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J. Service Science & Management, 2010, 3, 309-335 doi:10.4236/jssm.2010.33038 Published Online September 2010 (http://www.SciRP.org/journal/jssm) Copyright © 2010 SciRes. JSSM 309 A Statistical Analysis to Predict Financial Distress Nicolas Emanuel Monti, Roberto Mariano Garcia Department of Industrial Engineering, Instituto Tecnológico de Buenos Aires (ITBA), Buenos Aires, Argentina. Email: montinicolas@gmail.com, rmgarcia@fibertel.com.ar Received June11th, 2010; revised July 17th, 2010; accepted August 20th, 2010. ABSTRACT The aim of this study is to apply the statistical inference to identify if a firm is likely to become financially distressed in the short term. To do this, we decided to collect data from the firms’ financial statements. The analyses performed were based on a group of 45 financial ratios observed from a sample of 86 firms operating in Argentina. First, we used the principal component analysis to turn the information in the 45 original ratios into two new global variables named as ∆Risk and ∆Return. In this way, we can easily represent and compare in a graph the firms’ risk and return variations. By the computation of these new variables it is possible to quickly financially categorize a certain firm based on the risk the company has with regard to the nature of its business and the risk involved in the amount of debt it has taken in comparison to the profits that were generated during the last two fiscal years. Second, we performed a logistic regres- sion analysis to estimate the probability that a firm becomes financially distressed in the short term. The model finally selected managed to successfully identify 85% of the companies from the sample and it explains 65% of the total sample variability. The model is represented by the following variables: 1) Current Debt Ratio, 2) Total Cost of Debt, 3) Oper- ating Profit Margin, and 4) ∆ROE. The outcomes from this study are two tools that were developed based on the statis- tical inference from which we can quickly asses the financial status of a firm based on its risks and return’s variation as well as to estimate the probability that a firm becomes financially distressed in the short term. There are different ways of taking these tools into practice such as: 1) to control and follow up the financial performance of a company, 2) to support the decision of lending money to a company, 3) to support the decision of investing money or the decision of merging with a company, 4) to support market analysis from a financial perspective, and 5) to support actions or deci- sions related to the financial assessment of a company that declares itself to be financially distressed. Keywords: Financial Distress, Financial Risk, Principal Component Analysis, Logistic Regression Analysis 1. Introduction The objective of this study is to identify those companies that have financial problems based on the information contained on their financial statements. With this regard, it is considered that a company has financial problems when it has a high probability of becoming financially distressed in the short term. To do this, we applied the statistical inference to a group of 45 financial ratios ob- served from a sample of 86 firms operating in Argentina. In previous similar studies, as for example those pro- posed by Guzmán [1], Heine [2], De la Torre Martínez [3] or Kahl [4], it was suggested as an objective to find that financial ratio that could better identify a company with financial problems or to find that statistical model that could better predict if a company is financially distressed based on the discriminant analysis. Although all these approaches might be efficient to identify which aspects of a company we should focus on when trying to asses its financial situation, their statistical outcomes would typi- cally not be able to provide a good overview of the firms’ overall performance as they are based on just a few vari- ables. This means that with the current statistical models it would be possible to recognize when a company is financially unhealthy but it would be difficult to identify under what circumstances a firm reached that status or even to compare how critical its financial situation is in comparison to other business units or companies within the same industry. Moreover, most of the statistical stud- ies in the current literature do not take into consideration the variation of the firms’ financial ratios through the last fiscal periods. Instead they provide a financial diagnosis based on the most recent snapshot of the firms’ situation, which might result in wrong decisions being made. In an attempt to provide a financial study that can cover the issues previously discussed, we decided to A Statistical Analysis to Predict Financial Distress 310 combine two statistical analyses with the aim of devel- oping a set of tools that will provide a comprehensive and accurate financial diagnosis of a firm that can be used to take decisions within different business scenarios such as investments analysis, credits offering, and finan- cial management, among others. In this way, we first used the principal component analysis to turn all the data initially collected into two new variables. With this analysis we can obtain a financial overview of a certain firm and we can represent and compare its financial situation based on the risk the company has with regard to the nature of its business and the risk involved in the amount of debt it has taken in comparison to the profits that were generated during the last two fiscal years. Sec- ond, we used the logistics regression analysis to precisely determine when a firm has financial problems and to identify those ratios that have a higher influene on its financial condition. The rest of this paper is organized as follows. In Sec- tion 2, we present the sample design by defining its size and composition as well as the criteria used to collect all the data from the firms’ financial statements. In Section 3, we define the group of 45 financial ratios that were computed for each company in the sample. In Section 4, the principal component analysis is performed to turn the information contained in the 45 original ratios into a small group of 2 new variables named as ∆Risk and ∆Return. In Section 5, we developed different logistic regression models to estimate the probability that a firm becomes financially distressed in the short term. In Sec- tion 6, the tools developed from the principal component and the logistic regression analyses are applied to a new sample. The objective in this case is to evaluate the joint effectiveness of these tools to recognize those companies with financial problems. Finally, the conclusions of the present study together with its possible uses are described in Section 7. 2. Sample Design A very important aspect in this kind of statistical research is the sample design from which the statistical models will be developed. For example, if we consider a sample of companies that belong to the construction sector then the resulting statistical model can only be applied to companies of that sector. Also, if the sample is composed by 90% of companies that did not have any financial problems and only 10% of companies that were finan- cially distressed then the capacity of any resulting statis- tical model to discriminate companies with financial problems will not be significant. Because of these rea- sons, below we comment all the criteria considered to design the sample which will determine the scope of the analysis. The sample is composed by 86 firms that operate in Argentina, from which 43 did not have any financial problems (group 1) and the other 43 were financially dis- tressed during the period under analysis (group 2). See Appendix 1 for a complete sample description. All the information considered in the present study was obtained from the financial statements of each com- pany. In the case of those companies that did not have any financial problem, the financial statements were ob- tained from the Bolsa de Comercio de Buenos Aires (BCBA). For those companies that had financial prob- lems, the financial statements were obtained from the official reports made by the corresponding receivers that are published by the Cámara Nacional de Apelaciones en lo Comercial. Different authors from statistical books consider valid to collect at least information from 5 observations for each variable that is included in the statistical model. William Beaver [5] and Edward Altman [6] carried out similar statistical analysis working with a sample of 120 and 60 companies, respectively. In both cases, significant results were obtained and they both considered different models with no more than 5 variables. Therefore, based on these results and considering that in the present study we will not develop any model with more than 5 vari- ables, we can state that a sample of 86 firms is big enough to carry out any statistical analysis. With regard to the proportion of companies in the sample with and without financial problems, it is not strictly necessary to consider the same amount of obser- vations for each of these groups. However, this is rec- ommended to obtain a better representation of the mean and the deviation of the variables observed in each group. To better understand this issue, we can consider the ex- treme case of a sample with 1 company that did not have any financial problems and 99 companies that were fi- nancially distressed. Based on this sample, when it comes the moment to estimate the probability that a firm be- comes financially distressed it is reasonable to think that the corresponding model will have a clear tendency to classify any company as if it is going to have financial problems in the near future. This is because the sample, while not being representative from the population, does not “reveal” the different ways in which a company with- out financial problems can be found. In other words, the sample contains very little information about the behav- ior of the variables observed in companies without finan- cial problems, and therefore, it is more difficult for the model to recognize companies from this group. Another important aspect to consider is the period of time from which the information in the financial state- ments is collected, especially in the case of those compa- nies that had financial problems. With this regard, the Copyright © 2010 SciRes. JSSM A Statistical Analysis to Predict Financial Distress 311 sample considered in the present study includes informa- tion from companies that operated during the years 2003, 2004, and 2005. It is important to notice that if this period is too long, for