Financial Measurement of Capital Investments

Suppose each alternative in a capital investment decision can be represented as a cash flow without uncertainty, i.e., as a sequence of m + 1 real numbers. Then the problem of which financial criterion (e.g., present value, internal rate of return, return per unit expenditure, etc.) to use for the capital investment decision is the problem of defining a preference ordering (which usually means a utility function) on the vector space of dimension m + 1. A Set of axioms is proposed for the preference ordering. The axioms specify the directions of preference in case one cash flow dominates another in magnitude (at least as great in every period, greater in some period) or in time (same total revenue, but received sooner). Also, an axiom of marginal consistency is specified, i.e., one cash flow is preferred to another if and only if the difference (considered as a separate investment) is preferred to the do-nothing investment. In addition, there is an axiom of continuity. Our result is that the only consistent (i.e., consistent with the axioms) method for ranking investments according to their cash flows is to rank them according to the formula for "present value", with positive (undetermined) rates of interest, possibly different for different time periods. Finally, an axiom specifying "temporal consistency" leads to the use of a single rate of interest. The viewpoint is that an overall corporate capital budgeting problem has two aspects: (1) the determination of a criterion, and (2) the determination of that capital program which maximizes the criterion, subject to the relevant constraints, e.g., on available projects, capital markets, etc. This paper is concerned with the first aspect only.