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A re-examination of two major bankruptcy prediction models Jin, Ming 1993

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A RE-EXAMINATION OF TWO MAJOR BANKRUPTCY PREDICTION MODELSbyMING JINA THESIS SUBMITTED IN PARTIAL FULFILMENT OFTHE REQUIREMENTS FOR THE DEGREE OFMASTER OF SCIENCE IN BUSINESS ADMINISTRATIONinTHE FACULTY OF GRADUATE STUDIESCommerce and Business AdministrationWe accept this thesis as conformingTHE UNIVERSITY OF BRITISH COLUMBIAApril, 1993Ming Jin, 1993In presenting this thesis in partial fulfilment of the requirements for an advanceddegree at the University of British Columbia, I agree that the Library shall make itfreely available for reference and study. I further agree that permission for extensivecopying of this thesis for scholarly purposes may be granted by the head of mydepartment or by his or her representatives. It is understood that copying orpublication of this thesis for financial gain shall not be allowed without my writtenpermission.(Signature) Department ofThe University of British ColumbiaVancouver, CanadaDate Apr,/ .2g^P7f3DE-6 (2/88)ABSTRACTThis thesis examines two major bankruptcy prediction modelsexisting in the literature: Altman's Z-score model and Ohlson'sprobabilistic model. The objective is to test whether the modelparameters have changed from what they were when Altman and Ohlsonoriginally estimated their models. Two reasons for expecting theparameter change are examined: (i) the change in U.S. bankruptcylaw in the 1970s; and (ii) the increased use of financial leveragein the 1980s.The first portion of this thesis reviews the bankruptcyprediction literature and discusses the change in U.S. bankruptcylaw and capital structure. The evidence presented in this studyindicates that business failures have increased since 1980 andfinancial leverage follows an upward trend from the 1970s to the1980s.The following four hypotheses associated with the originalAltman and Ohlson models are developed: (1) the Type-I ErrorHypothesis: the change in U.S. bankruptcy law in the 1970sincreases the Type-I (classifying bankrupt firms as nonbankrupt)error rate; (2) the Type-II Error Hypothesis: the increased use ofleverage in the 1980s increases the Type-II (classifyingnonbankrupt firms as bankrupt) error rate; (3) the InterceptHypothesis: the change in the bankruptcy law in the 1970s willcause a significant increase in the intercept in Ohlson's model;and (4) the Leverage Hypothesis: the increased use of leverage iniithe 1980s will result in a significant decrease in the coefficienton TLTA (total liabilities /total assets) in Ohlson's model.The remaining portion of the thesis discusses sample design andtests the four hypotheses. Two samples from the 1980s are examined:a paired sample of 99 bankrupt and 99 nonbankrupt firms; and asample of 99 bankrupt firms and 1,980 nonbankrupt firms. Usingthese samples, the predictive abilities of Altman's and Ohlson'smodels are examined and the models are reestimated to test the fourhypotheses. For Altman's model, the empirical results areconsistent with the Type-II Error Hypothesis but inconsistent withthe Type-I Error Hypothesis. For Ohlson's model, the results arealso consistent with the Type-II Error Hypothesis but inconsistentwith the Type-I Error Hypothesis. While the empirical results ofreestimating Ohlson's model support the Leverage Hypothesis, theydo not support the Intercept Hypothesis.iiiTABLE OF CONTENTSPageABSTRACT ^  iiTABLE OF CONTENTS ^  ivLIST OF TABLES  viLIST OF FIGURES ^  viiACKNOWLEDGMENTS  viiiCHAPTER 1 - INTRODUCTION  ^1CHAPTER 2 - LITERATURE REVIEW ^  62.1 Financial Distress and Bankruptcy  ^62.2 Existing Bankruptcy Models in the Literature  ^82.2.1 Altman's Z-score Model  ^82.2.2 Ohlson's Probabilistic Model ^  122.3 The Role of Ratios in Predicting Bankruptcy ^ 182.3.1 Traditional Use of Ratios ^  182.3.2 Major Prediction Models  192.3.3 Choice of Predictive Variables ^  222.4 Reasons to Expect That the Model Parameters HaveChanged ^  252.4.1 Change in the Bankruptcy Law ^  252.4.2 Change in Capital Structure  362.5 Hypotheses and Plan for the Following Analysis ^ 42CHAPTER 3 - DATA COLLECTION AND DESCRIPTIVE STATISTICS ^ 453.1 Data Collection ^  45iv3.2 Descriptive Statistics ^  50CHAPTER 4 - MODEL TEST AND REESTIMATION ^  524.1 The Predictive Abilities of Altman's and Ohlson'sModels ^  524.1.1 Test of Altman's Z-score Model ^ 524.1.2 Test of Ohlson's Model ^  564.1.3 Summary of the Results on Predictive Ability ^ 584.2 Model Reestimation ^  614.2.1 Reestimation of Altman's Model ^ 614.2.2 Reestimation of Ohlson's Model  674.2.2.1 Maximum-Likelihood Estimation of LogitModel ^  674.2.2.2 Empirical Results ^  69CHAPTER 5 - CONCLUSIONS ^  79BIBLIOGRAPHY ^  84APPENDIX A Listing of Bankrupt and Liquidated Firms ^ 89LIST OF TABLESTable^ Page2-1 Ohlson's Estimated Bankruptcy Prediction Models ^ 172-2 Variables Used in Major Empirical Studies ofBankruptcy ^  242-3 Industrial and Commercial Failures ^  342-4 Total Debt-to-Total Assets Ratios  403-1 Distribution of Bankrupt Firms by Year and by StockExchange ^  483-2 Profile Analysis of the Bankrupt and NonbankruptFirms in the Sample ^  514-1 Comparison of Type-I & Type-II Error Rates FromApplying Altman's Model to His Own Sample Versusthe 1980s Sample ^  544-2 Comparison of Type-I & Type-II Error Rates FromApplying Ohlson's Model to His Own Sample Versusthe 1980s Sample ^  584-3 Profile Analysis of the Variables Used toReestimate Altman's Model ^  624-4 Comparison between Altman's Model and theReestimated Model ^  644-5 Predictive Ability of the Reestimated Altman ModelOne and Two Years Prior to Bankruptcy ^ 664-6 Profile Analysis of the Variables Used toReestimate Ohlson's Model ^  704-7 Correlation Matrix of the Independent VariablesUsed to Reestimate Ohlson's Model ^  724-8 Results of Reestimating Ohlson's Model  734-9 Test for a Significant Change in the Parameters ofOhlson's Model When Reestimated Using the 1980sData  ^764-10 Type-I & Type-II Errors for Selected Cutoff Points ... 78viLIST OF FIGURESFigure^ Page1 Annual Failure Rates 1961-1988 ^  352 Yearly Debt-to-Total Assets Ratios 1972-1990 ^ 41viiACKNOWLEDGEMENTSI am most grateful to Dr. Joy Begley who provided guidance andadvice throughout this study. I am also grateful to Dr. Susan Wattsfor her good suggestion and assistance with this thesis. Finally,I sincerely thank Dr. Ronald Giammarino who reviewed this thesisand made valuable comments.viiiCHAPTER 1INTRODUCTIONPrediction of corporate bankruptcy has long been an issue ofpractical and academic interest. A number of researchers haveattempted to construct statistical models to predict the potentialbankruptcy of corporate firms. The data used for the prediction isusually gathered from publicly available financial information. Thestatistical technique used extensively in the earlier studies isdiscriminant analysis. The aim is to classify firms into one of twogroups, bankrupt or nonbankrupt. Beaver (1966) first used suchanalysis to predict firm failure by examining individual financialratios. Later, Altman (1968) employed multiple discriminantanalysis to distinguish between bankrupt and nonbankrupt firmsbased on a set of predesignated variables. Altman's multivariatemodel overcomes the univariate model's problem of different ratiosgiving conflicting predictions.A different statistical approach is the probabilisticprediction model which was initially used in bankruptcy predictionby Ohlson in 1980. Ohlson's model estimates the probability ofbankruptcy occurring based on a set of predesignated variables. Themodel also improves upon previous bankruptcy prediction models incertain aspects such as sample selection and the inclusion of firmsize as an independent variable.A correct and early identification of the bankruptcy event isof particular importance to investors, creditors, auditors and1management itself. Foster (1986) indicates that a successfulbankruptcy prediction model can be of assistance to investors indebt securities when they assess the likelihood of a firmexperiencing problems in making interest and principal repayments.He also states that research on bankruptcy prediction has relevanceto lending institutions, both in deciding whether to grant a loan(and its conditions) and in devising policies to monitor existingloans. Altman and McGough (1974) suggest that a bankruptcyprediction model can also be a useful aid to an auditor in makinga going-concern judgement. Furthermore, Foster argues that"bankruptcy can mean that a firm incurs both direct and indirectcosts. Direct costs include fees to professionals such asaccountants and lawyers. Indirect costs include the lost sales orprofits due to the constraints imposed by the court-appointedtrustee. ... It may well be that if early warning signals ofbankruptcy were observed, these costs could be reduced bymanagement arranging a merger with another firm or adopting acorporate reorganization plan at a more propitious time."Therefore, Deakin (1972) points out that a model that correctlypredicts potential business failure well in advance can serve toreduce losses associated with bankruptcy by providing an earlyindication of impending bankruptcy to these interested parties.Altman's and Ohlson's models appear to be the two mostfrequently referenced bankruptcy prediction models in theaccounting literature. There is considerable evidence that thesemodels continue to be popular today. Altman's model is more popular2among financial analysts, while academic researchers appear toprefer to use Ohlson's model to estimate the relative probabilityof bankruptcy among firms. Academic books frequently suggestAltman's model as a potential tool used by analysts to forecastfinancial distress.1 Investment management books, designed forpractitioners, also suggest the use of Altman's model forinvestment decision making.2 Even some financial analysis softwarepackages incorporate Altman's model in their analysis.3 Altman'sand Ohlson's models are also very popular in academic research.Altman's model is frequently used by academics as an indicator ofbankruptcy risk.4 Ohlson's model is also often used and referencedin academic research.5Although both Altman's and Ohlson's models frequently appear inthe literature, they are by no means perfect measures of thelikelihood of bankruptcy. One potential limitation of both modelsis that they are estimated based upon data from the 1940s-1970s.'For example, the books of Foster (1986), Watts and Zimmerman(1986), Hawkins (1986), Brealey et al. (1986), Finnerty (1986),Yadav (1986), Brigham et al. (1987), Bernstein (1993) and Stickney(1993) all make references to the use of Altman's model. Inaddition, Foster (1986), Watts and Zimmerman (1986), and Yadav(1986) also reference Ohlson's model.2For example, Platt (1985), Shim and Siegel (1988), andRamaswami and Moller (1989).3Forexample, "FisCAL: Financial Analysis and Planning ComputerSoftware Package" distributed by the Halcyon Group.4For example, O'Neal (1988), Becker and Burns (1989), and Shim(1992).5For example, Lo (1986), Barnes (1986), Lau (1987), Burgstahleret al. (1989), Bell and Tabor (1991), and Han et al. (1992).3Their applicability outside of that period is, therefore,questionable. It is expected that the model parameters have changedfrom what they were when Altman and Ohlson developed their models.There are two major reasons why the model parameters are expectedto have changed. The first reason is that the bankruptcy law in theU.S. changed dramatically in the late 1970s. The change inbankruptcy law reduced the costs of filing bankruptcy, therefore,the law change is expected to increase the number of firms filingfor bankruptcy. The second reason is the increased use of financialleverage in the 1980s. Due to the proliferation of LeveragedBuyouts (LB0s) and other highly leveraged transactions in the1980s, capital structure has changed dramatically for more and morefirms.6 Brealey and Myers (1991) state that for the debt