Application of the Factor Analysis on the Financial Ratios and Validation of the Results by the Cluster Analysis: An Empirical Study on the Indian Cement Industry

Abstract

For saving considerable time and effort of the analyzers, it is necessary to select the most important financial ratios to be used for the financial analysis. To reduce the number of financial ratios and to find out the categories of financial ratios on the basis of empirical evidence, Factor Analysis technique is being used successfully by different researches during the last three decades. In this study Factor Analysis has been applied over audited financial data of selected cement companies of India for a period of 10 years. Initially 44 variables (financial ratios) grouped in 7 categories are selected for the study. Before conducting Factor Analysis, variables having low inter-correlation with the other variables are excluded. Factor Analysis, conducted over remaining variables, identifies 8 underlying categories (factors). Multiple Regression Analysis is conducted taking the factor scores for each such factor as dependent variable and constituent variables as independent variables. Statically insignificant variables, evident from the regression analysis, are eliminated from the study. Factor Analysis, conducted again over thus remaining 25 variables, resulted in 8 underlying categories with a few changes in their composition. To validate the results of Factor Analysis, Cluster Analysis is performed. Factors are named and representative ratios are identified for each of them. [PUBLICATION ABSTRACT]

Headnote

Abstract

For saving considerable time and effort of the analyzers, it is necessary to select the most important financial ratios to be used for the financial analysis. To reduce the number of financial ratios and to find out the categories of financial ratios on the basis of empirical evidence, Factor Analysis technique is being used successfully by different researches during the last three decades. In this study Factor Analysis has been applied over audited financial data of selected cement companies of India for a period of 10 years. Initially 44 variables (financial ratios) grouped in 7 categories are selected for the study. Before conducting Factor Analysis, variables having low inter-correlation with the other variables are excluded. Factor Analysis, conducted over remaining variables, identifies 8 underlying categories (factors). Multiple Regression Analysis is conducted taking the factor scores for each such factor as dependent variable and constituent variables as independent variables. Statically insignificant variables, evident from the regression analysis, are eliminated from the study. Factor Analysis, conducted again over thus remaining 25 variables, resulted in 8 underlying categories with a few changes in their composition. To validate the results of Factor Analysis, Cluster Analysis is performed. Factors are named and representative ratios are identified for each of them.

Key words: Financial Ratio Analysis; Factor Analysis; Multiple Regression Analysis; Cluster Analysis.

Introduction

Financial ratio analysis is a useful measure to provide a snapshot of a firm's financial position (Muresan and Wolitzer 2004) at any particular moment of time or to provide a comprehensive idea about the financial performance of the company over a particular period of time. Use of financial ratios in finance is multi-dimensional. It is not only useful for judging the financial health or performance of a particular firm over time, it is also a useful tool for comparing a firm's financial position and performance with respect to others in the same or different industry to pinpoint problem areas or to identify areas of further improvements (De, Bandyopadhyay and Chakraborty 2010).

Financial ratios are computed from financial statements of a company namely Balance Sheet, Profit & Loss Account or Income Statement, and Cash Flow Analysis. Interpretation of the financial ratios is complicated and multi-dimensional. While developing and computing the different financial ratios, consideration is given to capture the various aspects of financial position and financial performance of a company. In order to use a financial ratio, one needs to have a relatively decent knowledge of basic mathematical and accounting concepts. Over the years, there has been a proliferation in the number of financial ratios developed and applied by analysts and researchers (Hamdi and Abdelrazzak 1994).

However, it is impractical and sometimes improbable to compute all the ratios to reach to a conclusion desired for. With the presence of inter-relationships within and among the sets of financial ratios, a smaller number of representative ratios may be sufficient to capture most of the desired information (Hamdi and Abdelrazzak 1994). This inter-relationship is called as 'multicollinearity' in statistical language. Using some statistical methods we can reduce this effect by finding out the factors (latent variables) inherent into the total set of financial ratios. The traditional ad hoc grouping of ratio such as Earnings & Profitability, Liquidity, Leverage and Solvency, Asset efficiency, Operating efficiency, etc. is based on assumed relationships rather than empirical foundations. The need to use Inductive approach i.e. classification based on statistical techniques (Öcal, Oral, Erdis and Vura 2007) has grown momentum over the years. Factor Analysis is the most popular amongst them. Once the Factor Analysis identifies the latent factors (i.e. categories) inherent into the total set of financial ratios, at least one ratio may be selected from each such category on the basis of some criteria. In this way, we can identify a smaller number of financial ratios to be used for financial analysis.