example more than 10 years, then we would run the risk of mixing the financial information from companies that operated in different macroeconomic contexts. If that is the case, then the interpretation of any financial information should be done individually even for companies that operated in the same sector. In countries that have a stable economy, this effect would not introduce a high distortion in the data collected. However, this is not the case of Argentina. In addition, we should notice that it was decided not to include any financial information from companies that had financial problems during the years 2001 and 2002 because during that period there was an economic crisis that affected the normal operations of companies. In this way, we avoid to include in the present analysis any atypical variations that are not the object of study and that could bring distortions into the analysis. We should notice that only for a few companies we decided to consider the financial information from 2002 to be able to compute the variation of some financial ratios over two consecutive periods. In any case, the effect of introducing this information in the study is not significant because in 2002 the amount of companies that had financial problems was significantly lower in comparison to 2001 when the economic crisis was originated (see Figure 1). In the case of those companies that had financial prob- lems, the required information for the statistical analysis was obtained from the financial statements that correspond to the period during which each company was financially distressed and from the previous period. In this way, we can include in the analysis the evolution of some financial ratios from one period to another. In the case of those companies that did not have any financial problems, the required information was obtained from the financial statements of two consecutive periods, always within the period under analysis of the present study. 0 2,000 4,000 6,000 8,000 10,000 12,000 14,000 2000 2001 2002 2003 2004 2005 Nr. Firms Financially Distressed Figure 1. Yearly number of firms financially distressed in Argentina. In similar researches, it was decided to include in the statistical analyses financial information until five peri- ods before the companies were financially distressed. However, these studies analyzed the information from each period separately instead of including in one sample some variables that reflect the evolution of the ratios over two or more periods. The methodology used in these analyses consisted in using the financial information from previous periods as a separate sample to test the discrimination power of a certain statistical model. This model was developed through a group of financial ratios that correspond to the most recent period during which each company was financially distressed. As expected, the results obtained show that as long as the financial information in a sample was more far away in time from the period in which the company was financially dis- tressed then the capacity of the model to distinguish be- tween companies with and without financial problems was diminishing. Therefore, it can be concluded that it is not relevant to include in the analyses financial informa- tion from many periods before the companies become financially distressed. This is because by that time com- panies might show a good financial performance and if this information is taken into account then it will reduce the capacity of the model to distinguish those companies with financial problems. In this sense, it seems more reasonable to focus our attention on the information from those periods where the characteristics of the financial problems become evident in a company, i.e. some years before they become financially distressed. The companies included in the sample belong to dif- ferent economic sectors such as industry, commerce, agriculture, and services. The main reason of this choice is to develop a broad statistical model that can be applied in different type of companies. The financial theory states that it is not convenient to directly compare the financial ratios from two companies that belong to different economic sectors. This is because the economic dynamics in these sectors might differ sub- stantially. For example, a financially healthy company that operates in a certain sector can show a liquidity ratio of 2 while other company that performs a different type of activity can have the same value of this financial ratio and be in financial problems. Therefore, from this per- spective it seems not reasonable to include in the sample companies that perform different economic activities. This is because the sample could contain misleading in- formation with regard to those characteristics that allow identifying a company with financial problems, i.e. the relation between the financial ratios and the financial distressed could be distorted. However, we should con- sider that we are performing a multivariate analysis, and therefore, the characteristics that are observed in each Copyright © 2010 SciRes. JSSM A Statistical Analysis to Predict Financial Distress 312 individual are compared in a simultaneous and global way. In this way, it is more difficult that the particular behavior of certain ratios in some economic sectors af- fect the global profile of a company. Nevertheless, there are two precautions that can be implemented in order to diminish the effect that some characteristics inherit to each economic sector have in the identification of com- panies with financial problems. The first precaution con- sists of including in both groups of the sample companies from the same economic sectors. The second precaution consists of having the same amount of companies from each economic sector in both sample groups. Although the second precaution was not implemented for all the economic sectors because of the difficulties to find available financial data, the sample was design to keep the highest balance possible in both groups. William Beaver [5] designed a paired sample based on companies that operated in different economic sectors. In that sample, for every company that had financial prob- lems there was another financially healthy company from the same economic sector, and whenever it was possible, with the same size. With this regard, we should notice that the size of a company was measured through its total assets. In this way, Beaver performed a univariate statis- tical analysis, i.e. that the financial ratios of each com- pany were compared once at a time and that the distinc- tion of those companies with financial problems was made through a single ratio with a cut-off value. In his research, Beaver suggested doing a paired analysis with the objective of quantifying the effect that the economic sectors and the size of the companies have in the identification of those companies financially dis- tressed. In this way, for each pair of companies from the same economic sector and with similar sizes the differ- ence of each financial ratio was computed. Afterwards, these differences were evaluated to determine if there was sufficient statistical evidence that allowed the identi- fication of companies with financial problems. We should notice that because each difference of the financial ratios was determined based on companies from the same eco- nomic sector and with similar sizes, the effects of these factors in the sample were mitigated. In addition, it is important to mention that these differences were only computed to quantify the impact that the economic sec- tors and the size of the companies have on the identifica- tion of those companies with financial problems. How- ever, to classify each firm in one of the two groups a limit value from a single financial ratio was considered. This limit value was computed through a direct com- parison of the financial ratios, i.e. no differences between the financial ratios were considered. The reason of this is that it is not possible to get any conclusions from a single individual through a paired analysis because always two companies are compared at the same time. Once the paired analysis is performed, the capacity of each financial ratio to identify those companies with fi- nancial problems can be compared to those capacities that are obtained from a statistical analysis based on a global comparison of the companies. With this regard, one would expect these results to be similar as long as the effect of the economic sectors and the size of the companies were negligible. In fact, the findings from Beaver’s research support this statement. Therefore, everything seems to indicate that using a paired sample is the best approach to mitigate the possible effects from the economic sectors and the size of the companies. However, we must take into account that the research made by Beaver was based on a univariate statistical analysis, and therefore, each financial ratio was com- pared once at a time. This means that the effects of these factors when multiple financial ratios are compared at the same time were not evaluated. In this sense, we expect that by simultaneously comparing multiple financial ra- tios the effects of the economic sectors and the size of the companies should also be mitigated. Therefore, we can conclude that it is not strictly necessary to have a paired sample to continue with our study although keeping a certain balance in the sample can help to diminish the undesired effects of the economic sectors and the size of the companies. Another precaution that has been considered in the present study to facilitate the identification of companies with financial problems in different economic sectors is the incorporation of a variable that measures the per- formance of a given company in comparison to the aver- age performance of the sector. More details about the variables considered can be found in the following sec- tion. Finally, another important aspect to be considered in the sample design is the size of the companies. This as- pect has already been mentioned when referring to Bea- ver’s research. With this regard, the sample was designed not to include companies with high assets value, i.e. all the companies included in the statistical analysis have assets lower than 500 [Million $AR]. The reason of this is that there are just a few cases where big companies suffered financial problems, and therefore, it is reason- able to think that these firms belong to a different statis- tical population. With this regard, Alexander Sydney [7] suggests that there is theoretical evidence as well as em- pirical facts that demonstrate that the return rate of a company becomes more stable as the size of its assets increases. This could imply that a firm with a high assets value would have a lower risk of becoming financially distressed in comparison to a middle size or small com- pany even when they both show the same financial ratios Copyright © 2010 SciRes. JSSM A Statistical Analysis to Predict Financial Distress 313 values. As a result of this, we could first think that it is not convenient to compare the financial ratios of two companies that differ significantly in its size. Therefore, considering that a consistent statistical analysis requires that all the sample observations come from the same population, we have decided to include companies within a similar range of the assets value in the two sample groups considered. Nevertheless, it is not desirable to have a perfect homogeneity in the sample with regard to the size of the firms because this would decrease the ability of the model to identify those companies with financial problems. 