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Timo Salmi and Teppo Martikainen

A Review of the Theoretical and Empirical Basis of Financial Ratio Analysis

Published in The Finnish Journal of Business Economics 4/94, 426-448
Runeberginkatu 14-16
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Finland

This paper is reproduced at the University of Vaasa in the electronic format with the permission of The Finnish Journal of Business Economics. Copyright © 1994 by The Finnish Journal of Business Economics and the authors.

CONTENTS
 
Abstract

1. Introduction
2. Basic Properties of Ratios
2.1. Functional Form of Financial Ratios
2.2. Distributional Characteristics of Financial Ratios
2.3. Classification of Financial Ratios
2.3.1. Pragmatical Empiricism
2.3.2. Deductive Approach
2.3.3. Inductive Approach
2.3.4. Confirmatory Approach
3. Measurement of Profitability and Financial Ratios
3.1. ARR vs IRR
3.2. Estimating the IRR from Financial Statements
3.3.Estimating the IRR from the Cash Recovery Rate
4. Conclusions
 
References Section 2.1
References Section 2.2
References Section 2.3
References Section 3

Please use the following reference to this publication: Salmi, T. and T. Martikainen (1994), "A review of the theoretical and empirical basis of financial ratio analysis", The Finnish Journal of Business Economics 43:4, 426-448. Also available from World Wide Web: <URL:http://lipas.uwasa.fi/~ts/ejre/ejre.html>.


Timo Salmi
Professor of Accounting and Business Finance

Teppo Martikainen
Associate Professor of Accounting and Business Finance

A Review of the Theoretical and Empirical Basis of Financial Ratio Analysis

Abstract

This paper provides a critical review of the theoretical and empirical basis of four central areas of financial ratio analysis. The research areas reviewed are the functional form of the financial ratios, distributional characteristics of financial ratios, classification of financial ratios, and the estimation of the internal rate of return from financial statements. It is observed that it is typical of financial ratio analysis research that there are several unexpectedly distinct lines with research traditions of their own. A common feature of all the areas of financial ratio analysis research seems to be that while significant regularities can be observed, they are not necessarily stable across the different ratios, industries, and time periods. This leaves much space for the development of a more robust theoretical basis and for further empirical research.

Keywords: Financial statement analysis, financial ratios, review

Acknowledgments: Our thanks are due to Manuel Garcia-Ayuso Covarsi of the University of Sevilla, Spain, for his constructive comments.

Published as Timo Salmi and Teppo Martikainen (1994), "A Review of the Theoretical and Empirical Basis of Financial Ratio Analysis", The Finnish Journal of Business Economics 4/94, 426-448. Also published on the World Wide Web as http://www.uwasa.fi/~ts/ejre/ejre.html


1. Introduction

Financial ratios are widely used for modelling purposes both by practitioners and researchers. The firm involves many interested parties, like the owners, management, personnel, customers, suppliers, competitors, regulatory agencies, and academics, each having their views in applying financial statement analysis in their evaluations. Practitioners use financial ratios, for instance, to forecast the future success of companies, while the researchers' main interest has been to develop models exploiting these ratios. Many distinct areas of research involving financial ratios can be discerned. Historically one can observe several major themes in the financial analysis literature. There is overlapping in the observable themes, and they do not necessarily coincide with what theoretically might be the best founded areas, ex post. The existing themes include
The history of financial statement analysis dates far back to the end of the previous century (see Horrigan, 1968). However, the modern, quantitative analysis has developed into its various segments during the last two decades with the advent of the electronic data processing techniques. The empiricist emphasis in the research has given rise to several, often only loosely related research trends in quantitative financial statement analysis. Theoretical approaches have also been developed, but not always in close interaction with the empirical research.

Technically, financial ratios can be divided into several, sometimes overlapping categories. A financial ratio is of the form X/Y, where X and Y are figures derived from the financial statements or other sources of financial information. One way of categorizing the ratios is on the basis where X and Y come from (see Foster, 1978, pp. 36-37, and Salmi, Virtanen and Yli-Olli, 1990, pp. 10-11). In traditional financial ratio analysis both the X and the Y are based on financial statements. If both or one of them comes from the income statement the ratio can be called dynamic while if both come from the balance sheet it can be called static (see ibid.). The concept of financial ratios can be extended by using other than financial statement information as X or Y in the X/Y ratio. For example, financial statement items and market based figures can be combined to constitute the ratio.

In this paper we review the existing trends in financial statement analysis literature by focusing primarily on the theoretical and empirical basis of financial ratio analysis. This is an important task to carry out since the ratios are often used intuitively, without sufficient consideration to their theoretical meaning and statistical properties. In doing this it is our purpose to pinpoint the different directions taken in quantitative ratio based research. By critically considering financial ratio literature, we also aim to help the decision makers to use ratios in an efficient way.

We review four of the research areas listed above. In our opinion the primary areas of the literature concerning the theoretical and empirical basis of financial ratio analysis are the functional form of the financial ratios, distributional characteristics of financial ratios, and classification of financial ratios. These three research avenues are reviewed in Section 2. All the major financial ratio research avenues cannot be tackled within the limited space of this paper. Therefore, we select the estimation internal rate of return from financial statements as the fourth area. A fundamental task of financial analysis is evaluating the performance of the business firm. This area, reviewed in Section 3, directly concerns profitability measurement.


2. Basic Properties of Ratios

2.1. Functional Form of Financial Ratios

The traditionally stated major purpose of using financial data in the ratio form is making the results comparable across firms and over time by controlling for size. This basic assertion gives rise to one of the fundamental trends in financial ratio analysis (or FRA for short, in this paper). The usually stated requirement in controlling for size is that the numerator and the denominator of a financial ratio are proportional.

The seminal paper is this field is Lev and Sunder (1979). They point out, using theoretical deduction, that in order to control for the size effect, the financial ratios must fulfill very restrictive proportionality assumptions (about the error term, existence of the intercept, linearity, and dependence on other variables in the basic financial variables relationship models Y = bX + e and its ratio format Y/X = b + e/X). It is shown that the choice of the size deflator (the ratio denominator) is a critical issue. Furthermore, Lev and Sunder bring up the problems caused in multiple regression models where the explaining variables are ratios with the same denominator. This is a fact that has been discussed earlier in statistics oriented literature like in Kuh and Meyer (1955).

Two interrelated trends are evident. Theoretical discussions about the ratio format in FRA and empirical testing of the ratio model. While mostly tackling the former Whittington (1980) independently presents illustrative results finding the ratio specification inappropriate in a sample of U.K. firms. Whittington also discusses the usage of a quadratic form in FRA. Significant instability in the results was reported.

The proportionality considerations have implications on various facets of FRA. Barnes (1982) shows how the non-normality of financial ratios can result from the underlying relationships of the constituents of the financial ratios. He is thus able to tie in the ratio format aspects with the distributional properties of financial ratios (to be discussed later in this review). In the discussion on Barnes's paper (Horrigan, 1983, Barnes, 1983), Horrigan puts forward that financial ratio research should be more interested in the role of the financial ratios themselves than in "the nature of the ratios' components or to the ratios' incidental role as data size deflators".

To extrapolate from Horrigan's critique, in our own interpretation the validity of financial ratio analysis should be determined by its usefulness to the decision making process of the different interested parties (owners, management, personnel,...). To illustrate, consider the potential impact of economics of scale. To assess the efficiency of management a direct comparison of financial ratios of small and big firms would have to be adjusted for the size effect. On the other hand, an investor evaluating different investment targets might be more interested in the level of profitability regardless whether or not it is a result of the size effect.

