PREDICTING FINANCIAL DISTRESS OF COMPANIES: REVISITING THE Z-SCORE AND ZETA® MODELS

Edward I. Altman*

July 2000

*Max L. Heine Professor of Finance, Stern School of Business, New York University. This paper is adapted and updated from E. Altman, “Financial Ratios, Discriminant Analysis and the Prediction of Corporate Bankruptcy,” Journal of Finance, September 1968; and E. Altman, R. Haldeman and P. Narayanan, “Zeta Analysis: A New Model to Identify Bankruptcy Risk of Corporations,” Journal of Banking & Finance, 1, 1977.

Predicting Financial Distress of Companies: Revisiting the Z-Score and ZETA® Models

Background This paper discusses two of the venerable models for assessing the distress of industrial corporations. These are the so-called Z-Score model (1968) and ZETA® 1977) credit risk model. Both models are still being used by practitioners throughout the world. The latter is a proprietary model for subscribers to ZETA Services, Inc. (Hoboken, NJ). The purpose of this summary are two-fold. First, those unique characteristics of business failures are examined in order to specify and quantify the variables which are effective indicators and predictors of corporate distress. By doing so, I hope to highlight the analytic as well as the practical value inherent in the use of financial ratios. Specifically, a set of financial and economic ratios will be analyzed in a corporate distress prediction context using a multiple discriminant statistical methodology. Through this exercise, I will explore not only the quantifiable characteristics of potential bankrupts but also the utility of a much-maligned technique of financial analysis: ratio analysis. Although the models that we will discuss were developed in the late 1960’s and mid-1970’s, I will extend our tests and findings to include application to firms not traded publicly, to non-manufacturing entities, and also refer to a new bond-rating equivalent model for emerging markets corporate bonds. The latter utilizes a version of the Z-Score model called Z”. This paper also updates the predictive tests on defaults and bankruptcies through the year 1999. As I first wrote in 1968, and it seems even truer in the late 1990’s, academicians seem to be moving toward the elimination of ratio analysis as an analytical technique in assessing the performance of the business enterprise. Theorists downgrade arbitrary rules of thumb (such as

company ratio comparisons) widely used by practitioners. Since attacks on the relevance on ratio analysis emanate from many esteemed members of the scholarly world, does this mean that ratio analysis is limited to the world of “nuts and bolts?” Or, has the significance of such an approach been unattractively garbed and therefore unfairly handicapped? Can we bridge the gap, rather than sever the link, between traditional ratio analysis and the more rigorous statistical techniques which have become popular among academicians in recent years? Along with our primary interest, corporate bankruptcy, I am also concerned with an assessment of ratio analysis as an analytical technique. It should be pointed out that the basic research for much of the material in this paper was performed in 1967 and that several subsequent studies have commented upon the Z-Score model and its effectiveness, including an adaptation in 1995 for credit analysis of emerging market corporates. And, this author has co-developed a “second generation” model (ZETA) which was developed in 1976. Traditional Ratio Analysis The detection of company operating and financial difficulties is a subject which has been particularly amenable to analysis with financial ratios. Prior to the development of quantitative measures of company performance, agencies were established to supply a qualitative type of information assessing the credit-worthiness of particular merchants. (For instance, the forerunner of the well-known Dun & Bradstreet, Inc. was organized in 1849 in Cincinnati, Ohio, in order to provide independent credit investigations). Formal aggregate studies concerned with portents of business failure were evident in the 1930’s. One of the classic works in the area of ratio analysis and bankruptcy classification was performed by Beaver (1967). In a real sense, his univariate analysis of a number of bankruptcy

predictors set the stage for the multivariate attempts, by this author and others, which followed. Beaver found that a number of indicators could discriminate between matched samples of failed and nonfailed firms for as long as five years prior to failure. He questioned the use of multivariate analysis, although a discussant recommended attempting this procedure. The ZScore model did just that. A subsequent study by Deakin (1972) utilized the same 14 variables that Beaver analyzed, but he applied them within a series of multivariate discriminant models. The aforementioned studies imply a definite potential of ratios as predictors of bankruptcy. In general, ratios measuring profitability, liquidity, and solvency prevailed as the most significant indicators. The order of their importance is not clear since almost every study cited a different ratio as being the most effective indication of impending problems. Although these works established certain important generalizations regarding the performance and trends of particular measurements, the adaptation of the results for assessing bankruptcy potential of firms, both theoretically and practically, is questionable. In almost every case, the methodology was essentially univariate in nature and emphasis was placed on individual signals of impending problems. Ratio analysis presented in this fashion is susceptible to faulty interpretation and is potentially confusing. For instance, a firm with a poor profitability and/or solvency record may be regarded as a potential bankrupt. However, because of its above average liquidity, the situation may not be considered serious. The potential ambiguity as to the relative performance of several firms is clearly evident. The crux of the shortcomings inherent in any univariate analysis lies therein. An appropriate extension of the previously cited studies, therefore, is to build upon their findings and to combine several measures into a meaningful predictive model. In so doing, the highlights of ratio analysis as an analytical technique will be emphasized rather than downgraded. The questions are (1) which ratios are most important in

