
                               - 1 -


Timo Salmi
Professor of Accounting and Business Finance
University of Vaasa
Email: ts@uwasa.fi

Teppo Martikainen
Associate Professor of Accounting and Business Finance
University of Vaasa
Email: tlm@uwasa.fi


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.


                               - 2 -


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,
   and
 - 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.

                               - 3 -


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

                               - 4 -


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

                               - 5 -


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

                               - 6 -


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

                               - 7 -


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

                               - 8 -


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

                               - 9 -


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

                               - 10 -


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

                               - 11 -


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).




                               - 12 -


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

                               - 13 -


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).


                               - 14 -


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

                               - 15 -


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

                               - 16 -


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

                               - 17 -


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

                               - 18 -


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) =   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

                               - 19 -


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

                               - 20 -


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

                               - 21 -


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

                               - 22 -


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

                               - 23 -


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.


                               - 24 -


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

                               - 25 -


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

                               - 26 -


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,

                               - 27 -


 - 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

                               - 28 -


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.