McDonald and Morris (1984, 1985) present the first extensive empirical studies of the statistical validity of the financial ratio method. The authors use three models with two samples, one with a single industry the other with one randomly selected firm from each (four-digit SIC) industry branch to investigate the implications of homogeneity on proportionality. The first model is the traditional model for replacement of financial ratios by bivariate regression, with intercept
    Y(i) = a + bX(i) + e(i).
The above model is central in this area. It is characteristic that the testing for proportionality is considered in terms of testing the hypothesis H0: a = 0. Barnes (1986) points out for statistical testing that the residual is typically heteroscedastic. For a discussion also see Garcia-Ayuso (1994). The second model in McDonald and Morris is
    Y(i) = b'X(i) + e'(i)
that is without the intercept to tackle heteroscedasticity. Dropping the intercept from the model is not always enough to treat the heteroscedasticity (see Berry and Nix, 1991). The third model applies a (Box-Cox) transformation on the first model to tackle non-linearities. While they find support for financial ratio analysis for comparisons within industry branches, in inter-industry comparisons proportionality of financial ratios is not supported.

Berry and Nix (1991), however, cast doubt on the generality of McDonald and Morris results over time, over ratios and over industries. Similar results was obtained for Finnish data in Perttunen and Martikainen (1989) and for Spanish data by Garcia-Ayuso (1994). By comparing value and equal weighted aggregate financial ratios McLeay and Fieldsend (1987) find evidence based on samples of French firms that "the departure from proportionality varies from ratio to ratio, from size class to size class and from sector to sector".

Research on financial ratio proportionality has close connections to distributional questions. Testing the statistical significance of the parameters of the previous models involves, at least implicitly, assumptions of normality (see Ezzamel, Mar-Molinero and Beecher, 1987, p. 467). Fieldsend, Longford and McLeay (1987) draw on the fact that a number of accounting variables are expected to be lognormally distributed because of technical zero lower bounds. Consequently they test empirically a lognormal regression model
    lnY(ij) = a + blnX(ij) + g(j) + e(ij)
where the industry effect g(j) is explicitly specified in the model. Their empirical results on a single financial ratio (the current ratio) are in line with the earlier results supporting proportionality only if industry effects are included.

As was discussed in Introduction financial ratios can be extended to include market based data. We concentrate mainly on "pure" financial ratios with both the numerator and the denominator originating from the income statement and/or the balance sheet. Nevertheless, concomitant research has been presented with market based ratios. For example, Booth, Martikainen, Perttunen and Yli-Olli (1994) report deviations from proportionality in the E/P ratio.

 

2.2. Distributional Characteristics of Financial Ratios

It is typical of FRA research that there are several distinct lines with research traditions of their own. In some cases there is little link to the other FRA fields. The distributional characteristics of financial ratios have induced a research line of their own, but part of this research is intertwined with the proportionality research discussed above. In fact some of the papers reviewed tackle both the areas either separately or within the same framework.

The recurring motivation for looking into the distributional properties of financial ratios is that the normal distribution of the financial ratios is often assumed in FRA. This is because the significance tests in parametric methods prevalent in FRA research, such as regression analysis and discriminant analysis, rely on the normality assumption.

In the history of FRA it is common that professional journals and academic papers do not recognize each other. An early paper on financial ratio distributions was published in Management Accounting by Mecimore (1968). It is interesting to recognize that all ingredients of modern distribution analysis already appear incumbent in Mecimore's paper. Using descriptive statistical measures (average and relative deviations from the median) he observes cross-sectional non-normality and positive skewness for twenty ratios in a sample of randomly selected forty-four Fortune-500 firms.

The paper most often referred to in literature as the seminal paper in this field is, however, the much later published article by Deakin (1976). His chi-square findings reject (with one exception) the normality of eleven financial ratios in a sample of 1114 Compustat companies for 1954-72. Less extreme deviations from normality were observed when square-root and logarithmic transformations were applied, but normality was still not supported. Likewise, while not statistically significantly, industry grouping made the distributions less non-normal. Concomitant results are obtained by Lee (1985) using a stronger test (Kolmogorov-Smirnov) for a different set of data.

Bird and McHugh (1977) adopt an efficient Shapiro-Wilk small-sample test for the normality of financial ratios for an Australian sample of five ratios over six years. Like Deakin they find in their independent study that normality is transient across financial ratios and time. They also study the adjustment of the financial ratios towards industry means which is a different area of FRA research. Bougen and Drury (1980) also suggest non-normality based on a cross-section of 700 UK firms.

The results indicating non-normality of financial ratio distributions have led researchers into looking for methods of restoring normality to warrant standard parametric statistical analyses. Frecka and Hopwood (1983) observe that removing outliers and applying transformations in a large Compustat sample covering 1950-79 restored normality in the same financial ratios as tackled by Deakin (1976). They point out that if the ratios follow the gamma distribution, the square root transformation makes the distribution approximately normal. The gamma distribution is compatible with ratios having a technical lower limit of zero. There is, however, a certain degree of circularity in their approach, since instead of identifying the underlying causes of the outliers they employ a mechanistic statistical approach to identify and remove the outliers from the tails of the financial ratio distributions.

A varying and often a considerable number of outliers has to be removed for different financial ratios in order to achieve normality. The empirical results are supported by later papers such as So (1987). Ezzamel, Mar-Molinero and Beecher (1987) and Ezzamel and Mar-Molinero (1990) review and replicate the earlier analyses on UK firms with a particular emphasis on small samples and outliers, respectively. One of the avenues taken is to study new industries. Kolari, McInish and Saniga (1989) take on the distribution of financial ratios in banking. Buckmaster and Saniga (1990) report on the shape of the distributions for 41 financial ratios in a Compustat sample of more than a quarter million observations.

Foster (1978) points out the outlier problem in FRA. Later, he presented in Foster (1986) a list of alternatives for handling outliers in FRA. The list includes deleting true outliers, retaining the outlier, adjusting the underlying financial data, winsorizing that is equating the outliers to less extreme values, and trimming by dropping the tails. Foster also puts forward accounting, economic and technical reasons for the emergence of outliers in FRA. While improving the statistical results trimming and transformations can pose a problem for the theoretical rigor in FRA research. Instead of deleting or adjusting the observations McLeay (1986a) proposes using a better fitting distribution with fat tails for making statistical inferences in FRA. He seeks for a best fitting t-distribution for a cross-section of 1634 UK and Irish firms. Also his empirical results confirm non-normality. The best-fitting (in the maximum-likelihood sense) t-distribution varies across financial ratios (the t-distribution can be considered a family of distributions defined by its degrees of freedom). McLeay (1986b) also tackles the choice between equally weighted and value weighted aggregated financial ratios in terms of ratio distributions on a sample of French firms. Also the results by Martikainen (1991) demonstrate that normality can be approached by other procedures than removing outliers. In a sample of 35 Finnish firms, four ratios and fifteen years about half of the non-normal distributions became normal if economy-wide effects were first controlled for using the so-called accounting-index model. Martikainen (1992) uses a time-series approach to 35 Finnish firms in turn observing that controlling for the economy factor improves normality.

Typically, many later papers tackle the same basic question of ratio distributions using different samples and expanding on the methodologies. Buijink and Jegers (1986) study the financial ratio distributions from year to year from 1977 to 1981 for 11 ratios in Belgian firms corroborating the results of the earlier papers in the field. Refined industry classification brings less extreme deviation from normality. They also point to the need of studying the temporal persistence of cross-sectional financial ratio distributions and suggest a symmetry index for measuring it. Virtanen and Yli-Olli (1989) studying the temporal behavior of financial ratio distributions observe in Finnish financial data that the business cycles affect the cross-sectional financial ratio distributions.

The question of the distribution of a ratio format variable (financial ratio) has been tackled mathematically as well as empirically. Barnes (1982) shows why the ratio of two normally distributed financial variables does not follow the normal distribution (being actually skewed) when ratio proportionality does not hold. Tippett (1990) models financial ratios in terms of stochastic processes. The interpretation in terms of implications to financial ratio distributions are not, however, immediately evident, but the general inference is that "normality will be the exception rather than the rule".

Because of these results bringing forward the significance of the distributional properties of financial ratios many later papers report routinely about the distributions of financial ratios in connection with some other main theme. Often these themes are related to homogeneity and industry studies such as Ledford and Sugrue (1983). The distributional properties of the financial ratios also have a bearing in testing proportionality as can be seen, for instance, in McDonald and Morris (1984). In a bankruptcy study Karels and Prakash (1987) put forward that in applying the multivariate methods (like discriminant analysis) the multivariate normality is more relevant than the (univariate) normality of individual financial ratios. They observe that deviations from the multivariate normality is not as pronounced as the deviations in the earlier univariate studies.

