Percentage Gain on Investment - An Investment Decision Yardstick
Authors: Kaitz Melvin 
Published: December 2007

KAITZ, MELVIN, MEMBER AIME, MOBIL OIL CORP., NEW YORK, N.Y.

Abstract
A continuing discussion in both the petroleum engineering and economic literature is directed to the difficulties encountered in the use of discounted cash flow rate of return (DCF) as a measure of investment worth. Although useful in most instances. DCF has been criticized because it is time-consuming in its trial-and-error solution, theoretically invalid, not adaptable to cash flow streams yielding multiple return solutions and not entirely reliable in selecting between mutually exclusive investments. The theoretical in validity of DCF stems from the reinvestment assumption implicit in the calculation that earning are reinvested at the DCF rate. The emerging consensus of the economic literature is that the net present value or the present worth of the net cash flow stream discounting at the average opportunity or cost of capital rate) is more correct and reliable. Other criteria proposed have been ratios of net present value divided by initial in vestment or by present value of all investments in a project. All of these criteria are simple to determine and explicitly assume a reinvestment rate four the income generated by a project. This paper develops and discusses a theoretically valid profitability criterion which is simple to compute and retains the appeal of a percent return on investment. It is called "percentage gain on investment" or PGI. It measures the gain an investment is expected to realize over like capital invested in the average opportunity and explicitly considers reinvestment potential. Why add another concept to the large array of in vestment criteria now available, any one of which, or perhaps a combination of several. appears to embrace the firm's (or individual's) objectives? The answer is that not one of the existing criteria provides both a readily comprehensible and theoretically valid measure of risk coverage that has general application. The proposed PGI does fulfill these requirements.

Introduction
An ancient expression warns that "one must yield to the times" - there are better ways of doing things. A review of the petroleum engineering and economic literature on one topic alone, measurement of investment worth, certainly is witness to this truth. In use for a number of years. the DCF has recently received attention, directed mainly to its theoretical invalidity. Several alternatives to DCF have been proposed to provide a valid, simply determined criterion to describe investment worth and to overcome the criticisms previously mentioned. This paper introduces another method called percentage gain on investment (PGI) and is proposed as but one of several yardsticks that should be used in making investment decisions.

MEASURES OF INVESTMENT WORTH
This paper will consider only those criteria which give weight to the time pattern of future earnings. These criteria are usually compared with an average opportunity rate or cost of capital of the firm to judge the relative worth of the investment. For purposes of demonstration, a 9 percent average opportunity rate will be used throughout this paper. Implicit in the DCF calculation is the assumption that earnings are reinvested at the DCF rate. Some argue though. that there is no reinvestment assumption, that the DCF rate is simply that maximum rate of interest one can pay on the investment over the life of the project and break even. The determination of DCF is accomplished by discounting the net cash flow stream at that rate (DCF) which will yield zero. The question is: why should reinvestment potential be explicitly considered in calculating return on investment or other criteria measuring economic worth? Perhaps the answer lies in consistent or equal treatment of future cash flow. It appears entirely illogical to give different present worth value to $1 received, say, 10 years from now, which is the circumstance resulting in comparing projects with different DCF returns. In fact, $1 received in 10 years has the same value regardless of which project generated the income. DCF return thus favors investment projects which are expected to provide early income as compared to those providing long-term income. Not surprisingly, the controversy on reinvestment assumption is an old one. Hoskold discussed this same problem in 1877. He considered the future income from mineral properties as an annuity or a series of fixed future payments. (As will be demonstrated, his equation can be modified for variable income.) Prior to Hoskold, the value or what one could pay for the mine, was determined with the use of standard, single-interest tables. Here is what Hoskold said with regard to these tables.
JPT
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