Altman_1968

Financial Ratios, Discriminant Analysis and the Prediction of Corporate Bankruptcy Edward I. Altman The Journal of Finance, Vol. 23, No. 4. (Sep., 1968), pp. 589-609. Stable URL: http://links.jstor.org/sici?sici=0022-1082%28196809%2923%3A4%3C589%3AFRDAAT%3E2.0.CO%3B2-R The Journal of Finance is currently published by American Finance Association. Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at http://www.jstor.org/about/terms.html. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, non-commercial use. Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at http://www.jstor.org/journals/afina.html. Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printed page of such transmission. JSTOR is an independent not-for-profit organization dedicated to and preserving a digital archive of scholarly journals. For more information regarding JSTOR, please contact support@jstor.org. http://www.jstor.org Sun Jun 17 20:06:08 2007 The Journal of FINANCE VOL.XXIII SEPTEMBER 1968 No. 4 FINANCIAL RATIOS, DISCRIMINANT ANALYSIS AND T H E PREDICTION O F CORPORATE BANKRUPTCY ACADEMICIANSSEEM 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 compari- sons, widely used by practitioners. Since attacks on the relevance of 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 there- fore unfairly handicapped? Can we bridge the gap, rather than sever the link, between traditional ratio "analysis" and the more rigorous statistical tech- niques which have become popular among academicians in recent years? The purpose of this paper is to attempt an assessment of this issue-the quality of ratio analysis as an analytical technique. The prediction of corporate bankruptcy is used as an illustrative case.l Specifically, a set of financial and economic ratios will be investigated in a bankruptcy prediction context wherein a multiple discriminant statistical methodology is employed. The data used in the study are limited to manufacturing corporations. A brief review of the development of traditional ratio analysis as a technique for investigating corporate performance is presented in section I. In section I1 the shortcomings of this approach are discussed and multiple discriminant anal- ysis is introduced with the emphasis centering on its compatibility with ratio analysis in a bankruptcy prediction context. The discriminant model is devel- oped in section 111,where an initial sample of sixty-six firms is utilized to establish a function which best discriminates between companies in two mutu- ally exclusive groups: bankrupt and non-bankrupt firms. Section IV reviews empirical results obtained from the initial sample and several secondary sam- ples, the latter being selected to examine the reliability of the discriminant * Assistant Professor of Finance, New York University. The author acknowledges the helpful suggestions and comments of Keith V. Smith, Edward F. Renshaw, Lawrence S. Ritter and the Journal's reviewer. The research was conducted while under a Regents Fellowship a t the University of California, Los Angeles. 1. In this study the term bankruptcy will, except where otherwise noted, refer to those firms that are legally bankrupt and either placed in receivership or have been granted the right to re- organize under the provisions of the National Bankruptcy Act. 590 The Journal of Finance model as a predictive technique. In section V the model's adaptability to practi- cal decision-making situations and its potential benefits in a variety of situations are suggested. The final section summarizes the findings and conclusions of the study, and assesses the role and significance of traditional ratio analysis within a modern analytical context. The detection of company operating and financial difficulties is a subject which has been particularly susceptible to financial ratio analysis. 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 me r~han t s .~ Formal aggregate studies concerned with portents of business failure were evident in the 1930's. A study a t that time3 and several later ones concluded that failing firms exhibit significantly different ratio measurements than continuing entities.* In addition, another study was concerned with ratios of large asset-size corporations that experienced difficul- ties in meeting their fixed indebtedness obligation^.^ A recent study involved the analysis of financial ratios in a bankruptcy-prediction c o n t e ~ t . ~ This latter work compared a list of ratios individually for failed firms and a matched sample of non-failed firms. Observed evidence for five years prior to failure was cited as conclusive that ratio analysis can be useful in the prediction of failure. 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. The previous section cited several studies devoted to the analysis of a firm's condition prior to financial difficulties. Although these works established cer- tain important generalizations regarding the performance and trends of partic- ular measurements, the adaptation of their results for assessing bankruptcy 2 . For instance, the forerunner of well known Dun & Bradstreet, Inc. was organized in 1849 in Cincinnati, Ohio, in order to provide independent credit investigations. For an interesting and informative discussion on the development of credit agencies and financial measures of company performance see, Roy A. Foulke, Practical Financial Statement Analysis, 5th Ed., (New York, McGraw-Hill, 1961). 