detecting bankruptcy potential, (2) what weights should be attached to those selected ratios, and (3) how should the weights be objectively established. Discriminant Analysis After careful consideration of the nature of the problem and of the purpose of this analysis, I chose multiple discriminant analysis (MDA) as the appropriate statistical technique. Although not as popular as regression analysis, MDA has been utilized in a variety of disciplines since its first application in the 1930’s. During those earlier years, MDA was used mainly in the biological and behavioral sciences. In recent years, this technique has become increasingly popular in the practical business world as well as in academia. Altman, et.al. (1981) discusses discriminant analysis in-depth and reviews several financial application areas. MDA is a statistical technique used to classify an observation into one of several a priori groupings dependent upon the observation’s individual characteristics. It is used primarily to classify and/or make predictions in problems where the dependent variable appears in qualitative form, for example, male or female, bankrupt or nonbankrupt. Therefore, the first step is to establish explicit group classifications. The number of original groups can be two or more. Some analysts refer to discriminant analysis as “multiple” only when the number of groups exceeds two. We prefer that the multiple concepts refer to the multivariate nature of the analysis. After the groups are established, data are collected for the objects in the groups; MDA in its most simple form attempts to derive a linear combination of these characteristics which “best” discriminates between the groups. If a particular object, for instance, a corporation, has characteristics (financial ratios) which can be quantified for all of the companies in the analysis, the MDA determines a set of discriminant coefficients. When these coefficients are applied to the actual ratios, a basis for classification into one of the mutually exclusive groupings exists.

The MDA technique has the advantage of considering an entire profile of characteristics common to the relevant firms, as well as the interaction of these properties. A univariate study, on the other hand, can only consider the measurements used for group assignments one at a time. Another advantage of MDA is the reduction of the analyst’s space dimensionally, that is, from the number of different independent variables to G-1 dimension(s), where G equals the number of original a priori groups. This analysis is concerned with two groups, consisting of bankrupt and nonbankrupt firms. Therefore, the analysis is transformed into its simplest form: one dimension. The discriminant function, of the form Z = V1X1 + V2X2 +…+ VnXn transforms the individual variable values to a single discriminant score, or z value, which is then used to

classify the object where

V1, X2, . . . . Vn = discriminant coefficients, and V1, X2, . . . . Xn = independent variables

The MDA computes the discriminant coefficient; Vi while the independent variables Xi are the actual values. When utilizing a comprehensive list of financial ratios in assessing a firm’s bankruptcy potential, there is reason to believe that some of the measurements will have a high degree of correlation or collinearity with each other. While this aspect is not serious in discriminant analysis, it usually motivates careful selection of the predictive variables (ratios). It also has the advantage of potentially yielding a model with a relatively small number of selected measurements which convey a great deal of information. This information might very well indicate differences among groups, but whether or not these differences are significant and meaningful is a more important aspect of the analysis. Perhaps the primary advantage of MDA in dealing with classification problems is the potential of analyzing the entire variable profile of the object simultaneously rather than

sequentially examining its individual characteristics. Just as linear and integer programming have improved upon traditional techniques in capital budgeting, the MDA approach to traditional ratio analysis has the potential to reformulate the problem correctly. Specifically, combinations of ratios can be analyzed together in order to remove possible ambiguities and misclassifications observed in earlier traditional ratio studies. As we will see, the Z-Score model is a linear analysis in that five measures are objectively weighted and summed up to arrive at an overall score that then becomes the basis for classification of firms into one of the a priori groupings (distressed and nondistressed). Development of the Z-Score Model Sample Selection The initial sample is composed of 66 corporations with 33 firms in each of the two groups. The bankrupt (distressed) group (Group 1) are manufacturers that filed a bankruptcy petition under Chapter X of the National Bankruptcy Act from 1946 through 1965. A 20-years period is not the best choice since average ratios do shift over time. Ideally, we would prefer to examine a list of ratios in time period t in order to make predictions about other firms in the following period (t+1). Unfortunately, it was not possible to do this because of data limitations. Recognizing that this group is not completely homogeneous (due to industry and size differences), I attempted to make a careful selection of nonbankrupt (nondistressed) firms. Group 2 consists of a paired sample of manufacturing firms chosen on a stratified random basis. The firms are stratified by industry and by size, with the asset size range restricted to between $1 and $25 million. The mean asset size of the firms in Group 2 ($9.6 million) was slightly greater than that of Group 1, but matching exact asset size of the two groups seemed unnecessary. Firms in group 2 were still in existence at the time of the analysis. Also, the data collected are from the

same years as those compiled for the bankrupt firms. For the initial sample test, the data are derived from financial statements dated one annual reporting period prior to bankruptcy. The data were derived from Moody’s Industrial Manuals and also from selected annual reports. The average lead-time of the financial statements was approximately seven and one-half months. An important issue is to determine the asset-size group to be sampled. The decision to eliminate both the small firms (under $1 million in total assets) and the very large companies from the initial sample essentially is due to the asset range of the firms in Group 1. In addition, the incidence of bankruptcy in the large-asset-size firm was quite rare prior to 1966. This changed starting in 1970 with the appearance of several very large bankruptcies, e.g., PennCentral R.R. Large industrial bankruptcies also increased in appearance, since 1978. In all, there have been at least 100 Chapter 11 bankruptcies with over $1 billion since 1978 (the year of the existing Bankruptcy Code's enactment). A frequent argument is that financial ratios, by their very nature, have the effect of deflating statistics by size, and that therefore a good deal of the size effect is eliminated. The ZScore model, discussed below, appears to be sufficiently robust to accommodate large firms. The ZETA model did include larger sized distressed firms and is unquestionably relevant to both small and large firms. Variable Selection After the initial groups are defined and firms selected, balance sheet and income statement data are collected. Because of the large number of variables found to be significant indicators of corporate problems in past studies, a list of 22 potentially helpful variables (ratios) was complied for evaluation. The variables are classified into five standard ratio categories, including liquidity, profitability, leverage, solvency, and activity. The ratios are chosen on the

