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All capital investment decisions are made under varying degrees of risk and uncertainty. Evaluations of the desirability of capital investments require estimates of present conditions as well as forecasts of future events which involve these risks and uncertainties. Several recently developed models for capital investment decision-making have involved the random variable treatment of anticipated cash flows. When present worth calculation are made in these cases, a fixed interest rate is usually assumed. When internal rate of return calculations are made, the minimum acceptable rate of return is given a fixed value. This paper treats the minimum attractive rate of return (used with present worth calculations) and the minimum acceptable internal rate of return (used with internal rate of return calculations) as stochastic variables having subjective probability distributions. This procedure takes explicit account of the uncertainty of future investment opportunities. It is shown that, under certain circumstances, significant differences in the values of the mean and the variance of the criteria for making the investment decision are obtained when the results of this procedure are compared with results using the usual deterministic interest rate or minimum acceptable rate of return. [ABSTRACT FROM AUTHOR]

When uncertainty concerning costs, revenues, and project life exists, classical measures of capital investment return are limited in value. Sensitivity analysis indicates that relatively small over estimates and under estimates create relatively large errors in the discounted rate of return for different types of return schedules. Perhaps, then, businessmen are justified in seeking other methods of project evaluation. [ABSTRACT FROM AUTHOR]

The Payback Period has been dismissed as misleading and worthless by most writers on capital budgeting at the same time that businessmen continue to utilize this concept. This paper seeks to identify the problems which businessmen try to solve by use of the payback period, so that better tools can be provided for solving these, since neither the present value nor the internal rate of return does so. In the course of the analysis the payback concept is considered in its role as a criterion versus a payback constraint, payback and liquidity of capital assets and the liquidity requirements of the firm, payback as a break-even concept, and payback as crude measure of the rate of resolution of uncertainty. While payback is not advocated for capital investment decisions, the reasons for its popularity need to be understood before it is possible to develop superior alternatives. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

A method is developed for optimally selecting capital investments with uncertain returns, under conditions of limited funds and a constraint on the maximum average variance allowed in the final investment packages. The concepts involved in the analysis are somewhat related to Markowitz's work on the portfolio problem. Dynamic programming is used to compute solutions. [ABSTRACT FROM AUTHOR]

In this paper, a method is proposed for evaluating combinations of investments when the cash flows are not known with certainty. Various probability concepts are employed; and combinations are evaluated according to their incremental contribution of expected net-present value and variance to the firm as a whole. It is shown that existing investment projects must be considered if the total risk of a particular combination of investment proposals is to be evaluated realistically. Through diversification of investments, a firm is able to obtain the most desirable combination of expected net-present value and risk. [ABSTRACT FROM AUTHOR]

In this paper we consider a firm that must make a production decision and a capital decision at periodic intervals of time. The cost of production is assumed to be convex and the firm is allowed to hold inventories. For a class of inventory and capital costs the optimal production and capital decisions are obtained for an n-period problem. The optimality criterion used is minimization of the expected present value of costs in the n periods. [ABSTRACT FROM AUTHOR]

The article presents a commentary on the articles "Mathematical Analysis of Rates of Return Under Certainty" and "An Analysis of Criteria for Investment and Financing under Certainty," by Daniel Teichroew, Alexander A. Robichek, and Michael Montolbano. The articles detailed mathematical analyses pertaining to the measurement of rate of return. The author contends that one of the theorems contained in the former article is erroneous. The author presents an alternate theorem to correct the problem.

The article examines the problem of determining how to fund a capital investment by a corporation. One option is to sell new stock, and the profitability of an issue of new stock is analyzed. The authors present a definition of the rate of profit required by the market on a share of common stock, and note that the revenue stream from a share may be expected to grow. The article then examines some of the problems involved in using this definition of the rate of profit and the earnings yield in capital budgeting models. Taking out a loan, which is another option for acquiring funds for a capital investment, is discussed. An attempt is made to create a technique for estimating the future revenue from a capital outlay proposal.