3. R. F. Smith and A. H. Winakor, Changes i n the Financial Structure of Unsziccessful Corpora- tions. (University of Illinois: Bureau of Business Research, 1935). 4. For instance, a comprehensive study covering over 900 firms compared discontinuing firms with continuing ones, see C. Merwin, Financing Small Corporations (New York: Bureau of Eco- nomic Research, 1942). 5 . W. B. Hickman, Corporate Bond Quality and Zttvestor Experience (Princeton, N.J.: Princeton University Press, 1958). 6. W. H. Beaver, "Financial Ratios as Predictors of Failure," Empirical Research itt Accounting, Selected Studies, 1966 (Institute of Professional Accounting, January, 1967), pp. 71-111. Also a recent attempt was made to weight ratios arbitrarily, see M. Tamari, "Financial Ratios as a Means of Forecasting Bankruptcy," Management International Review, Vol. 4 (1966), pp. 15-21. 591 Financial Ratios and Discriminant Analysis potential of firms, both theoretically and practically, is q~estionable.~ In almost every case, the methodology was essentially univariate in nature and emphasis was placed on individual signals of impending problems.* Ratio analysis pre- sented 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 aver- age liquidity, the situation may not be considered serious. The potential am- biguity 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 pre- dictive model. In so doing, the highlights of ratio analysis as an analytical technique will be emphasized rather than downgraded. The question becomes, which ratios are most important in detecting bankruptcy potential, what weights should be attached to those selected ratios, and how should the weights be objectively established. After careful consideration of the nature of the problem and of the purpose of the paper, a multiple discriminant analysis (MDA) was chosen as the appropriate statistical technique. Although not as popular as regression anal- ysis, 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 biologi- cal and behavioral sciences.'O More recently this method had been applied successfully to financial problems such as consumer credit evaluationl1 and investment classification. For instance in the latter area, Walter utilized a MDA model to classify high and low price earnings ratio firms,12 and Smith applied the technique in the classification of firms into standard investment categories.13 MDA is a statistical technique used to classify an observation into one of several a prior; groupings dependent upon the observation's individual charac- teristics. I t is used primarily to classify and/or make predictions in problems 7. At this point bankruptcy is used in its most general sense, meaning simply business failure. 8. Exceptions to this generalization were noted in works where there was an attempt to empha- size the importance of a group of ratios as an indication of overall performance. For instance, Foulke, op. cit., chapters XIV and XV, and A. Wall and R. W. Duning, Ratio Analysis of Finan- cial Statements, (New York: Harper and Row, 1928), p. 159. 9. R. A. Fisher, "The Use of Multiple Measurements in Taxonomic Problems," Annals of Eugenics, No. 7 (September, 1936), pp. 179-188. 10. For a comprehensive review of studies using MDA see W. G . Cochran, "On the Performance of the Linear Discriminant Function," Technometrics, vol. 6 (May, 1964), pp. 179-190. 11. The pioneering work utilizing MDA in a financial context uras performed by Durand in evaluating the credit worthiness of used car loan applicants, see D. D. Durand, Risk Elements in Consumer Installment Financing, Studies in Consumer Installment Financing (New York: National Bureau of Economic Research, 1941), pp. 105-142. More recently, Myers and Forgy analyzed several techniques, including MDA, in the evaluation of good and bad installment loans, see H. Myers and E. W. Forgy, 'LDevelopment of Numerical Credit Evaluation Systems," Journal of American Statistical Association, vol. 50 (September, 1963), pp. 797-806. 12. J. E. Walter, "A Discriminant Function for Earnings Price Ratios of Large Industrial Cor- porations," Review of Economics and Statistics, vol. XLI (February, 1959), pp. 44-52. 13. K. V. Smith, Classification o f Investment Securities Using MDA, Institute Paper #I01 (Purdue University, Institute for Research in the Behavioral, Economic, and Management Sciences, 1965). The Journal of Finance where the dependent variable appears in qualitative form, e.g., male or female, bankrupt or non-bankrupt. Therefore, the first step is to establish explicit group classifications. The number of original groups can be two or more. After the groups are established, data are collected for the objects in the groups; MDA then attempts to derive a linear combination of these character- istics 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 ratio, 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 dimen- sionality, i.e., from the number of different independent variables to G - 1 dimension(s), where G equals the number of original a prior; groups.14 This paper is concerned with two groups, consisting of bankrupt firms on the one hand, and of non-bankrupt firms on the other. Therefore, the analysis is trans- formed into its simplest form: one dimension. The discriminant function of the form Z =VI XI +vs x2 +. . . +Vn Xn transforms individual variable values to a single discriminant score or Z value which is then used to classify the object where vl, va, . . .v, =Discriminant coefficients XI, x2, . ..X, = Independent variables The MDA computes the discriminant coefficients, vj, while the independent variables xj are the actual values where, j = 1, 2, . . .n. 