ratio ofmanufacturing corporations in the U.S. "there is a clear upwardshift from the 1950s to the 1980s. Recent events have dramatizedthe shift to debt financing. The rapid growth of the junk bondmarket means by definition that firms have levered up: Junk is junkbecause firms have borrowed beyond conventional targets." (p.331).Because financial leverage is a significant factor in both Altman'sand Ohlson's models, the increased use of debt in the 1980s islikely to change the parameters of the models.The purpose of this paper is to test whether the modelparameters have changed from what they were when Altman and Ohlsondeveloped their models. In order to do so, the predictive abilitiesof the two models are tested and the models are reestimated using6Empirical evidence on this point is presented in Chapter 2.4data from the 1980s. There are other ways in which Altman's andOhlson's models might be further improved to increase their abilityto predict bankruptcy.7 However, it is not the purpose of thisstudy to address these issues.The paper is organized as follows. Chapter 2 provides a reviewof the literature. The change in U.S. bankruptcy law and the changein capital structure are discussed. The evidence on businessfailures over three decades and evidence of increased use ofleverage in the 1980s are presented. Four hypotheses associatedwith Altman's and Ohlson's models are developed. Chapter 3discusses the data and sample design. Two samples are collectedfrom Compustat. The sample used to test Altman's model consists of99 bankrupt and 99 nonbankrupt firms and the sample for testingOhlson's model consists of 99 bankrupt and 1,980 nonbankrupt firms.Both samples cover the 1981-1990 time period. Chapter 4 tests thefour hypotheses given in Chapter 2. First, the predictive abilitiesof Altman's and Ohlson's original models are examined using the1980s samples. Then, Altman's and Ohlson's models are reestimatedin order to test for a significant change of the model parameters.Chapter 5 concludes the thesis.'For example, the predictive ability of the models could beimproved by adding additional variables that are expected to relateto the occurrence of bankruptcy. Also, different model estimationtechniques such as a Cox proportional hazard model or a stepwiseprocedure might yield superior models.5CHAPTER 2LITERATURE REVIEW2.1 FINANCIAL DISTRESS AND BANKRUPTCYIn the bankruptcy prediction literature,^the terms"bankruptcy" and "financial distress" are used frequently andalternatively. Many studies do not indicate their relation anddifference and sometimes confusion results. Therefore, it isnecessary to discuss them here.Foster (1986) defines financial distress as "severe liquidityproblems that cannot be resolved without a sizable rescaling of afirm's operations or structure." Liquidity problems result fromnon-availability of cash or near-cash resources for meeting thefirm's current obligations. As a firm increases its financialleverage, it increases the probability of its financial distress.When a firm is in financial distress, both creditors andshareholders may want it to recover. The firm may resolve itsliquidity problems via a dramatic rescaling of its operations (forexample, the firm can sell the portion of its asset base) or amerger with another firm. However, in other respects, raisingfinancial leverage increases the probability of potential conflictsbetween shareholders and creditors. "Shareholders are tempted toforsake the usual objective of maximizing the overall market valueof a firm and pursue narrow self-interest instead. They are tempted6to play games at the expense of their creditors." 8 In this case,creditors may utilize covenants to restrict shareholders'behaviours that will reduce the firm's value.Bankruptcy is a legal process and is usually easier to identifythan financial distress. Bankruptcy occurs when either creditors orshareholders petition for a bankruptcy order. Once a petition isfiled, a third party, the bankruptcy court, will enter, and thefirm will inevitably be reorganized or liquidated. Brealey andMyers (1984) state that liquidation is usually voluntary butsometimes involuntary. A licensed trustee will be appointed to takepossession of and distribute all the assets of a firm. Altman(1983) notes that a petition for reorganization can be enteredvoluntarily or involuntarily. When a firm faces temporary financialproblems and the business is viable in the long run, reorganizationmay be a suitable solution.Although bankruptcy is associated with financial distress, theyare not equivalent. Financial distress can lead to bankruptcy.However, as Brealey and Myers (1984) suggest "not every firm whichis financially distressed becomes bankrupt. As long as the firm canfind enough cash to pay its debt when due, it may be able to avoidbankruptcy for many years. Eventually, the firm may recover, payoff its debt, and escape bankruptcy altogether."Many models have been developed to predict bankruptcy. Why arepeople so interested in those models? The major reason is thatpeople want to avoid the costs resulting from doing business with8Brealey and Myers (1984), p.395.7a firm that may not meet its obligation. That is, people want to beable to predict the financial distress of the firm. However,financial distress cannot be observed with precision. People canobserve only something related to the distress - filingbankruptcy. Thus, the studies that would like to develop a modelpredicting distress, have instead been forced to limit themselvesto predicting bankruptcy.2.2 EXISTING BANKRUPTCY MODELS IN THE LITERATUREA number of studies have constructed statistical models topredict the potential bankruptcy of firms. Many statisticalmethodologies, such as, linear discriminant analysis, quadraticdiscriminant analysis, logit analysis and probit analysis, havebeen used. Altman's Z-score model and Ohlson's probabilistic modelare the two models most commonly mentioned in the literature.2.2.1^ALTMAN'S 2-SCORE MODELAltman (1968) develops a bankruptcy prediction model usingMultivariate Discriminant Analysis (MDA). This technique allows aresearcher to study the differences between two or more groups ofobjects with respect to several variables simultaneously. Thetechnique is primarily used for the classification or prediction ofqualitative variables, for example, bankrupt or nonbankrupt. Anobservation is classified into one of several a priori groups,8dependent upon the observation's individual characteristics.Therefore, first of all, two or more mutually exclusive groupsshould be established, based on objects. "Objects are the basicunits of analysis. They may be, for example, people, firms,countries, or the economy at different points in time. In the caseof bankruptcy, each firm is an object. The groups must be definedso that each object belongs to one, and only one, group."9"After the groups are established, data is collected for theobjects in the groups; MDA in its most simple form attempts toderive a linear combination of these characteristics which 'best'discriminates between the groups. If a particular object, forinstance, a firm, has characteristics (financial ratios) which canbe quantified for all of the companies in the analysis, the MDAdetermines a set of discriminant coefficients. When thesecoefficients are applied to the actual ratios, a basis forclassification into one of the mutually exclusive groups exists. "1°When the analysis is concerned with two groups, lineardiscriminant analysis for classification into two a priori groupsresults in one discriminant function of the form:Z = co + ciX, + c2X2 + ... +c,X,where9Klecka (1980), p.8.'°Altman (1971), p.59.9Xi = the i-th classification variable,ci = the coefficient value of Xi,Z = the discriminant score.The discriminant function thus transforms the value of theindividual variables (the Xis) of the object into a singlediscriminant score (Z). Z is then used to classify the object."The MDA technique has the advantage of considering an entireprofile of characteristics common to the relevant firms, as well asthe interaction of these properties. A univariate prediction model,on the other hand, can only consider the measurements used forgroup assignments one at a time. 01 "Another advantage of MDA isthe reduction in the analyst's space dimensionality, that is, fromthe number of different independent variables to G-1 dimension(s),where G equals the number of original a priori groups. linIn constructing his model, Altman uses a paired sampleconsisting of thirty-three pairs of manufacturing firms over theperiod 1946-1965. The range of the total assets (i.e., size of thebankrupt firms) is 0.7-25.9 million dollars one year prior tobankruptcy. For each of the bankrupt firms, a comparable match ischosen from the same industry and asset size and is measured overthe same chronological period. Twenty-two accounting andnonaccounting variables are considered in various combinations as"Ibid. p.59.12Ibid. p.59.10predictors of failure. The following combined ratios performed thebest:X1 = net working capital/total assetsX2 = retained earnings/total assetsX3 = earnings before interest and taxes/total assetsX4 = market value of equity/book value of total liabilitiesX5 = sales/total assetsWith the exception of X5, each ratio discriminates wellindividually between the groups. The mean values of the ratios forthe bankrupt group are significantly smaller than for thenonbankrupt group.The estimated discriminant function is"Z = .012X1 + .014X2 + .033X3 + .006; + .999X5By observing those firms which have been misclassified by thediscriminant model in the initial sample, Altman finds that allfirms having a Z-score greater than 2.99 clearly fall into thenonbankrupt group, while those firms having a Z-score below 1.81are all bankrupt. The area between 1.81 and 2.99 is defined as thezone of ignorance or gray area because of the susceptibility toerror classification. Since errors are observed in this range ofvalues, there is uncertainty about whether a new firm whose Z-scorefalls in this range is expected to go bankrupt or not. Hence, it is"With the exception of X5, all ratios are being measured inpercentages.11desirable to establish a guideline for classifying firms in thisarea. The process used by Altman begins with identification of thesample observations that fall within the overlapping range. Then,the minimum number of misclassifications is found. In the analysis,the best critical value falls between 2.67 and 2.68, and therefore2.675, the midpoint of the interval, is chosen as the Z-score thatdiscriminates best between the bankrupt and nonbankrupt firms.The accuracy of Altman's model in the prediction of bankruptcycan be measured by the total error rate in classifying his sample.He reports an overall error rate of 5 per cent one year prior tobankruptcy and 18 per cent two years prior to bankruptcy. Beyondtwo years the accuracy in prediction falls very rapidly: the errorrate is 48 per cent in the third year prior to bankruptcy.2.2.2 OHLSON'S PROBABILISTIC MODELOhlson (1980) uses a logit model to predict bankruptcy. Thelogit model is a conditional probability model. Conditionalprobability models assume that firms are faced with an outcomebetween two alternatives and that the outcome depends on theircharacteristics. A probability model is generally used when adependent variable is qualitative. There are many situations inwhich a dependent variable is qualitative, for instance, theoutcome of whether a firm goes bankrupt or not, or the choice ofwhether a household purchases a car or not. In these cases, onepurpose of a probability model is to determine the probability that12an event will occur. The interpretation of the dependent variableis that it is a probability measure for which the realized value is0 or 1.A cumulative probability distribution function is used toconstrain the predicted values within the acceptable [0,1] limitingvalues of a probability. The cumulative logistic probabilityfunction has the following form:P = F(Z) = [1+exp(-Z)]4 (2.1)where "exp" represents the base of nature logarithm. Z is atheoretical continuous index. P is the probability that an eventwill occur, given Z. It is easy to see that P is increasing in Z.If Z = +00, P is 1, and when Z = -00, P takes the value 0. Thus, Pcan never be outside the range [0,1].The logit probability model is based on the cumulative logisticprobability function. It is assumed that there exists a theoreticcontinuous index Z which is determined by an explanatory vector X.The form of a logit model isln[P/(1-P)] = Z = flx (2.2)In this notation, X is a vector of attributes; )3 is an unknownparameter vector to be estimated and P is the probability that anevent will occur, given X. The rationale for this form can be seenby solving equation (2.1) for Z. We then have equation (2.2).It is assumed the probability that an event will occur is alinear function of the firm attributes. The logit probability model13derives the probability of a dependent variable by assigningcoefficients to the independent variables. These coefficients canbe interpreted as the effect of a unit change in an independentvariable on the index Z.It should be noted that observations on Z are not available.Instead, we have data that distinguish only whether firmobservations are in one category (i.e., bankrupt), or a secondcategory (i.e., nonbankrupt). The dependent variable in equation(2.2) is the logarithm of the odds, P/(1-P), that a particularevent will occur. "One important appeal of the logit model is thatit transforms the problem of predicting probabilities within (0,1)interval to the problem of predicting the odds of an eventoccurring within the range of the real line. HMIf P happens to equal either 0 or 1, the odds will equal 0 orinfinity and the logarithm of the odds will be undefined. Thus, theapplication of ordinary least-squares estimation to equation (2.2)is inappropriate.15 Therefore, the most suitable procedure used insuch a case is the maximum likelihood method.16 Logit analysissolves the problem of how to obtain the parameters while at thesame time obtaining information about the underlying index Z.The data used in Ohlson's study is from the nineteen-seventies(1970-1976). The final sample consists of 105 bankrupt firms and2,058 nonbankrupt firms. The data for bankrupt firms is obtained"Pindyck and Rubinfeid (1991), p.259.IsIbid. p.260.MDetail will be discussed in Section 10-K financial statements as reported at the time. As Ohlsonstates, "This procedure has an important advantage: the reportsindicate at what point in time they are released to the public. Onecan therefore check whether the firm enters bankruptcy prior to orafter the date."17 Nonbankrupt firms are obtained from theCompustat tape. A sample of 2,058 nonbankrupt firms is chosen so asto be more representative of the proportion of bankrupt andnonbankrupt firms occurring naturally in the economy. Everynonbankrupt firm in the sample contributes with only one vector ofdata points. The year of any given firm's report is chosenrandomly.Ohlson uses the logit model to examine the effect of four basicfactors on the probability of bankruptcy. The four basic factorsare: (1) the size of the company; (2) a measure(s) of the financialstructure; (3) a measure(s) of performance; (4) a measure(s) ofcurrent^liquidity.^Nine^ratios^are^considered^as^independentvariables to represent the above four factors. They are:"1. SIZE = ln(total assets/GNP price-level index). The indexassumes a base value of 100 for 1968. Total assetsare as reported in dollars.2. TLTA = Total liabilities divided by total assets.3. WCTA = Working capital divided by total assets.4. CLCA = Current liabilities divided by current assets.°Ohlson (1980), p.110."Ibid. pp.118-119.155. OENEG = One if total liabilities exceeds total assets, zerootherwise.6. NITA = Net income divided by total assets.7. FUTL = Funds provided by operations divided by totalliabilities.8. INTWO = One if net income was negative for the last twoyears, zero otherwise.9. CHIN = (NIt - NIw)/(INId^+ INI01),^where NIt is netincome for the most recent period. The denominatoracts as a level indicator. The variable is thusintended to measure change in net income.Using these predictors, Ohlson computes three sets ofcoefficients. Model 1 predicts bankruptcy within one year; Model 2predicts bankruptcy within two years, given that the company doesnot fail within the subsequent year; Model 3 predicts bankruptcywithin one or two years. Table 2-1 shows the first two sets of theparameters of Ohlson's empirical results.With the exception of OENEG, all of the predictor signs forModel 1 are consistent with Ohlson's expectations. While Ohlsonexpects that the sign of OENEG is indeterminate, it is negative inModel 1. While three of the coefficients (WCTA, CLCA and INTWO)have t-statistics less than two, the others are all statisticallysignificant at a respectable level. In addition, SIZE appears asan important predictor of bankruptcy because it has a relativelylarge t-statistic.16An overall measure of goodness-of-fit is given by thelikelihood ratio index. For Model 1, the ratio is 84 percent, andthis is significant at an extremely low a-level. For Model 2, theratio is 79 percent. This decrease is in accordance with theexpectation that the accuracy decreases as the lead time increases.Table 2-1Ohlson's Estimated Bankruptcy Prediction ModelsVariablesSIZE TLTA WCTA CLCA OENEG NITA FUTL INTWO CHIN CONSTModel 1(Predicting bankruptcy within one year)Coefficients^-.407 6.03 -1.43 .0757 -1.72 -2.37 -1.83 .285 -.521 -1.32t-statistics^-3.78 6.61 -1.89 .761^-2.45 -1.85 -2.36 .812 -2.21 -.970Model 2(Predicting bankruptcy beyond one, but within two years)Coefficients^-.519 4.76 -1.71 -.297 -1.98 -2.74 -2.18 -.780 .4218^1.84t-statistics^-5.34 5.46 -1.78 -.733 -2.42 -1.80 -2.73 -1.92 ^2.10^1.38In Ohlson's model, the cutoff point which minimizes the sum ofthe Type-I and Type-II errors is .038. Ohlson defines Type-I andType-II errors in the opposite manner to Altman. For consistency,Altman's definition is also used for Ohlson's model in this study.That is, a Type-I error occurs when P is less than the cutoff pointand the firm is bankrupt. Similarly, a Type-II error occurs when Pis larger than the cutoff point and the firm is nonbankrupt. Usingthe cutoff point of .038, Ohlson finds that 17.4 percent of the2,058 nonbankrupt firms and 12.4 percent of the 105 bankrupt firms17are misclassified.2.3 THE ROLE OF RATIOS IN PREDICTING BANKRUPTCY2.3.1^TRADITIONAL USE OF RATIOS"The development of financial ratios for the purposes ofanalyzing accounting data is one of the important outcomes ofaccounting evolution."19 Ratios can be used to evaluate a firm'sperformance and assess its ability to pay its debt. Stickney (1990)states that ratios are useful tools because they summarize data ina form that is more easily understood, interpreted and compared infinancial statement analysis.The use of ratios dates back to the 1890s when the currentratio was used in credit decisions made by U.S. banks. Later theuse of ratios focusing on profitability measures both for creditpurposes and managerial analysis began. "Around 1919 the Du PontCompany began to use its famous ratio triangle system formanagerial decision making, providing the foundation for the moderninterfirm comparison scheme in accounting. umThere are two principal reasons for using financial ratios. Oneis that ratios can be used to make inferences based on changes ina firm's financial variables over a period of time. The use ofratios controls for the effect of changing firm size on the19Horrigan (1968), p.284.MBarnes (1987), p.449.18financial variables being examined in the time-series context. Thesecond reason for using ratios is to aid in comparisons between afirm and its industry by, once again, adjusting for differences infirm size. Firm-specific ratios can be compared with the industrystandard, and the firm's performance inferred based on thedifference between its ratios and the industry standard.21 Ineither case, ratios are used, as opposed to the actual values ofthe financial variables of interest, to facilitate comparison whilecontrolling for size.2.3.2 MAJOR BANKRUPTCY PREDICTIVE MODELS USING RATIOSRecently financial ratios have been used for predictivepurposes. The ratios are used as inputs by researchers instatistical models which predict a firm's credit rating, risk, itspotential for bankruptcy and its potential as a takeover target.The main focus, however, has been on developing statistical modelswhich use ratios to predict bankruptcy.Beaver (1966) uses financial ratios in predicting businessfailure. He uses a sample of 79 failed firms and a matched sampleof 79 non-failed firms and studies their financial ratios for aperiod of up to five years before failure. The nonfailed firms areselected using the paired-sample technique; that is, for eachfailed firm in the sample a nonfailed firm is chosen from the sameindustry and asset-size group one year prior to the year of failure2IThis is usually referred to as cross sectional analysis.19for the failed firm. The objective of such a sample design is tocontrol for systematic size and industry differences in financialratios.Financial ratios for the failed firms in Beaver's study areavailable for up to five years before failure. The data for eachfailed and nonfailed pair corresponds to the same time period.Thirty financial ratios from the various conventional ratiocategories are calculated for each firm in the sample. A cutoffpoint is chosen by ranking the value of each ratio. The cutoffpoint is the value that minimizes total misclassification. Beaverfinds that the mean values of the ratios of both groups lay in thepredicted directions: the cash flow and the reservoir of liquidassets are, on average, smaller for the failed firms than for thenonfailed firms. Although the failed firms have less capacity tomeet their obligations, they have more debt than the nonfailedfirms. Therefore, Beaver concludes that financial ratios havepredictive ability. The technique used in the study is referred toas classification analysis and is essentially univariate. Theshortcomings inherent in the univariate analysis is that differentratios can imply different predictions for the same firm.As mentioned previously, Altman (1968) uses multiplediscriminant analysis (MDA) to estimate a model that uses ratios todiscriminate between failed and nonfailed firms. Altman'smultivariate model overcomes the univariate model's problem ofdifferent ratios giving conflicting predictions.Altman et al. (1977) develops a "second-generation" model20called "Zeta analysis". The new model is essentially the same asthe old Z-score model, but takes great care in adjusting thefinancial statement data for information contained in the footnotes(e.g., lease data, contingent reserves, intangibles, minorityinterests, etc)  22 The ZETA model for bankruptcy classificationappears to be quite accurate for up to five years prior to failure.Over 90 percent of the sample is successfully classified one yearprior to bankruptcy and 70 percent up to five years prior.Furthermore, inclusion of retailing firms in the same model asmanufacturers does not seem to weaken the results. This model isbased on the data from 1969-1975.Another approach described in Section 2.2.2 is theprobabilistic bankruptcy prediction model. Ohlson (1980) developsa probabilistic model of bankruptcy prediction using LOGIT toestimate the coefficients of the variables in the model. Ohlsondoes not base his choice of variables on any theoretical frameworkbut chooses them on the basis of their reasonableness and their usein the previous bankruptcy prediction literature. The modelovercomes several problems encountered in discriminant analysisincluding the assumptions that financial ratios are normallydistributed and that bankrupt and nonbankrupt firms have the samevariance-covariance matrix.There are many other prediction models in the literature.However, the aforementioned models