basis of their popularity in the literature and their potential relevancy to the study, and there are a few “new” ratios in this analysis. The Beaver study (1967) concluded that the cash flow to debt ratio was the best single ratio predictor. This ratio was not considered in my 1968 study because of the lack of consistent and precise depreciation and cash flow data. The results obtained, however, were still superior to the results Beaver attained with his single best ratio. Cash flow measures were included in the ZETA model tests (see later discussion). From the original list of 22 variables, five are selected as doing the best overall job together in the prediction of corporate bankruptcy. This profile did not contain all of the most significant variable measured independently. This would not necessarily improve upon the univariate, traditional analysis described earlier. The contribution of the entire profile is evaluated and, since this process is essentially iterative, there is no claim regarding the optimality of the resulting discriminant function. The function, however, does the best job among the alternatives which include numerous computer runs analyzing different ratio profiles. In order to arrive at a final profile of variables, the following procedures are utilized: (1) observation of the statistical significance of various alternative functions, including determination of the relative contributions of each independent variable; (2) evaluation of intercorrelations among the relevant variables; (3) observation of the predictive accuracy of the various profiles; and (4) judgment of the analyst. The final discriminant function is as follows: Z = 0.012X1 + 0.014X2 + 0.033X3 + 0.006X4 +0.999X5 where X1 = working capital/total assets, X2 = retained earnings/total assets, X3 = earnings before interest and taxes/total assets, X4 = market value equity/book value of total liabilities, X5 = sales/total assets, and

Z = overall index. Note that the model does not contain a constant (Y-intercept) term. This is due to the particular software utilized and, as a result, the relevant cutoff score between the two groups is not zero. Other software program, like SAS and SPSS, have a constant term, which standardizes the cutoff score at zero if the sample sizes of the two groups are equal. X1, Working Capital/Total Assets (WC/TA). The working capital/total assets ratio, frequently found in studies of corporate problems, is a measure of the net liquid assets of the firm relative to the total capitalization. Working capital is defined as the difference between current assets and current liabilities. Liquidity and size characteristics are explicitly considered. Ordinarily, a firm experiencing consistent operating losses will have shrinking current assets in relation to total assets. Of the three liquidity ratios evaluated, this one proved to be the most valuable. Two other liquidity ratios tested were the current ratio and the quick ratio. There were found to be less helpful and subject to perverse trends for some failing firms. X2, Retained Earnings/Total Assets (RE/TA). Retained earnings is the account which reports the total amount of reinvested earnings and/or losses of a firm over its entire life. The account is also referred to as earned surplus. It should be noted that the retained earnings account is subject to "manipulation" via corporate quasi-reorganizations and stock dividend declarations. While these occurrences are not evident in this study, it is conceivable that a bias would be created by a substantial reorganization or stock dividend and appropriate readjustments should be made to the accounts. This measure of cumulative profitability over time is what I referred to earlier as a “new” ratio. The age of a firm is implicitly considered in this ratio. For example, a relatively young

firm will probably show a low RE/TA ratio because it has not had time to build up its cumulative profits. Therefore, it may be argued that the young firm is somewhat discriminated against in this analysis, and its chance of being classified as bankrupt is relatively higher than that of another older firm, ceteris paribus. But, this is precisely the situation in the real world. The incidence of failure is much higher in a firm’s earlier years. In 1993, approximately 50% of all firms that failed did so in the first five years of their existence (Dun & Bradstreet, 1994). In addition, the RE/TA ratio measures the leverage of a firm. Those firms with high RE, relative to TA, have financed their assets through retention of profits and have not utilized as much debt. X3, Earnings Before Interest and Taxes/Total Assets (EBIT/TA). This ratio is a measure of the true productivity of the firm’s assets, independent of any tax or leverage factors. Since a firm’s ultimate existence is based on the earning power of its assets, this ratio appears to be particularly appropriate for studies dealing with corporate failure. Furthermore, insolvency in a bankrupt sense occurs when the total liabilities exceed a fair valuation of the firm’s assets with value determined by the earning power of the assets. As we will show, this ratio continually outperforms other profitability measures, including cash flow. X4, Market Value of Equity/Book Value of Total Liabilities (MVE/TL). Equity is measured by the combined market value of all shares of stock, preferred and common, while liabilities include both current and long term. The measure shows how much the firm’s assets can decline in value (measured by market value of equity plus debt) before the liabilities exceed the assets and the firm becomes insolvent. For example, a company with a market value of its equity of $1,000 and debt of $500 could experience a two-thirds drop in asset value before insolvency. However, the same firm with $250 equity will be insolvent if assets

