showing how the approach can be implemented in practice. Secondly, the starting point of Hillier's analysis are the means and variances of cash flows. In many situations these may not be known directly. What may be available are the means and variances of factors which make up these cash flows. The present paper discusses methods for handling such situations.