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International Journal of Research in Engineering, Social Sciences (ISSN 2249-9482)
(Impact Factor: 4.16, Volume 5 Issue 2, February 2015)
Website: www.indusedu.org
THE EFFECT OF FINANCIAL RATIOS ON THE FINANCIAL
SITUATION OF INDIAN ENTERPRISES: A DISCRIMINANT ANALYSIS
Dr. Nitin Tanted
Associate Professor, Prestige Institute of Management and Research, Indore
Dr. Yogeshwari Pathak
Professor and Director, Prestige Institute of Management and Research, Indore
ABSTRACT
The present study aims to reveal the effect of and make evaluations on liquidity, financial,
activity and profitability ratios on the financial positions of enterprises (profit / loss). The
purpose of this paper is to assess the quality of ratio analysis as an analytical technique. The
prediction of Profit and loss is used as an illustrative case. Specifically, a set of financial and
economic ratios will be investigated in the profit and loss prediction wherein multiple
discriminant statistical methodology will be employed. The study is conducted on the selected
stocks from S and P 500 index.
Keywords: Financial Ratio, Banks, S & P, NSE
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International Journal of Research in Engineering, Social Sciences (ISSN 2249-9482)
(Impact Factor: 4.16, Volume 5 Issue 2, February 2015)
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INTRODUCTION
The persistent problem while employing financial ratio is that, which ratios, of available that can
be computed easily from the available financial data should be analyzed to obtain the
information for task at hand. Naturally, different researchers often include different ratios. Yet, it
is impossible to include most of the useful ratios in the literature. Which ratios, then, should be
deleted and which should be included has become very important. Ratio analysis has been a tool
of analysts for as long as financial statements have been prepared. However, discrimination is
needed to recognize a limited set of financial ratios. Discriminant Analysis is a technique, by
means of which researcher may categorize items into one or two or more mutually exclusive and
exhaustive groups on the basis of a set of independent variables. For performing discriminant
analysis researcher requires interval independent variables and a nominal dependent variable.
Discriminant analysis is considered an appropriate technique when the single dependent variable
happens to be non-metric and is to be classified into two or more groups, depending upon its
relationship with several independent variables which all happen to be metric. The objective of
performing discriminant analysis is to predict an items likelihood of belonging to a particular
group based on several independent variables (Kothari, 2004).
Discriminant analysis is a useful technique in the solution of three distinct but interrelated
problems (Tatsuoka, 1976) like to determine if there are significant differences among two or
more existing groups (populations) based on a combined set of descriptor variables, to explain
any significant differences among the groups with a number of underlying factors that is smaller
than the number of original descriptor variables and to predict group membership of future items,
assuming such items are truly members of one or another of the groups. Ramayah, (2010) said
that while a researcher analyzes the data, he has to identify the correct analysis technique and
interpret the output that he gets. While analysis is simple task and just on few click it can be
done.
LITERATURE REVIEW
Ramayah, (2010) said that while a researcher analyzes the data, he has to identify the correct
analysis technique and interpret the output that he gets. While analysis is simple task and just on
few click it can be done. The more challenging part is the interpretation of the output. Many
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International Journal of Research in Engineering, Social Sciences (ISSN 2249-9482)
(Impact Factor: 4.16, Volume 5 Issue 2, February 2015)
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researchers are very familiar and well exposed to the regression analysis technique whereby the
dependent variable is a continuous variable. But what happens if the dependent variable is a
nominal variable? Then the researcher has 2 choices: either to use a discriminant analysis or a
logistic regression. Discriminant analysis is used when the data are normally distributed whereas
the logistic regression is used when the data are not normally distributed.
Yıldız, (1995) said that the discriminant analysis is one of the multi variable statistical analysis
methods, in which the structures of predetermined populations are revealed through the samples
drawn from these populations and through a set of variables. Following the identification of
these structures, a selected individual or a group of individuals are assigned to the predetermined
groups (populations) on the basis of the observations concerning these individuals. Discriminant
analysis is used primarily to predict membership in two or more mutually exclusive groups.