3. Variables Considered The selection of the variables that afterwards are going to be used to carry out the statistical analysis is a very im- portant stage of this study. The reason of this is that at this moment we should take into account all those as- pects from the companies that we think they could have some relationship with the fact that these firms become financially distressed. In this sense, the selections of the variables together with the sample design define the scope and the applicability of this research. To select the variables considered in this study the following criteria was considered: 1) popularity of some ratios in the finan- cial literature and 2) the performance of some financial ratios in similar statistical analysis. The statistical analyses presented in the following sec- tions consider a total of 45 variables. The values of each of these ratios were computed for every firm included in the sample based on the criterias described in the previ- ous section. In Appendix 2, we present a list with all the formulas describing each ratio. In order to have a better representation of the selected ratios, we have decided to group them based on the following categories: 1) Liquid- ity Ratios, 2) Operating Efficiency Ratios, 3) Business Risk Ratios, 4) Financial Risk Ratios, 5) Return Ratios, and 6) Growth Ratios. It should be noted, that we have included a new financial ratio named Benchmarked Re- turn, with the aim of having a measurement that com- pares the return of each company against the average return of the sector that represents that company. In Ap- pendix 3, we provide the average return considered for each sector that was used to calculate this new ratio. We should notice that in this particular study we have considered a high number of explanatory variables in order to obtain a comprehensive data base that allow us to develop and compare multiple regression models. More- over, because we are implementing a principal compo- nent analysis there is no need to reduce the number of variables considered in the study, especially if many of them are correlated. 4. Principal Component Analysis In this section, we present the results obtained after ap- plying the principal component analysis to the data col- lected in the sample. To compute the principal compo- nents we followed the procedures proposed by Peña [8] and Johnson [9]. After calculating the eigenvalues from the covariance matrix C, we can see that the first two eigenvalues stand for 93% of the total variance (see Appendix 4). Because of this reason, it was decided to work with the first two principal components F1 and F2 to represent the sample data. We should notice that these results are significant considering that we managed to reduce the space of rep- resentation of the data set from 45 variables to a two di- mensional space. To represent each of the companies from the sample in a unique graph, we calculated the values that each of the principal components take for each firm (see Appendix 5). To do this, we first determined the eigenvectors ma- trix V. The results obtained are shown in Figure 2. We have represented in blue color those firms corresponding to group 1 (without financial problems) and in red color those firms from group 2 (with financial problems). This representation excludes two outliers, i.e. observations with particular characteristics that deviate from the rest of the sample. We have decided not to consider these outliers to avoid that the scale of the graph is set in such a way that the rest of the companies cannot be distin- guished. Although it seems that there is not a clear distinction between the two groups, the firms from group 2 tend to have higher values of the principal component F2 in comparison to the firms of group 1. In addition, we can observe a great concentration of companies with a similar negative value of the component F1 as well as some spread observations from both groups that present higher Figure 2. Representation of the firms based on the principal component values without considering the outliers. Copyright © 2010 SciRes. JSSM A Statistical Analysis to Predict Financial Distress 314 values of this component. To continue with the principal component analysis, the correlation between the original 45 variables and the se- lected principal components were computed. The results obtained indicate that the principal com- ponent F1 has a high positive correlation with the fol- lowing variables: X14 – Operating Leverage, X41 – ΔDebt Coverage, and X42 – ΔOperating Profit Margin. This suggests that F1 reflects two types of risks: 1) the risk that a company has based on how much money it has generated to cover its debt, and 2) the risk of the com- pany’s business based on the impact that the sales varia- tions have on the company’s profits. Therefore, we have decided to name this principal component as ΔRisk. A high value of F1 can be caused by: 1) a high operat- ing leverage, 2) an improvement of the debt coverage, 3) an improvement of the operating profit margin, or 4) a combination of all these alternatives. Nevertheless, we should keep in mind that based on the eigenvectors ma- trix the variable X14 – Operating Leverage is the one with a higher influence over F1. In this way, we can conclude that those companies that have high values of this prin- cipal component will most probably present a high lev- erage supported by an improvement of the debt coverage and the operating profit margin. With this regard, if we have a look at Figure 3 we can see that those firms that present high values of F1 with a value of F2 similar to the sample average show the characteristics previously men- tioned. In addition, we should consider those firms that present a high value of F1 together with a high value of F2. In these cases, we could verify that the corresponding companies present a strong decrease in the debt coverage as well as the operating profit margin. Consequently, the high value of F1 is exclusively due to a high value of the operating leverage. To summarize the analysis so far, we can state that the firms with a high ΔRisk (F1) only show an improvement of the debt coverage and the operating profit margin Figure 3. Categorization of the firms based on the values of F1 – ΔRisk. when they have a value of F2 similar or lower to the sample average. In addition, those companies that have high values of both principal components show a high variation of their operations together with a decrease in the debt coverage and the operating profit margin. Therefore, we would expect that a firm with financial problems would show the latter characteristics although these are not sufficient conditions to classify a firm as financially distressed. This means that a company with a negative value of the ΔRisk (F1) does not necessarily need to have financial problems. In other words, those companies that have higher risks in combination with good profits can be considered as financially healthy while those companies that have higher risks but show poor profits will most probable have financial problems in the short term. In Figure 3, we represent how the firms included in the sample can be differentiated based on the values of F1. The yellow bandwidth includes a big amount of compa- nies with a low value of the operative variation while the green bandwidth corresponds to a few companies with a high value of the operative variation. Considering that firms from groups 1 and 2 show low and high values of F1, it is difficult to distinguish those companies with fi- nancial problems by only having a look at this principal component. However, if we combine this information together with the analysis of F2 then we will find out that it is possible to recognize certain characteristics from the companies based on the principal components represen- tation. If we now consider the principal component F2, we see that it has a high negative correlation with the following variables: X33 – ΔNet Income, X43 – ΔNet Profit Margin, and X45 – ΔROA (see Appendix 6). In this way, we can conclude that this component is mainly reflecting two aspects: 1) the changes in the ability of a firm to generate revenues, and 2) the changes in the efficiency of a firm to generate revenues. This is the reason why it was decided to name the component F2 as ΔReturn. A high value of F2 can be caused by: 1) a decrease of the net income, 2) a decrease of the net profit margin, 3) a decrease of the return on assets, 4) a combination of all these alternatives. This means that those companies with a high value of this component would most probably show a deterioration of their return. In fact, if we have a look at Figure 2 we can see that most of the firms with a high value of F2 belong to group 2, i.e. that these compa- nies have had financial problems. In addition, we can see from Figure 2 a small number of firms that show a low value of F2 although they belong to group 2 as well. Therefore, in these cases we could conclude that the cor- responding companies are actually recovering from their financial problems by showing an improvement of their Copyright © 2010 SciRes. JSSM A Statistical Analysis to Predict Financial Distress 315 returns. In Figure 4, we represent how the firms included in the sample can be differentiated based on the values of F2. The red bandwidth includes those companies that have shown a high deterioration of their returns while the green bandwidth corresponds to those firms that have shown an improvement in their returns. In addition, we have defined a yellow bandwidth that corresponds to those companies that show a similar value of their ΔReturn that approximates to the sample average. After performing an analysis of each principal com- ponent, we can now combine all the information obtained