Watson (1990) examines the multivariate distributional properties of four financial ratios from a sample of approximately 400 Compustat manufacturing firms for cross-sections of 1982, 1983 and 1984. Multivariate normality is rejected for all the four financial ratios. Multivariate normality is still rejected after applying Box's and Cox's modified power transformations. However, when multivariate outliers are removed, normality is confirmed. Multivariate normality has particular bearing on research using multivariate methods, for example on bankruptcy prediction. It also has implications on univariate research, since while univariate normality does not imply multivariate normality, the opposite is true.

 

2.3. Classification of Financial Ratios

A central question both in FRA research and practice is finding a parsimonious set of financial ratios to cover the activities of the firm. The main approaches in this area are fairly clearcut. They are pragmatical empiricism (a term coined by Horrigan 1968), a data oriented classification approach, a deductive approach, and lately, the combination of the last two. An interesting early paper on financial ratios which has many of the later issues in a embroynic form can be seen in Horrigan (1965).

 

2.3.1. Pragmatical Empiricism

Several accounting and finance text-books present a subjective classification of financial ratios based on the practical experience or views of the authors. It is common that the classifications and the ratios in the different categories differ between the authors as pointed out in a tabulation by Courtis (1978, p. 376). In very general terms three categories of financial ratios are more or less common: profitability, long-term solvency (capital structure) and short-term solvency (liquidity). Beyond that there is no clear consensus. Pragmatical empiricism is exemplified by the text-books of Weston and Brigham (1972), Lev (1974a), Foster (1978, 1986), Tamari (1978), Morley (1984), Bernstein (1989), White, Sondhi and Fried (1994), Brealey and Myers (1988, Ch. 27), and handbook chapters such as Beaver (1977), and Holmes and Sugden (1990, Ch 24).

Official bodies also can give recommendations. For example, in Finland the Committee for corporate analysis (1990) guidelines influence Finnish reporting practices. More generally security exchange commission stipulations influence reporting of financial ratios in many countries.

 

2.3.2. Deductive Approach

The classic of deductive approach goes back to 1919 to the du Pont triangle system (profits/total assets), (profits/sales), (sales/total assets):
               profits
           sales     total assets
Courtis (1978) returns to the theme. He presents a diagram for a financial ratios framework based on financial ratios used in earlier studies, textbooks, "other sources", deliberation, and visual approximation of relationships in a sample of 79 ratios. Laitinen (1983) presents a model of the financial relationships in the firm with attached financial ratios. The model is based on Laitinen (1980). For the most part empirical evidence based on 43 publicly traded Finnish firms supports the structure of the model. Bayldon, Woods, and Zafiris (1984) evaluate a pyramid scheme of financial ratios. In a case study the pyramid scheme does not function as expected. The deductive approach to establish relevant financial ratio categories has more or less stalled, and this approach has become intermixed with confirmatory approach discussed later.

 

2.3.3. Inductive Approach

The emphasis on data and statistical methods is characteristic of the inductive approach to financial ratio classification like it is in the proportionality and distribution studies discussed earlier. The empirical rather than the theoretical foundations for grouping the financial ratios are central in this approach.

The seminal paper in empirically-based FRA classifications ("taxonomies") is Pinches, Mingo and Caruthers (1973). They apply factor analysis to classify 51 log-transformed financial ratios of 221 Compustat firms for four cross sections six years apart. The selection of the method was prompted by applications in other behavioral disciplines (e.g. psychology and organizational analysis). They identify seven factors, Return on investment, capital intensiveness, inventory intensiveness, financial leverage, receivables intensiveness, short-term liquidity, and cash position. These factors explain 78-92% (depending on the year) of the total variance of the 51 financial ratios. Moreover, the correlations for the factor loadings, and the differential R-factor analysis indicate that the ratio patterns are reasonably stable over time. The same study is replicated for adjacent years 1966-1969 in Pinches, Eubank, Mingo and Caruthers (1975).

Johnson (1978) runs the factor analysis for a single year 1972, but for two industries based on a sample of 306 primary manufacturing and 61 retail firms. Congruency coefficients of financial ratio patterns indicate a good stability of the nine factors for the two industries. Johnson (1979) repeats the study for a larger sample of firms and for two years.

Chen and Shimerda (1981) present a summary of the financial ratios used in a number of early studies which use the financial ratios for analysis and prediction. They note that there is an abundant 41 different financial ratios which are found useful in the earlier studies. They reconcile by judgement the factors in the earlier studies into financial leverage, capital turnover, return on investment, inventory turnover, receivables turnover, short-term liquidity, and cash position. They identify ten financial ratios which are representative of their seven factors. After a principal component factor analysis of 39 ratios of the Pinches, Eubank, Mingo and Caruthers (1975) they conclude that there is a high instability in always selecting the financial ratio with the highest absolute factor loading as the representative financial ratio for the observed factors.

Cowen and Hoffer (1982) study the inter-temporal stability of financial ratio classification in a single, homogeneous industry. Their findings do not support the Pinches, Mingo and Caruthers results about the stability of the ratio patterns. Cowen and Hoffer's sample consist of 72 oil-crude industry firms for 1967-75. Four or five factors are found for each year for the 13 financial ratios included. As the authors put it "there was little consistency and stability in the factor loadings across all years". The results are only slightly improved with log-transformations. Cowen and Hoffer also find applying cluster analysis that groupings of firms with respect to the financial ratios exist within the industry, but that they are not stable over time. Ezzamel, Brodie and Mar-Molinero (1987) detect instability in the factors of financial ratios for a sample of UK firms. Martikainen and Ankelo (1991) find that instability of financial ratio groups is more pronounced for firms about to fail than for healthy firms in a sample of 40 Finnish firms. Martikainen, Puhalainen and Yli-Olli (1994) observe significant instability of the financial ratio classification patters across industries in a sample typical of bankruptcy research.

Aho (1980) includes also cash-flow based profitability ratios in a factorization study for 24 financial ratios of 57 Finnish firms in 1967-1976. His financial characteristic factors become financial structure, profitability, liquidity, working capital turnover and financial opportunities for investments. Gombola and Ketz (1983) include cash-flow based (adjusted for all accruals and deferrals) financial ratios in their factorization of 40 financial ratios for a sample of 119 Compustat firms for 1962-80. Contrary to the earlier studies, the cash-flow based financial ratios load on a distinct factor. The results are not sensitive to using historical costs vs general price-level adjusted data. Similar results on the empirical distinctiveness of cash flow ratios are later obtained in Salmi, Virtanen and Yli-Olli (1990) in a study that also introduces market-based ratios to the analysis.

Yli-Olli and Virtanen (1986, 1989, 1990) introduce the usage of transformation analysis to study the stability of the financial ratio patterns. After aggregating financial ratios for 1947-75 for the US and 1974-84 for Finland they find that value-weighted aggregation produces ratio patterns that are stable both over time and across countries. The stability is further improved by using first differences of the financial ratios.

Factorization of financial ratios has also been a part in several multivariate studies analyzing the economic features of the firms. Pinches and Mingo (1973) screen a set of 35 financial variables into seven factors in a bond rating study. Likewise, Libby (1975) reduces an original 14-ratio set to five financial factors by a principal component analysis in connection with a bankruptcy study. Another example is Richardson and Davidson (1984). Hutchinson, Meric and Meric (1988) also classify ratios with principal component analysis in a study attempting to identify small firms which have achieved quotation on the UK Unlisted Securities Market. Martikainen (1993) classifies financial ratios and tests their stability with transformation analysis in a study on identifying the key factors which determine stock returns.

 

2.3.4. Confirmatory Approach

It seems that despite the initial optimism the inductive studies have been unable to agree on a consistent classification of financial ratio factors, at least beyond three to five factors. Consequently a number of later studies hypothesize an a priori classification and then try to confirm the classification with empirical evidence.

