Evaluando el modelo de Puntuación Z’’ de Altman para determinar su nivel de precisión en empresas mexicanas Testing Altman’s Z’’-Score to assess the level of accuracy of the model in Mexican companies

Introduction: in 1968, Altman developed a multivariable predictive Z-score model to assess the probability of a public manufacturing company going to bankruptcy based on financial ratios. Later, Altman (1983) re-stated a more improved Z’’-Score model designed to apply in public or private, manufacturing, or non-manufacturing firms, but also in emerging countries. Prediction of the updated model proved to be highly efficient. This research was conducted to prove the level of accuracy of the Z’’-Score model applied to firms listed in the Mexican Stock Exchange (MSE) since there is little relevant research on this subject. Method: this research was conducted under a quantitative approach as a census and its scope was situational with a non-experimental and longitudinal research design. The period covered by this research was 2012-2019 since the data was available for those years under a somehow stable economic situation without significant economic ups and downs. This research considered the integration of a large financial database and the design of a typology to classify and analyze 155 Pantoja-Aguilar, M. P. et al. No 27, Vol. 13 (3), 2021. ISSN 2007 – 0705, pp.: 1 – 25 3 firms based on a standard deviation and average results of 837 Z’’-scores. A second analysis was conducted to prove if the predicted situation (area) by the Z’’-Score corresponded to the real situation in the marketplace for every company. Results: the results showed that the accuracy level of the Altman model decreased when applied to Mexican firms. The error of the model applied to Mexican companies related to those classified in the bankruptcy prediction area was 75 % of misclassification cases. The total error of the model included all areas, or cases, was 18 % of misclassification cases. This model is supposed to be effective within a time frame of two years before a possible bankruptcy. Even considering a longer time frame, the companies located in the bankruptcy prediction area continued having misclassifications representing 57 % of error. The error for the model considering all cases and all areas, was 14 % of misclassification cases. This represented a high level of inefficiency of the model applied to an emerging country companies, such as Mexico. Discussion or conclusion: the model is certainly effective while predicting companies in the areas of non-bankrupt sector and grey, but it was inefficient when predicting the possibility of bankruptcy. It was also demonstrated that the time frame of two years is no longer effective when applying the model to Mexican companies. As a result, more research cases are needed to update the model to perform efficiently in emerging countries including country-specific conditions and considering a different time frame to predict bankruptcy.


Introduction
The history of financial evaluation of a firm using financial ratios is already more than a century old. Beaver (1966) points out that "At the turn of the [XX] century, ratio analysis was in its embryonic state. It began with the development of a single ratio, the current ratio, for a single purpose-the evaluation of creditworthiness" (p. 71). In 1969, Beaver mentioned that ratio analysis involved the use of several ratios by several users including credit lenders, credit-rating agencies, investors, and management. Today, "contemporary tools of financial analysis which always focus on the future and whose emerging is based on the criticism of traditional financial analysis indicators, particularly the profit indicator, measure either the company's potential to produce value for the owners (EVA) [Economic Value Added], cash flow return on investment (CFROI) or the value at risk (VaR); or assess a company as an investment opportunity" (Vimrova, 2015, p. 170). Testing Altman's Z''-Score to  The use of financial ratios analysis to predict or estimate the possibility that a firm may go into bankruptcy has been developed since the first decades of the 20th century until today. The interest regarding this subject has led to classify the consequences that the situation of probability of bankruptcy of a company may have in four categories. Those categories include: "(i) financial reporting and auditing consequences, (ii) firm-level operational consequences, (iii) capital market consequences and (iv) corporate governance consequences" (Habib et al., 2020(Habib et al., , p. 1023).
According to Horrigan (1968), the need to carry out a financial analysis grew in the last half of the 19th century when companies had industrial maturity and the banks needed to conduct more credit analysis. Among the main authors for bankruptcy prediction, Altman (1968) is well known for developing a Z-score model designed to predict bankruptcy in public manufacturing firms. Later, in 1983, Altman improved the model to also be applicable in private, non-manufacturing and emerging countries' firms. Altman's Z''-Score model has been widely disseminated but also tested by a various number of authors (Balcaen & Ooghe, 2006;Bauer & Agarval, 2014;Grice & Ingram, 2001;Jackson & Wood, 2013;Kumar & Ravi, 2007;Xu & Zhang, 2009)   The third section examines the results of the testing on accuracy of the Z''-Score model applied to Mexican firms. Finally, the last section presents the conclusions of the paper.

