Accounting Rates of Return

Abstract

Many economic studies provide empirical evidence regarding cross-sectional differences in firm profitability. In most of these studies, firm profitability is measured by an accounting rate of return (net income dividend by the book value of assets, hereafter, ARR) rather than an economic rate of profit.' Franklin Fisher and John McGowan define the firm's economic rate of profit (IRR) as that interest rate which equates the present value of its net revenue stream to its initial outlay (1983, p. 82). Fisher and McGowan examine the analytic relation between a firm's ARR and its IRR in a series of and conclude that the ARR is such a bad surrogate for the IRR that the results of ARR-based empirical studies are likely to be (p. 91). William Long and David Ravenscraft (1984) have criticized the theoretical work of Fisher and McGowan because the nature of the analytic relationship between the ARR and the IRR in the context of highly simplified hypothetical examples may not be indicative of the nature of the relationship in empirical settings. Their criticism adopts the utilitarian view that the ARR has to be treated as a suitable surrogate for the IRR as long as no preferable alternative measure of profitability is available for empirical work. This view has merit as long as the measurement error which is contained in the ARR is random rather than systematic. Unfortunately, the nature and extent of the measurement error which is contained in the ARR in a particular empirical setting can only be determined unequivocally if the IRR is unequivocally known. In such a case, of course, there would be no need to rely on the ARR at all. Due to this unhappy circle, empirical research on firm profitability has continued to rely on the ARR despite the fact that many persons reasonably believe that the results of such research may be totally misleading (Fisher and McGowan; G. C. Harcourt, 1965), while others reasonably believe that the results are reliable enough to form a basis for policy decisions (Long and Ravenscraft). Recent work by Y. Ijiri (1978; 1979; 1980) and by myself (1982) has shown that conditional IRR estimates can be obtained from data in firms' financial statements. While these IRR estimates are conditional, they do abstract from certain extraneous factors that influence ARRs and that differ across firms. Consequently the conditional IRR estimates are free from some of the sources of measurement error which are known to contaminate the ARR. Thus, the conditional IRR estimates can be used to provide evidence on whether these sources of measurement error have or have not affected the outcome of prior studies in which profitability was measured by the ARR. Such evidence can help to objectively resolve the conflict between the opposing views on the reliability of ARR-based profitability research. This paper uses conditional IRR estimates to examine the properties of the measurement error in the ARR in a study of the relationship between firm profitability and firm size. The remainder of the paper is organized as follows. In Section I, the theoretical work of Fisher and McGowan is used *Professor of Accounting, University of Iowa, Iowa City, IA 52242. I gratefully acknowledge the comments of William Albrecht, Dan Dhaliwal, Gary Fethke, Franklin Fisher, Scott Linn, William R. Kinney, Jr., and the participants of a workshop at the University of Florida on earlier versions of this paper. 1 Some authors (for example, William Long and David Ravenscraft, 1984) have used the sales margin ratio (earnings/sales) as a measure of profitability. However, if one views profitability as return per unit of sacrifice, the sales margin ratio is not a profitability measure since it ignores the sacrifice (or investment) required to generate a dollar of sales. Consequently, this paper does not attempt to shed any insight into prior studies that have relied on the sales margin ratio as a measure of profitability.

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