to define different clusters that can help us to identify the status of a certain firm with regard to its ΔRisk and ΔReturn. This classification of the sample is represented in Figure 5 together with a description of the type of evolution that a company belonging to a certain sector has suffered. Figure 4. Categorization of the firms based on the values of F2 – ΔReturn. Figure 5. Categorization of the firms based on the principal components. We would expect those firms with a higher disposition to have financial problems in the short term to fall into sectors 1 or 2. The sector 1 corresponds to firms showing a significant deterioration on their returns while sector 2 represents companies showing higher risks in combina- tion with a deterioration of their returns. In a similar way, we would expect those firms with a low disposition to have financial problems in the short term to fall into sec- tors 5 or 6. The sector 5 corresponds to those companies that show signs of stability, low risk and return im- provement. In a similar way, the sector 6 is represented by companies that show a significant return increase in combination with higher risks. In the case of sectors 3 and 4 it is not possible to link them to any of the groups considered, i.e. that for those companies falling into these sectors we are not able to make any conclusions with regard to their disposition of having financial problems in the near future. We could say that these companies have a financial situation similar to the sample average. However, we should keep in mind that those companies within sector 4 have higher risks in comparison to those firms from sector 3. To summarize, we have seen that the results obtained after performing the principal component analysis indi- cate that this technique has been very useful to achieve a better representation of the firms, especially considering the power of synthesis that it brings by compiling the information contained in the 45 original variables into only 2 new components. By the computation of these new variables it is possible to quickly financially catego- rize a certain firm based on the risk the company has with regard to the nature of its business and the risk in- volved in the amount of debt it has taken in comparison to the profits that were generated during the last two fis- cal years. In this way, depending on the sector to which a company belongs to it is possible—in some cases—to make an inference with regard to the disposition of this firm to have financial problems in the short term. In the next section, we will perform a logistics regression ana- lysis to develop a statistical model that allows us to esti- mate the probability that a firm becomes financially dis- tressed in the short term. In this way, we will be able to compute a new quantitative measure that will help us to identify those firms with financial problems. 5. Logistics Regression Analysis Because the principal components F1 – ΔRisk and F2 – ΔReturn have been useful to represent the firms from the sample and because they hold 93% of the total variance from the 45 original variables included in the analysis, it would be reasonable to use these components to build a logistics regression model. To do this we followed the procedures proposed by Hosmer and Lemeshow [10]. In Copyright © 2010 SciRes. JSSM A Statistical Analysis to Predict Financial Distress 316 this way, this model would allow us to estimate the proba- bility that a firm becomes financially distressed in the short term, which in the end could be used as a quantita- tive measure to help us to identify those companies with financial problems. However, the results obtained from the model validation based on the coefficients of deter- mination indicate that the model only explains a small percentage (31.87%) of the behavior of the dependant variable we are trying to estimate: Y – Financial Distress (Y = 1 if the firm IS financially distressed, Y = 0 if the firm is NOT financially distressed). Therefore, we de- cided to further investigate if it is possible to find a re- gression model that can better adjust to the data collected. If we keep in mind that the principal components are actually a linear combination of the 45 ratios considered in this study, we could then make the following question: What would happen if we develop a regression model only with those ratios that are representative of each prin- cipal component? The reason of this question is that the variance of each principal component can be negatively affected by the values of some ratios that are not useful to identify those firms with financial problems. This does not mean that the regression model based on the principal components is useless but it brings the opportunity of finding a new model that better explains the behavior of the firms in the sample. To answer our question, we decided to build a new re- gression model based only on those ratios that have a me- dium or high correlation with the principal component F2 – ΔReturn. In this case, the result obtained from the model validation indicates that this group of ratios can explain 35.63% of the variance of the dependant variable Y – Financial Distress. In this way, we verified the idea that the new model is more efficient to identify those firms with financial problems in comparison to the prin- cipal components model. This is because we can obtain similar results but with much more less information. Therefore, following this reasoning, we can state that al- though the principal components analysis has been useful to represent companies with different financial profiles it is not effective to use these results in a regression model. In fact, we have demonstrated that with a few ratios we can develop a model that manages to identify a similar percentage as the model based on the principal compo- nents, which contains data collected from all the 45 ratios. To summarize, we have demonstrated that in this par- ticular study it is difficult to combine the principal com- ponent and the logistic regression analyses. This situation brings us a new problem. It might be the case that there are some ratios that are effective to estimate the prob- ability that a firm becomes financially distressed in the short term but that they have a low correlation with the principal components. To solve this problem, it was de- cided to carry out a global analysis that contemplates the 45 financial ratios included in this study. It is clear that if we consider all the possible combina- tions that can be obtained based on the 45 ratios to de- velop a regression model with no more than 5 variables then it would be very hard to evaluate and compare all these alternatives by trial and error. Because of this rea- son, we decided to implement a methodology that allows us to reduce the number of models to be compared. This methodology consists in focusing our attention on the first 22 ratios with the highest coefficient of determina- tion based on a regression model with a single inde- pendent variable. In this way, the objective is to develop different models only with those variables that by them- selves are more effective to identify those firms with financial problems. It is important to keep in mind that this methodology does not guarantee an optimal solution. This is due to the fact that a certain ratio can show a low R2 in a regression model with a single independent vari- able but when it is combined with other ratios then the information that brings to identify those firms with fi- nancial problems can be much higher. Nevertheless, the methodology implemented is still a valid procedure to find a near optimal solution especially if we consider the high amount of ratios included in the analysis and that many of these variables are correlated. In Table 1, we present the ranking of the coefficients of determination. From these results, we can see that those variables that had a higher correlation with the prin- cipal components are spread all over the ranking. How- ever, we should notice that most of the ratios that are cor- related with the component F2 have a R2 higher than 0.1. This could be explained by the fact that the parameter value from the component F2 in the regression model is higher than the component F1. In addition, it is important to mention that most of the ratios that can better individu- ally explain the behavior of the firms are related to prof- itability and return aspects. Based on the first 22 ratios shown in Table 1, a total of 57 regression models were tested (see Appendix 7). We should notice that we have not included the outliers identified in the principal component analysis when de- veloping any of these logistics regression models. We limited each model to 5 independent variables at most. In addition, the ratios were first grouped based on their cor- relations to avoid including in the same model more than one ratio that brings the same type of information. For example, it is not reasonable to include in the same re- gression model only ratios related to liquidity aspects given that we would miss some important financial in- formation from the companies related to aspects such as operational performance, debt, profit, and growth. The models tested were compared based on the value Copyright © 2010 SciRes. JSSM A Statistical Analysis to Predict Financial Distress Copyright © 2010 SciRes. JSSM 317 Table 1. Ranking of the coefficients of determination for a regression model based on a single financial ratio. Independent Variable R2 Independent Variable R2 X29. ROA 0.3687 X40. ∆Debt Turnover 0.0596 X27. Return on Capital Employed (ROCE) 0.3116 X11. Current Assets Turnover 0.0429 X25. ROE 0.3088 X8. Average Inventory Processing Period 0.0378 X44. ∆ROE 0.2505 X35. ∆Fixed Assets Ratio 0.0369 X24. Net Profit Margin 0.2386 X36. ∆Working Capital 0.0335 X43. ∆Net Profit Margin 0.2326 X6. Average Receivables Collection Period 0.0334 X26. Benchmarked Return 0.2258 X42. ∆Operating Profit Margin 0.0332 X16. Current Debt Ratio 0.2242 X14. Operating Leverage 0.0233 X15. Total Debt Ratio 0.2236 X10. Total Assets Turnover 0.0226 X23. Operating Profit Margin 0.1977 X38. ∆Total Assets Turnover 0.0198 X45. ∆ROA 0.1894 X18. Non-Current Debt Ratio 0.0127 X19. Equity to Debt Ratio 0.1885 X22. Gross Profit Margin 0.0102 X32. ∆Assets 0.1762 X7. Payables Payment Period 0.0101 X2. Working Capital Ratio 0.1672 X12. Fixed Assets Turnover 0.0093 X33. ∆Net Income 0.1642 X37. ∆Current Ratio 0.0056 X3. Current Ratio 0.1627 X1. Fixed Assets Ratio 0.0053 X20. Debt Coverage 0.1502 X41. ∆Debt Coverage 0.0053 X5. Cash Ratio 0.1464 X31. ∆Sales 0.0038 X21. Total Cost of Debt 0.1110 X9. Cash Conversion Cycle 0.0037 X39. ∆Total Debt Ratio 0.1037 X28. Operating