Literature review
The research studies conducted during the first two decades of the 20 th century related to financial ratios included, among others, the one from Wall (1912). Wall compiled seven ratios of 981 firms for an unspecified period and stratified them by industry and geographic location. Another study carried out by the Du Pont Company in 1919 included the triangle system of profit, assets, and sales as a foundation for ratio analysis. These two studies did not focus directly on ratios as predictors of business failure, but they set the basis for a new explosion of ratio analysis during the 1920s (Horrigan, 1968). This would become the starting point for later research studies related to bankruptcy conducted by Beaver and Altman in late 1960s.
According to Swart (1936) and Beaver (1968), the first study on failing firms to appear was in 1932, when Fitz Patrick examined a sample of thirty-eight companies including failed and nonfailed companies. The study determined that there were significant changes in ratios for at least three years prior to failure. This result was the foundation for later authors to explore the time prediction variable. Horrigan (1968) mentions that: Winakor and Smith (1935) began their analysis on a sample of firms which had experienced financial difficulties during the 1923-1931 period. They analyzed the prior ten years' trends of the means of 21 ratios and concluded that the ratio of net working capital to total assets was the most accurate and steady indicator of failure, with its decline beginning ten years before the occurrence of financial difficulty. By this research they added the concept of impact of the cash measures to the actual models of bankruptcy. However, their study suffered the shortcoming of lacking a contrasting control group of successful firms; this was a serious shortcoming (p. 288).
The first serious and sophisticated ratio analysis study as a predictive and statistic credible business failure predictor was by Mervin (1942). Mervin conducted a statistic method during a period of eleven years on five different types of industries to analyze failure and non-failure businesses. The author found that "a comparison of selected credit ratios for continuing and discontinuing companies reveals signs of comparative weakness in the latter as early as four or five years before the date of discontinuance" (Mervin, 1942, p. 3). Mervin's research was indeed one of the major  Beaver (1966) conducted a study to develop a mechanism for financial analysis applied to prediction of a firm's failure. Beaver's (1966) research included five years prior to failure financial data of 79 failed firms and five years prior according to the years that were assigned to their failed paired samples of 79 nonfailed firms within the period of 1954-1964. Firms were selected from the Moody´s Industrial Manual that were only industrial publicly owned. The selected failed firms were bankrupt, involved non-payment of preferred stock dividends, and had bond defaults or had an overdrawn bank account. Firms were also selected according to industry classification (38) and asset size using a pair-sample design. Beaver (1966) recognized that the study's results applied only to this kind of firms and that there was a major need to also study non-publicly owned and non-industrial firms. As well, the paired-sample design that Beaver used was not able to predict the failure of a firm under a single observation. In his study, the author (1966) selected all the firms with 30 ratios divided into six groups. The analysis was carried out by using a comparison of means (profile), a dichotomous classification (failed/non-failed) test, and an analysis of likelihood ratios (histogram). The results identified six financial ratios that were most likely predictive based on the highest percentage of failure prediction in each group: 1) cash flow/total debt; 2) net income/total assets; 3) total debt/total assets; 4) working capital/total assets; 5) current ratio; and 6) no-credit interval. This prediction was based on a bivariate normality, with some limitations, but Beaver's study demonstrated that asset size was not a directly correlated variable that would affect the prediction power of the proposed study. Recognizing the limitations of his study, Beaver (1966) also demonstrated that not all selected ratios have the same impact on prediction of a firm's failure, but each ratio has a different level of impact on it. This finding set up the basis for other authors to conduct further research on a weighted analysis of ratios. Beaver (1968) conducted another study related to alternative accounting measures as predictors of failure. He used the very same number of firms, period, and source of information that was used in his 1966 study. The new study included the selection of 14 ratios placed into three groups, one group of non-current assets including three ratios, and two more groups of current assets including 11 ratios. The research was based on the initial premise that current assets-based ratios were better predictors in the previous years of failure. Beaver (1968) also found that contrary to the initial premise, the error in predicting a failure classification for a firm through non-current assets was much lower than the ratios calculated on current assets, cash flow or net income. In addition, he found that many of the traditional assumptions for selecting the main or popular ratios for failure prediction were not a reliable criterion. For example, in his study he found "that the two less frequently advocated measures, net working capital and cash, outperformed current assets and quick assets, the two more frequently advocated measures" (Beaver, 1968, p. 119).