This paper provides a computational technique for the evaluation of the distribution of the net present value (NPV) of an investment, in which the cash inflows occur at random time points, as in the case of venture capital. The initial cash outlay is deterministic and the magnitudes of the cash inflows are nonnegative, random variables with known distributions. The lengths of the intervals between successive cash inflows are independently distributed and independent of the magnitude of the inflows. The Laplace transforms and the first two moments of the distribution are computed for both independent and perfectly correlated inflows. It is shown that the use of constant time intervals when the timing of the inflows is random underestimates the variance of the distribution of the NPV. [ABSTRACT FROM AUTHOR]

This paper investigates the potential reduction in decision-making effort in capital budgeting problems obtainable through the use of measures of risk in addition to variance. Specific measures of risk treated are Baumol's lower confidence limit and the maximum probability of loss. The primary purpose of the paper is to present a methodology which imposes certain "constraining relations" on acceptable investment programs rather than one which appeals to a specific utility function as the basis for ordering choices. In this connection a discussion of several different utility functions is presented, along with an analysis of their usefulness when the probability distributions of net present values for various investment portfolios cannot be taken as known. In addition, some of the logical problems involved in constructing a utility function are examined. [ABSTRACT FROM AUTHOR]

This paper treats the following problem. How much money should be invested at time to at an interest rate of I for a time T such that the probability of the funds required "K(T)" exceeding those available "X(T)" equals at most p. That is P{K(T) > X(T)} ≤ p, where X(T) = X(t0) exp {I(T - t0)}. The parameters I, T, X(T) and K(T) are taken to be random variables. The theory to solve the stated problem is presented and solutions to certain specific cases are given. [ABSTRACT FROM AUTHOR]

A study of irrigation, economics was conducted in 1963 on a 10,000 acre sugar plantation in Hawaii and repeated in 1964 on three additional plantations covering 34,000 acres. The objective of the study was to recommend, on an agronomic and economic basis, a program for investing large amounts of capital in newly developed automatic and semi-automatic irrigation systems. Although basically a problem in capital budgeting, a number of complicating factors precluded the straightforward application, of traditional investment analysis techniques. The more important of these factors were; 1. Many Alternatives. The wide range of physical conditions found on each plantation ruled out the selection of a single "best" irrigation system. As a result, a number of systems had to be evaluated for each of several hundred cane fields. 2. Combinatorial Aspects. Investments in individual cane fields were interdependent since groups of fields shared common water sources; thus, combinations of investments had to be analyzed, increasing the number of investment alternatives astronomically. 3. Opportunity Value of Scarce Resources. New irrigation systems offered substantial water savings. However, the value of these savings arises from the "opportunity" value of water in alternative uses. Alternative uses, in turn, depend on how much water is saved. Thus, no value for potential savings on the plantation could be established until the investment analysis was run, first for individual alternatives and then for combinations of alternatives. 4. Complicated Timing. Because of crop planting schedules, new systems would be installed on small increments of acreage over a period of 8 to 10 years. Thus, "nonconventional" investments (outlays interspersed with benefits such that the stream of cash flows had multiple sign changes) occurred in multiple time periods; furthermore, because of crop harvesting schedules, returns from these investments also were distributed over multiple time periods with varying amounts of delay between investments and returns. The approach used to solve this problem is described in the paper. [ABSTRACT FROM AUTHOR]

Practically all existing analyses covering the obsolescence or the improvement of productive facilities are concerned with equipment replacement. An extension of such considerations to general capital investment analysis would seem to be a natural development. The present analysis is related to an investment decision on the expansion of productive capacity in discrete steps with facilities which undergo technological improvement. First, the analysis for expansion in one step is developed after the effects of technological improvement on the price and operating cost of a future facility have been introduced. The discussion of one-step expansion is then extended to an N-step expansion. In both types of expansion, the necessary conditions for optimum values of investment decision variables are obtained in order to maximize the present value of the net profit over the planning period. [ABSTRACT FROM AUTHOR]