The objectives of the discriminant analysis could be grouped under five main categories (Eroğlu,
2008). He stated that it could be used to predict the group membership and to decide about in
which variable group a particular data will be included, through the discriminant function
equation, it helps classifying the data into groups, it could be used to determine how the
arithmetic means of the independent variables change across groups, it can be used to identify
the variables that are effective and ineffective in distinguishing between groups and it could be
used to test whether the data has been classified as predicted.
Dimitras, etal., (1996) studied that predicting enterprise failures constitutes one of the most
important activities in supervising enterprise risks and/or variables. The term enterprise failure is
a definable phenomenon: for instance, failure to cover external debts, exceeding budget limits,
failure to effect payment to suppliers, incurring losses, etc. Altaş, Giray (2005) reported that
financial failure is quite an important problem in terms of its socio-economic results; thus, it
needs an examination of its underlying variables. Furthermore, the increasing number of
enterprise failures in Turkey during the last years is another case that also needs investigation
Ahn, Cho, Kim, 2000; Balcaen, Ooghe, (2006) said that financial analysis model developed to
predict enterprise failure is a quite helpful tool for executives and provides concerned decisionmakers (authorities) with the possibility to avoid failures through an early warning system.
Furthermore, this model is of assistance to the decision makers of the financial institutions
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International Journal of Research in Engineering, Social Sciences (ISSN 2249-9482)
(Impact Factor: 4.16, Volume 5 Issue 2, February 2015)
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during the investment evaluation stage or in selecting potential enterprise partners. There are a
few leading studies on predicting financial failure.
Beaver (1967) studied on bankruptcy and financial situation of enterprises. The study covers 79
successful and failing enterprises during the period between 1954 and 1964, his study discusses
the reasons of failure such as bankruptcy, failure in due payment of the bond yield and failure to
pay the profit shares. Beaver performed his analysis in 3 stages and over 30 financial ratios
which he classified under 6 categories (Cash Flow Ratios, Profit Rates, Total Liabilities / Total
Assets Ratio, Liquid Assets / Total Assets Ratio, Liquid Assets / Short-Term Liabilities Ratios
and Turnover Ratios). In the first stage, he compared the average values of the financial ratios.
The subsequent stage involved a dual comparison to demonstrate the predictory power of the
ratios, while in the final stage, he calculated the ratio distribution for the successful and failing
enterprises. Consequently, he concluded that the cash flow/total assets ratio is the most effective
ratio in predicting enterprise failure.
On the other hand, Altman (1968) uses the multiple discriminant analysis in his study. Within the
scope of his analysis, he categorizes the enterprises into two groups: bankrupt and non-bankrupt
enterprises. Analyzing 33 bankrupt and 33 non-bankrupt enterprises according to the 22 ratios he
identified under the category of basic ratios (liquidity ratio, financial leverage ratios, solvency
ratios, efficiency and profitability ratios), the author achieved a successful prediction rate of 94%
by obtaining the discriminant scores which yield the best results (Z score). In order to
demonstrate the effect of the analyzed ratios on enterprise financial situation (profit / loss), the
present study as well apply the discriminant analysis.
OBJECTIVES OF THE STUDY
To study the ability of various financial ratios in discriminating between profit and loss making
firms.
•
To test whether the data has been classified as predicted.
•
To devise a model which shows the extent to which various financial ratios can be
used to predict profit and loss making firms.
METHODOLOGY
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International Journal of Research in Engineering, Social Sciences (ISSN 2249-9482)
(Impact Factor: 4.16, Volume 5 Issue 2, February 2015)
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The Study: The present study is an analytical in nature as it aims at identifying and assessing the
ability of various financial ratios in discriminating between profit and loss making firms.