represent the major empirical220n1y some of these adjustments are made in the ZETA modelbecause the data for the nonbankrupt firms are taken from theCompustat Annual Industrial Tape.21research conducted in the area.2.3.3^CHOICE OF PREDICTIVE VARIABLESKarels and Prakash (1987) suggest that "the causes of businessfailure have been attributed to internal and external factors.Internal factors stem from poor management which is manifestedthrough lack of responsiveness to change, inadequate communication,over expansion, mishandling of major projects and fraud. Externalfactors can include labor problems, governmental regulation andnatural causes such as weather disasters. Researchers have usedfinancial ratios to account for these factors." The various ratiosare used to indicate aspects of a company's health such asprofitability, liquidity and solvency.As early as 1942, Merwin studied financial ratios and concludedthat failing firms exhibit significantly different ratio measuresthan continuing entities. For example, generally, current ratios offailed firms are less than those of the industry as a whole.Watts and Zimmerman (1986) point out that accounting data isuseful in predicting bankruptcy because lending agreements oftenuse financial ratios to restrict managers' actions. For example, afirm may be required to maintain a minimum current ratio. Breach ofthe financial ratio covenant places the firm in default and canlead to bankruptcy.However, Watts and Zimmerman also argue that breach of acovenant involving financial ratios does not necessarily lead to22bankruptcy. Hence, although defaults are defined using ratios thereis no mechanical association between ratios and bankruptcies. Afirm's bondholders will not file for bankruptcy if the costs offiling (lawyer and accounting fees and the opportunity costs ofusing a trustee) outweigh the benefits of eliminating theshareholder's option.Watts and Zimmerman finally conclude that while technicaldefault does not automatically lead to bankruptcy, the use ofaccounting numbers in covenants to signal default providesdebtholders with the option to force bankruptcy. It is, therefore,not surprising that studies use these financial ratios (e.g.,current ratio and debt-to-assets ratio) to predict bankruptcy.There is no consensus as to which ratios are most important forpredicting bankruptcy. The reason for this is that theoreticalmodels provide little foundation as a guide in the choice. Forexample, Beaver (1966) computes 30 ratios and selects six as"best". Altman (1968) chooses five variables as predictors which heconsiders most important. Ohlson (1980) frankly states:"No attempt was made to select predictors on the basis ofrigorous theory. To put it mildly, the state of the art seems topreclude such an approach. The first six predictors were partiallyselected simply because they appear to be the ones most frequentlymentioned in the literature."(p.118).Table 2-2 presents the ratios employed by several researchersin their empirical studies of bankruptcy. The diverse selection offinancial ratios used in predicting bankruptcy is apparent from thetable. Such diversity is not surprising given the limitedtheoretical basis for choosing the ratios.23Table 2-2Variables Used in Major Empirical Studies of BankruptcyVariables^ Beaver Altman Altman et al. Ohlson(1966)^(1968)^(1977)^(1980)working capital/total assets^X^X Xcurrent assets/current liabs^X X^Xcash flow/total assets^X^ Xtotal debt/total assets X XMVCE/total assets'^ Xsales/total assets XEBIT/total assets^ X^XEBIT/(interest+lease payments)2^ Xnet income/total assets^X^ Xretained earnings/total assets^X^XMVCE/(MVCE+book value of^ Xother equities)std err of EBIT/total assets Xfirm size^ X^Xno credit interval^ Xnet income dummy variable3^ Xtwo year % change in NI Xnet worth dummy variable4^ X1MVCE = market value of common equity.2EBIT = earnings before interest and taxes.3one if net income is negative for two years,zero otherwise.4one if total liabilities exceeds total assets,zero otherwise.242.4 REASONS TO EXPECT THAT THE MODEL PARAMETERS HAVE CHANGEDThis study investigates two potential reasons why theparameters of Altman's and Ohlson's models are expected to havechanged from what they were when they were originally estimated.One reason is that the bankruptcy law in the U.S. changeddramatically in the late 1970s. The change is expected to increasethe number of firms filing for bankruptcy. The second reason theparameters are expected to change is because of the increased useof debt in the 1980s. Due to the proliferation of LBOs and otherhighly leveraged transactions in the 1980s, the capital structureof many firms has changed. In the remainder of this section,changes in the bankruptcy law and in capital structure arediscussed and evidence of a change is reported.2.4.1^CHANGE IN THE BANKRUPTCY LAWThe Bankruptcy Act in the United States emerged in 1898. TheAct applied only to corporate liquidation and contained noprovision for corporate reorganization. The Bankruptcy Act servedthe U.S. until 1938 when it was repealed and replaced with a newBankruptcy Act. The new Bankruptcy Act appeared to be in responseto the massive social and economic upheaval caused by the GreatDepression. The new Bankruptcy Act, which was well known as theChandler Act, made a remarkable change to the original act. Underthe Chandler Act, corporations could choose to either liquidate25under Chapter VII or reorganize under Chapter X or XI.LIQUIDATIONLiquidation could happen either through a court petition or atrustee decision. "When it is deemed that there is no hope forrehabilitation or if prospects are so poor as to make itunreasonable to invest further efforts, costs, and time, the onlyalternative remaining is liquidation. Economically, liquidation isjustified when the value of the assets sold individually exceedsthe capitalized value of the assets in the marketplace." 23Liquidation was sometimes referred to as "straight bankruptcy"under the former Bankruptcy Act. "Its purpose is to achieve a fairdistribution to creditors of whatever nonexempt property the debtorhas and to give the individual debtor a fresh start through thedischarge in bankruptcy. 'INCHAPTER XChapter X proceedings applied to publicly held corporations andsecured creditors. "This bankruptcy procedure could be initiatedvoluntarily by the debtor or involuntarily by three or morecreditors with total claims of $5,000 or more."25"Chapter X automatically provided for the appointment of anindependent, disinterested trustee or trustees to assume control of23Altman (1983), p.12.24Treister et al. (1988), p.17.25Altman (1983), p.10.26the company for the duration of the bankruptcy proceeding. Actuallythe act provided for the appointment of the independent trustee inevery case in which indebtedness amounted to $250,000 or more.Where the indebtedness was less than $250,000, the judge couldeither continue the debtor in possession or appoint a disinterestedtrustee."26 "The trustee appointed by a court had wideinvestigative powers and had the first opportunity to propose aplan of reorganization. All other interested parties, except thedebtor, might also file proposals. The debtor could not file a planuntil the trustee's time to file had elapsed." fl Chapter X gavecreditors preferential treatment relative to shareholders.When a petition for Chapter X was filed, the committeesrepresenting each class of creditors and shareholders would beformed. The trustee or a representative committee would confer withthe creditors' committees and prepare a reorganization plan. Theplan could provide for the exchange of securities, the selection ofnew management, and an adequate means of executing the plan.The plan had to be approved by two-thirds of each class ofcreditors by value. Also, the plan had to be approved byshareholders unless total liabilities exceeded total assets.Finally, if the plan was fair and feasible, the court would alsoapprove and confirm it. "Chapter X followed the principles ofabsolute priority. The junior creditors had no interest under the26Ibid. p.10.flIbid. p.11.27plan until most senior creditors were paid in full."28 The ChapterX proceeding was the least common, but it was an important type ofcorporate bankruptcy reorganization.CHAPTER XIChapter XI applied to corporate and non corporate entities andto individuals. It could only be initiated voluntarily by a debtorand affected only unsecured creditors.A court had the power to appoint an independent trustee tomanage the corporate property or, as was frequently the case, topermit the old management team to continue its control during theproceedings. Chapter XI placed the bankrupt's assets strictly inthe custody of the court and made them free from any prior pendingcourt proceeding. "The bankrupt's petition for reorganizationusually contained a preliminary plan for financial relief. Theprospect of continued management control and reduced financialobligations made Chapter XI particularly attractive to presentmanagement."29During the proceedings, after a plan was proposed by a debtor,a referee called the creditors together to go over the proposedplan and any new amendments that had been proposed. If a majorityin number and amount of each class of unsecured creditors consentedto the plan, the court could confirm the plan and make it binding28See U.S. Congress (1973), Report of the Commission on theBankruptcy Law of the United States, Part I, p.245.29Altman (1983), p.9.28on all creditors."Usually, the reorganization plan provided for a scaling-downof the size and composition of creditor's claims and/or anextension of payments over time."" New financial instruments couldbe issued to creditors in lieu of their old claims. The debtorcould borrow new funds that had preference over all unsecuredindebtedness. Although the interest rate on such new credit wasexpected to be high, it still enabled the firm to secure animportant new source of financing.Chapter XI arrangements, if successful, tended to be fasterthan the more complex Chapter X cases. Also, Chapter XI was usuallyless costly than the proceedings that involved all securityholders. Successful out-of-court settlements, however, were usuallyeven less costly.THE BANKRUPTCY REFORM ACT OF 1978In 1978, U.S. Congress enacted the Bankruptcy Reform Act. TheChandler Act was officially repealed on October 1, 1979. Sincethen, the bankruptcy practices for most companies have beengoverned by the Bankruptcy Reform Act which is usually referred toas the Bankruptcy Code.Altman (1983) states that the major reason for revising theChandler Act is that "it was no longer functioning in its intendedmanner due to changes in social and economic conditions of thecountry over three decades. The bankruptcy courts were faced with"Ibid. p.9.29an increasing number of bankruptcies as more and more consumers andbusinesses made use of the process. More than one-quarter of thereferees in bankruptcy had problems in the administration of theirduties and suggested modifications to the Chandler Act."Altman also points out that "one of the major goals of theBankruptcy Reform Act of 1978 is to speed up the process becausethe longer a firm spends in bankruptcy, the higher the costs todebtors, creditors and society in general. ... In an attempt toreduce the time spent in bankruptcy, the Bankruptcy Reform Act laysdown several time limits and generally makes it easier to enter thebankruptcy process."The chapters of the Bankruptcy Code that are of interest inthis study are Chapter 7 (liquidation) and Chapter 11(reorganization). An extremely important change appears in Chapter11. Chapter 11 is a consolidated chapter for businessrehabilitation. It adopts much of the old Chapter XI arrangementsand incorporates a good portion of Chapter X.Under Chapter 11, a petition for reorganization can be filedvoluntarily by a debtor or involuntarily by creditors. "If thedebtor has more than 12 creditors, three creditors whose claimsmust total at least $5,000 in aggregate must join in