drop only one-third in value. This ratio adds a market value dimension which most other failure studies did not consider. The reciprocal of X4 is a slightly modified version of one of the variables used effectively by Fisher (1959) in a study of corporate bond yield-spread differentials. It also appears to be a more effective predictor of bankruptcy than a similar, more commonly used ratio; net worth/total debt (book values). At a later point, we will substitute the book value of net worth for the market value in order to derive a discriminant function for privately held firms (Z’) and for non-manufacturers (Z”). More recent models, such as the KMV approach, are essentially based on the market value of equity and its volatility. The equity market value serves as a proxy for the firm's asset values. X5, Sales/Total Assets (S/TA). The capital-turnover ratio is a standard financial ratio illustrating the sales generating ability of the firm’s assets. It is one measure of management’s capacity in dealing with competitive conditions. This final ratio is quite important because it is the least significant ratio on an individual basis. In fact, based on the univariate statistical significance test, it would not have appeared at all. However, because of its unique relationship to other variables in the model, the sales/total assets ratio ranks second in its contribution to the overall discriminating ability of the model. Still, there is a wide variation among industries in asset turnover, and we will specify an alternative model (Z”), without X5 at a later point. A Clarification The reader is cautioned to utilize the model in the appropriate manner. Due to the original computer format arrangement, variables X1 through X4 must be calculated as absolute percentage values. For instance, the firm whose net working capital to total assets (X1) is 10%

should be included as 10.0% and not 0.10. Only variable X5 (sales to total assets) should be expressed in a different manner: that is, a S/TA ratio of 200% should be included as 2.0. The practical analyst may have been concerned by the extremely high relative discriminant coefficient of X5. This seeming irregularity is due to the format of the different variables. Table 1 illustrates the proper specification and form for each of the five independent variables. Over the years many individuals have found that a more convenient specification of the model is of the form: Z = 1.2X1 + 1.4X2 + 3.3X3 + 0.6X4 + 1.0X5. Using this formula, one inserts the more commonly written percentage, for example, 0.10 for 10%, for the first four variables (X1-X4) and rounds the last coefficient off to equal 1.0 (from 0.99). The last variable continues to be written in terms of number of times. The scores for individual firms and related group classification and cutoff scores remain identical. We merely point this out and note that we have utilized this format in some practical application, for example, Altman and LaFleur (1981). Table 1 Variable Means and Test Significance Bankrupt Nonbankrupt n Group Mean Group Meann -6.1% 41.4% -62.6% 35.5% -31.8% 15.4% 40.1% 247.7% 1.5X 1.9X

Variable X1 X2 X3 X4 X5 N = 33. F1.60 (0.001) = 12.00; F1.60 (0.01) = 7.00; F1.60 (0.05) = 4.00 *Significant at the 0.001 level. Variable Tests

F Ration 32.50* 58.86* 26.56* 33.26* 2.84

A test to determine the overall discriminating power of the model is the F-value which is the ratio of the sums-of-squares between-groups to the within-groups sums-of-squares. When this ratio is maximized, it has the effect of spreading the means (centroids) of the groups apart

and, simultaneously, reducing dispersion of the individual points (firm Z-values) about their respective group means. Logically, this test (commonly called the F-test) is appropriate because the objective of the MDA is to identify and utilize those variables which best discriminate between groups and which are most similar within groups. The group means of the original two-group sample are: Group 1 = -0.29 Group 2 = +5.02 F = 20.7 F4n (0.01) = 3.84

The significance test therefore rejects the null hypothesis that the observations come from the same population. Variable means measured at one financial statement prior to bankruptcy and the resulting F-statistics were shown in Table 1. Variables X1 through X4 are all significant at the 0.001 level, indicating extremely significant differences in these variables among groups. Variable X5 does not show a significant difference among groups and the reason for its inclusion in the variable profile is not apparent as yet. On a strictly univariate level, all of the ratios indicate higher values for the nonbankrupt firms. Also, all of the discriminant coefficients display positive signs, which is what one would expect. Therefore, the greater a firm’s distress potential, the lower its discriminant score. It is clear that four of the five variables display significant differences between groups, but the importance of MDA is its ability to separate groups using multivariate measures. Once the values of the discriminant coefficients are estimated, it is possible to calculate discriminant scores for each observation in the samples, or any firm, and to assign the observations to one of the groups based on this score. The essence of the procedure is to compare the profile of an individual firm with that of the alternative groupings. The

comparisons are measured by a chi-square value and assignments are made based upon the relative proximity of the firms’ score to the various group centroids. Initial Sample (Group 1) The initial sample of 33 firms in each of the two groups is examined using data compiled one financial statement prior to distress. Since the discriminant coefficients and the group distributions are derived from this sample, a high degree of successful classification is expected. This should occur because the firms are classified using a discriminant function which, in fact, is based upon the individual measurements of these same firms. The classification matrix for the original sample is shown in Table 2. Table 2 Classification Results, Original Sample Number Percent Percent Correct Correct Error

n

Predicted____ Actual Group 1 Group 2 Group 1 31 2 Group 2 1 32

Type 1 Type II Total

31 32 63

94 97 95

6 3 5

33 33 66

The model is extremely accurate in classifying 95% of the total sample correctly. The Type I error proved to be only 6% while the Type II error was even lower at 3%. The results, therefore, are encouraging, but the obvious upward bias should be kept in mind, and further validation techniques are appropriate. Results Two Statements Prior to Bankruptcy The second test observes the discriminating ability of the model for firms using data compiled two statements prior to distress. The two-year period is an exaggeration since the average lead time for the correctly classified firms is approximately 20 months, with two firms having a 13-month lead. The results are shown on Table 3. The reduction in accuracy is

understandable because impending bankruptcy is more remote and the indications are less clear. Nevertheless, 72% correct assignment is evidence that bankruptcy can be predicted two years prior to the event. The Type II error is slightly larger (6% vs. 3%) in this test, but still it is extremely accurate. Further tests will be applied below to determine the accuracy of predicting bankruptcy as much as five years prior to the actual event. Table 3 Classification Results, Two Statements Prior to Bankruptcy Number Percent Percent Predicted_________ Correct Correct Error n Actual Group 1 Group 2 (Bankrupt) (Non-Bankrupt) Group 1 23 9 Group 2 2 31 Type 1 23 72 28 32 Type II 31 94 6 33 Total 54 83 17 65