A tentative emergence of this idea can be detected in Laurent (1979). As noted earlier Courtis (1978) presents a pyramid scheme of financial ratios based on a mix of experience, deduction and visual approximation of data. This can be considered an a priori classification. Laurent performs a standard principal component factorization for a set of 45 financial ratios presumably for a single year of 63 Hong Kong companies. He compares his results with the deductive classification by Courtis (1978) and finds a good correspondence. With the exception of administration Laurent identifies and locates each of his ten empirical factors in Courtis's framework. Such a comparison has the hallmarks of the basic idea of the confirmatory approach.

Pohlman and Hollinger (1981) test two a priori classification schemes based an a sample of Compustat firms for 1969-78. They call the first the "traditional" scheme. (It practically is Lev's (1974) categorization.) The second is not actually a priori classification but the empirical classification by Pinches, Eubank, Mingo and Caruthers (1975) with seven factors. They use the redundancy indexes produced by canonical correlation analysis to evaluate how well financial ratios fit the relevant factor. They find that the a priori categories are correlated with each other. Thus they caution against using too few financial ratios in FRA.

Luoma and Ruuhela (1991) present five a priori "dimensions" for the financial ratios, profitability, financial leverage, liquidity, working capital, and revenue liquidity. Rather than using cross-sections across firms their data consist of time series of 40 Finnish firms for 1974-84. They apply cluster analysis to group the 15 initial ratios separately for each firm in the sample, and compare the empirical clusters with the a priori dimensions. Profitability and revenue liquidity appear almost invariably as distinct clusters. The other three dimensions turn out more commonly to be interrelated.

Kanto and Martikainen (1991) evaluate Lev's (1974) a priori classification of financial ratios by introducing the usage of confirmatory factor analysis to testing a priori classifications of financial ratios. Confirmatory factor analysis provides statistical significance tests for the existence and stability of the a priori factor structure. Using Compustat firms it is observed for 1947-75 that the a priori financial ratio categories are significantly correlated. Thus Lev's classification is not corroborated. Similar results are observed for a sample of Finnish firms in Kanto and Martikainen (1992).


3. Measurement of Profitability and Financial Ratios

3.1. ARR vs IRR

The fundamental task of accounting is income determination and the evaluation of the firm's assets. The measurement of profitability is intimately linked with both. There is a significant body of literature which considers profitability assessment. In terms of economic theory the profitability of a firm could be defined as the internal rate of return of the capital investments constituting the firm, although Salamon (1973) casts doubt of this view. There is a strong tradition in literature that seeks to estimate the internal rate of return, either from a time series of the financial statements of the firm, or, more narrowly, by considering the relationship between the familiar accounting rate of return (the firm's annual profit in relation to its assets) and the internal rate of return. They will be called IRR and ARR below since there is some variance in the full terms in literature, especially for the latter. The ARR vs IRR discussion can also be deemed as seeking a reconciliation between accounting based measurement and the economic theory of income. The relationship has been considered both as a purely mathematical relationship and from the empirical estimation point of view.

To recount the general, formal definitions, ARR is defined in literature as
    a(t) = (F(t) - D(t))/K(t),
where F(t) is the funds flows from operations in period t, D(t) is the depreciation in period t, and K(t) is the net book value of assets at the beginning of year t. (The average of K(t) and K(t+1) is also often used.) IRR is naturally defined as r by

          n            t
  I(o) = sum R(t)/(1+r),
         t=1
where I(o) is the initial capital investment outlay, R(t) the net cash flow in period t, and n is the life-span of the capital investment. (The existence conditions for a rational solution for r, and the multiple solutions of the polynomial equation have been tackled in the relevant literature but are not reviewed in this paper).

British economists present one tradition of tackling the question of the divergence between the ARR and IRR since Harcourt (1965) put forward his position that the accountant's rate of return is "extremely misleading". Using four different cases of accumulation of assets (growth) he asserts that it is not possible to develop rough rules of thumb to adjust ARR to reflect IRR under different life-spans of investments, the net cash flow patterns generated by the investments, different growth rates, and different depreciation methods. He concludes by an explicit warning about profitability comparison between firms in different industries or different countries if accountants' measurements are used. It can only be deduced that he implicitly gives very little value for the financial statements annually prepared by the accounting profession.

The formal mathematical relationship between the ARR and IRR is independently considered by Solomon (1966). Using both a zero-growth and a growth model he demonstrated that the ARR (book-yield in Solomon's terms) is not a reliable measure of the IRR (true-yield in Solomon's terms). His paper shows that the difference between the two measures involves project lives, the depreciation method, and the lag between the investment outlays and their recoupment. Further numerical examples to illustrate the disparity of accounting and economic profitability measurement are provided in Solomon and Laya (1967). Interestingly these two papers are practically devoid of references to other literature. Vatter (1966) ponders the content of Solomon's paper at great length. He questions both the realism of Solomon's assumptions and the validity of IRR as a practical measure of profitability.

The relationship between the ARR and IRR is also indirectly involved in studies considering the relation between rules of thumb for capital investment decisions (payback reciprocal) and the ARR on the other hand and IRR on the other. See Sarnat and Levy (1969, p. 483).

Livingstone and Salamon (1970) build on Solomon's model and conduct a simulation analysis of the ARR-IRR relationship by extending the assumptions of the previous models into more general cases. They observed under their assumptions that ARR shows a dampening cyclical behavior determined by the project life-spans, pattern of cash flows generated by the projects making up the firm, the reinvestment rate, and the level or IRR. They also include the effect of growth. McHugh (1976) and Livingstone and Van Breda (1976) have an exchange of views about the mathematical derivations and the generality of the results of Livingstone and Salamon (1970).

Stauffer (1971) presents a generalized analysis of the ARR vs IRR relationship using continuous mathematics under several cash profile assumptions. He demonstrates that the depreciation schedule affects the relationship. Also he puts forward that the accounting and the economic measurements (ARR/IRR) are irreconcilable, and that the situation is aggravated by the introduction of taxation into the analysis. From the accounting point of view it is interesting that he points to the task of estimating the real rates of return from historical accounting data.

Also Bhaskar (1972) arrives at the conclusion that "in general ARR does not perform satisfactorily as a surrogate for the IRR". He also points out that the using the annuity method of depreciation makes ARR a more accurate reflection of the IRR, but points out that the annuity method has undesirable side-effects for accounting measurement. Bhaskar augments his deductions with a statistical analysis of his simulation results on ARR and IRR levels. Likewise, for example, Fisher and McGowan (1983) consider economic rate of return (IRR) the only correct measure of economic analysis. They conclude that the accounting rate of return is a misleading measure of the economic rate of return and see little merit in using the former. Long and Ravenscraft (1984) present a critical view on Fisher and McGowan's claim of the prevalence of the IRR, the assumptions in their examples, and their mathematical derivations. Fisher (1984) discards the criticism insisting that ARR does not relate profits with the investments that produce it.

Gordon (1974, 1977) takes a more optimistic view on the potential reconciliation between ARR and IRR. He shows that ARR can be a meaningful approximation of the IRR when "the accountant's income and asset valuations approximate the economic income and asset values". The central condition is linked to the depreciation method. The accountant's accumulated depreciation must approximate the accumulated economic depreciation for the ARR and IRR to converge. Gordon concludes by pointing out that even if no general "cook-book tricks" can be devised for converting the ARR to the IRR, the managers can be able to make sufficient adjustments. To us this view appears logical because it is unlikely that profit oriented business firms could, in the long run, indulge in totally unsound measurement and management practices. Stephen (1976), on the other hand, claims that Gordon fails to resolve the difference between ARR and IRR.

Kay (1976) refutes Salamon's conclusion and contends that IRR can be approximated by the ARR irrespective of the cash flow and depreciation patterns. The crucial requirement is that the accountant's evaluation of the assets (their book value) and the economist's evaluation (the discounted net cash flow) are equal. He also applies his results to estimate the profitability of the British manufacturing industry 1960-1969 from aggregate accountant's data. Key and Mayer (1986) revisit the subject coming to the conclusion that "accounting data can be used to compute exactly the single project economic rate of return". Wright (1978) considers Kay's (1976) view too optimistic and claims that one cannot easily translate ARR into IRR except under special circumstances. Salmi and Luoma (1981) demonstrate using simulated financial statements that applying Kay's results require more restrictive assumptions than originally indicated by Kay (1976). Stark (1982) recounts Key's results by including working capital, loan financing and taxation.