theinvoluntary petition. If there are fewer than 12 creditors, twocreditors or a single creditor holding claims of at least $5,000may file." In order to file an involuntary petition, thecreditors must "show that the debtor is generally not paying his31Altman (1983), p.15.30debts as such debts become due or that within 120 days before thefiling of petition, a custodian was appointed and took possessionof the debtor's assets.""A debtor may propose his plan of reorganization within 120 daysafter filing his petition. After this period, if a trustee has beenappointed by the court, any interested party may file a plan aswell. The court holds hearings on the plan and will approve andconfirm it if it is fair and feasible. The confirmation requiresthat the plan be accepted by two thirds in amount and one half innumber of each class of creditors and by two thirds in amount,regardless of number of shareholders. "The court may confirm a planeven if a class of creditors object if the court finds that theinterests of that class are not impaired by the plan.""Chapter 11 also provides for the appointment of committees torepresent the interests of certain classes of claimholders beforethe court. The committees normally consist of the seven largestmembers of a particular class who are willing to serve, and areempowered to hire legal counsel and other professional help.Committees' operating expenses are paid out of the bankrupt firm'sassets. Appointment of a committee of unsecured creditors ismandatory in Chapter 11 cases; additional committees can beappointed to represent other classes, including shareholders, atthe discretion of the judge.Chapter 11 permits the debtor to continue running his business."Ibid. p.15."Ibid. p.22.31The bankrupt firm is expected to continue as a going concern afterleaving bankruptcy. To protect the firm from creditor harassmentwhile it tries to reorganize, Chapter 11 imposes an automatic stay.The stay prevents creditors from collecting on their debt orforeclosing on their collateral until the firm leaves bankruptcy.Due to the change in the bankruptcy law, the rate ofbankruptcies is expected to increase. One reason for expecting thisis that under the new law, it is likely to be easier to enter andlater leave the bankruptcy process therefore the reorganization isexpected to take less time. As a result, more firms are expected totake advantage of this option. Altman (1983) indicates that "theattempt to reduce reorganization time is important, since there isa positive correlation between the time spent in reorganization andthe direct cost of bankruptcy. The latter includes legal andaccounting fees, trustee and filing fees, and other tangible costsinvolved with the bankruptcy process." (p.26). The other reasons, asRamaswami and Moeller (1990) state, are "the Bankruptcy Code hasbecome an increasingly popular management tool for companiesseeking not only protection from creditors but also as a bargainingploy in their confrontations with the labor unions."(p.4).Table 2-3 contains information on business failures fromBusiness Statistics 1961-1988. This data is supplied by Dun &Bradstreet Inc. (hereafter D & B) which defines business failuresto include businesses that (1) ceased operations followingassignments or bankruptcy with losses to creditors, (2) voluntarilywithdrew, leaving unpaid obligations, or (3) were involved in a32court action such as receivership, reorganization, or arrangement.As of January 1984, D & B expanded the compilation of businessclosing statistics in certain industry groupings. As a result,calculations of industrial breakdowns have been changed to reflectthe new collection criteria, and data reported for individualindustries prior to 1984 are not comparable with succeeding years.However, the annual failure rate can still be used for a relativecomparison between years.Table 2-3 lists the number of industrial and commercialfailures and the annual failure rate which is expressed as theannual number of failures per the 10,000 industrial and commercialenterprises followed by the D & B. The rate is the most continuoustime series bankruptcy statistic. The last column of Table 2-3shows that the annual failure rate is relatively low in the 1970s.However, since 1980, the rate has increased dramatically. Thistendency is illustrated by Figure 1.The change in bankruptcy law in 1978 is expected to havecontributed to the increased rate of bankruptcies in the 1980s andis likely to have led to a change in the parameters of Altman's andOhlson's bankruptcy prediction models.33Table 2-3Industrial and Commercial FailuresYear Total CommercialServiceNumber of FailuresManufactur-Construction^ing andminingTrade--------------------Retail Wholesaleannualfailure rate(Number offailures per10,000 firms)1961 17,075 1,472 2,752 2,825 8,292 1,734 64.41962 15,782 1,339 2,703 2,575 7,552 1,613 60.81963 14,374 1,373 2,401 2,409 6,681 1,510 56.31964 13,501 1,226 2,388 2,254 6,241 1,392 53.21965 13,514 1,299 2,513 2,097 6,250 1,355 53.31966 13,061 1,368 2,510 1,852 6,076 1,255 51.61967 12,364 1,329 2,261 1,832 5,696 1,246 49.01968 9,636 1,106 1,670 1,513 4,366 981 38.61969 9,154 1,159 1,590 1,493 4,070 842 37.31970 10,748 1,392 1,687 2,035 4,650 984 43.81971 10,326 1,464 1,545 1,932 4,428 957 41.71972 9,566 1,252 1,375 1,576 4,398 965 38.31973 9,345 1,182 1,419 1,463 4,341 940 36.41974 9,915 1,320 1,840 1,557 4,234 964 38.41975 11,432 1,637 2,262 1,645 4,799 1,089 42.61976 9,628 1,331 1,770 1,360 4,139 1,028 34.81977 7,919 1,041 1,463 1,122 3,406 887 28.41978 6,619 773 1,204 1,013 2,889 740 23.91979 7,564 930 1,378 1,165 3,183 908 27.81980 11,742 1,594 2,355 1,599 4,910 1,284 42.11981 16,794 2,366 3,614 2,224 6,882 1,708 61.31982 24,908 3,840 4,872 3,683 9,730 2,783 88.41983 31,534 6,617 5,267 4,433 11,429 3,598 109.71984 52,078 12,787 6,936 5,759 13,787 4,882 107.01985 57,252 16,647 7,004 5,662 13,501 4,835 115.01986 61,601 20,966 7,110 5,699 13,623 4,865 120.01987 61,384 23,928 6,775 4,912 12,272 4,353 102.01988 57,093 22,756 6,811 4,703 11,485 4,451 98.0Source: Business Statistics 1961-1988, Supplementto "Survey of Current Business".34Figure 1Source: Business Statistics 1961-1988, Supplement to "surveyof Current Business".352.4.2 CHANGE IN CAPITAL STRUCTUREDuring the 1980s, highly leveraged transactions becameextremely popular among U.S. corporations. This increased use ofleverage has emerged as one of the important economic and politicalissues of the 1980s. Several factors could explain this economicphenomenon.First, entering the 1980s, as Ramaswami and Moeller (1990)point out, "the U.S. corporate sector could no longer afford thelow debt/equity of the 1950s and 1960s - the golden era for U.S.industry. ... The business and financial environment of the 1980sis quite different from that of the 1960s and early 1970s. Rapidtechnological change, worldwide competition for major products, andthe fluctuating global financial market conditions are importantcharacteristics of the business environment in the 1980s. Thesewere not present in 1960s and early 1970s."Ramaswami and Moeller also state that " the more competitive,globalized market environment of the 1980s and beyond calls for agreater measure of risk-taking by U.S. managers. Increasing thedebt-equity ratio is one way of institutionalizing that attitudewith some discipline. When one's survival is in question, betterhusbanding of resources, sharper focus, and quicker response tochanging market conditions could be expected."Second, obtaining tax benefits is one of the most importantfactors leading corporations to finance through debt. The purposeis to enhance shareholder value. Larger amounts of debt used in36LB0s, leveraged asset acquisitions, and asset recapitalizationssuch as leveraged share repurchases generate larger interestdeductions reducing taxes and increasing shareholder wealth.Third, entering the 1980s, "commercial banks were undertremendous pressure after the deregulation of deposits. They didnot have good places to put their money. ... They needed somethingnew."m They began to look at the cash flow coverage of the companyrather than the value of total assets to determine the level ofsenior debt the firm could carry. The appearance of junk bondsfurther increased the availability of debt.Fourth, LBOs had a significant effect on the American financialscene in the 1980s. "An LBO is a purchase of a company's stock withborrowed money."35 That is, it is characterized by a generalsubstitution of debt for equity in the capital structure of theacquired entity.In essence, an LBO is a transaction in which a buying groupacquires ownership of a corporation or a subsidiary of acorporation. The group consists generally of outsider investors,members of management, other employees and some shareholders. "AnLBO is financed primarily through borrowings from one or morelenders. The lenders will look to the assets and/or the cash flowof the company as the source of repayment of the debt."36"Before 1981, LBOs were characterized as relatively smallmAmihud (1989), p.106.35Ramaswami and Moeller (1990), p.xx.36Amihud (1989), p.175.37transactions, generally less than $50 million, where the purchaseprice was approximately equal to the assets, and the financing wasa mortgage."37 Furthermore, their size was restricted due to theconvention of financing the transaction by taking back a securityover the assets."In 1981, this was changed by Kohlberg, Kravis, Roberts & Co.in a transaction called 'Houdaille'. For the first time, a $400million transaction was done where the financing wasn't tieddirectly to the amount of assets. The bank financing was the first'cash flow loan' in which the banks decided that, instead oflooking strictly at current assets and plant and equipment todetermine the amount of senior debt, they would look at the cashflow coverage of the enterprise."m Since then, LBOs withsubstantial amounts of money involved have become popular. In 1985,the use of junk bonds proliferated, changing from simply financingfor companies that were either in trouble or growing to acquisitionfinancing.Today, many companies have adopted new thinking with respect totheir debt loads. Management now pays more attention to thebenefits of debt. It is argued that as long as a firm rests itsdebt-raising ability on both the firm's ability to generate cashand the protection offered by the intrinsic value of its assets,the use of debt makes sense. The use of debt also enables a firm toreduce tax payments through the interest deduction. Finally, LBOs37Ibid. p.103.mIbid. p.104.38allow large shareholders to be bought out, and thus act as a usefuldefense tactic against hostile takeovers. Danzi et al. (1990)suggest that an ideal LBO firm should have a healthy, stable cashflow, marketable tangible assets, scope for improving assetmanagement, and potential for asset redeployment.As evidence of the increased use of leverage in the 1980s,leverage ratios from the Compustat database for all industrialfirms, the S & P 500 and S & P industrial firms are summarized inTable 2-4. Debt-to-total assets ratios from year to year for eachgroup of firms are computed. The results indicate that, on average,leverage in the 1980s follows an upward trend. Figure 2 also showsthis tendency. To determine whether the increased use of leveragefrom the 1970s to 1980s is significant, a t-test of the differencebetween the mean leverage ratio in the 1970s and in the 1980s isperformed for the S & P 400 and the S & P 500 firms. For the S & P400 firms, the leverage increase is not significant. For the S & P500 firms, the leverage increase is significant at the 10% level.The increased use of debt by otherwise healthy firms in the1980s is expected to lead to a change in the parameters of Altman'sand Ohlson's models.39Table 2-4Total Debt-to-Total Assets RatiosaYEAR S & P 400 S & P 500 ALL INDUSTRIAL')1972 25.31% 21.26%1973 24.33% 20.29%1974 25.17% 20.83%1975 24.76% 20.74%1976 23.35% 19.68%1977 22.60% 18.96%1978 22.37% 18.93%1979 21.68% 18.77%1980 21.67% 18.84%1981 22.36% 19.52%1982 22.29% 20.36% 24.47%1983 20.87% 19.59% 22.81%1984 21.73% 21.26% 24.88%1985 22.41% 22.50% 26.48%1986 23.84% 22.44% 28.01%1987 22.90% 22.04% 27.30%1988 31.84% 26.90% 33.57%1989 33.59% 27.37% 36.25%1990 34.07% 27.37% 35.34%'Source: S & P Compustat PC PLUS.bThe ratios from 1972 to 1981 for all industrial are unavailable.40Figure 2Source: S & P Compustat PC PLUS412.5 HYPOTHESES AND PLAN FOR THE FOLLOWING ANALYSISWith regard to the expectation for the parameter change inAltman's and Ohlson's models, four hypotheses are developed.