A follow-up paper
Counting since 15.10.2005 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 FIN-00100 Helsinki 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: .
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 functional form of the financial
ratios, i.e. the proportionality discussion, distributional
characteristics of financial ratios, classification of financial
ratios, comparability of ratios across industries, and industry
effects, time-series properties of individual financial ratios,
bankruptcy prediction models, explaining (other) firm
characteristics with financial ratios, stock markets and financial
ratios, forecasting ability of financial analysts vs financial
models, estimation of internal rate of return from financial
statements. 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 (BoxCox)
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 maximumlikelihood 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
(bookyield 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 ARRIRR 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 sideeffects 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 handbook 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 marketbased
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: the functional form of the financial ratios, i.e. the
proportionality discussion, distributional characteristics of
financial ratios, classification of financial ratios, and
estimation of internal rate of return from financial statements. 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
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Salmi, T., Virtanen, I., and Yli-Olli, P. (1992), "Measuring the
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3. Measurement of Profitability and Financial Ratios
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published financial statements", Journal of Business Finance and
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abstract]
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rate of return", Oxford Economic Papers 30/3, 464-468.
Other scientific publications by Timo Salmi in electronic
format
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