Tamminen (1976) presents a thorough mathematical analysis (with continuous time) of ARR and IRR profitability measurement under different contribution distribution, growth conditions, and depreciation methods. As one result he derives a growth-dependent formula for a conversion between IRR and ARR assuming realization depreciation. (For the definition of the realization depreciation see e.g. Bierman, 1961, and Salmi, 1978). The analysis is conducted under steady-state growth conditions, then extended to structural changes and for under cyclical fluctuations.

Whittington (1979) points out that the ARR vs IRR discussion should also consider whether ARR, instead of IRR, already inherently is a valid and useful variable especially in the positive research approach. He also studied the possibility of extenuating circumstances that could reduce the ARR vs IRR discrepancy in statistical analysis. Peasnell (1982b) goes on to consider the usefulness of ARR as a proxy of IRR for FRA. Applying a standard variation measure he comes to the conclusion that the usage of ARR does not lead to serious valuation errors in FRA provided that the variations in the ARRs are not too great. He presents an iterative weighting scheme for estimating the IRR from the ARR. Peasnell (1982a) also considers economic asset valuation and yield vs accounting profit and return in a discontinuous (discrete time) mathematical derivation framework (while Kay, 1976 used continuous time). He proves that if there are no opening and closing valuation errors of assets with respect to their economic values, and ARR is a constant, then the constant ARR equals the IRR. Under constant growth equal to IRR he proves that IRR can be derived as the mean of ARRs. He also studies the relationship when IRR is not equal to the growth rate of assets.

Luckett (1984) reviews and summarizes the ARR vs IRR discussion. He also stresses the fact that the measures are conceptually different by nature. The IRR is a long-term, average-type ex ante measure, while the ARR is a periodic ex post measure. His main conclusions are pessimistic. He points to the results stating that the annual ARR is a surrogate of the IRR only under very special circumstances. He also claims that it estimating the IRR in actual practice from the annual ARRs is not generally practical. Kelly and Tippett (1991) present a stochastic approach to estimating the IRR and ARR, and find them significantly different in a sample of five Australian firms. Shinnar, Dressler, Feng, and Avidan (1989) estimate the IRR, ARR and the cash flow pattern for 38 U.S. companies for 1955-84.

Jacobson (1987) takes another approach to the IRR vs ARR controversy. He evaluates the validity of ARR as a proxy for IRR by examining the association between corporate level ARR and the stock return for 241 Compustat firms for 1963-82. He concludes that while ARR has serious limitations as a measure of business performance, claiming that ARR has no relevance is an overstatement. However, he does not take on examining the association between IRR and stock returns, possibly because of the difficulty of estimating the IRR from the published data.

 

3.2. Estimating the IRR from Financial Statements

The problem with the studies reviewed in the above, at least until Gordon (1974), is that while they extensively analyze the ARR - IRR relationship they are barren from the accountant's point of view since their economist's analysis does not present any guidance to conducting better profitability estimation or profit measurement in actual practice from annual financial reports. Their main point is subjecting accounting measurement to severe doubt.

The pioneering work from the account's point of view in estimating the internal rate of return from the firms financial statements is Ruuhela (1972). He presents a model of firm's growth, profitability and financing. Assuming constant growth and that the firm is constituted of a series of capital investments, he establishes a general method to estimate the firm's long-run profitability (IRR) from published financial statements. He also points out that the annual income of the firm can be measured from this IRR estimate and the capital stock of the firm. Furthermore, they point out that the long-run financial policy of the firm manifests itself in growth-discounted average balance sheet.

The mathematical derivation of Ruuhela's model is streamlined in Salmi (1982). The IRR estimation procedure is later enhanced in Ruuhela, Salmi, Luoma and Laakkonen (1982). The paper also presents an empirical application to compare the long-run profitability of eight major Finnish pulp and paper firms for 1970-1980. Salmi, Ruuhela, Laakkonen, Dahlstedt, and Luoma (1983a, 1983b, 1984) present hand-book type instructions for IRR estimation from published financial statements for the accounting profession. Jegers (1985), Salmi and Ruuhela (1985), Van der Hagen and Jegers (1993), and Salmi and Ruuhela (1993) exchange views about the validity of the presented IRR estimation methods.

An integral part of in Ruuhela's method is the estimation of the firm's growth rate. Salmi, Dahlstedt and Luoma (1985) consider how the growth estimation can be improved by eliminating cycles from the accounting data. Ruuhela's method requires about 11-13 years of data and thus often covers different phases of business cycles.

Steele (1986) criticizes Ruuhela's model for its strong steady-state assumptions. Based on Kay's model and Peasnell's results he presents an iterative process for estimating the IRR from published financial statements without the steady-state assumption. On the other hand his approach requires market-based values and thus limits the range of firms that can be the target of the profitability evaluation. Brief and Lawson (1991a, 1991b) derive a simplified error term for the IRR estimation. Using simulation they cast doubt especially on the accuracy of IRR estimation for a small number of observations.

 

3.3. Estimating the IRR from the Cash Recovery Rate

A parallel line of research with the ARR vs IRR debate emanates from the concept of cash recovery rate (CRR). In brief CRR means the ratio of the cash paybacks to the gross investment which generates these cash inflows. The advantage of CRR is that it is readily estimated from the cash flows calculated from the financial statements of the firm. For the details see Ijiri (1978).

Ijiri (1979, 1980) shows that under certain general conditions the recovery rate converges to the "discounted cash flow rate" which is similar to economist's measure of the firm's profitability. The conceptual difference is that the economist's valuation is based on the future cash flows while in the profitability estimation only the historical data is used. By not involving the ARR, this approach circumvents the major ARR vs IRR controversy, that is the disagreement whether ARR can be a proxy of the IRR under any realistic assumptions. Salamon (1982) indicates explicitly that Ijiri's discounted cash flow rate is the firm's IRR. According to Salamon "Ijiri has shown that if the measure of a firm's IRR is desired it can be obtained by analyzing a model of the relationship between the IRR and the firm's cash recovery rate rather than by analyzing a model of the relationship between the IRR and the firm's accounting rate of return". Salamon extends Ijiri's analysis to the case where the firm does not reinvest all its cash flows. Furthermore, Salamon examines the relationship between the firm's CRR and IRR under inflation. Later Salamon (1988) utilizes the CRR method for studying the usefulness of ARR in IRR estimation. He casts doubt on the usefulness of ARR-based measures in economics.

The CRR method does not remain unchallenged. Brief (1985) casts doubt on the practicality of the CRR method. He notes that in the CRR method for IRR estimation requires information about a firm's past as well as its future cash flows. He argues that the CRR papers do not deal with the problem of predicting the future cash flows. Lee and Stark (1987) reject Ijiri's CRR method as "unsound". They put forward mathematically, and using numerical examples, that Ijiri's method can produce investment evaluations which differ from the conventional discounted cash flow approach. The conclusion would be that CRR cannot be used for unique IRR estimation. Also Stark (1987) casts doubt on the operationality of the CRR approach.

Gordon and Hamer (1988) present a more optimistic view on the CRR method. They extend the CRR method to a concave cash flow pattern. Estimating the IRR and CRR profitability from the same sample which Ijiri (1980) and Salamon (1982) used, they come to the conclusion that the rankings given by the two methods are sufficiently consistent. Griner and Stark (1988) develop an alternative approach making explicit predictions of the future cash flows in order to estimate the CRR. They claim using a sample of 307 Compustat firms that their method gives different rankings than Ijiri's method, and that their estimates are better correlated with the economic rates of return. Unfortunately it is not clear to us how the IRR estimates are assessed, and how a circular deduction has been avoided. In a later paper Stark, Thomas and Watson (1992) revisited Griner and Stark (1988) using simulation. Buijink and Jegers (1989) comment on the effects of various depreciation methods on the relationships between IRR, ARR and CRR. Stark (1994) analyzes the consequences for CRR based IRR estimation of incorrectly formulating the outflow/inflow patterns and the effect of growth.