Return on Capital Employed 0.0028 X30. Operating Profit on Assets 0.1026 X13. Equity Turnover 0.0008 X17. Debt Turnover 0.1003 X4. Quick Ratio 0.0003 X34. ∆Liabilities 0.0003 of the different coefficients of determination. We should notice that usually when some liquidity ratio was in- cluded in a certain model then the corresponding esti- mated parameter was not coherent with the expected be- havior of that variable. In other words, we found out that in many of these models a higher liquidity implied a higher probability of the firm becoming financially dis- tressed, which is not coherent with the observed behavior of this variable. This is the reason why some models had to be ignored even when they presented high values for the coefficient of determination. In Table 2 we present the ratios that belong to the re- gression model selected as the output for this analysis. This model was mainly selected based on the value of the coefficient of determination but also based on the coher- ence of the estimated parameters with the expected be- havior of each variable as well as the author’s judgment with regard to the relevance of the different ratios con- sidered. To develop this model, we estimated the correspond- ing parameters through three different methods: 1) least squares, 2) weighted least squares, and 3) maximum like- lihood. The results obtained are summarized in Table 3. Table 2. Variables included in the regression model se- lected. Symbol Name Type of Variable X16 Current Debt Ratio Independent and Continue Variable X29 ROA Independent and Continue Variable X21 Total Cost of Debt Independent and Continue Variable X23 Operating Profit Margin Independent and Continue Variable X44 ∆ROE Independent and Continue Variable Y Financial Distress Dependent and Dicotomic Variable A Statistical Analysis to Predict Financial Distress 318 Table 3. Estimation of the regression model parameters. Estimated Parameter Estimation Method b0 b1 (X16) b2 (X29) b3 (X21) b4 (X23) b5 (X44) Least Squares –2.6012 2.4251 –9.0192 13.3503 –3.1242 –0.2422 Weighted Least Squares –1.3466 1.4257 –0.2317 7.5672 –1.3062 –0.2490 Maximum Likelihood –2.2748 2.1978 –2.4296 12.3765 –2.7072 –0.2648 Considering that many of the validation tests for the regression model require that the parameters were esti- mated through the maximum likelihood method then we are going to keep these results as representative of the model. In this way, the regression model is defined through the following expression: 162921 23 44 ( 2.2748 2.19782.429612.37652.70720.2648) 1 ˆ 1XX XXX Ye (1) where represents the probability that a firm becomes financially distressed in the short term. From this model, we can see that an increase of the current debt ratio or an increase of the total cost of debt implies a higher prob- ability for a company to become financially distressed. In addition, an increase of the ROA, an increase of the op- erating profit margin, or an increase of the ROE deter- mines a lower probability of a firm to become financially distressed in the short term. In this way, we can verify that the estimated values of the parameters are coherent with the expected financial impact that these ratios should have on a firm. Y ˆ As a next step, we performed different tests to validate the logistics regression model obtained as suggested by García [11]. We should notice that in all these validation tests we have considered a significance level of 5%. The first validation test corresponds to the following hypothesis: H0) the model fits the data. To perform this validation, we determined the corresponding statistics through the following expressions: 2 2 11 ntt ttt YX XX (2) 2DLn (3) The results obtained are shown in Table 4. We can see that the hypothesis considered is not rejected, and there- fore, we do not have enough statistical evidence to prove that the model does not fit the data. The second validation test corresponds to the follow- ing hypothesis: H0) 12 0 k . In this case, the corresponding statistic was determined through the following expression: 0 2( )GLnLn (4) The results obtained for this validation test are shown in Table 5. Considering that the hypothesis is rejected then we have enough statistical evidence to state that at least one of the estimated parameters in the model is not null. To continue with the model validation, we performed the significance tests of the estimated parameters. The results obtained through the Wald and Wilks methods are shown in Table 6. These results indicate that there is not enough statisti- cal evidence to state that the estimated parameters for the variables X16 – Current Debt Ratio and X21 – Total Cost of Debt are null. In the case of the variables X23 – Oper- ating Proft Margin and X44 – ΔROE, the Wald validation method indicates that there is enough statistical evidence to think that the corresponding estimated parameters are null. However, when we consider the Wilks method the results obtained are the opposite. Therefore, to decide if these variables should be included in the model we de- cided to calculate the maximum probabilities of rejecting the hypothesis H0) 40 and H0) 50 when they are actually true. These probabilities are 40.1448 and 50.0871 , respectively. In this way, given that Table 4. Validation results for H0) the model fits the data. Hypothesis H0) The model fits the data Statistic Computed Value 249.0968 60.8275D Critical Value 2 80;095 108.6479 2 80;095 108.6479 Rejection Condition 22 80;095 2 80;095 D Result Do Not Reject Do Not Reject Table 5. Validation results for H0) 12 0 k . Hypothesis 01 2 H) 0 k Statistic Computed Value 58.3938G Critical Value 2 5;095 11.0705 Rejection Condition 2 5;095 G Result Reject Copyright © 2010 SciRes. JSSM A Statistical Analysis to Predict Financial Distress 319 Table 6. Validation results for the significance tests of the estimated parameters. Estimated Parameters Wald Method b1 (X16) b2 (X29) b3 (X21) b4 (X23) b5 (X44) Hypothesis 01 H) 0 02 H) 0 03 H) 0 04 H) 0 05 H) 0 Statistic Computed Value 2.2064t 0.5036t 1.6817t 1.0661t 1.3713t Critical Value 80;0.95 1.6641t 80;0.95 1.6641t 80;0.95 1.6641t 80;0.95 1.6641t 80;0.95 1.6641t Rejection Condition 80;0.95 tt 80;0.95 tt 80;0.95 tt 80;0.95 tt 80;0.95 tt Result Reject Do Not Reject Reject Do Not Reject Do Not Reject Estimated Parameters Wilks Method b1 (X16) b2 (X29) b3 (X21) b4 (X23) b5 (X44) Hypothesis 01 H) 0 02 H) 0 03 H) 0 04 H) 0 05 H) 0 Statistic Computed Value 29.7588 20.3969 24.4051 24.2093 26.6551 Critical Value 2 1;0.9 2.7055 2 1;0.9 2.7055 2 1;0.9 2.7055 2 1;0.9 2.7055 2 1;0.9 2.7055 Rejection Condition 22 1;0.9 22 1;0.9 22 1;0.9 22 1;0.9 22 1;0.9 Result Reject Do Not Reject Reject Reject Reject these probabilities are quite low, we concluded that there is not enough statistical evidence to think that the esti- mated parameters of the variables X23 and X44 are null. Finally, we need to consider the estimated parameter associated with the variable X29 – ROA. In this case, the hypothesis H0) 20 2 is not being rejected in the Wald validation method nor in the Wilks method. In fact, the maximum probability of rejecting this hypothesis when it is actually true is 0.308 0.528 according to the Wald’s statistic and 27 according to the Wilks’ statis- tic. These results indicate that there is enough statistical evidence to believe that the corresponding variable should not be included in the regression model given that it does not help to identify those firms with financial problems. To verify this statement we compared the re- gression model that includes the variable X29 – ROA against that model that does not include this ratio based on the coefficients of determination and the ability of each model to identify a firm with financial problems1. The results obtained—as shown in Tables 7 and 8— indicate that the additional information provided by the variable X29 – ROA is negligible, and therefore, we have decided not to include this variable in the regression mo- del. To finalize with the validation process, we can analyze the results obtained in Tables 7 and 8. The most impor- tant thing to notice is the improvement that the model based on the original variables shows in comparison to the model based on the principal components. If we have a look at the coefficients of determination then the maximum value obtained for the model based on the original variables is 0.654 while for the model based on the principal components is 0.3187. In a similar way, the model based on the original variables managed to cor- rectly identify 84.88% of the firms—either as a firm with or without financial problems—while the principal com- ponents model correctly identified 78.57% of the firms in the sample. All in all, these validation metrics reflect the robustness of the regression model selected. Given that from the model validation we concluded that the variable X29 – ROA should not be considered, the new regression model can be represented as follows: 1621 23 44 ( 2.4567 2.281314.23153.5630.271) 1 ˆ 1XXXX Ye (5) where the parameters corresponding to each financial ratio were again estimated through the maximum likeli- hood method. As in the previous model, the relation be- tween the estimated parameters and the variables consid- ered is coherent as we can see from Expression (5). The validation of this new model is quite straight for- ward since we only left out one financial ratio in com- parison to the previous model. As in previous validations, first we tested the hypothesis H0) the model fits the data and we found that there was not enough statistical evi- dence to reject it. Second, we tested the hypothesis H0) 12 0 k and in this case we found out that there was enough statistical evidence to state that not all the estimated parameters are null. To continue with the validation process we also performed the significance tests of the regression coefficients. The results obtained are shown in Table 9. In this case, we can see that Copyright © 2010 SciRes. JSSM A Statistical Analysis to Predict Financial Distress 320 Table 7. Comparison of the coefficients of determination. Regression Model based on X16, X29, X21, X23, and X4 Regression Model based on X16, X21, X23, and X44 Coefficients of Determination Value Coefficients of Determination Value 2 R 0.5858 2 R 0.5504 2 M cFadden R 0.4898 2 M cFadden R 0.4865 2 A ldrich Nelson R 0.4044 2 A ldrich Nelson R 0.4028 2 Cox Snell R 0.4929 2 Cox Snell R 0.4905 2 ker Nagel ke R 0.6572 2 ker Nagel ke R 0.6540 Table 8. Comparison of the ability of the models to identify a firm with financial problems. Regression Model based on X16, X29, X21, X23, and X44 Regression Model based on X16, X21, X23, and X44 Correct Classifications Incorrect Classifications Total Correct