(1)The Type-I Error Hypothesis: The change in U.S. bankruptcylaw in the 1970s is predicted to increase the Type-I (classifyingbankrupt firms as nonbankrupt) error rate for both Altman's andOhlson's models with respect to the 1980s data. The reason for thisargument is that the change in bankruptcy law leads to an increasednumber of firms filing for bankruptcy.(2)The Type-II Error Hypothesis: The increased use of leverageby healthy firms in the 1980s is predicted to increase the Type-II(classifying nonbankrupt firms as bankrupt) error rate for bothAltman's and Ohlson's models with respect to the 1980s data. Sincefinancial leverage is one factor in both models, the higher levelof debt will result in a lower Z-score and a higher predictedprobability of bankruptcy for firms. Thus, a firm having a highlevel of debt is more likely to be predicted to go bankrupt, evenwhen the firm is profitable, healthy and growing.Ideally, these two hypotheses should be tested by comparing theresults from the 1980s sample with those from a true holdout sampleapplied to Altman's or Ohlson's original model. For Altman's model,Moyer's 1970s sample" can be treated as a holdout sample. ForOhlson's model, unfortunately, such a holdout sample isunavailable. Given the lack of a true holdout sample for Ohlson's"See Moyer (1977).42model, we would expect the Type-I and Type-II error rates toincrease when the model is applied to a sample outside of theoriginal estimation sample. This leads to a bias in favour offinding evidence in support of the above two hypotheses.(3) The Intercept Hypothesis: The change in bankruptcy law inthe late 1970s is predicted to lead to a significant increase inthe intercept of Ohlson's model. It is possible that thecoefficients of some of the other ratios in Ohlson's model may havechanged as a result of the change in the bankruptcy law. However,it is not immediately obvious which ratios they would be.Therefore, we look for an effect of the change in the bankruptcylaw by looking for an increase in the average likelihood ofbankruptcy that is independent of the ratios in the model. That is,we look for an increase in the intercept to the model. To theextent that the effect of the change in the bankruptcy law isrelated to one or more of the ratios in Ohlson's model, this testwill not capture that effect.(4) The Leverage Hypothesis: The increased use of leverage inthe 1980s is predicted to result in a significant decrease in thecoefficient on TLTA (total liabilities/total assets) in Ohlson'smodel. That is, for the same level of leverage, the estimatedprobability of bankruptcy is expected to be lower in the 1980s thanwhat it was in Ohlson's sample from the 1970s.Because statistics such as standard errors and t-values are notavailable for individual variables in the discriminant model asignificant change in the coefficients of Altman's model cannot be43tested.The remaining chapters are organized in the following format.Chapter 3 describes in detail the data and sample design. Twosamples are selected from the Compustat database. The data isrestricted to the period from 1981 to 1990. A profile analysis isconducted to describe the sample characteristics. Chapter 4 firstexamines both Altman's model and Ohlson's model based on the datadiscussed in Chapter 3. The predictive abilities of the two modelsare examined and the Type-I and Type-II Error Hypotheses aretested. Then, Altman's and Ohlson's models are reestimated usingthe 1980s samples. The purpose is to determine whether the modelparameters have changed since 1980. In particular, for Ohlson'smodel, the Intercept and Leverage hypotheses are tested. Chapter 5gives the conclusions of this study.44CHAPTER 3DATA COLLECTION AND DESCRIPTIVE STATISTICS3.1 DATA COLLECTIONThe majority of the data for this study is obtained from the1991 Compustat database which contains financial statement data ona large number of companies for the period of 1971-1990. Thedatabase includes information on over 7,000 industrialcorporations, banks, utilities, and telecommunications companies.The Compustat data is collected from company annual reports, SEC10-K and 10-Q reports. The majority of companies covered byCompustat are publicly traded rather than smaller privatecompanies. Therefore, there is a sample bias toward larger publiclytraded firms in this study.For a firm to be included in the sample, the followingconditions must hold:1. The firm's financial statement data is available fromCompustat for at least two consecutive years during theperiod 1981-1990.2. For firms which COMPUSTAT indicates as bankrupt or inliquidation, the firm's bankruptcy filing date isavailable from the Capital Changes Reporter, from SEC 10-Kreports or from the Moody's Manuals.3. The firm's stock price at fiscal year end is available fromthe Compustat database or from the Daily Stock Price Record.454. The firm is not a utility, transportation or financialservices firm.The first condition is required because data from the 1980s isused to examine the predictive power of the existing bankruptcyprediction models. In order to reestimate Altman's and Ohlson'smodels financial statement data for at least two years is required.The second condition is required to avoid an ex post bias. As wasnoted in Ohlson (1980), "financial statement data for the bankruptfirms must be selected carefully to ensure that it is availableprior to the date of bankruptcy filing. Otherwise, 'back-casting'for many of the bankrupt firms may occur."4° To avoid this problem,financial statement data for the bankrupt firms is obtained fromCompustat in the year prior to the year it filed for bankruptcy.The third condition is imposed because share prices are used tocalculate market value, one of the five predictors in Altman's Z-score model. The fourth condition excludes utilities,transportation and financial service firms because "firms in theseindustries are regulated, are structurally different, and have adifferent environment,11141 all of which are expected to affect thelink between financial performance and expected bankruptcy. As aconsequence, the sample is restricted to mainly commercial andindustrial companies.The bankrupt and nonbankrupt firms are collected separately. Inthis study, a firm is identified as bankrupt if it is coded by40Ohlson (1980), p.110.41Ibid. p.114.46Compustat as bankrupt. A firm is identified as nonbankrupt ifCompustat does not indicate that it was in bankruptcy. Compustatclassifies a firm as bankrupt if a petition for bankruptcy orliquidation, either voluntary or involuntary, has been filed.There are three steps to selecting the sample of bankruptfirms. The bankruptcy footnote on Compustat is used to identifycompanies, other than utilities, transportation and financialservice firms that went bankrupt during the period 1981-1990. Onehundred and sixty-two bankrupt firms are identified by thisprocess. The date a firm filed for bankruptcy or liquidation isobtained from the Capital Changes Reporter, SEC 10-K reports or theMoody's Manuals. Forty-nine firms are deleted from the samplebecause the bankruptcy or liquidation dates are unavailable,reducing the sample to 113 firms. Nine of the 113 firms are deletedfrom the sample because financial statement data is not availableon Compustat, reducing the sample to 104 firms. Thirty-eight ofthese 104 firms are missing share prices on Compustat. The stockprices of 33 of these 38 firms are obtained from the Daily StockPrice Record (hereafter DSPR) and used to calculate market values.The share prices for the remaining 5 firms are unavailable, andthey are dropped from the sample. Thus, in total, 63 bankrupt firmsare dropped due to missing data leaving a final sample of 99 firms.A list of the 99 bankrupt firms in the sample is shown in AppendixA.The distribution of these bankrupt firms across years andacross stock exchanges appears in Table 3-1. As Table 3-147indicates, most of the bankrupt firms are listed on the OTC justprior to their bankruptcy. No bankrupt firms listed on regionalexchanges are included in the sample. This is because the marketvalues for these firms are unavailable either from Compustat orfrom the DSPR.Table 3-1Distribution of Bankrupt Firms by Year and by Stock ExchangeYEARExchange 81 82 83 84 85 86 87 88 89 90 Total PercentNYSE^0^1^1^3^5^2^1^2^1^5^21^21AMSE^0^1^0^1^1^1^2^3^2^2^13^13OTC^4^4^3^2^8^6^6^7 11 14^65^66TOTAL^4^6^4^6 14^9^9 12 14 21^99^100The sample of bankrupt firms in this study contains a higherpercentage of NYSE and OTC firms than is present in Ohlson'ssample. Ohlson reports that, in his sample, 8 percent of the firmsare listed on the NYSE, 41 percent on the AMSE, and 51 percent ofthe firms are listed on the OTC or regional exchanges.Table 3-1 shows that, in general, the number of bankrupt firmsin the sample is increasing over time. This is expected given theincreasing rate of corporate failures during the 1980's documentedby the Dun & Bradstreet Inc. and reproduced in Table 2-3.48The nonbankrupt firms are also selected from Compustat. ForAltman's model, a sample of 99 nonbankrupt firms is collected inorder to form a paired sample. This paired sample is matched on thebasis of industry, asset size and calendar year.For Ohlson's model, ideally, both bankrupt and nonbankruptfirms should be selected simultaneously as a single random samplefrom the database. Once the sample is obtained, firms should beidentified as bankrupt or nonbankrupt. Given that all bankruptCOMPUSTAT firms with data available are included, all nonbankruptCOMPUSTAT firms should form the nonbankrupt sample. This wouldresult in a sample of approximately 72,830 nonbankrupt firmyears.42 Such a large sample is very difficult to handle inpractice due to computer memory limitations.As a result of these constraints, the following procedures areused in this study to select a smaller sample of nonbankrupt firms.The proportion of bankrupt to nonbankrupt firms is set to 1:20.43Thus, 1,980 nonbankrupt firms are required given the sample of 99bankrupt firms. One hundred and ninety-eight nonbankrupt firms arerandomly selected for each year during the 1981-1990 period. It ispossible that the same nonbankrupt firm could appear more than oncein the sample, due to its inclusion in different years. Theseprocedures result in a sample of 99 bankrupt and 1,980 nonbankruptfirm years.42The number of firm years is defined as the number of activenonbankrupt firms on Compustat multiplied by the number of years.43This ratio of one bankrupt to 20 nonbankrupt firms is similarto the proportions used in Ohlson (1980) and in Zmijewski (1983).493.2 DESCRIPTIVE STATISTICSIn order to better describe the sample characteristics, aprofile analysis is conducted. Seven financial ratios commonly usedin bankruptcy prediction are reported in Table 3-2. The table showsthat the ratios deteriorate as one moves from nonbankrupt firms tobankrupt firms two years prior to bankruptcy to bankrupt firms oneyear prior to bankruptcy. This tendency is in accordance with whatone would expect. To determine if there is a significant differencein the ratios between the bankrupt firms one year prior tobankruptcy and nonbankrupt firms, an F-test of the mean differencebetween the two groups is conducted for each financial ratio. Withthe exception of SLTA (sales/total assets), all the ratios aresignificantly different across the two groups at the 1% level. SLTAis significant at the 5% level. This indicates that a significantdifference in the