To summarize the section on "Measurement of Profitability", the following main trends are evident in the ARR vs IRR discussion. 1) A prevalent conclusion is that the IRR is a theoretically well-founded profitability concept even if it is pointed out that the ARR can have managerial relevance as a practical profitability concept. 2) The question whether it is possible and sound to calculate the firm's IRR from its ARR (or CRR) remains unresolved. 3) The estimation of the IRR from published financial data is one of the directions for measuring the long-run profitability of the firm.


4. Conclusion

In this paper we review four areas of financial ratio analysis research: It is obvious that the existing main research areas in financial ratio analysis are fairly separate from each other sometimes with traditions of their own. Historically, these trends have developed to a degree on their own without a distinct theoretical framework to encompass the entire field of financial statement analysis. Of the four areas reviewed in this paper only the first and the second are closely interrelated.

The research on the functional form of financial ratios has been characterized by theoretical discussions about the ratio format in financial ratio analysis and empirical testing of the ratio model. We conclude from the review that the proportionality assumption for financial ratios is stronger within an industry than between industries. Moreover, proportionality varies from ratio to ratio, and between time periods indicating problems in temporal stability.

The research on the distributional characteristics of financial ratios has focused much on the question of normality of the financial ratio distributions because normality would be very convenient in statistical analysis. The empirical results, however, indicate that in many cases the financial ratios follow other than the normal distribution. Part of the research has sought to restore normality by transformations of the data or by eliminating outlier observations. Some improvement towards normality has been observed, but in many cases it has been inadequate.

The research on classifying financial ratios into parsimonious sets can be in our opinion best characterized as the following trends: pragmatical empiricism, deductive approach, inductive approach, and confirmatory approach. The review shows that the number of essential financial ratios often can be reduced to about 4-7 essential ratios. However, empirically based categorizations are not stable across the different studies, that is there is no clear consensus what the categories are, except that profitability and solidity commonly appear. This dispersion of the inductive empirical results has given rise to using theoretical classifications and then seeking empirical confirmation of a priori classifications. The most prevalent method has been factor analysis, although also other options have been used.

The fourth area we reviewed was the estimation of internal rate of return from financial statements. The discussions center on three trends, the relationship between IRR and ARR, the usage of CRR for IRR estimation, and direct estimation of IRR from the financial statements. This area is characterized by much debate both on the concepts of economists' and accountants' views, and the validity of both the theoretical and empirical results. No unique consensus whether successful IRR estimation is possible has been reached in the literature.

A common feature of all the areas of financial ratio analysis research seems to be that while significant regularities can be observed, they are not necessarily stable across the different ratios, industries, and time periods. Thus there remains much to be done to find a tenable theoretical background to improve the generalizability of financial ratio analysis. A systematic framework of financial statement analysis along with the observed separate research trends might be useful for furthering the development of research. If the research results in financial ratio analysis are to be useful for the decision makers, the results must be theoretically consistent and empirically generalizable.


Articles marked with a (*) only apprear in this electronic format of our reference list. These additional references have been discovered or published right after writing the actual text of the article. No later changes have or will be made.

2.1. Functional Form of Financial Ratios; Refereces

Barnes, P. (1986), "The statistical validity of the ratio method in financial analysis: an empirical examination: a comment", Journal of Business Finance and Accounting 13/4, 627-635.

Berry, R.H., and Nix, S. (1991), "Regression analysis v. ratios in the cross-section analysis of financial statements", Accounting and Business Research 21/82, 107-117.

Booth, G., Martikainen, T., Perttunen, J., and Yli-Olli, P. (1994), "On the functional form of earnings and stock prices: international evidence and implications for the E/P anomaly", Journal of Business Finance and Accounting 21/3, 395-408.

Ezzamel, M., Mar-Molinero, C., and Beecher, A. (1987), "On the distributional properties of financial ratios", Journal of Business Finance and Accounting 14/4, 463-481.

Fieldsend, S., Longford, N., and McLeay, S. (1987), "Industry effects and the proportionality assumption in ratio analysis: a variance component analysis", Journal of Business Finance and Accounting 14/4, 497-517.

Garcia-Ayuso, M. (1994), "The functional form of financial ratios: further empirical evidence", paper presented at the XVII annual meeting of the European Accounting Association, April 1994, Venice.

Kuh, E., Meyer, J.R. (1955), "Correlation and regression estimates when the data are ratios", Econometrica 23/4, 400-416.

Lee, C.-W.J. (1985), "Stochastic properties of cross-sectional financial data", Journal of Accounting Research 23/1, 213-227.

Lev, B., and Sunder, S. (1979), "Methodological issues in the use of financial ratios", Journal of Accounting and Economics 1/3, 187-210.

McDonald, B., and Morris, M.H. (1984), "The statistical validity of the ratio method in financial analysis: an empirical examination", Journal of Business Finance and Accounting 11/1, 89-97.

McDonald, B., and Morris, M.H. (1985), "The functional specification of financial ratios: an empirical examination", Accounting and Business Research 15/59, 223-228.

McDonald, B., and Morris, M.H. (1986), "The statistical validity of the ratio method in financial analysis: an empirical examination: a reply", Journal of Business Finance and Accounting 13/4, 633-635

McLeay, S., and Fieldsend, S. (1987), "Sector and size effects in ratio analysis: an indirect tests of a ratio proportionality", Accounting and Business Research 17/66, 133-140.

Perttunen, J., and Martikainen, T. (1989), "On the proportionality assumption of financial ratios", Finnish Journal of Business Economics 38/4, 343-359.

Perttunen, J., and Martikainen, T. (1990), "Distributional characteristics and proportionality of marked-based security ratios", Finnish Economic Papers 3/2, 125-133.

Triqueiros, D. (1992), "The cross-sectional characterization of accounting data", Working Paper, ISCTE.

Whittington, G. (1980), "Some basic properties of accounting ratios", Journal of Business Finance and Accounting 7/2, 219-232.

 

2.2. Distributional Characteristics of Financial Ratios

Barnes, P. (1982), "Methodological implications of non-normally distributed financial ratios", Journal of Business Finance and Accounting 9/1, 51-62.

Barnes, P. (1983), "Methodological implications of non-normally distributed financial ratios: a reply", Journal of Business Finance and Accounting 10/4, 691-693.

Bird, R.G., and McHugh A.J. (1977), "Financial ratios - an empirical study", Journal of Business Finance and Accounting 4/1, 29-45.

Bougen, P.D., and Drury, J.C. (1980), "U.K. statistical distributions of financial ratios, 1975", Journal of Business Finance and Accounting 7/1, 39-47.

Buckmaster, D., and Saniga E. (1990), "Distributional forms of financial accounting ratios: Pearsons's and Johnson's taxonomies", Journal of Economic and Social Measurement 16, 149-166.

Buijink, W., and Jegers, M. (1986), "Cross-sectional distributional properties of financial ratios in Belgian manufacturing industries: aggregation effects and persistence over time", Journal of Business Finance and Accounting 13/3, 337-363.

Deakin, E.B. (1976), "Distributions of financial accounting ratios: some empirical evidence", Accounting Review, January 1976, 90-96.

Ezzamel, M., Brodie, J., and Mar-Molinero, C. (1990), "The distributional properties of financial ratios in UK manufacturing companies", Journal of Business Finance and Accounting 17/1, 1-29.

Frecka, T.J., and Hopwood, W.S. (1983), "The effects of outliers on the cross-sectional distributional properties of financial ratios", Accounting Review 58/1, 115-128.

Horrigan, J.O. (1983), "Methodological implications of non-normally distributed financial ratios: a comment", Journal of Business Finance and Accounting 10/4, 683-689.

