Altman’s Bankruptcy Prediction Model: Test on a Wide Out of Business Private Companies Sample

This study tests the accuracy of the Altman bankruptcy prediction model for a wide private companies’ sample that went bankrupt in the years 1985 to 2013. Financial ratios used in the model calculations, Z’-Score (Altman’s Z for private companies) also provide useful information on the solvency and probability of bankruptcy for privately held companies from the sample. The findings do not support the assertion that the Z’-Score can be generalized to countries and sectors different from industrial sector. The general number of bankruptcies may be an antecedent variable to certain economic and/or financial crises, but the results indicate a correct identification of bankruptcy risk only to two thirds of the sample of companies.


Introduction
The economic literature suggests that business activity is closely linked to the process of uncertainty. In this case, organizations, irrespective of the nature of their activity, may go through certain financial difficulties, even in periods that are not characterized by financial instabilities. [1] addressed the issue of corporate bankruptcy as an important phenomenon, because it compromises the financial performance and the continuity of business activity. Therefore, they stress that it is of interest to identify a possible signaling of this scenario, so that it is possible to decide with the purpose of reversing adversity and properly structuring the organization with the aim of reducing the possibility of bankruptcy. A seminal contribution on the subject was made by DOI: 10.4236/ib.2018.101002 22 iBusiness [2], with the aim of evaluating the prediction of bankruptcies of industrial companies through financial and accounting information, based on the multiple discriminant analysis technique. To do so, the author developed a set of ratios that generated higher explanation power for this issue. [3] pointed out that indicators of profitability, liquidity and solvency are relevant in a univariate analysis. However, in a univariate system, the order of importance among the indicators is not clear in the empirical literature; therefore, it is important to consider a combination of prediction measures for a better understanding of the issue.
Accordingly, it is in the interest of organizations to observe the validity of indicators capable of indicating a situation of bankruptcy of companies aimed at promoting changes, whether structural or managerial. On the other hand, public policy makers can appropriate this information to predict adverse scenarios and to carry out alternatives that mitigate this effect, since this context implies effects on the real economy, primarily on employment and income.
Thus, the main objective of this research is to test the validity of the Z'-Score proposed by [4], the focus of which consists of an understanding of the dynamics of solvency for private (i.e., closely-held) companies. For such, it is based on the multiple discriminant analysis with the respective weights determined by the author, from a sample with a set of 622 companies, represented by several segments and countries, derived from Capital IQ® between 1985 and 2013.
The main contribution of the study is to test the validity of Altman's model [4], not only for industrial companies, but also for a set of data from more than ten countries and nine different sectors of economic activity. Validity provides a broader understanding, in such a way that financial and accounting instruments, when properly constructed, can extract information relevant to the proposed theme. It is also relevant to determine whether this model can provide an instrument to observe scenarios of financial and/or economic crises-a context that would allow effective actions such as reversion measures.
The paper is divided into three sections, beside introduction and conclusion.
The first section describes the theoretical model of the Altman Z'-Score, the second one comprises an empirical review of the literature on such method, the third consists of the database and research method, and the last section presents the results and a discussion on the implications thereof. [2] reveals that detection of a scenario of companies in financial difficulties has been of interest in the literature but understanding the phenomenon of bankruptcy requires measures of ratios of financial indicators. Until that time, the literature indicated that profitability, liquidity and solvency were the most representative indicators, but they encompassed a univariate understanding of the indicators, which raises questions about the validity of their generalizations, since companies have different relative performances.

Corporate Bankruptcy
In which: X 1 : working capital/total assets X 2 : retained earnings/total assets X 3 : earnings before interest and taxes/total assets X 4 : market value of equity/total liabilities X 5 : sales/total assets Z: Z-Score (general ratio) The possible results of the Z-Score are presented in ranges, according to the following criteria: 1) Z-Score ≤ 1.80: comprises the low performance range, i.e., bankrupt zone; 2) 1.81 ≤ Z-Score ≤ 2.99: consists of the region of the gray zone, as it is susceptible to classification error; 3) Z-Score > 2.99: includes the area of companies with good financial performance, i.e., in healthy condition (non-bankrupt).
The results obtained by the author indicated that 94% of the companies of the sample were correctly identified, being this statistically significant result. [2] also considers that the results of the prediction model are accurate for up to two years before bankruptcy, although such accuracy diminishes with increasing analysis time, and considers applicability to be particularly useful for bankers, credit managers, executives and investors for decision making.
Subsequently, [4] constructed the Z'-Score model, specifically directed to closely-held industrial companies. Thus, the author revised the initial model of the Z-Score, substituting X 4 market value by the equity book value. Thus, the iBusiness discriminant model becomes:

Empirical Evidence
Based on the seminal works of Altman, several authors made use of the methods with two primary objectives. The first one consists of validating the multiple discriminant model proposed by the author, while the second one seeks to make diagnoses and projections regarding the companies' results, i.e., it comprises a more practical character in the sense of applying the method for use in evaluating companies.
The first group of studies is particularly interesting for this paper, since it not only encompasses the discussion of the Z-Score and Z'-Score as a method, but also broadens the discussion by inserting issues of an economic, institutional and legal nature, as well as allowing to identify any possible applications and generalizations.
First, it should be noted that some works, such as that of [6], [8], and [9] have a small sample of companies. Such a condition limits the results to the scope of generalizations, and suggests that they should be observed with caution by the Similarly, [6] considers the importance of the level of development of the capital market. A more solid and consolidated market attracts more investor resources, not only to speculative capital but also to the real sector of the economy.
Therefore, it allows for the expansion of the number of companies in the economy and increases the investment capacity of organizations.

Methodology
As the main objective of the paper is to test the accuracy of Altman's [4] model of prediction of bankruptcy for private companies, Z'-Score, the following hypotheses are proposed: H1: The Z'-Score is valid for private companies, that is, it has representative explanatory power, as evidenced by [2] [4].
H2: The Z'-Score is valid for companies from different countries. iBusiness One of contributions of the research is to test the validity of the Altman model [4] not only for North American companies, but for several different countries.
H3: The Z'-Score is valid for companies in different sectors, that is, it is explanatory for forecasting bankruptcy for any segment of economic activity.
Another contribution of the research is to test the validity of Altman's model [4], not only for industrial companies, but for a set of nine different sectors of economic activity, including the financial sector.
H4: From the sample selected by the Z'-Score criterion, it is possible to identify some variable antecedent to economic and/or financial crises.
H5: Crises of an economic and/or financial nature also affect the target sectors of the study under the premise of selecting the Z'-Score sample.
For the accomplishment of the tests, the procedures of collection, selection, cleaning, classification and synthesis are executed for later analysis.
The first collection is done in the database of Capital IQ® with all the companies that have registered in this and subsequently failed (status: out of business).   There is no significant difference between the Z-Score calculation methods.
The results were not very expressive, whose explanation is directly linked to the local characteristics, different sectors, and the limited period Size of the sample available for the capital market of Serbia. The financial indicators of taxes on profit were not published for some companies, which reduces the power of analysis. Moreover, the capital market in Serbia does not reflect the real value of the shares (it is an incipient market that is of little relevance in the country's economy) [7] Z-Score and Z'-Score The synthesis procedure for the characterization of the sample is started by grouping the companies by country, then ordering these from the largest to the smallest number of companies before calculating the cumulative percentage. Figure 1 presents the sample information of the five countries with the largest number of companies that have failed. They represent more than 91% of the total, 568 of 622. That does not mean that these countries have bigger problems with the survival of companies, but merely that they are countries which have companies that present data.
The second synthesis is done by grouping the companies by sectors, ordering from highest to lowest percentage (quantity) and calculating the percentage accumulated. The first five are: discretionary consumption (non-essential), information technology, industry and agriculture, financial, and health. They account for 84.72% of the total number of companies.