Potential Bias and Validation Techniques When the firms used to determine the discriminant coefficients are reclassified, the resulting accuracy is biased upward by (1) sampling errors in the original sample; and (2) search bias. The latter bias is inherent in the process of reducing the original set of variables (22) to the best variable profile (5). The possibility of bias due to intensive searching is inherent in any empirical study. While a subset of variables is effective in the initial sample, there is no guarantee that it will be effective for the population in general. The importance of secondary sample testing cannot be overemphasized. One type of secondary sample testing is to estimate parameters for the model using only a subset of the original sample, and then to classify the remainder of the sample based on the parameters established. A simple t-test is then applied to test the significance of the results. Five different

replications of the suggested method of choosing subsets (16 firms) of the original sample are tested. The test results reject the hypothesis that there is no difference between the groups and substantiate that the model does, in fact, possess discriminating power on observations other than those used to establish the parameters of the model. Therefore, any search bias does not appear significant. Secondary Sample of Bankrupt Firms In order to test the model rigorously for both bankrupt and nonbankrupt firms, two new samples are introduced. The first contains a new sample of 25 bankrupt firms whose asset size range is similar to that of the initial bankrupt group. On the basis of the parameters established in the discriminant model to classify firms in this secondary sample, the predictive accuracy for this sample as of one statement prior to bankruptcy is described in Table 4. The results here are surprising in that one would not usually expect a secondary sample’s results to be superior to the initial discriminant sample (96% vs. 94%). Two possible reasons are that the upward bias normally present in the initial sample tests is not manifested in this investigation and/or that the model, as stated before, is not optimal.

Table 4 Classification Results, Secondary Sample of Bankrupt Firms Bankrupt Group (Actual) Predicted_________ Number Percent Percent Correct Correct Error Bankrupt Non-Bankrupt 24 n = 25 1

Type I (Total)

24

96

4

Testing the Model on Subsequent Distressed Firm’s Samples In three subsequent tests, I examined 86 distressed companies from 1969-1975, 110 bankrupts from 1976-1995 and 120 from 1997-1999. I found that the Z-Score model, using a cutoff score of 2.675, was between 82% and 94% accurate. For an in-depth discussion of these studies, see below. In repeated tests up to the present (1999), the accuracy of the Z-Score model on samples of distressed firms has been in the vicinity of 80-90%, based on data from one financial reporting period prior to bankruptcy. The Type II error (classifying the firm as distressed when it does not go bankrupt), however, has increased substantially with as much as 15-20% of all firms and 10% of the largest firms having Z-Scores below 1.81. Recent tests, however, show the average Z-Score increasing significantly with the average rising from the 4-5 level in 1970-1995 period to almost 10 (ten) in 1999 (see Osler and Hong [2000] for these results, shown below in Figure 1. But, the media level has not increased much. The majority of increase in average Z-Scores was due to the dramatic climb in stock prices and its impact on X4. I advocate using the lower bond of the zone-of-ignorance (1.81) as a more realistic cutoff Z-Score than the score 2.675. The latter resulted in the lowest overall error in the original tests. In 1999, the proportion of U.S. industrial firms, comprised in the Compustat data tapes, that had Z-Scores below 1.81 was over 20%.

FIG U R E 1
Average Z-Scores: US Industrial Firms 1975-1999
12

10

8

6

M ean

4

2

0 Mar-75 Mar-77 Mar-79 Mar-81 Mar-83 Mar-85 Mar-87 Mar-89 Mar-91 Mar-93 Mar-95 Mar-97 Mar-99

Source: Osler and Hong, 2000.

Secondary Sample of Nonbankrupt Firms Up to this point, the sample companies were chosen either by their bankruptcy status (Group I) or by their similarity to Group I in all aspects except their economic well-being. But what of the many firms which suffer temporary profitability difficulties, but actually do not become bankrupt? A bankruptcy classification of a firm from this group is an example of a Type II error. An exceptionally rigorous test of the discriminant model’s effectiveness would be to search out a large sample of firms that have encountered earning problems and then to observe the Z-Score’s classification results. In order to perform the above test, a sample of 66 firms is selected on the basis of net income (deficit) reports in the years 1958 and 1961, with 33 from each year. Over 65% of these firms had suffered two or three years of negative profits in the previous three years. The firms are selected regardless of their asset size, with the only two criteria being that they were manufacturing firms which suffered losses in the year 1958 or 1961. The companies are then evaluated by the discriminant model to determine their bankruptcy potential. The results show that 14 of the 66 firms are classified as bankrupt, with the remaining 52 correctly classified. Therefore, the discriminant model correctly classified 79% of the sample firms. This percentage is all the more impressive when one considers that these firms constitute a secondary sample of admittedly below-average performance. The t-test for the significance of the result is 5=4.8; significant at the 0.001 level. Another interesting facet of this test is the relationship of these “temporarily” sick firms’ Z-Scores and the “zone of ignorance.” The zone of ignorance is that range of Z-Scores where misclassification can be observed. Of the 14 misclassified firms in this secondary sample, 10 have Z-Scores between 1.81 and 2.67, which indicates that although they are classified as bankrupt, the prediction of their

