Rate of Return and Optimal Investment in an Imperfect Capital Market

Abstract

The analysis of a firm's investment decision under certainty involves two basic topics: The determination of the optimal initial total invest ment and the selection of investment projects among alternatives. Following the suggestion first made by Keynes (pp. 135-146), the optimal level of total initial investment is determined by the intersection of marginal efficiency of investment (MEI) and marginal cost of capital (MCC) curves. Hirshleifer promoted an alternative approach. In his 1958 paper, he extended Fisher's idea of the inter temporal allocation of investment funds between two periods. Essential to this approach is the concept of productive and market opportunity curves. If, in addition, the decision unit is assumed to possess a conventional preference function, it can also determine the optimal income and consumption pattern over time. This two-stage procedure of first maximizing invest ment return and then consumption is known as Fisher's Separation Theorem. In order to implement either one of these two approaches, it is necessary to evaluate the rates of return from all feasible investment projects and rank them properly. The current economic literature, however, does not satisfactorily address the question of how to measure investment returns. Two commonly used tech niques are net present value (NPV) and internal rate of return (IRR). The NPV technique, which measures projects by magnitudes instead of rates, disengages itself from the aforesaid investment decision theories. In fact, ranking investment projects by NPVs favors those with large initial outlays. It can lead to erroneous investment decisions if the firm's borrowing capacity is limited at the given cost of capital. On the other hand, the IRR method is beset by its questionable reinvestment assumption and the possibility of multiple rates. Most of these problems were documented, for example, by Brigham (pp. 309-444), McGuigan and Moyer (pp. 494-517), and Solomon, to mention just a few. McGuigan and Moyer (pp. 497) warned that there are some practical difficulties in implementing the Keynesian approach. The basic problem lies in ranking the n-period investment projects and deriving the MEI curve. The same problem would arise with the introduction of Hirshleifer's approach. In such a case, the difficulty would be ranking the projects and deriving the productive opportunity curve. The purpose of this paper is two-fold. The authors propose a generalized rate of return concept designed to evaluate the rates of return from alternative investment projects in an imperfect capital market. Based on these rates of return, the decision maker can rank investment projects properly and perform the analysis of optimal total initial investment along the lines suggested by Keynes or Hirshleifer. In this paper we consider multi-period (N >: 2) investment projects in an imperfect capital market. There are no stringent assumptions imposed on the cash flow pattern of the investment projects, as was the case in the studies by Canton and Lippman, and Dorfman. Our emphasis has been on methods of determin ing the optimal total investment and consump tion in the initial period. As such, it is consistent with the general treatment of the subject in the current literature, but is less ambitious than what was attempted by Hirshleifer (pp. 200-205): Ascertaining optimal investment and consump tion in each and every period. In his analysis, the use of the NPV rule was shown to be not utility-free and a filtering procedure was sug gested to define the opportunity frontier. In section II, the concept of a generalized rate of return is introduced. This rate of return is