Analysis and Discussion of Results
The some companies may have achieved healthy Z'-Score results but signaled an adverse financial scenario a few years before bankruptcy. This is the scenario that guides the choice to observe the last five years in which there are data for the company before its bankruptcy.
Therefore, the definitive sample includes the 622 companies for the last five years of their activities, making 3110 firm-years Z'-Score calculations that are grouped into three classes: bankrupt, gray and non-bankrupt. This information is reported in Table 2. The precision column of the tables in this study shows the correctness and error values, given that the sample is from failed companies. The gray class is not considered in this analysis. Table 3 presents Z'-Score results at the company level. As the analysis is temporal, distinct from the version conducted by [4], the analysis is divided into three perspectives.
In   The second analysis perspective, presented in Table 4, involves some more rigid Z'-Score analysis criteria. Over the five years prior to bankruptcy, the number of bankruptcy evidences is considered. In this most rigorous scenario, five bankruptcies (bankruptcy results) are counted before companies' bankruptcy.  Table 5.
The result shows that the model could be still valid, but not robust, by correctly assigning only 53.38% bankruptcy condition of the data sample. The result   Therefore, inconsistencies were identified in the Altman method [4] in relation to the set of companies in this research, either in the temporal perspective or in the static perspective. This evidence converges with the findings of [10], and those of [11].
In this case, the temporal nature was not able to better explain the phenome- Many companies in the sample had a non-bankruptcy class but had a reversal of class one year before their bankruptcy. In these cases, the frequency of semiannual or quarterly data may yield more adequate results in this temporal issue.
The H2 hypothesis, which inquires if the Z'-Score is valid for companies from different countries, is tested by adopting this firm-year classification of Z'-Score of three classes and through the analysis of two. The correctness and error results are deployed per country. These results do not support the claim that the Z'-Score is valid for companies from different countries, that is, it has no support to the possibility of being generalized to jurisdictions different from the United States, its country of creation. One possible explanation could be as [9]   of accounting and financial indicators.
Hypothesis H3 asks if the Z'-Score is valid for companies of different sectors.
Adopting two classes, the results of correctness and error are deployed by sector, being valid for the period immediately before the break. It should be mentioned that the success rate is higher than 67% for the sectors of information technology, health, energy, materials, and telecommunications services. On the other hand, the non-essential consumption, essential consumption, and financial sectors had the lowest hit rates (below 50%). Therefore, it is possible to observe a higher rate of adjustment for companies in the service sector, given the lower performance of the indicator for trade and industry.
The H4 hypothesis inquires if, based on the selection criteria of the sample that meet the factors simultaneity, minimum amount of years, and continuity of data for each company for the calculation, the Z'-Score may present some antecedent variable of crises of an economic and/or financial nature. In other words, the sample was constituted considering all the accounting factors required to estimate the Z'-Score and, from this premise, the percentage change of bankruptcy of companies before and after some crisis-triggering period is verified.
The data set in Table 8 shows the rate of growth of corporate bankruptcy in the years before the outbreak of some economic/financial crises. There was a considerable increase in the number of corporate failures before the crises in Brazil (1999) and in the United States (2000 and 2008).
These results indicate that, possibly, a good part of the financial performance of the companies could be linked to the economic growth of the developed and emerging countries, or even to the American economy, and that financial stability, reduction in the economic trajectory, and even the flow of business was adversely affected, even if they originated in different countries. This scenario could explain the increase in bankruptcies, since it is a strong and adverse shock for entrepreneurs.   Similarly, it is noticeable that in the year after these crisis, many companies still went bankrupt, possibly due to the optimistic expectation of the entrepreneurs or the restrictive measures adopted by the governments that did not have a positive effect in the short term, to avoid a more representative fall in companies.
In the case of the United States (US) the variation between the year before the crisis cited is that it stands out. For the Internet bubble, it is possible to observe a variation of 205.88% a continuation of business downturn, with even more company failures after the crisis began, but with a decreasing rate that reached preceding. This factor could be attributed to the growth trajectory of bankruptcies in years before the crisis, that is, the adverse shock is smoothed over time, up to the event. Therefore, companies broke down at a more pronounced pace before the crisis, acting as a signal that the main event was yet to come. It is iBusiness worth mentioning that the epicenter of the crisis occurred in the United States, whose economy has a greater dynamism, and where government actions were representative of efforts to immediately contain the adverse effects on the economy, including in the recovery of companies and the re-heating of economic activity. In this context, the use of the Z'-Score criterion to define the sample could be relevant to try to help identify economic and/or financial crises as antecedent variables.
Hypothesis H5, from the selected sample with the criteria of the Z'-Score, asks if crises of an economic and/or financial nature also affect the target sectors of the study.
For this demonstration, the companies are grouped by year of their respective bankruptcies and by sector. The year of bankruptcy is understood as the first year in which the accounting information is no longer available for all the indicators necessary for the calculation of the Z'-Score.
