* Assistant Professor, University of Florida. author wishes to thank Professors Bodenhorn, Greenball, and Livingstone of Ohio State University for their valuable comments on an earlier version of this paper. This paper is part of Gerald L. Salamon, Comparison of the Accounting and Internal Rates of of Firms With Nonnegative Growth Rates and Infinitive Lives, unpublished Ph.D. dissertation, Ohio State University, 1971. 'R. S. Carlson, Measuring Period Profitability: Book Yield Versus True Yield, unpublished Ph.D. dissertation, Stanford University, 1964. M. N. Greenball, Appraising Methods of Accounting for Accelerated Tax Depreciation: A Relative Accuracy Approach, Journal of Accounting Research (Autumn 1969), pp. 26289. G. C. Harcourt, The Accountant in a Golden Age, Oxford Economic Papers, March 1965, pp. 66-80. J. L. Livingstone and G. L. Salamon, Relationship Between the Accounting and the Internal Rate of Measures: A Synthesis and An Analysis, Journal of Accounting Research (Autumn 1970), pp. 199-216. E. Solomon, Return on Investment: Relation of Book Yield to True Yield, Research in Accounting Measurement, ed. R. K. Jaedicke, Y. Ijiri, and O. Nielsen (Menasha, Wise.: American Accounting Association, 1966), pp. 232-44. 2 scope of this investigation will be restricted to the research which is cited in footnote 1. In order to avoid the frequent repetition of several authors' names we will use the term prior to denote that group of researchers whose work is cited in the footnote 1. 'Ezra Solomon, Alternative Rate of Concepts .. ., op. cit., p. 68.

Willem Buijink and Marc Jegers have pointed out that the conditional internal rate of return estimates contained in my 1985 paper are dependent on estimates of the useful life of the firms' depreciable assets and that my estimates of such useful lives are contaminated by depreciation method differences across the firms. I think their point is correct and the intent of this reply is to use their formulas to obtain corrected useful life and conditional internal rate of return estimates and to report the impact of these corrections on the relationship between profitability and firm size for the sample of firms that was the focus of my 1985 paper.

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.

ABSTRACT: Previous analytical work has shown that a firm's cash recovery rate (the ratio of cash recovery during a period to gross investments outstanding during the period) is related to the internal rate of return of firm projects in the event that the firm reinvests all of its cash flows. This paper extends the previous analytical work by establishing a link between a firm's cash recovery rate and the internal rate of return of firm projects in circumstances when the firm does not reinvest all of its cash flows. Additionally, this paper applies the extended model to a group of firms in order to obtain estimates of their internal rates of return. Work of this kind would seem to be of particular interest to economic researchers who are interested in theoretically defensible empirical measures of firm profitability.

William R. Kinney, Jr., Gerald L. Salamon, Regression Analysis in Auditing: A Comparison of Alternative Investigation Rules, Journal of Accounting Research, Vol. 20, No. 2, Part I (Autumn, 1982), pp. 350-366

John Leslie Livingstone, Gerald L. Salamon, Relationship between the Accounting and the Internal Rate of Return Measures: A Synthesis and an Analysis, Journal of Accounting Research, Vol. 8, No. 2 (Autumn, 1970), pp. 199-216

This article examines the impact of one form of sales seasonality on the response of equity returns to earnings announcements in different quarters. We regress unexpected announcement period returns on unexpected earnings and compare the results for seasonal firms—those with sales consistently concentrated in the same quarter each year—to those of other firms. For seasonal firms, we find robust evidence of a greater regression intercept and some evidence of a greater earnings response coefficient in peak sales quarters than in nonpeak quarters. These results are consistent with a greater resolution of the uncertainty about seasonal firms' prospects in their peak sales quarters than in other quarters. Our evidence also shows that fourth‐quarter earnings announcements have smaller stock price response coefficients than do interim announcements. Some prior has found smaller fourth‐quarter earnings response coefficients for small but not large firms. We find some evidence that fourth‐quarter earnings response coefficients are smaller than interim‐quarter response coefficients for large firms as well as for small firms. This suggests that explanations for smaller fourth‐quarter earnings response coefficients need to be applicable to both large and small firms. Résumé. Les auteurs examinent, pour différents trimestres, l'incidence d'une forme de caractère saisonnier des ventes sur la réaction du rendement des actions aux déclarations de bénéfices. Ils effectuent une analyse de régression des rendements imprévus des trimestres par rapport aux bénéfices imprévus et comparent les résultats obtenus dans le cas des entreprises dont les activités sont saisonnières—c'est‐à‐dire dont les ventes sont systématiquement concentrées dans le même trimestre chaque année—aux résultats obtenus dans le cas des autres entreprises. Dans le cas des entreprises dont les activités sont saisonnières, les résultats de l'analyse démontrent vigoureusement que l'intersection de la régression est supérieure et confirment avec moins de fermeté que le coefficient de réaction aux bénéfices déclarés est supérieur pour les trimestres où le volume des ventes culmine, par rapport aux autres trimestres. Ces résultats permettent de conclure à une plus grande résorption de l'incertitude relative aux perspectives des entreprises dont les activités ont un caractère saisonnier dans les trimestres où les ventes de ces entreprises culminent que dans les autres trimestres. Les résultats de l'analyse démontrent également que les déclarations de bénéfices au quatrième trimestre donnent lieu à des coefficients plus faibles de réaction du cours des actions que les déclarations des trimestres intermédiaires. Certains travaux antérieurs ont établi que les coefficients de réaction aux déclarations de bénéfices du quatrième trimestre étaient plus faibles pour les petites entreprises que pour les grandes. L'analyse des auteurs tend ici à démontrer que les coefficients de réaction aux déclarations de bénéfices du quatrième trimestre sont plus faibles que les coefficients de réaction des trimestres intermédiaires pour les grandes entreprises aussi bien que pour les petites entreprises. Ces constatations donnent à penser que les facteurs qui expliquent les coefficients de réaction plus faibles aux déclarations de bénéfices du quatrième trimestre devraient pouvoir s'appliquer tant aux grandes qu'aux petites entreprises.

ABSTRACT: This paper presents a detailed example regarding whether to continue to generate service internally or to acquire the service externally. The example demonstrates that most of the basic data required for the correct decision on closing one service department can be obtained from the information normally presumed to be available when service department costs are allocated to producing departments by the algebraic (simultaneous equation) method. The example includes variable and nonvariable service department costs. Finally, the decision to close more than one service department is examined.