Since Beaver's (1968)  selected, a total of 22 financial ratios were compiled for evaluation and they were classified in five categories: liquidity, profitability, leverage, solvency, and activity. The discriminant function was transformed to a single discriminant score, or Z value where discriminant coefficients (weights) and independent variables (ratios) were determined. Altman (1968) concluded that all firms having a Z score of greater than 2.99 clearly fall into the "non-bankrupt" sector, while those firms having a Z score below 1.81 are all bankrupt. The area between 1.81 and 2.99 was defined as the "zone of ignorance" or "gray area" because of the susceptibility to error classification. So, the Z-score discriminant function remained as follows: Z= 1.  (Altman, 1983).
The discriminant model proved to be exceptionally accurate using financial information of one year prior to bankruptcy but, it was also significantly accurate with results of two years prior to bankruptcy.
The Z''-Score could be applied to all kinds of firms, including small and medium companies.
The model was tested under the univariate and multivariate discriminatory tests and Altman (1983) concluded that the results of the analysis "showed impressive evidence that bankruptcy can be predicted as much as two reporting periods prior to the event" (p. 125). This new version

Application of the Z''-Score model in developing countries
Regarding the application of Z''-Score model in developing countries, Altman et al. (2017) mention that, Grice and Ingram (2001)  also tested other similar techniques to MDA such as the logistic regression analysis (LRA), but performance results were similar. Even additional variables were tested, and the improvement of the model was not strong but variation in the effects were stronger by country. Consequently, Altman et al. (2017) found that "it is obvious that while a general international model works reasonably well, for most countries, the classification accuracy may be somewhat improved with country-specific estimation" (p. 167). In this sense Xu and Zhang (2009)

Method
The firms for this research were selected as a population of companies listed in the Mexican Stock Exchange, an emerging market. The specific source for the researched data were the annual reports since the data was available for those years under a somewhat stable economic situation without significant economic ups and downs. Since there could be a possible impact of previous economic crisis in the selected companies' financial performance, the 2012 year was selected as the initial year of study to allow at least three years of recovery from the latest known crisis in 2008. In that sense, the selected period provides a more standardized and stable period of financial information.
A methodological analysis proposal was elaborated as described in fig. 1. Since Altman et al.