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 necessitates careful selection of the predictive variables (ratios), it also has the advantage of yielding a model with a relatively small number of selected measurements which has the potential of conveying a great deal of information. This information might very well indicate differences between groups but whether or not these differences are significant and meaningful is a more im- portant aspect of the analysis. To be sure, there are differences between bank- rupt firms and healthy ones; but are these differences of a magnitude to facilitate the development of an accurate prediction model? Perhaps the primary advantage of MDA in dealing with classification prob- lems is the potential of analyzing the entire variable profile of the object simultaneously rather than sequentially examining its individual characteristics. 14. For a formulation of the mathematical computations involved in MDA, see J. G . Bryan, '(The Generalized Discriminant Function, Mathematical Foundation & Computational Routine,'' Harvard Educational Review, vol. XXI, no. 2 (Spring, 1951), pp. 90-95, and C. R. Rao, Advanced Statistical Methods in Biometric Reseclrch (New York: John Wiley & Sons, Inc., 1952). 593 Financial Ratios and Discriminant Analysis Just as linear and integer programming have improved upon traditional tech- niques in capital budgeting15 the MDA approach to traditional ratio analysis has the potential to reformulate the problem correctly. Specifically, combina- tions of ratios can be analyzed together in order to remove possible ambiguities and misclassifications observed in earlier traditional studies. Given the above descriptive qualities, the MDA technique was selected as most appropriate for the bankruptcy study. A carefully devised and interpreted multiple regression analysis methodology conceivably could have been used in this two group case. Sample Selection. The initial sample is composed of sixty-six corporations with thirty-three firms in each of the two groups. The bankrupt group (1) are manufacturers that filed a bankruptcy petition under Chapter X of the National Bankruptcy Act during the period 1946-1965." The mean asset size of these firms is $6.4 million, with a range of between $0.7 million and $25.9 million. Recognizing that this group is not completely homogeneous, due to industry and size differences, a careful selection of non-bankrupt firms was attempted. Group 2 consisted of a paired sample of manufacturing firms chosen on a strati- fied random basis. The firms are stratified by industry and by size, with the asset size range restricted to between $1-$25 million.ls Firms in Group 2 were still in existence in 1966. 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 one reporting period prior to bankruptcy.ls 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 is quite rare today while the absence of comprehensive data negated the representation of small firms. A frequent argument is that financial ratios, by their very nature, have the effect of deflating statistics by size, and therefore a good deal of the size effect is eliminated. T o choose Group 1 firms in a restricted size range is not feasible, while selecting firms for Group 2 a t random seemed unwise. However, subsequent tests to the original sample do not use size as a means of stratification.'' 15. H. M. Weingartner, Mathematical Programming and the Analysis o f Capital Budgeting, Budgeting Problems, (Englewood Cliffs, New Jersey: Prentice-Hall, 1963). 16. The choice of a twenty year period is not the best procedure 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. However, the number of bankruptcies were approximately evenly distributed over the twenty year period in both the original and the secondary samples. 17. 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. 18. The data was derived from Moody's Industrial Manuals and selected Annual Reports. The average lead time of the finanaal statements was approximately seven and one-half months prior to bankruptcy. 19. One of these tests induded only firms that experienced operating losses (secondary sample of non-bankrupt firms). 594 The JournaE of Finance 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 twenty-two potentially helpful variables (ratios) is compiled for evaluation. The variables are classified into five standard ratio categories, including liquid- ity, profitability, leverage, solvency, and activity ratios. The ratios are chosen on the basis of their 1) popularity in the literature:' 2 ) potential relevancy to the study, and a few "new7' ratios initiated in this paper. From the original list of variables, five variables are selected as doing the best overall job together in the prediction of corporate bankr~ptcy.~ ' In order to arrive a t 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 vari- able; ( 2 ) evaluation of inter-correlations between the relevant vari