Data: The Data is secondary nature and uses ratios of 95 companies grouped into 51 profit and
44 loss making companies. A profit making company had consistent profit for 5 years and
similarly loss making firms were defined.29 ratios grouped in to 5 categories namely EPS,
Profitability, Liquidity, Leverage and Payout Ratios.
A Total 2755 (95*29) data were subjected to discriminant analysis through. The analysis drew
upon dummy variables by coding “1” for the profit-making companies and “2” for the lossmaking companies. The data were obtained from Rediffmoneywiz.com. During the course of the
research; the software packages Microsoft Office Excel 2007 and SPSS 11.5 for Windows were
used. Table 1 presents the major ratio categories, the ratios included in each category and their
codes.
Tool for Data Collection: For the purpose of study secondary data was collected regarding
financial positions and financial ratios of banks for the period 2006 to 2010.
Tool for Data Analysis: For analysis of data Microsoft Office Excel 2007 and SPSS 15.0 for
Windows were used as a tool for performing Discriminant Analysis on selected sample. The
discriminant function is a linear combination of the independent variables. An examination of the
function demonstrates the following configuration.
Zi = α + b1X1i + b2X2i + …………. + bnXni
where Zi: the ith individual Discriminant Score (Z Score)
α: Constant Coefficient
bn: Discriminant Coefficients of nth variable
X1: the ith individual value of the jth independent variables
Zcrit. : The critical value for the discriminant score
The classification procedure in such a case would be
If Zi > Zcrit., Classify individual i as belonging to Group I
If Zi < Zcrit., Classify individual i as belonging to Group II
The equation presented here is similar to the configuration in the multiple regression analysis.
Nevertheless, the coefficients maximize the distance between the mean scores of the independent
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International Journal of Research in Engineering, Social Sciences (ISSN 2249-9482)
(Impact Factor: 4.16, Volume 5 Issue 2, February 2015)
Website: www.indusedu.org
variables. This equation helps formulating a prediction model which could be used in classifying
new observations.
FINDINGS
The Results of the Analysis and Evaluation
Table 1: The Eigenvalue Statistic
Function Eigenvalue % of Variance Cumulative % Canonical
Correlation
1
1.913
100.0
100.0
.810
a First 1 canonical discriminant functions were used in the analysis.
The eigenvalue, which is another important statistical value for our purposes, is used to evaluate
the degree of significance for the discriminant analysis, and it follows that as the eigenvalue
increases, the function explains an increasing part of the variance in the dependent variable. Even
though there is not any absolute value, eigenvalues higher than 0.40 are considered as optimum
(Eroğlu, 2008). The eigenvalue , which is another important statistical value for our purpose , is
used to evaluate the degree of significance for the discriminant analysis , and it follow that as the
eigenvalue increases the function explains an increasing part of the variance in the dependent
eigenvalue higher than 0.40 are consider as optimum .
An examination of table -1 suggests that, since the eigen value statistics is 1.913 in our analysis,
this function provides a through differentiation
An eigenvalue indicates the proportion of variance explained. (Between-groups sums of squares
divided by within-groups sums of squares). A large eigenvalue is associated with a strong
function. The canonical relation is a correlation between the discriminant scores and the levels of
the dependent variable. A high correlation indicates a function that discriminates well. The
canonical correlation measures the correlation between the discriminant scores and the Group ,
and also indicates the explained variance .
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As seen in table - 2, this value is 0.810. An interpretation of this value requires squaring , where
the resulting value is
0.6561. Hence, it could be suggested that our model explains 65.61% of
the variance for dependent variable.
Table 2: Wilks' Lambda Statistics
Test of Function(s)
1
Wilks' Lambda
.343
Chi-square
98.379
Df
2
Sig.
.000
Wilks‟ Lambda statistic value, which is presented in Table 2, has a range of values between 0-1
and refers to the unexplained part (ratio) of the total variance in the discrimination scores left
unexplained by the differences between the groups. Furthermore, it is possible to determine the
significance of the function‟s eigenvalue statistic. While greater Wilks‟ Lambda values indicate
that mean scores are not dissimilar for groups, discriminatory character of the model increases as
the value gets smaller.