(2017) proved in their latest research that the variables of age, industry and statistical method were not of significant impact on the Z''-Score model prediction, the census of firms listed in the BMV constituted a homogenous data based. Even reputation was a homogenous variable according to Diogenes et al. (2020) that found signs that companies with a high reputation have a lower risk of bankruptcy, which was the case of firms in the BMV.  As a first step, a census of the total listed Mexican companies was conducted, and a typology was identified. According to the BMV typology, a total of 170 companies whose shares are listed in the Mexican Stock Market A typology for all companies was created to determine the tendency of the Z''-Score and to allocate companies into one of the 17 classifications identified based on the propensity to bankruptcy or not in a company. The 17 classifications were place into two groups: 1) non-bankrupt sector and grey area group, and 2) the bankruptcy prediction group, including the number of periods in which the Z''-Score appeared to predict a bankruptcy. Later, a second analysis was conducted to determine the operational situation of the companies in the real market to confirm their actual situation regarding four possible options: continuous operation, financial challenges, financial distress, or legal bankruptcy. The first two situations would provide evidence that a company has either none or not significant financial problems that could possibly make them fall into bankruptcy. The last two situations would provide evidence to predict significant financial distress or even existence of a legal bankruptcy process in the companies. The results obtained were used to conduct the third and final analysis to determine in which cases the Z''-Score tendency agreed with the real situation of the company in the marketplace and hence established the percentage of assertiveness or error in the two predicted groups. The Z''-Score model was proved in an emerging economy such as Mexico and its level of effectiveness was demonstrated. The results are presented in the next section. companies to perhaps become a bankruptcy prediction. Also, the average indicator for each category was calculated, and the first two categories showed an average result far from the lower limit of each area, but also from the bankruptcy prediction. When results were analyzed as a percentage of the total indicators per year as shown in table 2, it was found that the non-bankrupt sector and grey areas had the largest variability measured by the     The categories were also grouped into two sub-groups. Sub-group 1 includes those companies which showed a level of Z''-Score indicators with a tendency to fall into the non-bankrupt sector and the grey area, and sub-group 2 includes those companies with a tendency to fall into the A second analysis was conducted in the 115 companies selected reviewing each one of the companies' information in the BMV, institutional webpage, financial information reports, stock market brokers reports, and financial newspapers of prestige. Information was gathered to prove if the predicted situation (area) by the Z''-Score corresponded to the real situation in the marketplace.

Results
In sub-group 1, a total of 87 companies were reviewed and support evidence was collected. In all the cases, evidence showed that the companies classified with a tendency of falling in the nonbankrupt sector and grey area, in fact, did not have significant financial distress that could possibly make them fall into bankruptcy. They could not have entered a bankruptcy process, operationally or legally. In sub-group 2, a total of 28 companies were reviewed to collect enough evidence to confirm, or not, if the companies were falling into the bankruptcy process, operationally, or legally.
This review was conducted within the two following years when the Z''-Score resulted under the 1.10 level established by the model. A greater detail on each one of the years in which the Z''-Score failed under the 1.10 level was needed since the prediction is established to happen within the next two years of operation of the company. Some companies had one or two years of a Z''-Score falling under the 1.10 level, but some others had even eight years. Based on the evidenced gathered, the results of the sub-group 2 showed that only seven companies classified as bankruptcy prediction by the Z''-Score were effectively in significant financial distress or started a legal process for bankruptcy under the Mexican legislation, or even under the USA legislation (those also listed in the New York Stock Exchange, NYSE). On the other hand, 21 companies showed enough evidence to assume that their financial situation was not distressful enough to go into bankruptcy or to start a legal process. This situation was contrary to the prediction of the model.
The model failed to predict the real situation of these companies within the two years following the Z''-Score indicator under the 1.10 level. The analysis conducted in sub-group 1 and sub-group 2 is summarized in table 5. As we can see, according to the original Z''-Score prediction model 82 % of the total predictions were verified as correct, but 18 % of the total predictions were incorrect.  There is a high level of error since Altman (1983)  Since several companies showed financial distress after more than two years of obtaining a Z''-Score level under 1.10, a reconsideration of the correctly and incorrectly predicted companies was conducted regardless of the number of years that happened. In this case, the results in table 6 demonstrate the changes for five companies located in the bankruptcy sector; that is, twelve companies were correctly classified in the bankruptcy prediction area. For some companies it took more than two years after the Z''-Score had fallen under the 1.10 level to start a bankruptcy process, or to show strong financial distress. On the other hand, without considering the time variable, 16 companies were still not classified correctly according to the Z''-Score indicators obtained. This consideration changed the results reaching an overall level of effectiveness for the model to an 86 % of the total prediction cases. However, 14 % of the total companies were misclassified since those companies never entered a bankruptcy process or showed significant financial distress. The evidence showed that the Z''-Score model still had a significantly high level of error that was much  Altman (1983). Even considering these new calculations, all the companies located by the Z''-Score model as non-bankrupt sector and grey area continued to be classified correctly. Nevertheless, the companies located in the bankruptcy prediction remained having all the misclassification cases, although the percentage of error went down to 57 %. Yet it was a too high error for prediction if a company has possibilities to be classified between sub-group 1 or sub-group 2. The model still failed in predicting these companies' real propensity to bankruptcy. It is also important to mention that nine out of 28 analyzed companies started a legal process of bankruptcy under the corresponding legislation. So, from the 12 companies that were correctly predicted in the bankruptcy prediction area, three companies had not started a legal process under the corresponding legislation. Those companies solved their financial situation by either conducting an internal re-structure of negotiating debt, bringing new financing to the company, or improving operational decisions, or doing all of them.