Karels, G.V., and Prakash, A.J. (1987), "Multivariate normality and forecasting of business bankruptcy", Journal of Business Finance and Accounting 14/4, 573-593.

Kolari, J., McInish, T.H., and Saniga, E.M. (1989), "A note on the distribution types of financial ratios in the commercial banking industry", Journal of Banking and Finance 13/3, 463-471.

Ledford, M.H., and Sugrue, P.K. (1983), "Ratio analysis: application to U.S. motor common carriers", Business Economics, September 1983, 46-54.

Martikainen, T. (1991), "A note on the cross-sectional properties of financial ratio distributions", Omega 19/5, 498-501.

Martikainen, T. (1992), "Time-series distributional properties of financial ratios: empirical evidence from Finnish listed firms", European Journal of Operational Research 58/3, 344-355.

McLeay, S. (1986a), "Students' t and the distribution of financial ratios", Journal of Business Finance and Accounting 13/2, 209-222.

McLeay, S. (1986b), "The ratio of means, the means of ratios and other benchmarks: an examination of characteristics financial ratios in the French corporate sector", Finance, The Journal of the French Finance Association 7/1, 75-93.

Mecimore, C.D. (1968), "Some empirical distributions of financial ratios", Management Accounting 50/1, 13-16.

Smith, D.B., and Pourciau, S. (1988), "A comparison of the financial characteristics of december and non-december year-end companies", Journal of Accounting and Economics 10/4, 335-344.

So, J.C. (1987), "Some empirical evidence on the outliers and the non-normal distribution of financial ratios", Journal of Business Finance and Accounting 14/4, 483-496.

Tippet, M. (1990), "An induced theory of financial ratios", Accounting and Business Research 21/81, 77-85.

Virtanen, I., and Yli-Olli, P. (1989), "Cross-sectional and time-series persistence of financial ratio distributions; Empirical evidence with Finnish Data", European Institute for Advanced Studies in Management, Working paper 89-04, Brussels.

Watson, C.J. (1990), "Multivariate distributional properties, outliers, and transformation of financial ratios", Accounting Review 65/3, 682-695.

 

2.3. Classification of Financial Ratios

Aho, T. (1980), "Empirical classification of financial ratios", Management Science in Finland 1980 Proceedings, ed. C.Carlsson.

Bayldon, R., Woods, A., and Zafiris, N. (1984), "A note on the pyramid technique of financial ratio analysis of firms performance", Journal of Business Finance and Accounting 11/1, 99-106.

Beaver, W. (1977), "Financial Statement Analysis", Handbook of Modern Accounting, eds Davidson, S. and Weil, R., 2nd ed. McGraw-Hill.

Bernstein, L. (1989), Financial Statement Analysis: Theory, application, and interpretation. Richard D. Irwin, 4th ed.

Brealey, R., and Myers, S. (1988). Principles of Corporate Finance. McGraw-Hill, 3rd ed.

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Courtis, J.K. (1978), "Modelling a financial ratios categoric framework", Journal of Business Finance and Accounting 5/4 , 371-386.

Cowen, S.S., and Hoffer, J.A. (1982), "Usefulness of financial ratios in a single industry", Journal of Business Research 10/1, 103-118.

Ezzamel, M., Brodie, J., and Mar-Molinero, C. (1987), "Financial patterns of UK manufacturing companies", Journal of Business Finance and Accounting 14/4, 519-536.

Fornell, C., and Larcker, D.F. (1980), "The use of canonical correlation analysis in accounting research", Journal of Business Finance and Accounting 7/3, 455-473.

Foster, G. (1978), Financial Statement Analysis. Prentice-Hall, first ed.

Foster, G. (1986), Financial Statement Analysis. Prentice-Hall, 2nd ed.

Gombola, M.J., and Ketz, J.E. (1983), "A note on cash flow and classification patterns of financial ratios", Accounting Review 63/1, 105-114.

Holmes, G., and Sugden, A. (1990), Interpreting Company Reports and Accounts. University Press, Cambridge, 4Th ed.

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Hutchinson, P., Meric, I., and Meric, G. (1988), "The financial characteristics of small firms which achieve quotation on the UK unlisted securities market", Journal of Business Finance and Accounting 15/1, 9-19.

Johnson, W.B. (1978), "The cross-sectional stability of financial patterns", Journal of Business Finance and Accounting 5/2, 207-214.

Johnson, W.B. (1979), "The cross-sectional stability of financial ratio patterns", Journal of Financial and Quantitative Analysis 14/5, 1035-1048.

Kanto, A.J., and Martikainen, T. (1991), "A confirmatory test of an a priori classification pattern of financial ratios: empirical evidence with U.S. data", Finnish Journal of Business Economics 1, 22-38.

Kanto, A.J., and Martikainen, T. (1992), "A test of a priori financial characteristics of the firm", European Journal of Operational Research 57/1, 13-23.

Laitinen, E.K. (1983), "A multivariate model of the financial relationship in the firm", Finnish Journal of Business Economics 32/4, 317-333.

Laurent, C.R. (1979), "Improving the efficiency and effectiveness of financial ratio analysis", Journal of Business Finance and Accounting 6/3, 401-413.

Lev, B. (1974a), Financial Statement Analysis; A new approach, Prentice-Hall.

Libby, R. (1975), "Accounting ratios and the prediction of failure: some behavioral evidence", Journal of Accounting Research 13/1, 150-161.

Luoma, M., and Ruuhela, R. (1991), "Consistency and comovement of financial ratios: a firm-specific approach", Finnish Journal of Business Economics 1, 39-49.

Martikainen, T. (1993), "Stock returns and classification pattern of firm-specific financial variables: empirical evidence with Finnish data", Journal of Business Finance and Accounting 20/4, 537-557.

Martikainen, T. and Ankelo, T. (1991), "On the instability of financial patterns of failed firms and the predictability of corporate failure", Economics Letters 35/2, 209-214.

Martikainen T., Puhalainen, K. and Yli-Olli, P. (1994), "On the industry effects on the classification patterns of financial ratios", Scandinavian Journal of Management 10/1, 59-68.

Morley, M.F. (1984), Ratio Analysis. The Institute of Chartered Accountants of Scotland.

Pinches, G.E., and Mingo, K.A. (1973), "A multivariate analysis of industrial bond ratings", Journal of Finance, 28/1, 1-18.

Pinches, G.E., Eubank, A.A., Mingo, K.A., and Caruthers, J.K. (1975), "The hierarchical classification of financial ratios", Journal of Business Research 3/4, 295-310.

Pinches, G.E., Mingo, K.A., and Caruthers, J.K. (1973), "The stability of financial patterns in industrial organizations", Journal of Finance, May 1973, 389-396.

Pohlman, R.A., and Hollinger, R.D. (1981), "Information redundancy in sets of financial ratios", Journal of Business Finance and Accounting 8/4, 511-528.

Richardson, F.M., and Davidson, L.F. (1984), "On linear discrimination with accounting ratios", Journal of Business Finance and Accounting 11/4, 511-525.

Salmi, T., Virtanen, I., and Yli-Olli, P. (1990), "On the classification of financial ratios. A factor and transformation analysis of accrual, cash flow, and market-based ratios", Acta Wasaensia, no 25. Also published on the World Wide Web as http://www.uwasa.fi/~ts/sera/sera.html

Salmi, T., Virtanen, I., and Yli-Olli, P. (1992), "Measuring the generalized association between financial statements and security characteristics: A canonical correlation approach", EURO XII/TIMS XXXI Joint International Conference, Operational Research / Management Science, Helsinki, Finland, June 29-July 1, 1992.

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Yli-Olli, P., and Virtanen, I. (1990), "Transformation analysis applied to long-term stability and structural invariance of financial ratio patterns: U.S. vs. Finnish firms", American Journal of Mathematical and Management Sciences 10/1-2, 73-125.


3. Measurement of Profitability and Financial Ratios

Bhaskar, K.N. (1972), "Rates of return under uncertainty", Accounting and Business Research (Winter 1972), 40-52.

Bierman, H.J. (1961), "Depreciable assets - timing of expenditure recognition", The Accounting Review 36, 693-699.