To get rid of the heterogeneous behavior of financial ratios, companies belonging to a single type of industry are chosen for the analysis. In this backdrop, the companies belonging to the cement, asbestos and abrasive producing industry of India is identified for the study. This industry is one of the most important and extensive industries of India. The cement industry in India has been moving from strength to strength, over the years, it has emerged as the world's second largest cement producing industry (April, 2009).

For the purpose of the study, a set of 44 of financial ratios categorized in 7 distinct categories was identified. These categories are Earnings and Profitability, Liquidity, Cash Flow, Cash Balance, Long-term Solvency, Assets Management, and Operating Efficiency. Since the objective of this study is to identify smaller number of financial ratios which are able to capture the desired information, the ratios which have weak inter-correlation (i.e. < ±0.5) are identified and excluded from the study. On the remaining financial ratios (variables) Factor Analysis is conducted. Factor Analysis is a statistical tool which identifies the latent variables (i.e. factors) inherent in the total set of observed variables. Each such factor comprises of different variables (financial ratios) which are most similar in terms of correlation with each other. In an attempt to reduce the effects of a (possibly) incorrect presence of variable in the factors, Multiple Regression Analysis is conducted taking the Factor Scores of different factors as dependant variables and the constituent variables in the respective factor as independent variables. Variables with low t-values (i.e. |t| 2) and the corresponding high p-values (i.e. p-values >0.05) are excluded. On the remaining set of variables, Factor Analysis is conducted once again. With an attempt to validate and improve the results of the Factor Analysis, another statistical method, Cluster Analysis, is conducted on the final set of variables. Cluster Analysis involves categorization by dividing a large group of observations into groups so that observations within each group are relatively similar. Proper determination of number of clusters is an important aspect of Cluster Analysis. However, the objective of Cluster Analysis here is to test the composition of categories (i.e. factors) as indentified by the Factor Analysis and to reach to a final conclusion.

Literature Review

Factor Analysis was first applied to financial ratios by Pinches, Mingo and Caruthers (1973) in an attempt to develop an empirically-based classification of financial ratios. Since then, researchers are using Factor Analysis as a mean of eliminating redundancy and reducing the number of financial ratios needed for empirical research. Hamdi and Charbaji (1994) applied Factor Analysis to 42 financial ratios of International Commercial Airlines for the year of 1986 to reduce them to underlying factors. Tan, Koh and Low (1997) used the Factor Analysis on 29 financial ratios of the companies listed on the Stock Exchange of Singapore (SES) from 1980 to 1991 to derive 8 underlying factors. Öcal, Oral, Ercan Erdis and Vural (2007) applied Factor Analysis on 25 financial ratios of Turkish construction industry during 1998 to 2001 to derive 5 underlying factors. De, Bandyopadhyay and Chakraborty (2010) made an empirical study on the 44 financial ratios of selected companies from Indian iron & steel industry and derived 10 underlying factors.

Application of Cluster Analysis on financial ratios is also not a new one. Few researchers have done it before. Wanga and Leeb (2008) applied a new clustering method based on a fuzzy relation between financial ratio sequences. They also conducted an empirical study on 24 financial ratios of four Taiwan shipping companies using Cluster Analysis. De, Bandyopadhyay and Chakraborty (2010) also validated the results derived from the Factor Analysis by the Cluster Analysis.

Objectives of the Study

This study is aimed at confirming or modifying the conventional as well as previous researchers' identified categorization of financial ratios with the help Factor Analysis as validated by the Cluster Analysis and reducing the number of financial ratios to a smaller number of representative financial ratios which can capture almost the same amount of information available in the original larger set of ratios. It may help to understand the financial position and perf

Variables Selection

For the purpose of this study, 44 most commonly used financial ratios were selected. These ratios were drawn from two main sources: Foster, G. (1986) and a monograph by Koh, H C, M H Lee, A M Low and T M Tan (1989). However, a few more ratios are added and a few are modified. These ratios are grouped into 7 categories to represent 7 different aspects of a business namely earnings and profitability, liquidity, cash flow, cash balance, long-term solvency, assets management and operating efficiency. The detail list of ratios along with their formula to compute them has been produced in the Appendix A. While conducting Factor Analysis, we had to exclude either of the LTDTCE (LS3) or NWTCE (LS4). These two variables, being complementary to each other (LTDTCE + NWTCE = 1), made the determinant value of the correlation matrix to zero with their simultaneous presence in the matrix. Therefore, we were left with the choice of excluding either of the two variables and we retained the Net Worth to Capital Employed (NWTCE) and eliminated Long-term Debt to Capital Employed (LTDTCE). Hence, the study is conducted on 43 financial ratios.