ratios of the bankrupt and nonbankrupt firmsexists.50Table 3-2Profile Analysis of the Bankrupt and Nonbankrupt Firms in theSampleNonbankruptFirmsBankrupt FirmsTwo Years Prior^One Year Priorto Bankruptcy to BankruptcyVariablea mean std dev mean std dev mean std devTLTA .5026 .2854 .8873 .5274 1.1068 .7179WCTA .3504 .2631 .0329 .5017 -.0864 .5668CLCA .5512 1.2445 1.4235 3.0260 1.9642 3.7041NITA .0876 .1561 -.2783 .5666 -.3930 .8135FUTL .4076 .7477 -.2005 .6882 -.2197 .5137RETA .3477 0.2045 -.0083 1.0639 -.7268 1.5556SLTA 1.5685 .8439 1.2827 1.0416 1.1998 .7188Number of firms^1980^ 95^ 99'FLTA = Total Liabilities/Total AssetsWCTA = Working Capital/Total AssetsCLCA = Current Liabilities/Current AssetsNITA = Net Income/Total AssetsFUTL = Funds from Operations/Total LiabilitiesRETA = Retained Earnings/Total AssetsSLTA = Sales/Total Assets51CHAPTER 4MODEL TEST AND REESTIMATIONIn this Chapter, the predictive abilities of Altman's andOhlson's bankruptcy prediction models are tested using the samplesof firms from the 1980s. Altman's and Ohlson's models are then re-estimated to test whether the parameters have changed.4.1 THE PREDICTIVE ABILITIES OF ALTMAN'S AND OHLSON'S MODELSIn this section, Altman's Z-score model is applied to firmsfrom the 1980s and its ability to correctly classify bankrupt andnonbankrupt firms is reported. Ohlson's model is also tested in asimilar manner.4.1.1^TEST OF ALTMAN'S 2 -SCORE MODELAltman's Z-score model" is estimated using data from theperiod 1946-1965. In this section, the predictive ability ofAltman's model is tested on data from the 1980s.Altman determines that a cutoff of Z=2.675 minimizes the errorclassification rate for his sample.45 If Z < 2.675, a firm is"Altman's Z-score model is described in Section 2.2.1 ofChapter 2.45Altman chooses this cutoff point to minimize the total numberof Type-I and Type-II errors for his sample. Choosing a cutoff inthis manner is equivalent to assuming that the costs of Type-I andType-II errors are equal. However, in general, Type-I errors are52classified as bankrupt. Otherwise, the firm is classified asnonbankrupt.Type-I (classifying bankrupt firms as nonbankrupt) and Type-II(classifying nonbankrupt firms as bankrupt) error rates forAltman's original sample are summarised in Panel A of Table 4-1.Altman reports the overall error rate for his sample is 5 percentone year prior to bankruptcy. The Type-I and Type-II error ratesare 6 and 3 percent, respectively. Two years prior to bankruptcythe overall error rate is 17 percent.Altman also uses a non-random "hold-out" sample toevaluate the predictive ability of his mode1.47 The sample consistsof 25 bankrupt and 66 nonbankrupt firms. When Altman's initialmodel is applied to this sample, the overall error rate is 16.5percent. The Type-I and Type-II error rates are 4 and 21 percent,respectively.likely to be more costly than Type-II errors.Natts and Zimmerman (1986) point out that "The use of aholdout sample is important methodologically. Knowledge of a firm'sratios and whether it went bankrupt or not is used to determine thediscriminant function and the 'optimal' z score cutoff for theestimation sample. Essentially, hindsight is used. When thediscriminant function and 'optimal' cutoff is applied to anothersample, the effect of hindsight is not present and the discriminantfunction will not predict as well. Hence, the use of a holdoutsample is necessary to evaluate the discriminant function'spredictive ability."47Altman points out the non-random naturesample: "a sample of sixty-six firms is selectednet income (deficit) reports in the years 1958thirty-three from each year. Over 65 per cent ofsuffered two or three years of negative profitsthree years reporting."of his holdouton the basis ofand 1961, withthese firms hadin the previous53Table 4-1Comparison of Type-I & Type-II Error Rates From ApplyingAltman's Model to His Own Sample Versus the 1980s SamplePanel A: Altman's Original SampleaPredictive Ability One Year Prior to BankruptcyNumberCorrectPercentCorrectPercentError NType-I" 31 94 6 33Type-IIc 32 97 3 33Total 63 95 5 66Predictive Ability Two Years Prior to BankruptcyNumber^Percent^PercentCorrect Correct ErrorType-I 23 72 28 32Type-II 31 94 6 33Total 54 83 17 65Panel B: 1980s Paired SamplePredictive Ability One Year Prior to BankruptcyNumber^Percent^PercentCorrect Correct ErrorType-I 88 89 11 99Type-II 67 68 32 99Total 155 78 22 198Predictive Ability Two Years Prior to BankruptcyNumber^Percent^PercentCorrect Correct ErrorType-I 67 71 24 95Type-II 62 67 33 93Total 129 69 31 188aAltman's original sample is the sample Altman used to estimatehis bankruptcy prediction model.bbankrupt predicted to be nonbankrupt.cnonbankrupt predicted to be bankrupt.54The new paired sample of 99 bankrupt and 99 nonbankrupt firmsfrom the 1980s is used to test Altman's original model. Panel B ofTable 4-1 shows the results of applying Altman's model to the newpaired sample." The overall error rate is 22 percent one yearprior to bankruptcy. The Type-I error rate is 11 percent and theType-II error rate is 32 percent. The overall error rate two yearsprior to bankruptcy increases substantially to 31 percent.Ideally, it is preferable to compare the results for the 1980ssample with those for a 'random' holdout sample from a periodbefore the change in the bankruptcy law and the change in the useof debt. The analysis in Moyer (1977) provides such a holdoutsample. Moyer examines the predictive ability of Altman's Z-scoremodel applying Altman's model and cutoff point to 27 bankrupt and27 nonbankrupt firms from 1965-1975. Moyer's results can thereforebe thought of as applying to a random holdout sample of bankruptand nonbankrupt firms taken from a period before the legal andcorporate changes this current study is concerned with. Moyerreports an overall error rate of 25 percent. The Type-I error rateone year prior to bankruptcy is 39 percent and the Type-II errorrate is 12 percent. Comparing these with the results for the 1980ssample, the Type-I error rate has declined and the Type-II errorrate has increased in the 1980s period. These results areconsistent with the Type-II Error Hypothesis, but are inconsistentwith the Type-I Error Hypothesis.If Type-I errors are more costly than Type-II errors then the"Here, Altman's cutoff point of 2.675 is used.55fact that Altman's model leads to less Type-I errors and more Type-II errors in the 1980s sample may be preferable for many decisions.4.1.2^TEST OF OHLSON'S MODELIn this section, Ohlson's bankruptcy prediction model" isapplied to the sample of firms from the 1980s to assess itspredictive ability. This sample consists of 99 bankrupt and 1,980nonbankrupt firms. Fitting the 1980s sample firms to Ohlson'smodel, P (the estimated probability of bankruptcy during thefollowing year) is obtained.Table 4-2 reports for both Ohlson's sample and the currentsample the percentage of Type-I and Type-II errors93 that occurwhen various values of P are used to classify firms as predictedbankrupt or nonbankrupt. As the cutoff for P increases, the numberof Type-I errors increases while the number of Type-II errorsdecreases.The results in Table 4-2 are similar to those reported in theprevious section when Altman's model is applied to Moyer's sampleand then to the 1980s sample. For almost all cutoffs for P,applying Ohlson's model to firms from the 1980s results in a higherrate of Type-II error and a lower rate of Type-I error than49Ohlson's model is described in Section 2.2.2 of Chapter 2.50For consistency, Altman's definition for Type-I and Type-IIerrors is also used for Ohlson's model in this analysis. In hisstudy Ohlson uses the opposite definition of Type-I and Type-IIerrors.56occurred in Ohlson's sample. Ohlson reports that a cutoff point ofP=0.038 minimizes the sum of Type-I and Type-II errors for hissample. Like the cutoff used by Altman, this cutoff point isdetermined based on the assumption that the cost of a Type-I erroris equal to the cost of a Type-II error. This cutoff point resultsin a Type-I error rate of 12.4 percent and a Type-II error rate of17.4 percent for Ohlson's sample. Applying the same cutoff point tothe 1980's sample, the Type-II error rate increases to 26.8 percentwhile the Type-I error rate falls to 9.1 percent.m For the 1980ssample, the cutoff point which minimizes the sum of Type-I andType-II error rates is 0.1. At this point, 15.15 percent of thebankrupt firms and 11.57 percent of the nonbankrupt firms aremisclassified.Ohlson reports that, in his sample, the mean probabilities ofbankruptcy are 0.03 for the nonbankrupt firms, 0.39 for thebankrupt firms one year prior to bankruptcy and 0.20 for thebankrupt firms two years prior to bankruptcy. For the 1980s sample,Ohlson's model predicts mean probabilities of 0.043 for thenonbankrupt firms and 0.555 and 0.395 for the bankrupt firms oneand two years prior to bankruptcy, respectively. Given theincreased rate of bankruptcy in the 1980s, it is to be expectedthat Ohlson's model will predict a higher probability of bankruptcywhen applied to 1980s data for all three types of firms in themIn evaluating Ohlson's model, it would be preferable tocompare the results from the 1980s sample with those from a 'hold-out' sample from an earlier period. Unfortunately, Ohlson does notreport results for a 'hold-out' sample and there are no otherpublished studies testing the predictive power of Ohlson's model.57sample.The decreased predictive power of Ohlson's model and theincreased mean probabilities using the data from the 1980s impliesthat the model parameters are likely to have changed from what theywere during the early 1970's. To test this hypothesis theseparameters will be re-estimated, using the 19805 sample, in Section4.2.Table 4-2Comparison of Type-I & Type-II Error Rates From Applying Ohlson'sModel 1 to His Own Sample Versus the 1980s SampleEstimated Probabilityof Bankruptcy usedas Cutoff PointsOhlson'sType-ISampleType-II1980'sType-ISampleType-II0.00 0% 100% 0% 100%0.02 7.6 28.7 5.05 36.570.04 14.3 16.7 9.09 26.770.06 20.6 11.6 13.13 18.740.08 25.7 9.3 13.13 13.890.10 26.7 7.2 15.15 11.570.20 44.8 3.3 26.26 4.900.30 48.6 1.75 35.35 3.280.40 57.1 1.07 39.39 2.370.50 67.6 0.63 45.46 1.820.60 71.4 0.29 52.52 1.110.70 76.2 0.19 57.58 0.760.80 81.9 0.15 63.64 0.560.90 88.6 0.049 69.70 0.451.00 100 0 100 04.1.3^SUMMARY OF THE RESULTS ON PREDICTIVE ABILITYChapter 2 suggests two potential reasons why the modelparameters are expected to have changed from what they were whenAltman and Ohlson estimated their models. The first reason is the58change in U.S. bankruptcy law in the late 1970s. This change isexpected to increase the number of firms filing for bankruptcy.The change in bankruptcy law is, therefore, expected to increasethe Type-I error rate with respect to the 1980s sample.The second reason for expecting a change in the modelparameters is the increased use of financial leverage in the 1980s.Financial leverage is a significant factor in both Altman's andOhlson's models. The higher level of debt observed in the 1980s isexpected to result in a lower z-score and a higher predictedprobability of bankruptcy for firms in the 1980s. That is, a firmhaving a high level of debt is more likely to be classified aspredicted to go bankrupt, even when the firm is profitable, healthyand growing. This increase in the use of leverage by healthy firmsis, therefore, expected to result in an increase in the Type-IIerror rate for the 1980s sample.Applying Altman's model to his original estimation sample, bothType-I and Type-II error rates have increased for the 1980s sample.These results are consistent with both the Type-I Error Hypothesisthat the change in U.S. bankruptcy law in the 1970s increases theType-I error rate and Type-II Error Hypothesis that the increaseduse of leverage in the 1980s increases the Type-II error rate.However, treating Moyer's 1970s sample as a holdout sample forAltman's original model, the conclusion for the Type-I ErrorHypothesis is different. Because the Type-I error