bankruptcy is not as definite as it is for the vast majority in the initial sample of bankrupt firms. In fact, just under one-third of the 66 firms in this last sample have Z-Scores within the entire overlap area, which emphasizes that the selection process is successful in choosing firms which showed signs (profitability) of deterioration. Although these tests are based on data from over 40 years ago, they do indicate the robustness of the model which is still in use in the year 2000. Long-Rang Accuracy The previous results give important evidence of the reliability of the conclusions derived from the initial and holdout samples of firms. An appropriate extension would be to examine the overall effectiveness of the discriminant model for a longer period of time prior to bankruptcy. To answer this question, data are gathered for the 33 original firms from the third, fourth, and fifth years prior to bankruptcy. One would expect on an a priori basis that, as the lead time increases, the relative predictive ability of any model would decrease. This was true in the univariate studies cited earlier, and it is also quite true for the multiple discriminant model. We will shortly see, however, that the more recent model (e.g., ZETA®) has demonstrated higher accuracy over a longer period of time. Based on the above results, it is suggested that the Z-Score model is an accurate forecaster of failure up to two years prior to distress and that accuracy diminishes substantially as the lead time increases. We also performed a trend analysis on the individual ratios in the model. The two most important conclusions of this trend analysis are (1) that all of the observed ratios show a deteriorating trend as bankruptcy approaches, and (2) that the most serious change in the majority of these ratios occurred between the third and the second years prior to bankruptcy. The degree of seriousness is measured by the yearly change in the ratio values. The latter observation is extremely significant as it provides evidence consistent with conclusions derived

from the discriminant model. Therefore, the important information inherent in the individual ratio measurement trends takes on deserved significance only when integrated with the more analytical discriminant analysis findings. Average Z-Scores Over Time As Table 5 shows, we have tested the Z-Score model for various sample periods over the last 30 years. In each test, the Type I accuracy using a cutoff score of 2.67 ranged from 82-94%, based on data from one financial statement prior to bankruptcy or default on outstanding bonds. Indeed, in the most recent test, based on 120 firms which defaulted on their publicly held debt during 1997-1999, the default prediction accuracy rate was 94% (113 out of 120). Using the more conservative 1.81 cutoff, the accuracy rate was still an impressive 84%. The 94%, 2.67 cutoff accuracy is comparable to the original sample’s accuracy which was based on data used to construct the model itself. We can, therefore, conclude that the Z-Score model has retained its reported high accuracy and is still robust despite its development over 30 years ago. In the last decade, however, the Type II accuracy, has increased to about 15-20% of those manufacturing firms listed on Compustat. Adaptation for Private Firms’ Application Perhaps the most frequent inquiry that I have received from those interested in using the Z-Score model is, “What should we do to apply the model to firms in the private sector?” Credit analysts, private placement dealers, accounting auditors, and firms themselves are concerned that the original model is only applicable to publicly traded entities (since X1 requires stock price data). And, to be perfectly correct, the Z-Score model is a publicly traded firm model and ad hoc

Table 5 Classification & Prediction Accuracy Z-Score (1968) Failure Model*
Year Prior To Failure 1 2 3 4 5 Original Sample (33) 94% (88%) 72% 48% 29% 36% Holdout Sample (25) 96% (92%) 80% 1969-1975 Predictive Sample (86) 82% (75%) 68% 1976-1995 Predictive Sample (110) 85% (78%) 75% 1997-1999 Predictive Sample (120) 94% (84%) 74% -

* Using 2.67 as cutoff score (1.81 cutoff accuracy in parenthesis)

adjustments are not scientifically valid. For example, the most obvious modification is to substitute the book value of equity for the market value and then recalculate V4X4. Prior to this writing, analysts had little choice but to do this procedure since valid alternatives were not available. A Revised Z-Score Model Rather than simply insert a proxy variable into an existing model to calculate z-scores, I advocate a complete reestimation of the model, substituting the book values of equity for the Market Value in X4. One experts that all of the coefficients will change (not only the new variable’s parameter) and that the classification criterion and related cutoff scores would also change. That is exactly what happens. The results of our revised Z-Score model with a new X4 variable is: Z’ = 0.717(X1) + 0.847(X2) + 3.107(X3) + 0.420(X4) + 0.998(X5) The equation now looks different than the earlier model; note, for instance, the coefficient for X1 went from 1.2 to 0.7. But, the model looks quite similar to the one using Market Values. The actual variable that was modified, X4, showed a coefficient change to 0.42 from 0.6001; that is, it now has less of an impact on the Z-Score. X3 and X5 are virtually unchanged. The univariate F-test for the book value of X4 (25.8) is lower than the 33.3 level for the market value but the scaled vector results show that the revised book value measure is still the third most important contributor. Table 5 lists the classification accuracy, group means, and revised cutoff scores for the Z'-Score model. The Type I accuracy is only slightly less impressive than the model utilizing market value of equity (91% vs. 94%) but the Type II accuracy is identical (97%). The nonbankrupt group's mean Z'Score is lower than that of the original model (4. 14 vs. 5.02). Therefore, the distribution of scores is now tighter with larger group overlap. The gray area (or