Sample Selection

This study is conducted on the selected companies of Indian Iron and Steel industry. Using CMIE Prowess 3.1 database software, a list of 224 companies which are registered under Indian Companies Act was derived first. Out of these 224 companies, a list of 74 companies was derived which were listed or permitted either in Bombay Stock Exchange (BSE) or National Stock Exchange (NSE) of India or both. Using the same database software, audited financial statements during the periods from 1999-2000 to 2008-2009 (i.e. 10 years) were collected. The companies which were not in operation during any of this 10 years period or where data were not available during any of these years were eliminated. 38 companies fulfilled all the criteria and were used for this study.

Statistical Methods

For the various statistical analysis required for this study, we have taken the help of statistical software, SPSS 16.0 version.

At first, inter-correlation matrix amongst the variables has been derived. An intercorrelation matrix is a k×k (k = the number of variables) array of the correlation coefficients of the variables with each other. With the help of this matrix, variables (financial ratios) with weak correlation (i.e. < ±0.5) with other variables are identified and excluded. However, elimination is effected only after exercising domain knowledge to ensure that no important variable (financial ratio) is excluded from the study.

After that, Factor Analysis with Principal Component extraction method is performed on the remaining set of variables. VARIMAX rotation is used to get better final results. Cut off value of factor loadings is kept more than 0.5. For the purpose of regression analysis, factor scores are saved as variables.

Statically, each such factor should be highly explained by the constituent variables of the same. In an attempt to reduce the effects of a (possibly) incorrect presence of variable in the factors, Multiple Regression Analysis is conducted taking the Factor Scores of different factors as dependant variables and the constituent variables in the respective factor as independent variables. Variables with low t-values (i.e. |t| 2) and the corresponding high p-values (i.e. pvalues >0.05) are eliminated on the basis of the regression results. On the remaining set of variables, Factor Analysis is conducted once again to identify the latent variables (or factors).

To validate the indentified categories (i.e factors) of variables ascertained by the Factor Analysis, Cluster Analysis is applied on the same set of variables and with the predefined number of clusters (same with the number of factors). To emphasize the degree of correlation amongst the variables as a measurement of similarity, hierarchical clustering approach using Ward's Method with the Pearson Correlation interval measure is applied here.

After the validation of the results of Factor Analysis is done, representative variables (financial ratios) are selected from each such factor so as to derive a smaller set of financial ratios than the original larger set of ratios.

Results and Implications

1.1 Correlation Study Results

With the help of inter-correlation matrix (43 X 43), 6 variables are excluded from the study because they had a very weak correlation (i.e. < ±0.5) with the other variables in the study. However, before elimination domain knowledge is exercised to ensure that no important variable (financial ratio) is excluded from the study. These variables are produced in Table 1 below:

1.2 Multiple Regression Analysis Results

Factor Analysis is conducted on remaining 37 variables (43 minus 6) and it is resulted in 8 factors. Multiple regression analysis is conducted taking the Factor Scores of different factors as dependant variables and the constituent variables in the respective factor as independent variables. It is found that R-square (coefficient of determination) for each such regression analysis is very high. It signifies the presence of strong regression relationship amongst the factors and their constituent variables. However, presence of variables with low t-value (i.e. < 2) and the corresponding high p-value (i.e. > 0.05) are found in different factors. These variables are considered to be incorrectly present in the respective factors and hence liable to be eliminated from the study. 12 variables are eliminated on this basis. Details of these variables along with tvalues and corresponding p-values are given in Table 2 below:

Results of the regression analysis (relevant portions only) have been given in the Appendix B.

1.3 Factor Analysis Results

Factor Analysis is conducted once again on the remaining 25 variables (37 minus 12). The Rotated Component Matrix is produced in the Appendix C. It is observed that 25 variables have been categorized in 8 factors. These factors account for about 89% of the total variance, which can be considered as excellent. Results of KMO and Bartlett's Test produced below in the Table 3:

KMO sample adequacy is more than 0.7, which can be considered as reasonably good (Öcal, Oral, Erdis and Vural 2007).

1.4 Cluster Analysis Results

Cluster Analysis has been performed on the same set of 25 variables on which Factor Analysis has been performed already. No of clusters is also pre-defined, which is 8 (i.e. the number of factors already ascertained). The results of Cluster Analysis are produced in the Appendix D.