Classifications Incorrect Classifications Total Group 1 97.67% 2.33% 100% Group 1 95.35% 4.65% 100% Group 2 76.74% 23.26% 100% Group 2 74.42% 25.58% 100% Total 87.21% 12.79% 100% Total 84.88% 15.12% 100% Table 9. Validation results for the significance tests of the estimated parameters. Estimated Parameters Wald Method b1 (X16) b3 (X21) b4 (X23) b5 (X44) Hypothesis 01 H) 0 03 H) 0 04 H) 0 05 H) 0 Statistic Computed Value 2.3395t 2.1002t 1.6862t 1.7514t Critical Value 81;0.95 1.6639t 81;0.95 1.6639t 81;0.95 1.6639t 81;0.95 1.6639t Rejection Condition 81;0.95 tt 81;0.95 tt 81;0.95 tt 81;0.95 tt Result Reject Reject Reject Reject Estimated Parameters Wilks Method b1 (X16) b3 (X21) b4 (X23) b5 (X44) Hypothesis 01 H) 0 03 H) 0 04 H) 0 05 H) 0 Statistic Computed Value 29.8813 26.4451 26.4641 215.2369 Critical Value 2 1;0.9 2.7055 2 1;0.9 2.7055 2 1;0.9 2.7055 2 1;0.9 2.7055 Rejection Condition 22 1;0.9 22 1;0.9 22 1;0.9 22 1;0.9 Result Reject Reject Reject Reject every hypothesis tested H0) 0 i is rejected through both the Wald and Wilks methods, being the validation results more robust that in the previous regression model validation. The validation concludes with the calculation of the coefficients of determination and the ability of the model to correctly classify the firms in the sample, which were already presented in Tables 7 and 8, respectively. In this way, we can finish with the regression analysis by com- puting the 95% confidence intervals for each of the esti- mated parameters from the selected regression model. The results obtained are the following: 12.2813 1.9407 (6) 314.2315 13.4856 (7) 43.563 4.2052 (8) Copyright © 2010 SciRes. JSSM A Statistical Analysis to Predict Financial Distress 321 50.271 0.308 (9) To summarize, we have found a logistic regression model based on a reduced group of financial ratios that is defined by Expression (5). The validation results indicate that this model can better explain the total variance of the firms in the sample and that it has a higher ability to identify those firms with financial problems in compari- son to that model based on the principal components. In this way, we confirm that in this particular study a big amount of information is lost if we use the principal components to develop a logistic regression model. Nev- ertheless, we should keep in mind that the principal component analysis has resulted very useful to represent and quickly asses the financial status of a firm based on the risk the company has with regard to the nature of its business and the risk involved in the amount of debt it has taken in comparison to the profits that were gener- ated during the last two fiscal years. In fact, both the principal component and the regression analyses have resulted in two complementary tools that allow us to evaluate and summarize the financial status of a firm based on the data from its balance sheets. 6. Applying the Analyses to a New Sample The objective of this section is to evaluate the effective- ness that the principal component and the regression analyses have to identify those firms with financial prob- lems when they are applied over a new sample. Given to the difficulties involved in the data collection, the new sample is composed by 14 companies from which only 3 of them have had financial problems (see Appendix 8 for the sample details). Moreover, we should notice that the data collected from these firms corre- sponds to periods previous than 2002, which means that there might be some unusual variation in the data due to the financial crisis that occurred in Argentina between 2001 and 2002. Nevertheless, despite of these data limi- tations the evaluation performed is still valid although the results will have to be carefully interpreted. To start with, the values of the principal components F1 – ∆Risk and F2 – ∆Return have been computed for each firm and are represented in Figure 6. From this fig- ure we can see that the 3 companies that have had finan- cial problems are located within sector 2, which corre- sponds to a high risk level together with a return deterio- ration. At the same time, most of the companies that did not have financial problems are also located in the same sector with the exception of 2 firms that are located in sector 6, which corresponds to a high level of risk to- gether with a return improvement. In this way, if we would have to classify the firms from the new sample based uniquely on the principal components analysis we would say that all those firms within sector 2 have a higher probability of becoming financially distressed in the short term while the opposite occurs with those com- panies from sector 6. The higher probability of having financial problems for those companies in sector 2 is mainly derived from the higher risk they have due to the nature of the business—as determined by the operating leverage—and the higher risk they are taking when in- creasing their debts without generating enough resources to cover it. Nevertheless, in order to obtain a more pre- cise classification we should performed the regression analysis as shown next. To finalize with the evaluation of the effectiveness of the tools developed, we performed the logistic regression analysis over the new sample and we computed for each firm the probabilities of becoming financially distressed in the short term as shown in Table 10. Based on these results and keeping in mind that those firms with a prob- ability equal or higher than 0.5 are considered to have financial problems, we can conclude that all companies were correctly classified within one of the two groups considered. This suggests that the tools developed are useful and effective to identify those firms with financial problems. Of course, we can always expect some classi- fication error but in this case it seems not to be signifi- cant. It is important to mention how the two analyses per- formed complement each other. From the principal component analysis we can quickly identify those com- panies that are taking a higher risk—based on the nature Figure 6. Categorization of the firms from the new sample based on the principal components. Copyright © 2010 SciRes. JSSM A Statistical Analysis to Predict Financial Distress 322 Table 10. Probabilities for a firm to become financially dis- tressed in the short term. Firm Nr Group Nr Probability 1 1 0.0045 2 1 0.2164 3 1 0.1569 4 1 0.3691 5 1 0.2479 6 1 0.0863 7 1 0.2680 8 1 0.4766 9 1 0.1244 10 1 0.3013 11 1 0.2462 12 2 0.5593 13 2 0.7444 14 2 0.5279 of the business and based on the higher debts—and to identify those companies that have a better coverage against that risk. From the regression analysis we are able to quantify through a unique indicator—the prob- ability of becoming financially distressed in the short term—how big is the risk involved and how good is the company covering against that risk. In addition, we can use this probability to identify those firms that already have financial problems. 7. Conclusions Through this study we managed to verify based on the statistical analyses performed that the financial ratios show a different behavior between those firms that have had financial problems and those which did not. Al- though not all these ratios have by themselves the same ability to allow the identification of those firms with fi- nancial problems, it is possible to combine and summa- rize all that information into 2 principal components that we have named as ∆Risk and ∆Return. By the computa- tion of these new variables it is possible to quickly finan- cially categorize a certain firm based on the risk the company has with regard to the nature of its business and the risk involved in the amount of debt it has taken in comparison to the profits that were generated during the last two fiscal years. The conclusive results obtained from the principal component analysis suggest that there would be no ap- parent reason not to consider any financial ratio origi- nally collected to estimate the probability that a firm be- comes financially distressed in the short term. However, after developing different regression models we have seen that we can obtain better estimations of these prob- abilities if we just consider a few financial ratios that all together show a higher ability to identify a firm with fi- nancial problems in comparison to a situation where the data collected from all the 45 ratios is used (as in the case of the principal components model). In this way, we managed to develop a more efficient model given that we can obtain better results with less data. This efficiency can be explained due to the fact that the principal com- ponents are a linear combination of 45 ratios, which means that many of them might not be useful to distin- guish between a financially healthy firm and one that it is not. This finding shows how important is to have a com- plete and broad database before starting any statistical analysis so that fewer limitations are introduced when trying to find a near optimal solution, i. e. the regression model with the available ratios combination that best estimates the probability of a firm of becoming finan- cially distressed in the short term. In the same way, we should emphasis the benefits that can be obtained when combining more than one statistical analysis together to better understand the nature of the process under study and to more effectively achieve the objective proposed, which in our case is to identify those firms with financial problems. We have seen that those ratios that have more capa- bilities to identify those firms with financial problems are all related to the return aspects of the companies. In fact, we have seen that the principal component that resulted more conclusive to identify financially unhealthy firms was the ∆Return as opposite to the ∆Risk component. Nevertheless, the information contained in these ratios can always be complemented with information from other type of ratios to identify those firms with financial problems more precisely and effectively. After perform- ing a logistic regression analysis based on the 45 ratios collected in the sample, we have selected a small group of them that can explain 65% of the firms’ behavior. The related model consists of the following ratios: 1) Current Debt Ratio, 2) Total Cost of Debt, 3) Operating Profit Margin, and 4) ∆ROE. It is interesting to notice that in most of the logistic regression models tested it was found that there is higher probability to incorrectly classify a firm with financial problems, i.e. to assume that a com- pany is financially healthy when actually it is not. This could be mainly explained due to the fact that the finan- cial ratios collected have a higher variability in those Copyright © 2010 SciRes. JSSM A Statistical Analysis to Predict Financial Distress Copyright © 2010 SciRes. JSSM 323 companies that are financially distressed in comparison to those that do not have any financial problem. Never- theless, the possibility of combining the regression and the principal component analyses helps to reduce the probability of misclassifying a certain firm. With this regard, we should notice that the present study does not include any analysis related to the costs involved in the decision making process of identifying firms with finan- cial problems. Nevertheless, whenever there are not con- clusive results that clear define the financial status of a company then the most conservative decision would be to assume that the firm has financial problems. The outcomes from this study are two tools that were developed based on the statistical inference from which we can quickly asses the financial status of a firm based on its risks and return’s variation as well as to estimate the probability that a firm becomes financially distressed in the short term. There are different ways of taking these tools into practice such as: 1) to control and follow up the financial performance of a company, 2) to support the decision of lending money to a company, 3) to support the decision of investing money or the decision of merg- ing with a company, 4) to support market analysis from a financial perspective, and 5) to support actions or deci- sions related to the financial assessment of a company that declares itself to be financially distressed. This study could be further developed by trying to in- corporate new explanatory variables that are rather not financial ratios but instead qualitative measurements that could contribute to more precise and effective estimation of the probability of a firm of becoming financially dis- tressed in the short term. Another alternative would be to incorporate a tool from which the costs involved in tak- ing the wrong decision—i.e. to assume that a company has no financial problems when it actually has or vice versa—could be minimized. Finally, the statistical analy- ses performed in this study could be replicated with firms that have a significant amount of assets with the objec- tive of determining the main characteristics that derive in a solid financial structure. As we can see, there are many different ways to continue with this study and the statis- tics offers interesting tools for that. REFERENCES [1] I. 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Beaver, “Financial Ratios as Predictors of Failure,” Empirical Research in Accounting, selected studies (in supplement to the Journal of Accounting Research, Janu- ary, 1967), 1966, pp. 71-111. [6] E. I. Altman, “Financial Ratios, Discriminant Analysis and the Prediction of Corporate Bankruptcy,” The Journal of Finance, Vol. 23, No. 4, 1968, pp. 589-609. [7] S. S. Alexander, “The Effect of Size of Manufacturing Corporation on the Distribution of the Rate of Return,” Review of Economics and Statistics, Vol. 31, No. 3, 1949, pp. 229-235. [8] D. Peña, “Análisis de Datos Multivariantes,” McGraw- Hill, 2002. [9] D. Johnson, “Métodos Multivariados Aplicados Al Análisis de Datos,” Thomson, 2000. [10] D. W. Hosmer and S. Lemeshow, “Applied Logistic Re- gression,” 2nd Edition, John Wiley & Sons Inc., 2000. [11] R. M. García, “Inferencia Estadística y Diseño de Experi- mentos,” Eudeba, 2004. [12] L. García, “Las Empresas Más Rentables,” Revista Mercado, 2004, pp. 76-80. [13] L. García, “Las Empresas Más Rentables,” Revista Mercado, 2005, pp. 110-114. http://www.ax5.com/antonio/publica- ciones/delatorre2002aplicacion.pdf [14] L. García, “Las 100 Empresas Más Rentables,” Revista Mercado, 2006, pp. 134-138. A Statistical Analysis to Predict Financial Distress 324 Appendices Appendix 1 Table A1. Details of the firms included in the sample. Firm Nr Group Nr Name Period Analyzed Firm’s Industry 1 1 Alvarez Hnos. S.A. 2005-2004 Mills and oils 2 1 Compañía Internacional de Alimentos y Bebidas S.A. 2004-2003 Food 3 1 Establecimiento Metalúrgicos Cavanna S.A.C.I.F.I. 2005-2004 Technology and communications 4 1 Andreani Logística S.A. 2004-2003 Transport 5 1 Compañía de Servicios Telefónicos S.A. 2005-2004 Telecommunications 6 1 Compumundo S.A. 2005-2004 Retail 7 1 Caputo S.A. 2005-2004 Construction 8 1 Ediar S.A. 2005-2004 Printing and publishing 9 1 Agrometal S.A.I. 2005-2004 Machinery and equipment 10 1 Electromac S.A. 2005-2004 Machinery and equipment 11 1 Gijon S.A. 2005-2004 Construction 12 1 Green S.A. 2005-2004 Construction 13 1 Esat S.A. 2004-2003 Plastic and chemical 14 1 Grafex S.A. 2004-2003 Printing and publishing 15 1 Lihue Ingeniería S.A. 2005-2004 Machinery and equipment 16 1 Laboratorio LKM S.A. 2004-2003 Laboratories 17 1 Guilford Argentina S.A. 2005-2004 Textiles and footwear 18 1 Rovella Carranza S.A. 2005-2004 Construction 19 1 Yar Construcciones S.A. 2005-2004 Construction 20 1 Mardi S.A. 2004-2003 Fishing 21 1 Mercoplast S.A. 2005-2004 Plastic and chemical 22 1 Bonafide Golosinas S.A. 2005-2004 Food 23 1 Bonesi S.A. 2005-2004 Household goods 24 1 Molinos Juan Semino S.A. 2004-2003 Mills and oils 25 1 City Pharma S.A. 2005-2004 Retail 26 1 Morixe Hnos. S.A. 2005-2004 Mills and oils 27 1 Coniglio S.A. 2005-2004 Textiles and footwear 28 1 Curtiduría A. Gaita S.R.L. 2005-2004 Tanneries and leather goods 29 1 Domec S.A.I.C. y F. 2005-2004 Household goods 30 1 Dulcor S.A. 2005-2004 Food 31 1 Distribuidora Santa Bárbara S.A. 2005-2004 Fishing 32 1 Outdoors S.A. 2004-2003 Textiles and footwear 33 1 Frutucumán S.A. 2003-2002 Export and import 34 1 García Reguera S.A. 2005-2004 Wholesale 35 1 Instituto Rosenbusch S.A. 2005-2004 Healthcare 36 1 Insumos Agroquímicos S.A. 2005-2004 Retail 37 1 Industria Textil Argentina (INTA) S.A. 2005-2004 Textiles and footwear 38 1 SAT Médica S.A. 2005-2004 Healthcare 39 1 Leyden S.A.I.C. y F. 2005-2004 Machinery and equipment 40 1 Lodge S.A. 2004-2003 Agricultural Copyright © 2010 SciRes. JSSM A Statistical Analysis to Predict Financial Distress 325 41 1 Longvie S.A. 2005-2004 Household goods 42 1 Ovoprot International S.A. 2004-2003 Food 43 1 Magalcuer S.A. 2005-2004 Tanneries and leather goods 44 2 Aero Vip S.A. 2003-2002 Transport 45 2 Alunamar S.A. 2005-2004 Fishing 46 2 American Falcon S.A. 2003-2002 Transport 47 2 AS Sistemas S.A. 2003-2002 Technology and communications 48 2 Bascoy S.A. 2003-2002 Transport 49 2 Cartex S.A. 2004-2003 Textiles and footwear 50 2 Casamen S.A. 2003-2002 Food 51 2 Celeritas S.A. 2004-2003 Healthcare 52 2 Comercial Mendoza S.A. 2003-2002 Household goods 53 2 Crédito José C. Paz S.A. 2003-2002 Construction 54 2 D´Vigi S.A. 2004-2003 Retail 55 2 Droguería Sigma S.A. 2003-2002 Retail 56 2 Ecourban S.A. 2004-2003 Waste 57 2 El Manzanar de Macedo S.A. 2004-2003 Food 58 2 Espejos Versailles S.A. 2003-2002 Glass and construction materials 59 2 FrigoFruit S.A. 2003-2002 Agricultural 60 2 Humberto Nicolás Fontana S.A.C. 2004-2003 Household goods 61 2 Impresiones Arco Iris Córdoba S.A. 2003-2002 Printing and publishing 62 2 Industrias Badar S.A. 2003-2002 Technology and communications 63 2 Diabolo Menthe S.R.L. 2003-2002 Textiles and footwear 64 2 La Tribu S.R.L. 2003-2002 Food 65 2 Loucen International S.A. 2004-2003 Beverages 66 2 Luicar S.R.L. 2003-2002 Turism 67 2 Manfisa Mandataria y Financiera S.A. 2003-2002 Construction 68 2 Norte Asistencia Empresaria S.A. 2003-2002 Post 69 2 Parmalat Argentina S.A. 2003-2002 Dairy 70 2 Pto. S.A. 2004-2003 Waste 71 2 Redes Excon S.A. 2003-2002 Gas 72 2 Sanatorio Ezeiza S.A. 2004-2003 Healthcare 73 2 Sanatorio Modelo Quilmes S.A. 2004-2003 Healthcare 74 2 Security Consulting S.A. 2003-2002 Technology and communications 75 2 Sepia Beauty S.A. 2004-2003 Cleaning and cosmetics 76 2 Sol de Brasa S.A. 2005-2004 Agricultural 77 2 Sycon Argentina S.A. 2003-2002 Gas 78 2 UOL Sinectis S.A. 2004-2003 Technology and communications 79 2 Yearling S.A. 2003-2002 Security services 80 2 Fundición de Aceros S.A. 2003-2002 Metallurgical and steel 81 2 Inmar S.A. 2003-2002 Construction 82 2 Carpintería Metálica San Eduardo S.A. 2003-2002 Glass and construction materials 83 2 Marmolería Sierra Chica S.A. 2003-2002 Mining 84 2 Avaca S.A. 2003-2002 Textiles and footwear 85 2 Bellas S.A. 2003-2002 Textiles and footwear 86 2 Ianson S.A. 2004-2003 Textiles and footwear Copyright © 2010 SciRes. JSSM A Statistical Analysis to Predict Financial Distress 326 Appendix 2 Table A2. Description of the financial ratios included in the analyses. Liquidity Ratios X1. Fixed Assets Ratio Non Current Assets / Total Assets X2. Working Capital Ratio Working Capital / Total Assets X3. Current Ratio Current Assets / Current Liabilities X4. Quick Ratio (Current Assets - Inventory) / Current Liabilities X5. Cash Ratio Cash & Equivalents / Current Liabilities X6. Average Receivables Collection Period Receivables / Sales X7. Payables Payment Period Accounts Payable / Purchases X8. Average Inventory Processing Period Average Inventory / COGS X9. Cash Conversion Cycle Avg. Inventory Processing Period + Avg. Receivables Collection Period - Avg. Payables Payment Period Operating Efficiency Ratios X10. Total Asset Turnover Sales / Total Assets X11. Current Assets Turnover Sales / Current Assets X12. Fixed Asset Turnover Sales / Non Current Assets X13. Equity Turnover Equity / Sales Business Risk Ratios X14. Operating Leverage | (%ΔOperating Income) / (%ΔSales) | Financial Risk Ratios X15. Total Debt Ratio Total Liabilities / Total Assets X16. Current Debt Ratio Current Liabilities / Total Assets X17. Debt Turnover Total Liabilities / Sales X18. Non Current Debt Ratio Non Current Liabilities / (Non Current Liabilities + Equity) X19. Equity To Debt Ratio Equity / Total Liabilities X20. Debt Coverage Operating Profit / Total Liabilities X21. Total Cost of Debt Interests / Total Liabilities Return Ratios X22. Gross Profit Margin Gross Profit / Sales X23. Operating Profit Margin Operating Profit / Sales X24. Net Profit Margin Net Income / Sales X25. Return on Equity (ROE) Net Income / Equity X26. Benchmarked Return (ROE - ROE sector) / ROE sector X27. Return on Capital Employed (ROCE) Net Income / (Total Liabilities + Equity) X28. Operating Return on Capital Employed Operating Profit / (Total Liabilities + Equity) X29. Return on Assets (ROA) Net Income / Total Assets X30. Operating Profit on Assets Operating Profit / Total Assets Growth Ratios X31. ΔSales (Sales j - Sales j-1) / Sales j-1 Copyright © 2010 SciRes. JSSM A Statistical Analysis to Predict Financial Distress 327 X32. ΔAssets (Total Assets j - Total Assets j-1) / Total Assets j-1 X33. ΔNet Income (Net Income j - Net Income j-1) / Net Income j-1 X34. ΔLiabilities (Total Liabilities j - Total Liabilities