ignorance zone) is wider, however, since the lower boundary is now 1.23 as opposed to 1.81 for the original Z-Score model. All of this indicates that the revised model is probably somewhat less reliable than the original, but only slightly less. Due to lack of a private firm data base, we have not tested this model extensively on secondary sample distressed and nondistressed entities. A recent model from Moody’s (2000) utilizing data on middle market firms and over 1600 defaults, concentrates on private firms. A Further revision - Adapting the Model for Non-Manufacturers The next modification of the Z-Score model analyzed the characteristics and accuracy of

Table 6

Revised Z'Score Model: Classification Results, Group Means, and Cutoff Boundaries ________________________________________________________________________ Actual Classified ______________________________________________________________________________ Bankrupt Nonbankrupt Total Bankrupt 30 3 33 (90.9%) (9.1%) Nonbankrupt 1 32 33 ( 3.0%) (97.0%) ______________________________________________________________________________ Note: Bankrupt group mean = 0.15; nonbankrupt group mean = 4.14. Z' 1, then there will be an added cost element in C1. This added element involves the lost interest on that remaining part of the loan which is not recovered (GLLLLR) for the duration of the defaulted loan. We will examine C11 below, but will not include this added element in our calculation of C1. Again, however, it is clear that we are underestimating C1 somewhat.

Recoveries in the Public Bond Market While there has been almost no rigorous studies published which quantify the effective costs of lending errors for loans and other private placements, a number of recent studies have documented losses in the public bond markets, e.g., Altman & Eberhart (1994), Moody's (1995) and Standard & Poor's (1995). The former documents recoveries at default and also upon emergence from Chapter 11. These public bond market studies observe recoveries stratified by bond seniority. For commercial loans, the most likely equivalents to the public bond market are the straight (non-convertible) senior secured and senior unsecured classes. Table 10 lists these recoveries at the time of default and upon emergence from Chapter 11. ______________________________________________________________________________ Table 10 Bond Recoveries (Percent of Par Value), By Seniority, at Default and Upon Emergence from Chapter 11 ______________________________________________________________________________ Recovery At Recovery Upon Bond Priority N Default Emergence ______________________________________________________________________________ Senior Secured 24 60.51% 100.91% Senior Unsecured 71 52.28 81.05 Senior Subordinated 35 30.70 23.38 Subordinated 54 27.96 32.41 ______________________________________________________________________________ Source: Altman & Eberhart (1994) and Altman (1993). We have measured C1 based on annual report data from 26 of the largest U.S. commercial banks and questionnaire returns from a sample of smaller, regional banks in the Southeast U.S. A questionnaire was sent to approximately 100 Southeast banks with 33 usable responses. The range of commercial bank asset sizes in this small-bank sample was between $12 million and $3 billion, with the average equal to $311 million and the median equal to $110 million. The large-bank sample's asset size averaged $13.4 billion with a $10 billion median.

Both the data sources encompass a five-year period, 1971-1975 inclusive, and we measure the average loan loss recovery statistics for senior unsecured loans on a contemporary and a one-year lag (recoveries lagging charge-offs) basis. The results of this investigation show that the average C1 on a contemporary basis is in the 76.7 - 83.0% range; when measured on a one-year lag basis, the averages are lower (68.6 - 72.2%). The year 1975 was an abnormally high loan charge-off year in the U.S. banking system and since this data is included in the contemporary statistics but not in the one-year lag data, we believe the more representative result for C1 is in the vicinity of 70%. We use this statistic for C1. The simple formula for C11 specifies that the decision not to lend to an account that would have repaid successfully forgoes the return on that loan, but the loss is mitigated by the alternative use of loanable funds. In its strictest sense, the bank's opportunity cost implies another loan at the same risk which is assumed to pay off. In this case, C11 is probably zero or extremely small. Conservatively speaking, however, an account is rejected due to its high risk characteristics and alternative uses probably will carry lower risk attributes. Hence, r-i will be positive but still quite low. Carried to the other extreme, the alternative use would be an investment in a riskless asset, i.e., government securities of the same maturity as the loan, and r-i will be somewhat higher - perhaps 2-4%. The relationship between r-i will vary over time and is particularly sensitive to the demand and supply equilibrium relationship for loanable funds. As an approximation, we specify C11 = 2%, hence C1/C11 is equal to 35 times (0.70/0.02). Revised cutoff score and model efficiency tests With respect now to the calculation of the critical or cutoff score ZETAc, we have,