1.5 Comparison of the results of Factor Analysis and Cluster Analysis

Final results of Factor Analysis and Cluster Analysis have been arranged in a manner so that comparison is possible against each other. This comparison is produced in Table 4 below:

Clusters are plotted against the identical or most identical (on the basis of constituent variables) factors. After a careful study on Table 4, it is observed that Factor 2, Factor 4, Factor 5, Factor 7 and Factor 8 are same with their corresponding clusters i.e. Cluster 5, Cluster 8, Cluster 3, Cluster 2 and Cluster 4. Factor 1 and Cluster 1 are almost identical excepting the presence of CF3_CPTSHF in the Cluster 1. Presence of variable CF3_CPTSHF (Cash Profit to Share-holders' Fund) is a mismatch in Factor 6, which is evident from the corresponding cluster (i.e. Cluster 6). CF3_CPTSHF is best suited in Factor 1 which is confirmed by its corresponding cluster (i.e. Cluster 1). Only two variables namely LS6_NFATCE and LS8_TDTTA are making the difference in the remaining 2 factors (i.e. Factor 3 and Factor 8) with their corresponding clusters (i.e. Cluster 7 and Cluster 6). These deviations are not significantly challenging the outcome of the Factor Analysis, rather the outcome it is improved and validated by the cluster analysis results. Therefore, we can accept the 8 factors as validated by the Cluster Analysis.

1.6 Naming the Factors

Factors names have been given considering the variables (financial ratios) featuring in each of them as well as in the corresponding clusters. Care is taken so that constituent variables in a particular factor as well as corresponding cluster are best represented by the factor name. This is provided in the Table 5 below:

1.7 Selection of Representative Variables (Financial Ratios)

Selection of representative variable from each factor should be based upon some appropriate criteria as well as their relative importance in the same group (here, factor) of variables. Variables having maximum factor loadings (absolute value) in the respective factors should have the strongest correlation with their respective factors. Factor loadings are the correlation of individual variables with its factor. Therefore, 10 representative variables (financial ratios) can be selected from the 10 finally concluded factors on the basis of maximum absolute value of the factor loadings on the respective factors. This approach has been adopted in the previous research studies also (for example, Tan, Koh and Low 1997). Care has been taken to somehow ensure that these selected variables should be able to reasonably explain the behavior of other variables in the same factor. In our study, representative ratios have been selected on the basis of maximum absolute value of factor loadings as well as their relative importance in the same factor. 7 out of 8 representative variables selected on the basis of maximum absolute factor loadings because these variables are able to represent their respective factors. In case of Factor 6 only, the representative variable is selected on the basis of domain knowledge because the selection on the basis of absolute value of factor loadings is unable to represent the factor. However, this selection is influenced by the corresponding cluster (i.e Cluster 6) composition as well. List of representative financial ratios have been produced in Table 6.

Conclusion

The initial objective of the study was to identify the underlying categories present amongst the financial ratios so as to confirm or modify the conventional categorization of financial ratios. Another objective of this study was to reduce the number of financial ratios to a smaller number of financial ratios which can capture almost the same amount of desired information as the original larger set of ratios could do. We started the study with 44 financial ratios of 130 India Iron and Steel companies for a period of 10 years grouped in 7 conventional categories. However, with the help of a series of statistical analysis, we could reach to a final conclusion which speaks about the presence of 8 underlying categories. A comparison can be made between the categories of financial ratios used in the study and categories appeared in the final results. It is shown in Table 7.

It is found that only two original categories (Liquidity, Cash Balance) of financial ratios held their place in the final results, though Liquidity is renamed as "Short-term Liquidity" because composition of this category indicates towards short-term solvency of a firm. "Longterm Solvency" has though held its place, but it has sacrificed a few of its constituent ratios to a new category i.e. "Capital Structure". "Profitability & Return on Investment" and "Dividend Policy" have emerged out of the 1st (Earnings and Profitability) and 3rd (Cash Flow) original categories. 6th (Assets Management) and 7th (Operating Efficiency) original categories together have given birth to new category of "Asset & Material Management", however in this process they have lost a few of their constituent variables. The last new category i.e. "Productivity of Working Capital" has emerged out taking one variable each from the original categories of "Assets Management" and "Cash Flow". The last i.e. 7th original category "Operating Efficiency" has lost its place in the final results after given one of its constituent variables to the new category of "Asset & Material Management".

Once the eight underlying categories are identified, at least one variable (financial ratio) is selected from each such category to represent eight different aspects of a business. Therefore, it can be concluded that while analyzing the performance and financial position of the companies of the cement industry of India with the help of financial ratio analysis, proper emphasis may be given to these eight financial ratios as indentified in this study. Considerable time and effort of the analyzers would be saved in this process.

However, it is to be noted that this study is industry as well as country specific and to some extent time specific. So, there is a huge research scope ahead for the future researchers across the globe.

References

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Appendix

(ProQuest: Appendix omitted.)