j-1) / Total Liabilities j-1 X35. ΔFixed Assets Ratio (Fixed Asset Ratio j - Fixed Asset Ratio j-1) / Fixed Asset Ratio j-1 X36. ΔWorking Capital (Working Capital j - Working Capital j-1) / Working Capital j-1 X37. ΔCurrent Ratio (Current Ratio j - Current Ratio j-1) / Current Ratio j-1 X38. ΔAssets Turnover (Assets Turnover j - Assets Turnover j-1) / Assets Turnover j-1 X39. ΔTotal Debt Ratio (Total Debt Ratio j - Total Debt Ratio j-1) / Total Debt Ratio j-1 X40. ΔDebt Turnover (Debt Turnover j - Debt Turnover j-1) / Debt Turnover j-1 X41. ΔDebt Coverage (Debt Coverage j - Debt Coverage j-1) / Debt Coverage j-1 X42. ΔOperating Profit Margin (Operating Profit Margin j - Operating Profit Margin j-1) / Operating Profit Margin j-1 X43. ΔNet Profit Margin (Net Profit Margin j - Net Profit Margin j-1) / Net Profit Margin j-1 X44. ΔROE (ROE j - ROE j-1) / ROE j-1 X45. ΔROA (ROA j - ROA j-1) / ROA j-1 Copyright © 2010 SciRes. JSSM A Statistical Analysis to Predict Financial Distress 328 Appendix 3 In Table A3 we present the average ROE per industry based on data published on [12-14]. These average returns have been used to compute the Benchmarked Return ratio for each company in the sample. Table A3. Average ROE per industry for companies operating in Argentina. Year Firm’s Industry 2003 2004 2005 Agricultural 26.81 29.23 27.02 Household goods 68.18 29.17 39.83 Automotive 31.09 28.27 29.64 Beverages 33.51 34.01 29.01 Pulp and paper 34.75 17.28 18.87 (*) Wholesale 38.81 36.43 33.44 Retail 51.69 32.95 67.25 Road concessionaire 86.56 (*) 95.16 103.89 (*) Construction 94.78 47.44 649.63 Post 44.75 48.79 (*) 53.27 (*) Tanneries and leather goods 42.31 52.54 73.68 Gas 33.24 37.66 28.04 Export and import 43.65 (*) 47.99 52.39 (*) Finance 257.69 64.35 53.62 Meat 115.63 40.12 43.80 (*) Oil and gas 128.53 28.81 46.18 Turism 3.24 3.53 (*) 3.86 (*) Printing and publishing 450.50 33.94 23.91 Fishing 31.19 (*) 34.29 37.43 (*) Lanoratories 79.01 55.35 60.43 Dairy 39.20 (*) 43.10 87.80 Cleaning and cosmetics 158.33 172.63 (*) 188.48 (*) Machinery and equipment 124.00 48.32 40.18 Metallurgical and steel 58.72 30.03 31.82 Mining 162.68 22.22 45.05 Mills and oils 74.89 24.18 47.77 Rubber products 28.59 31.17 (*) 28.42 Other 32.61 (*) 35.85 (*) 39.47 Production and distribution of electrical energy 46.30 18.01 56.93 Food 35.35 42.88 38.85 Film Products 14.98 (*) 16.47 17.98 (*) Plastic and chemical 65.97 18.64 77.78 Chemical and petrochemical 62.35 36.03 36.26 Copyright © 2010 SciRes. JSSM A Statistical Analysis to Predict Financial Distress 329 Waste 6.90 (*) 7.57 (*) 8.32 Healthcare 27.69 (*) 30.43 33.23 (*) Security services 41.31 (*) 45.41 (*) 50.00 Tobacco 23.69 (*) 26.04 (*) 28.67 Technology and communications 61.96 (*) 68.12 (*) 75.00 Telecommunications 58.82 363.10 57.18 Textiles and footwear 15.16 (*) 16.67 18.20 (*) Transport 60.13 163.61 100.65 Glass and construction materials 1100.00 22.19 29.56 (*) These returns are estimations based on the return of that sector from other years adjusted by the corresponding ∆GDP. Copyright © 2010 SciRes. JSSM A Statistical Analysis to Predict Financial Distress 330 Appendix 4 In Table A4 we present the eigenvalues for each principal component obtained through the covariance matrix. We can see from these results that the first two components already accumulate approximately 93% of the total sample vari- ance. Table A4. Eigenvalues for the principal components. Eigenvalues Cumulative Variance Eigenvalues Cumulative Variance F1 17862.89 84.69% F23 0.33 99.99% F2 1792.07 93.19% F24 0.29 100.00% F3 576.15 95.92% F25 0.21 100.00% F4 455.55 98.08% F26 0.18 100.00% F5 134.53 98.72% F27 0.15 100.00% F6 88.47 99.14% F28 0.11 100.00% F7 62.48 99.44% F29 0.09 100.00% F8 50.57 99.68% F30 0.06 100.00% F9 19.58 99.77% F31 0.06 100.00% F10 11.70 99.82% F32 0.04 100.00% F11 9.40 99.87% F33 0.03 100.00% F12 5.51 99.89% F34 0.02 100.00% F13 4.74 99.92% F35 0.02 100.00% F14 4.25 99.94% F36 0.01 100.00% F15 3.89 99.96% F37 0.01 100.00% F16 2.13 99.97% F38 0.01 100.00% F17 1.94 99.97% F39 0.01 100.00% F18 1.11 99.98% F40 0.00 100.00% F19 0.95 99.98% F41 0.00 100.00% F20 0.71 99.99% F42 0.00 100.00% F21 0.50 99.99% F43 0.00 100.00% F22 0.39 99.99% F44 0.00 100.00% F45 0.00 100.00% Copyright © 2010 SciRes. JSSM A Statistical Analysis to Predict Financial Distress 331 Appendix 5 In Table A5 we present the values that the two principal components selected have in each firm from the sample. Based on these values, it is possible to represent the firms in a unique graph as shown in Section 4. Table A5. Values of the principal components for each firm included in the sample. Firm Nr F1 F2 Firm Nr F1 F2 1 2.89 –8.73 44 –21.32 –11.43 2 –7.46 –13.63 45 –24.91 –10.17 3 –29.61 –9.03 46 –29.61 –8.20 4 –28.65 –9.93 47 –27.52 –12.12 5 –25.48 –11.18 48 –27.59 –8.34 6 –28.02 –9.82 49 –19.58 56.95 7 –24.38 –11.21 50 –27.25 –2.63 8 –29.96 –23.40 51 –10.80 348.78 9 –25.94 –9.77 52 –28.00 77.40 10 6.56 –29.62 53 83.18 –0.38 11 –27.35 –12.27 54 22.53 28.75 12 –13.12 –8.80 55 –24.40 –7.53 13 –26.62 –10.99 56 –19.52 –4.45 14 –27.68 –12.63 57 –16.61 –0.07 15 –21.24 –10.02 58 –27.95 –8.51 16 –9.81 –6.73 59 –29.01 –10.73 17 –29.29 –9.85 60 –29.00 –8.98 18 –28.17 –17.67 61 –18.88 –11.57 19 –29.11 –21.38 62 1,168.66 –28.96 20 21.88 –6.99 63 143.16 65.74 21 –27.91 –9.38 64 –9.03 5.18 22 –23.66 –11.65 65 –23.78 –24.24 23 –29.71 –10.96 66 –29.17 –8.94 24 –28.14 –11.62 67 –18.11 –2.91 25 –29.48 –9.49 68 –28.57 –11.15 26 44.80 16.75 69 –28.76 65.83 27 –26.62 –11.21 70 –25.86 –13.43 28 20.48 –6.61 71 –29.66 –7.74 29 –26.89 –11.24 72 –29.15 –9.30 30 –16.64 –8.22 73 –23.67 –8.33 31 –26.94 –10.14 74 –30.66 –3.28 32 –28.95 –10.66 75 –14.80 –5.93 33 49.83 0.62 76 –26.39 6.42 34 –18.95 –21.99 77 –28.18 17.90 35 –28.73 –10.61 78 –26.25 –8.48 36 –28.63 –9.81 79 –29.34 –2.67 37 –29.95 –9.09 80 –27.60 –7.34 38 –27.47 –11.72 81 –29.40 –7.81 39 –25.99 –10.93 82 296.70 55.26 40 –18.58 –7.64 83 –29.29 –10.68 41 –22.00 –14.59 84 0.38 –7.52 42 –28.22 –11.83 85 –29.25 5.02 43 –29.07 –8.22 86 –27.74 4.48 Copyright © 2010 SciRes. JSSM A Statistical Analysis to Predict Financial Distress 332 Appendix 6 In Table A6 we present the correlation between the two principal components selected and each of the financial ratios included in this study. We have highlighted those ratios that have a higher correlation with one of the principal compo- nents. Table A6. Correlation between the principal components selected and the financial ratios included in the analyses. Variable F1 F2 Variable F1 F2 X1 –0.0450 0.0003 X23 –0.0032 –0.1069 X2 0.0092 –0.1531 X24 –0.0039 –0.0835 X3 –0.0218 0.0707 X25 0.0158 –0.1549 X4 –0.0395 0.0364 X26 0.0056 –0.1566 X5 –0.0744 –0.0786 X27 0.0149 –0.1681 X6 –0.0150 –0.0299 X28 –0.0453 –0.1014 X7 –0.0251 –0.0285 X29 –0.0167 –0.4457 X8 0.0005 0.0194 X30 –0.0304 –0.3643 X9 0.0031 –0.0038 X31 –0.0262 0.0885 X10 –0.0297 0.1808 X32 –0.0842 –0.0678 X11 –0.0395 0.1606 X33 –0.0033 –0.9688 X12 –0.0299 –0.0295 X34 –0.0819 0.2591 X13 –0.0203 –0.0365 X35 –0.0251 0.1044 X14 0.9984 0.0221 X36 –0.0677 –0.0351 X15 –0.0457 0.1748 X37 –0.0223 0.1054 X16 –0.0357 0.1921 X38 0.0124 0.2825 X17 –0.0323 –0.0277 X39 –0.0323 0.5329 X18 –0.0480 –0.0363 X40 –0.0752 –0.0004 X19 –0.0285 –0.2219 X41 0.8628 –0.2082 X20 –0.0700 –0.3777 X42 0.8120 –0.2345 X21 0.2276 0.0313 X43 –0.0141 –0.7122 X22 –0.0650 –0.0932 X44 –0.0294 –0.4114 X45 –0.0143 –0.9859 Copyright © 2010 SciRes. JSSM A Statistical Analysis to Predict Financial Distress 333 Appendix 7 In Table A7 we present the 57 logistic regression models that were tested based on the standard and the Nagelkerke regression coefficients. Table A7. Ranking of the logistic regression models based on the regression coefficients. Model Nr Variables Considered 2 R 2 ker Nagel ke R 1 X16 X19 X21 X8 X44 0.57 0.67 2 X16 X29 X21 X23 X44 0.58 0.66 3 X16 X29 X5 X21 X44 0.55 0.65 4 X16 X29 X5 X21 X23 0.56 0.65 5 X16 X29 X26 X23 X44 0.55 0.65 6 X16 X25 X29 X8 X43 0.53 0.64 7 X16 X25 X29 X8 X21 0.54 0.64 8 X16 X29 X5 X23 X44 0.53 0.64 9 X16 X29 X5 X44 X17 0.50 0.64 10 X16 X29 X26 X24 X44 0.53 0.64 11 X16 X29 X21 X24 X44 0.57 0.64 12 X16 X29 X5 X21 X17 0.52 0.63 13 X16 X19 X21 X2 X44 0.54 0.63 14 X16 X25 X8 X29 X19 0.52 0.62 15 X16 X29 X5 X21 X43 0.52 0.62 16 X16 X29 X5 X44 X42 0.50 0.62 17 X16 X29 X21 X44 - 0.54 0.62 18 X16 X19 X21 X3 X44 0.54 0.62 19 X16 X25 X8 X29 - 0.51 0.61 20 X16 X25 X29 X5 X21 0.52 0.61 21 X16 X29 X5 X21 X33 0.51 0.61 22 X16 X29 X5 X21 X32 0.60 0.61 23 X16 X29 X5 X21 X45 0.51 0.61 24 X16 X29 X5 X21 X34 0.51 0.61 25 X16 X29 X5 X23 - 0.50 0.61 26 X16 X29 X5 X44 - 0.48 0.61 27 X16 X29 X5 X44 X20 0.49 0.61 28 X16 X29 X5 X44 X33 0.49 0.61 29 X16 X29 X5 X44 X11 0.51 0.61 30 X16 X29 X2 X21 X43 0.52 0.60 31 X16 X29 X21 X3 X25 0.53 0.60 32 X16 X25 X29 X21 X3 0.53 0.60 33 X16 X25 X29 X21 X2 0.52 0.60 34 X16 X29 X5 X21 - 0.50 0.60 35 X16 X29 X5 X21 X42 0.50 0.60 Copyright © 2010 SciRes. JSSM A Statistical Analysis to Predict Financial Distress 334 36 X16 X29 X5 X21 X26 0.51 0.60 37 X16 X29 X21 X23 - 0.54 0.60 38 X16 X3 X25 X33 X8 0.49 0.59 39 X16 X25 X29 X5 - 0.48 0.58 40 X16 X25 X29 X5 X20 0.48 0.58 41 X16 X3 X25 X33 X29 0.49 0.57 42 X15 X29 X2 X43 X21 0.50 0.57 43 X16 X29 X8 - - 0.47 0.57 44 X16 X25 X29 X3 - 0.49 0.57 45 X16 X25 X29 X2 - 0.49 0.57 46 X16 X29 X5 - - 0.45 0.57 47 X16 X25 X29 - - 0.48 0.56 48 X16 X29 X21 - - 0.49 0.56 49 X16 X3 X25 X33 X19 0.44 0.55 50 X16 X29 X3 - - 0.47 0.55 51 X16 X25 X3 - - 0.41 0.53 52 X45 X43 X33 X39 - 0.28 0.36 53 X45 X43 X39 - - 0.27 0.36 54 X14 X41 X42 X45 X33 0.27 0.34 55 X45 X33 X43 - - 0.25 0.34 56 X45 X43 - - - 0.24 0.33 57 X14 X41 X42 - - 0.12 0.14 Copyright © 2010 SciRes. JSSM A Statistical Analysis to Predict Financial Distress Copyright © 2010 SciRes. JSSM 335 Appendix 8 In Table A8 we present the companies that were included in the second sample to evaluate the performance of the prin- cipal component and the logistics regression analyses to identify those firms with financial problems. Table A8. Details of the firms included in the new sample. Firm Nr Group Nr Name Period Analyzed Firm’s Industry 1 1 Patricios S.A. 2004-2003 Plastic and chemical 2 1 Fiplasto S.A. 2005-2004 Export and import 3 1 Grupo Inplast S.A. 2003-2002 Agricultural 4 1 Grimoldi S.A. 2005-2004 Textiles and footwear 5 1 Limpiolux S.A. 2005-2004 Other 6 1 La Agraria S.A. 2005-2004 Agricultural 7 1 Amercian Plast S.A. 2004-2003 Plastic and chemical 8 1 Compañía argentina de semillas 2005-2004 Agricultural 9 1 Schiarre S.A. 2004-2003 Machinery and equipment 10 1 Sports Life S.A. 2005-2004 Retail 11 1 UOLE S.A. 2005-2004 Household goods 12 2 Sweet Victorian S.A. 2001-2000 Textiles and footwear 13 2 Metcasa Metalúrgica Callegari S.A. 2001-2000 Metallurgical and steel 14 2 Midan S.A. 2000-1999 Automotive |