For the Decision Maker—An Analytical Approach to Evaluating Risky Capital Investments

Hertz David B. , “Risk Analysis in Capital Investment,” Harvard Business Review, Jan.-Feb. 1964, pp. 95–106.

Hillier Frederick S. , “The Derivation of Probabilistic Information for the Evaluation of Risky Investments,” Management Science, April 1963, pp. 443–457.

“Cash flow” is used herein to refer to net cash flow, i.e., cash receipts less cash disbursements.

Consideration will typically be given to such things as a firm's cost of capital and returns available from alternate uses of capital in arriving at this figure.

Schlaifer Robert , Introduction to Statistics for Business Decisions (New York: McGraw-Hill Book Company, 1961). See chapter 15 for a discussion of the normal distribution.

An acronym for Program Evaluation and Review Technique, a control device using the network plan concept developed in 1958 as a control system for the Polaris project. For an explanation, see Moder Joseph Phillips Cecil R. , Project Management with CPM and PERT (New York: Reinhold Publishing Corporation, 1964).

Actually, the assumption that the normal distribution is applicable is more of a convenience than a necessity. The consequences, if this assumption should be violated, often are not very serious. This is discussed in a later section and, in more detail, in Hillier , op. cit.

Present Worth = −3,860,000+300,000/(1.08) + 500,000/(1.08)² + … + 650,000/(1.08)¹⁰.

If the company is in poor financial condition, an estimate of the extent to which losses may be incurred should be of vital concern to management.

Inasmuch as cash flows in the distant future are discounted more than those that are more imminent, the procedure is not too sensitive to errors in estimating remote cash flows.

This conclusion is obtained from the “Central Limit Theorem,” which is discussed in Hillier, op. cit., p. 446, and in Schlaifer , op. cit., pp. 252 ff.

A small error will be introduced to the extent that, for each year's cash flow, the estimated most likely value deviates from the “expected value” (as defined by probability theory) and the estimated maximum deviation deviates from three “standard deviations” (as defined by probability theory). To counteract this, the estimated maximum deviation should be roughly the average of the maximum deviation above and below the most likely value.

If this distribution is skewed rather than normal, one approach would be to obtain an optimistic, a pessimistic, and a most likely estimate of each year's cash flow; the discounted sum of the estimates of each type would provide a corresponding estimate (optimistic, pessimistic, and most likely, respectively) of present worth. This approach is valid only for the high correlation case.