It was also found that some companies are of a high public interest, such as the airlines, and they are in constant re-structure and being helped to survive. in the year 2020 and the high economic impact in all the world economies. The previous information based on the warning confirmed by Moreno and Bravo (2018) in their research of Spanish firms proving that Altman's Z''-Score indicator is highly conditioned by market values and does not seem to have sufficient predictive capacity in a time of economic and financial crisis.

Conclusions
Predicting financial distress ahead of time is of great interest for all administrators. It is not an easy task but certain signals in the financial indicators can become a warning light and this predicting feature needs to be organized and turned into a useful tool. The Z-score model developed by Altman (1969) proved to be an efficient tool since its creation. As time and economic and social conditions change, the existing models needed to be reconsidered and re-tested. Findings in the latest research showed that the Z''-Score model was still highly accurate, but Altman (2005Altman ( , 2017Altman ( , 2018 also found that there was still a possibility for the model to grow in accuracy by considering some other variables that are country-specific, such as economic environment, legislation, culture, financial markets, accounting practices and, in the case of Mexico, government support or intervention. It was also proved by Grice and Ingram (2001) and by the authors of this paper that the Z''-Score model, in its actual version, does not perform with enough accuracy in the Mexican companies listed in the BMV. The percentage of error of the model is 18 % based on the original time frame.
Moreover, even if we do not consider the two years of time frame established in the Z''-Score model for the prediction of bankruptcy, the level of error is 14 %. This error is high enough to confirm the low accuracy of the model. So, it can be said that in general the actual Z''-Score model is efficient in detecting propensity to bankruptcy in developed countries. Nevertheless, based on the findings of this paper, it cannot be said that the actual Z''-Score model can predict bankruptcy in Mexican companies listed in the BMV with a high accuracy. The model needs to be re-calibrated through a set of country-specific variables in more research. Those characteristics can include specifics to the Mexican companies, such as propensity to re-organizing the internal finance, renegotiation of debt, and the survival attitude before financial challenges. Xu and Zhang (2009) also support this reasoning based on their research on Japanese listed companies, as well as AlAli (2018) who shows that the specific situations in Kuwait companies affect the result of the Z''-Score.
Several Mexican companies have tried to re-structure the company for several years even before on Ecuadorian companies, although the emerging economies have some parallel conditions or situations, it is believed that every single economy and stock market have differential characteristics that need to be taken into consideration when proving a model of prediction, in this case of bankruptcy. Based on the research findings it can be inferred that the Z''-Score model needs to be constantly updated and calibrated accordingly to conditions of several variables existing in each market. This paper has pointed out the three main variables that should be adjusted: prediction time, weights of variables, and zone values. The findings of this paper show enough evidence to suggest that the Z''-Score model cannot be applied accurately in all emerging markets. There will always be economical, cultural, social, and governmental conditions that will impact the performance of the companies in such a different manner. Regarding this, future research on the Z''-Score bankruptcy prediction model must be sequential, periodical, and situational. For future research, there is also an opportunity to test the different variables that bankruptcy prediction that the authors have identified with the different models. Despite the selection they have made of the most convenient variables (ratios) to predict bankruptcy in an accurate way, other ratios could be explored under the conditions of the emerging markets to confirm the previous findings or tom propose new variables. Concerning this study's limitations, further research could also be carried out of other authors' models. It also is crucial to mention that this research was conducted in large public corporations. There is also a considerable niche to conduct more research on the bankruptcy model applied to micro, small, and medium enterprises that are not listed in the stock market.
Although their financial statements are not published. That is a major challenge to engage in that kind of research, but there is an important need of new knowledge to help that kind of companies