Wilks‟ Lambda is the ratio of within-groups sums of squares to the total sums of squares. This is
the proportion of the total variance in the discriminant scores not explained by differences among
groups. A lambda of 1.00 occurs when observed group means are equal (all the variance is
explained by factors other than difference between those means), while a small lambda occurs
when within-groups variability is small compared to the total variability. A small lambda
indicates that group means appear to differ. The associated significance value indicate whether
the difference is significant.
Wilk‟s Lambda statistics value indicate that mean scores are not dissimilar for group,
discriminatory character of the model increases as the value gets smaller .
As a result of the analysis , The Wilk‟s Lambda was found to be 0.343 and the function failed to
explain 34.3% of the total variance in the discriminant scores .
The significance value of the test, which is 0.000, demonstrates that the test result are statistically
significant at the levels of 5%.
Table 3: Classification Results
Predicted Group Membership
Profit/Loss
Original Count Profit
Total
Profit
Loss
46
1
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%
Loss
7
41
48
Profit
97.9
2.1
100.0
Loss
14.6
85.4
100.0
a 91.6% of original grouped cases correctly classified.
„Classification Results‟ is a simple summary of number and percent of subjects classified
correctly and incorrectly. The „leave-oneout classification‟ is a cross-validation method, of
which the results are also presented.
The higher the percentage of accurate classification, the more successful is the analysis. the
percentage of accurate classification for the 1st group is 97%, 85.4% and 91.6% in total all
signify an optimum classification
Table 4: Standardized Canonical Discriminant Function Coefficients
Function
1
Earning Per Share Ratio
.387
Payout Ratio
.968
An evaluation of the significance of the independent variables requires considering the
discriminant function coefficients and the load of each variable in the structure matrix. An
examination of Table 4 reveals that all variables used in grouping the profit-making and lossmaking enterprises are significant discriminatory variables. Here, the reason for using
standardized coefficients is to eliminate the effects of the different mean scores and standard
deviations in the independent variables.
Otherwise, variables with smaller standard deviations might have greater discrimination
coefficients, which will make difficult to evaluate the relative significance of the independent
variables. While evaluating these coefficients, higher coefficients make greater contributions and
the sign (either positive or negative) of the coefficients do not indicate any particular meaning.
The standardized canonical Discriminant function gives the Two category of ratios viz EPS and
Payout Ratio from the five identified.
Table 5: Structure Matrix
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Function
1
Payout Ratio
.923
Earning Per Share Ratio
.276
Leverage Ratio
.179
Profitablity Ratio
.095
Liquidity Ratio
.077
Structure matrix is a matrix which could be employed to evaluate the significance of the
independent variables. It presents the correlation between the discriminant function and each of
the variables. An examination of Table 5 reveals that the variables payout ratio (0.923) and
Earning Per share ratio (0.276) are the independent variables with the highest correlation with
the discriminant function
Table 6: Canonical Discriminant Function Coefficients
Function
1
Earning Per Share Ratio
.008
Payout Ratio
.071
(Constant)
-2.451
Unstandardized coefficients
The „Canonical Discriminant Function Coefficients‟ indicate the unstandardized scores
concerning the independent variables. It is the list of coefficients of the unstandardized
discriminant equation. Each subject‟s discriminant score would be computed by entering his or
her variable values (raw data) for each of the variables in the equation.
The equation below presents the Z score values obtained for each sample as a result of applying
to the values of relevant samples the above-mentioned discriminant function, which was
formulated through the analysis.
Z=-2.451+.008*eps+.071*payout ratio
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The result of the analysis shows that the ratio with the highest correlation to discriminant
function is payout ratio .923 and .276.It could be observed that variable with the highest effect
on the Z Score function.