ZETAc = ln

q1C1 0.02 ⋅ 0.70 = = ln 0.714, q 2 C11 0.98 ⋅ 0.02

ZETAc = − 0.338.
Before comparing the efficiency of the various alternative bankruptcy classification strategies, it should be noted that the observed classification accuracy of a model such as ZETA will change with the new cutoff score. For example, with the cutoff score of -0.337, the number of type I errors increases from two (3.8%) to four (7.6%), while the type II errors decreases from 6(10.3%) to 4(7.0%). Adjustments to the Cutoff Score and Practical Applications In addition to the utilization of prior probabilities of group membership and cost estimates of classification errors for comparative model efficiency assessment, these inputs could prove valuable for practical application purposes. For instance, the bank lending-officer or loanreview analyst may wish to be able to logically adjust the critical cutoff score to consider his own estimates of group priors and error costs and/or to reflect current economic conditions in the analysis. One could imagine the cutoff score falling (thereby lowering the acceptance criterion) as business conditions improve and the banker's prior probability of bankruptcy estimate falls form say 0.02 to 0.015. Or, a rise in cutoff scores could result from a change (rise) in the estimate of the type I error cost vis-à-vis the type II error cost. The latter condition possibly will occur for different decision-makers. For instance, the cost to a portfolio manager of not selling a security destined for failure is likely to be extremely high relative to his cost of not investing in a stock (which does not fail) due to its relatively low ZETA. The portfolio manager may indeed want to raise the cutoff or threshold level to reduce the possibility of intangible (law suit costs) as well as tangible (lower prices) costs involved with holding a failed company's stock. Another example of a practical application of cutoff score adjustment is the case of an accounting auditor. He might wish to use the model to decide whether a 'going concern'

qualified opinion should be applied. His expected cost for doing so is likely to be quite high (loss of client) relative to the expected cost of a stockholder law suit. This might lead to a fairly low cutoff score. On the other hand, the environment may be such that the law suit expected cost is prohibitive. Conclusions The ZETA model for assessing bankruptcy risk of corporations demonstrates improved accuracy over existing failure classification model (Z-Score) and, perhaps more importantly, is based on data more relevant to current conditions and to a larger number of industrial firms. Recall, however, our use of the Z" model for non-manufacturers. We are concerned with refining existing distress classification techniques by the use of the most relevant data combined with developments in the application of discriminant analysis to finance. The ZETA model's bankruptcy classification accuracy ranges from over 96 (93% holdout) percent one period prior to bankruptcy to 70% five annual reporting periods prior. We have assessed the effect of several elements involved with the application of discriminant analysis to financial problems. These include linear vs. quadratic analysis for the original and holdout samples, introduction of prior probabilities of group membership and costs of error estimates into the classification rule, and comparison of the model's results with naïve bankruptcy classification strategies. The potential applications of the ZETA bankruptcy identification model are in the same spirit as previously developed models. These include credit worthiness analysis of firms for financial and non-financial institutions, identification of undesirable investment risk for portfolio managers and individual investors and to aid in more effective internal and external audits of firms with respect to going-concern considerations, among others.

Appendix A

Listing of all Variables, Group Mean, and F-tests Based on one Period Prior to Bankruptcy Data (ZETA Model Sample) ______________________________________________________________________________ Variable Population Means Univariate ______________________________________________________________________________ No. Name Failed Non-Failed F-Test ______________________________________________________________________________ (1) EBIT/TA -0.0055 0.1117 54.3 (2) NATC/TC -0.0297 0.0742 36.6 (3) Sales/TA 1.3120 1.6200 3.3 (4) Sales/TC 2.1070 2.1600 0.0 (5) EBIT/Sales 0.0020 0.0070 30.2 (6) NATC/Sales -0.0153 0.0400 33.1 (7) Log tang. Assets 1.9854 2.2220 5.5 (8) Interest coverage -0.5995 5.3410 26.1 (9) Log no. (8) 0.9625 1.1620 26.1 (10) Fixed charge coverage 0.2992 2.1839 15.7 (11) Earnings/debt -0.0792 0.1806 32.8 (12) Earnings 5 yr. Maturities -0.1491 0.6976 8.8 (13) Cash/flow fixed charges 0.1513 2.9512 20.9 (14) Cash flow/TD -0.0173 0.3136 31.4 (15) WC/LTD 0.3532 2.4433 6.0 (16) Current ratio 1.5757 2.6040 38.2 (17) WC/total assets 0.1498 0.3086 40.6 (18) WC/cash expenses 0.1640 0.2467 5.2 (19) Ret.earn/total assets -0.0006 0.2935 114.6 (20) Book equity/TC 0.2020 0.5260 64.5 (21) MV equity/TC 0.3423 0.6022 32.1 (22) 5yr.MV equity/TC 0.4063 0.6210 31.0 (23) MV equity/total liabilities 0.6113 1.8449 11.6 (24) Standard error of estimate of EBIT/TA (norm) 1.6870 5.784 33.8 (25) EBIT drop -3.2272 3.179 9.9 (26) Margin drop -0.2173 0.179 15.6 (27) Capital lease/assets 0.2514 0.178 4.2 (28) Sales/fixed assets 3.1723 4.179 3.5 ______________________________________________________________________________ Notation: EBIT = earnings before interest and taxes NATC = net available for total capital TA = total tangible assets LTD = long term debt MV = market value of equity TC = total capital TD = total debt WC = working capital CF = cash flow (before interest #13,after interest #14)

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Osler, C. and G. Hong, “Rapidly Rising Corporate Debt: Are Firms Now Vulnerable to an Economic Slowdown?” Current Issues in Economics & Finance, Federal Reserve Bank of New York, June 2000. Standard & Poor's, "Corporate Defaults Level Off in 1994," L. Brand, T. K. Ho, and R. Bahar, CreditWeek, May 1, 1995.