Brief, R.P. (1985), "Limitations of using the cash recovery rate to estimate the IRR: a note", Journal of Business Finance and Accounting 12/3, 473-475.

Brief, R.P., and Lawson, R.A. (1991a), "Approximate error in using accounting rates of return to estimate economic returns", Journal of Business Finance and Accounting 18/1, 13-20.

Brief, R.P., and Lawson, R.A. (1991b), "Approximate error in using accounting rates of return to estimate economic returns: A correction", Journal of Business Finance and Accounting 18 (November), 915-916.

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Fisher, F.M., and McGowan, J.J. (1983), "On the misuse of accounting rates of return to infer monopoly profits", American Economic Review 73/1, 82-97.

Fisher, F.M. (1984), "The misuse of accounting rates of return: Reply", American Economic Review 74/3, 509-517.

Gordon, L.A. (1974), "Accounting rate of return vs. economic rate of return", Journal of Business Finance and Accounting 1/1, 343-356.

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Gordon, L.A., and Hamer, M.M. (1988), "Rates of return and cash flow profiles: an extension", Accounting Review 63/3, 514-521.

Griner, E.H., and Stark, A.W. (1988), "Cash recovery rates, accounting rates of return, and the estimation of economic performance", Journal of Accounting and Public Policy 7, 293-311.

Harcourt, G.C. (1965), "The accountant in a golden age", Oxford Economic Papers. New Series 17/1, 66-80.

Ijiri, Y. (1978), "Cash-flow accounting and its structure", Journal of Accounting, Auditing and Finance (Summer 1978), 331-348.

Ijiri, Y. (1979), "Convergence of cash recovery rate", in: Quantitative Planning and Controlling. Essays in Honor of William Wager Cooper on the Occasion of His 65th Birthday (ed. Y., Ijiri and A.B., Whinston), Academic Press, New York.

Ijiri, Y. (1980), "Recovery rate and cash flow accounting", Financial Executive (March 1980), 54-60.

Jegers, M. (1985), "Estimating the internal rate of return from published financial statements: a comment", Journal of Business Finance and Accounting 12/4, 609-610.

Jegers, M. (1985), "The ARR-IRR controversy: a critical review and some extensions", Paper presented at the European Accounting Association Congress, Brussels, April 1985.

Van der Hagen, K., and Jegers, M. (1993), "Measurement of the internal rate of return of a firm: an empirical comparison of accounting based methods", Finnish Journal of Business Economics 41/1, 16-23.

Kanniainen, V., and Hernesniemi, H. (1986), "Asset structure, indebtedness, and the rate of return on capital in a sample of Finnish manufacturing firms", Kansantaloudellinen aikakauskirja 3, 278-288.

Kay, J.A. (1976), "Accountants, too, could be happy in a golden age: the accountants rate of profit and the internal rate of return", Oxford Economic Papers (New Series) 28/3, 447-460.

Kay, J.A. (1978), "Accounting rate of profit and internal rate of return; a reply", Oxford Economic Papers 30/3, 469-470.

Kay, J.A., and Mayer, C.P. (1986), "On the application of accounting rates of return", Economic Journal 96 (March 1986), 199-207.

Kelly, G., and Tippett, M. (1991), "Economic and accounting rates of return: a statistical model", Accounting and Business Research 21/84, 321-329.

Livingstone, J.L., and Breda Van, M.F. (1976), "Relationship between accounting and the internal rate of return measures. A reply", Journal of Accounting Research 14/1, 187-188.

Livingstone, J.L., and Salamon, G.L. (1970), "Relationship between the accounting and the internal rate of return measures: a synthesis and an analysis", Journal of Accounting Research 8/2, 199-216.

Long, W.F., and Ravenscraft, D.J. (1984), "The misuse of accounting rates of return: Comment", American Economic Review 74/3, 494-500.

Luckett, P.F. (1984), "ARR vs. IRR: a review and an analysis", Journal of Business Finance and Accounting 11/2, 213-231.

Martin, S. (1984), "The misuse of the accounting rate of return: Comment", American Economic Review 74/3, 501-508.

McHugh, A.J. (1976), "Relationship between accounting and the internal rate of return measures", Journal of Accounting Research 14/1, 181-186.

Peasnell, K.V. (1982a), "Some formal connections between economic values and yields and accounting numbers", Journal of Business Finance and Accounting 9/3, 361-381.

Peasnell, K.V. (1982b), "Estimating the internal rate of return from accounting profit rates", The Investment Analyst, April, 26-31.

Ruuhela, R. (1972), Yrityksen kasvu ja kannattavuus. Summary: A capital investment model of the growth and profitability of the firm. Acta Academiae Helsingiensis, Series A:8. Helsinki.

Ruuhela, R., Salmi, T., Luoma, M., and Laakkonen, A. (1982), "Direct estimation of the internal rate of return from published financial statements", Finnish Journal of Business Economics 4, 329-345.

Salamon, G.L. (1973), "Models of the relationship between the accounting and the internal rate of return: An examination of the methodology", Journal of Accounting Research 11/2, 296-303.

Salamon, G.L. (1982), "Cash recovery rates and measures of firm profitability", Accounting Review 57/2, 292-302.

Salamon, G.L. (1988), "On the validity of accounting rates of return in cross-sectional analysis: theory, evidence, and implications", Journal of Accounting and Public Policy 7/4, 267-292.

Salmi, T. (1978), "A comparative review of the Finnish expenditure- revenue accounting", European Institute for Advanced Studies in Management: Working Paper 78-2. Revised in 1993 as "Review of Finnish expenditure- revenue accounting", University of Vaasa electronic library, ftp://garbo.uwasa.fi/pc/ts/tscmpacc.zip.

Salmi, T. (1982), "Estimating the internal rate of return from published financial statements", Journal of Business Finance and Accounting 9/1, 63-74. [Link to abstract]

Salmi, T., Dahlstedt, R., and Luoma, M. (1985), "Improving firm-level growth estimates by eliminating cycles", Finnish Journal of Business Economics 4, 383-410. [Link to abstract]

Salmi, T., and Luoma, M. (1981), "Deriving the internal rate of return from accountant's rate of profit: analysis and empirical estimation", Finnish Journal of Business Economics 1, 20-45.

Salmi, T., and Ruuhela, R. (1985), "Estimating the internal rate of return from published financial statements: a reply", Journal of Business Finance and Accounting 12/4, 611-612.

Salmi, T., Ruuhela, R., Laakkonen, A., and Luoma, M. (1983a), "Extracting and analyzing the time series for profitability measurement from published financial statements. With results on publicly traded Finnish metal industry firms. Part I", Finnish Journal of Business Economics 2, 135-174.

Salmi, T., Ruuhela, R., Laakkonen, A., and Luoma, M. (1983b), "Extracting and analyzing the time series for profitability measurement from published financial statements. With results on publicly traded Finnish metal industry firms. Part II", Finnish Journal of Business Economics 3, 209-241.

Salmi, T., Ruuhela, R., Laakkonen, A., Dahlstedt, R., and Luoma, M. (1984), "Extracting and analyzing the time series for profitability measurement from published financial statements. With results on publicly traded Finnish metal industry firms. Part III", Finnish Journal of Business Economics 1, 23-48. [Link to abstract]

Salmi T., and Ruuhela, R. (1993), "Comment: Measurement of the internal rate of return of a firm: an empirical comparison of accounting based methods", Finnish Journal of Business Economics 41/2, 98-99.

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Stark, A.W. (1987), "On the observability of the cash recovery rate", Journal of Business Finance and Accounting 14/1, 99-108.

Stark, A.W., Thomas, H.M., and Watson, I.D. (1992), "On the practical importance of systematic error in conditional IRRs", Journal of Business Finance and Accounting 19/3, 407-424.

Stark, A.W. (1994), "Some analytics of why conditional IRRs can contain growth rate related measurement error", Journal of Business Finance and Accounting 21/2, 219-229.

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Wright, F.K. (1978), "Accounting rate of profit and internal rate of return", Oxford Economic Papers 30/3, 464-468.


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