CONCLUSION
The present study is an analytical in nature as it aims at identifying and assessing the ability of
various financial ratios in discriminating between profit and loss making firms.
The Data used is secondary in nature and uses ratios of 95 companies grouped into 51 profit and
44 loss making companies. A profit making company had consistent profit for 5 years and
similarly loss making firms were defined.29 ratios grouped in to 5 categories namely EPS,
Profitability, Liquidity, Leverage and Payout Ratios.
A Total 2755 (95*29) data were subjected to discriminant analysis through. The analysis drew
upon dummy variables by coding “1” for the profit-making companies and “2” for the lossmaking companies. An examination of the basis statistics result of the discriminant analysis
demonstrated that the model has an accurate classification rate of 100 percent and that it explains
65.61 percent of the total variance for dependent variable. Furthermore, the eigenvalue statistics
is 1.993 which was obtained as a result of the analysis provides the evidence that the
discriminant analysis achieved a good discrimination, and that Wilk‟s Lambda was found to be
.343 and the function failed to explain 34.3 percent of the total variance in the discriminant
scores.
The result of the analysis show that the ratios with the highest correlation to discriminant
function are payout ratio (0.968), and earning per share (0.387), it could be observed that the
variable with the highest effect on the Z score function. In conclusion, it can be said that all
included variables having a discriminatory character, the payout ratio and the earning per share
have an important effect. Thus, it was found that out of five categories of ratios only two
category of ratio have the predictive ability to discriminate between profit and loss making firms
of which pay out ratio
REFERENCES
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International Journal of Research in Engineering, Social Sciences (ISSN 2249-9482)
(Impact Factor: 4.16, Volume 5 Issue 2, February 2015)
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1. Ahn, B. S.; Cho, S. S. and Kim, C. Y. (2000). The Integrated Methodology of Rough Set
Theory and Artificial Neural Network for Business Failure Prediction. Expert Systems
with Applications, 18, 65–74.
2. Altaş, D. and Giray, S. (2005). Multivariate Statistical Methods Determination of
Financial Failure: The Case of Textile Industry. Journal of Social Sciences at Anadolu
University , 2, 13-26.
3. Beaver, W. H. (1966). Financial Ratios as Predictors of Failure. Journal of Accounting
Research, 4, 71-111.
4. Edward, Altman I. (1968). Financial Ratios, Discriminant Analysis and the Prediction of
Corporate Bankruptcy. The Journal of Finance, 23(4), 589-609. Published by: Blackwell
Publishing for the American Finance Association.
5. Eroglu, A. (2008). SPSS Applied Multivariate Statistical Techniques. Editor: Honor
Kalayci, 3 Printing, Publishing Distribution Ltd. Noble. Sti.: London, 342.
6. Kothari, C. R. (2004). Research Methodology: Methods and Techniques. Second Edition
2nd New Age International Limited: New Delhi, 319.
7. Kung, Chen H. and Shimerda, Thomas A. (1981). An Empirical Analysis of Useful
Financial Ratios. Financial Management, 10(1), (Spring, 1981), 51-60 Published by:
Blackwell Publishing on behalf of the Financial Management Association International.
8. Ramayah, T.; Noor Hazlina Ahmad; Hasliza Abdul Halim; Siti Rohaida; Mohamed
Zainal and May-Chiun, Lo (2010). Discriminant Analysis: An Illustrated Example.
African Journal of Business Management, 4(9), 1654-1667.
9. Smith, P. (1990). Data Envelopment Analysis Applied to Financial Statements. Omega,
18(2), 131-138. Copyright © 1990 Published by Elsevier Science Ltd.
10. Tatsuoka, M.M. (1976). Discriminant Analysis, in Data Analysis Strategies and Designs
for Substance Abuse Research. Edited by P.M. Bentler, D.J. Lettieri and G.A. Austin
(Rockville, MD: National Institute on Drug Abuse, 1976), 201-20.
Email id:- [email protected]
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