Because of selected economic and financial crises, especially speculative in the period of analysis, it is particularly important to identify the segment that signaled the largest volume of corporate failures, since some may be more vulnerable to financial market crises, while others are more affected by events in the real economy.
In Figure 2 and Figure     In this case, the peak of bankruptcy of these segments occurs in the actual year of the crisis or in the immediately subsequent period.
On the other hand, the essential goods consumption sector points to a slightly upward trend in the period up to the year of the internet bubble crisis, with a peak just in that year. Already in later years, there is practically no representative variation in the series. This fact can be explained by the importance of the product offered by these companies having an inelastic demand, such that it is more persistent during periods of financial difficulty in the economy. The credit constraint-or even the increase in the interest rates of the contracts-could explain the periods of greater oscillation. This behavior indicates that this industry has specific characteristics, and little helps the method in identifying the crisis context.
The materials sector has an opposite behavior to the consumption of essential  In the context of this study, hypothesis H5, which states that economic and/or financial crises also affect the target sectors of the study, is weakened under the Z'-Score perspective, which may be particularly important for the performance of decision makers in order to conduct measures to stimulate economic activity or even mitigate the bankruptcy of companies with a view to preserving a more favorable economic environment for both the real economy and the financial point of view.
Therefore, it is possible to observe that even in a different economic context, with a more representative and segmented sample in more sectors and other economies, the Z'-Score model, containing multivariate data analysis of privately-held companies, needs further studies to infer if this is a valid instrument for the analysis of sector bankruptcy. However, the findings for the selected sample indicate, for now, that the model has only limited ability to predict company bankruptcy, since two-thirds of the sample of companies that effectively failed were correctly diagnosed with a bankruptcy scenario.
When analyzing the factors and their weights, it is possible to characterize the emphasis that the Z'-Score model has (multivariate discriminant model). Taking a temporal perspective as the basis, it is possible to classify these into factors more related to liquidity and more related to profitability. Each factor can be correctly interpreted as impacting the short and long term. In this analysis, it is assumed that a lack of profitability, for the short term, does not lead the company to bankruptcy, while a lack of liquidity does. Factors X 1 , X 2 and X 4 are classified iBusiness as more liquidity-related, factor X 3 to profitability, and X 5 cannot be classified since it can be in both categories.
Factor X 1 connotes the extent to which the operational aspects (working capital) are generators or cash takers versus the asset applications. The X 2 factor refers to the dividend policy, which, in the short term, impacts on the immediate cash level. Factor X 4 is related to leverage. This indebtedness is a liability that periodically impacts on the cash level in the short term. Factor X 3 is an indicator of profitability since it is measuring the operational return, i.e., it regards the long term. Factor X 5 is associated with asset turnover, where the level of sales substantially impacts on the available cash level. Discrimination in the form of receipt is not explicitly present, which compromises the liquidity analysis.
By observing the weights given to the factors, it is possible to do a proportionality analysis, taking the lowest weight (X 2 ) and dividing all the weights by it.
The result is shown in Table 9.
Short-term factors (X 1 , X 2 and X 4 ) that are directly linked to liquidity have weights that are significantly lower than the factor linked to profitability, X 3 , which is more than 36 times greater than the weight of the factor linked to the dividend policy. Even factor X 5 , which can be tied from the short to the long term, has a weight of less than a third of factor X 3 . Therefore, it is possible to infer that the model privileges the long-term factor over the short-term factor. This may also be indicative of improvements in the model in relation to the forecast of insolvency.
There is also the possibility that other factors not observed in the Altman multivariate model are important in identifying the risk of corporate bankruptcy. Intangible assets, information asymmetry, indicators of performance, risk, and efficiency, as well as the growth trajectory can help in understanding the phenomenon.

Conclusions
In testing the accuracy of the Altman bankruptcy forecasting model for a wide "out of business status" private companies sample that failed between 1985 and 2013, it can be seen that the 1993 model presented predictive power around 60%.
The financial ratios used in the model calculations and the Z'-Score was not supported that provides useful information on the chance of bankruptcy for the privately-held companies in the sample.
The results do not support that the Z'-Score has the potential to be generalized to jurisdictions different from the United States, its country of creation. Hig-iBusiness hlighting there may be distinctions between the models of accounting regimes between countries. It has also been shown to not be applicable to different industrial sectors, including financial ones. This fact does not support the robustness of the methodology proposed by Altman.
The presence of limitations on the results obtained, the method needs more investigations to assure if it acts as an instrument of analysis by both credit and financial companies, the managers of the companies themselves, and also in the strategy of public policies that can reflect directly on the activity of economic sectors.
Therefore, it is still open if this model may contribute to the understanding of an instrument prior to economic and/or financial crises, since it signals shortand medium-term trajectories of corporate bankruptcy.
It is important to continue these studies with the inclusion of other variables that can better understand the phenomenon, since a third of the sample indicated a non-bankruptcy scenario or was without result (gray), or else, the model itself may need revision before the distribution of the composition of weights for each indicator.