rate is lower andthe Type-II error rate is higher for the 1980s sample than forMoyer's sample, the Type-I Error Hypothesis is rejected and the59Type-II Error Hypothesis is still supported.For Ohlson's model, the Type-I error rate is less and the Type-II error rate is larger for the 1980s sample. The increased Type-II error rate is consistent with the Type-II Error Hypothesis, butthe decreased Type-I error rate does not support the Type-I ErrorHypothesis.Ideally, the 1980's error rates using Ohlson's model should becompared with the error rates using a true holdout sample from anearlier period. Unfortunately, such a holdout sample isunavailable. Given that Ohlson's error rates are for the sample offirms used to estimate his model, we would expect the Type-I andType-II error rates to increase when the model is applied to asample outside of the original estimation sample. This holdoutsample effect is an alternative reason for expecting to findsupport for the Type-I and Type-II Error hypotheses.As mentioned above, the Type-I error rate (classifying bankruptfirms as nonbankrupt firms) is lower in the 1980s than in the 1970sfor both Altman's and Ohlson's models. This is the reverse of whatis predicted if the change in the bankruptcy law in the late 1970smade it less costly for otherwise healthy firms to enter bankruptcyto gain concessions from their creditors. One possible explanationfor the lower rate of the Type-I errors in the 1980s is that theincreased rate of bankruptcy filings during the 1980s is not due tothe change in the bankruptcy law at all, but rather is due tochanges in operating and financing strategies that threaten firmviability. Altman (1983) mentions that "since 1980 there has been60a continuous economic malaise of the economy combined with otherfactors such as the deterioration in firm liquidity, increasedleverage, and dramatically reduced coverage of financial paymentsof interest and principal." These factors may lead to an increasein the risk of bankruptcy, that is related to variables alreadypresent in Altman's and Ohlson's models.4.2 MODEL REESTIMATION4.2.1^REESTIMATION OF ALTMAN'S MODELIn light of the results in Section 4.1, reestimation of theparameters of Altman's model using the 1980s data appearswarranted. The paired sample mentioned in Section 4.1.1 is used toreestimate Altman's model. The model is estimated using the samefive variables as in Altman's original model. These variables are, X2, X3, X4 and X5   52To test the discriminating ability of the individual variables,a univariate F-test of a difference in the means is conducted foreach variable. Table 4-3 shows the statistical characteristics ofthe five variables one year prior to bankruptcy for the 1980spaired sample. Variables XI, X2, X3 and X4 areall significant at the52As defined in Section 2.2.1, X1 = working capital/totalassets, X2 = retained earnings/total assets, X3 = earnings beforeinterest and taxes/total assets, X4 = market value of equity/bookvalue of total liabilities and X5 = sales/total assets. As inAltman's original model, variables XI, X2, X3 and X4 are measured inpercentage terms while X5 is a simple ratio.611% level and X5 is significant at the 5% level. This indicatessignificant differences exist in these variables between thebankrupt and nonbankrupt groups.Table 4-4 reports the results of reestimating Altman's modelusing the 1980s paired sample. In the same manner as Altman, thediscriminant analysis technique suggested by Fisher (1936) is usedto estimate the coefficients of a linear combination of thevariables. Fisher's approach is based on the assumption of equalprior probabilities and equal costs of misclassification. Thediscriminating power of the model is determined by maximizing XTable 4-3Profile Analysis of the Variables Used to Reestimate Altman's ModelVariablebbankrupt groupamean^std devnonbankrupt groupmean^std dev ^univariatecxl -.0864 .5668 .2893 .2728 35.32"X2 -.7268 1.5556 .1184 .5072 26.42"X3 -.1206 .3204 .0657 .1238 29.13"X4 .3701 .7038 1.5532 1.3288 61.28"X5 1.1998 .7188 1.4466 .9054 4.51*"Significant at the 1% level.*Significant at the 5% level.'Weans and standard deviations for the variables one year priorto bankruptcy.$C1 = working capital/total assetsX2 = retained earnings/total assetsX3 = earnings before interest and taxes/total assetsX4 = market value of equity/book value of total liabilitiesX5 = sales/total assetsTnivariate F-test of the mean difference between the two groups.62which is the ratio of between-groups sums-of-squares to within-groups sums-of-squares." Then, a related F-value is computed totest the null hypothesis that the observations come from the samepopulation. Table 4-4 shows that F-value is 21.8 which rejects thenull hypothesis at less than the 1% level. Therefore, a significantdifference exists between the bankrupt and nonbankrupt groups andthe model has discriminating power.The model parameters are scaled by a constant so that thecutoff point that minimizes the total number of errors remains at2.675 as in Altman's original model.In comparing the reestimated model with Altman's originalstudy, the magnitudes have changed. In particular, the coefficienton X4 for the new paired sample is larger than in Altman's study.This implies that, for the same level of leverage, the Z-score islarger in the 1980s than in Altman's original study predicting alower likelihood of bankruptcy. An increase in the coefficient onX4 is expected given the increased use of financial leverage in the1980s. This result is consistent with the Leverage Hypothesis.However, since statistics such as standard errors for individualvariables are not available for the discriminant function, thesignificance of the change in this parameter cannot be measured.Table 4-4 also lists the scaled vectors of Altman's and thereestimated models. The scaled vectors are used to measure therelative contribution of each variable to the total discriminant53See Tatsuoka (1971), p.159.63Table 4-4Comparison Between Altman's Model and the Reestimated ModelPanel A: Altman's Original ModelZ = 0.012X1+ 0.014X2 + 0.033X3 + 0.006; + 0.999X5F-value = 20.7Relative Contribution of the VariablesVariablea^Scaled Vector^RankingXi 3.29^ 5X2^ 6.04 4X3 9.89 1X4 7.42^ 3X5^ 8.41 2Panel B: Reestimated Model'Z = 0.013X1+ 0.006X2 + 0.032X3 + 0.017X4 + 0.826X5F-value = 21.8Relative Contribution of the VariablesVariablea^Scaled Vector^RankingX1 0.245 5X2^ 0.272 3X3 0.321^ 2X4 0.831 1X5^ 0.267 4aX1 = (Working Capital/Total assets)*100X2 = (Retained Earnings/Total assets)*100X3 = (Earnings before interest and taxes/Total assets)*100X4 = (Market value of equity/Book value of totalliabilities)*100X5 = Sales/Total assetsb(1) For comparison, the reestimated model is scaled by afactor of 2.548=(2.675/1.05) to keep the same cutoff as inAltman's original model.(2) Using the aforementioned sample of 99 bankrupt and 1,980nonbankrupt firms from 1981-1990, the reestimated model isZ=0. 315)(1+0. 048X2+0. 003X3+0. 001X4+1. 063X5. However, this modelis not suitable for comparison due to the small number ofbankrupt firms relative to nonbankrupt firms in the sample.64power of the mode1.54The rankings of the five variables in the reestimated model aredifferent than in Altman's original model. Panel A shows that X3(earnings before interest and taxes/total assets) had the greatestcontribution to Altman's original model. However, in Panel B, X4(market value of equity/book value of total liabilities) makes thegreatest contribution to the reestimated model. Since X4 is ameasure of leverage, this result indicates that financial leverageis a very important factor in predicting bankruptcy in the 1980s.Table 4-5 reports the Type-I and Type-II error rates for thereestimated model using the new paired sample. As mentionedpreviously, a cutoff point of Z=2.675 minimizes the total number oferrors when the reestimated model is applied to the sample. Withthis cutoff, the Type-I error rate one year prior to bankruptcy is12 percent and the Type-II error rate is 22 percent. The overallerror rate is 17 percent. Two years prior to bankruptcy the Type-Ierror rate is 20 percent and the Type-II error rate is 23 percent.The overall error rate is 21 percent.Table 4-1 summarises the error rates of Altman's originalmodel. Comparing Table 4-5 to Table 4-1, the Type-I and Type-IIerror rates and the overall error rates one and two years beforebankruptcy are, in general, higher for the reestimated model thanfor Altman's original model.54The scaled vectors are computed by multiplying a variable'scoefficient by the square root of the corresponding diagonalelement of the sample variance-covariance matrix.65Table 4-5Predictive Ability of the Reestimated Altman ModelOne and Two Years Prior to BankruptcyOne Year Prior to BankruptcyNumber^Percent^PercentCorrect Correct Error NType-I 87 88 12 99Type-II 77 78 22 99Total 164 83 17 198Two Years Prior to BankruptcyNumber Percent PercentCorrect Correct Error NType-I 76 80 20 95Type-II 72 77 23 93Total 148 79 21 188It appears, therefore, that even when Altman's model isreestimated using 1980's data, its ability to identify bankrupt andnonbankrupt firms is less than what it was when it was originallyestimated.In many cases, it is more serious to make one type of errorthan the other. That is, the cost of the Type-I error is differentfrom the cost of the Type-II error. Thus, in constructing aclassification procedure the objective is to minimize the totalcost of misclassification. In this case, Fisher's approach is notappropriate. We must use a general approach called Bayes solution.Fisher's approach is only a special case of Bayes solution.66Anderson (1984) shows that using Bayes general solution theprior probabilities and costs of misclassification can beincorporated into the modelling effort. "The general Bayes solutionto the classification problem compares the ratio of the groupprobability density functions to a classification criterion. Thespecification of this criterion varies depending upon whether theprior probabilities and/or costs of misclassification arerecognized. In either case, the specification of the classificationcriterion reduces to the selection of the cutoff point used toseparate groups."As Lachenbruch (1975) states, "the main problem with minimizingthe cost of misclassification is the difficulty in specifying thesecosts. The specification of costs is usually done by the user. Mostusers are not able to do so. In reality, all that is needed is theratio of costs, but even this is hard to get."4.2.2 REESTIMATION OF OHLSON'S MODEL4.2.2.1 MAXIMUM-LIKELIHOOD ESTIMATION OF LOGIT MODELAs mentioned in Section 2.2.2, OLS estimation of the logitmodel is inappropriate. This is because in the case of adichotomous dependent variable, the residuals are heteroscedastic,and OLS yields inefficient estimates. Therefore, the parameters inthe logit model are typically estimated by Maximum LikelihoodEstimation (MLE).67Recall the logit model:in[p/(1-P)] = Oxwhere X is a vector of attributes and 0 is a vector of unknownparameters. Take the bankruptcy event as an example, then P is theprobability of bankruptcy, given X. P is not observed, instead, wehave information for each observation on whether a firm is bankruptor nonbankrupt.Assume there are n bankrupt firms and m nonbankrupt firms.Then, a likelihood function is given bymlnL(0) = ElnPi + Eln(1-P)i=1MLE is used to find parameter estimates for all variables bymaximizing the likelihood of distinguishing the bankrupt firms fromthe nonbankrupt firms."Maximum likelihood estimators possess some very attractiveasymptotic properties. All parameter estimates are asymptoticallyconsistent and efficient. In addition, the asymptoticaldistribution of all maximum likelihood estimators is normal,regardless of the distribution from which the sample is drawn."mThis means that provided the sample is sufficiently large,inference can be based on the normal distribution. Therefore, theanalog of the regression chi-square can be calculated.mPindyck and Rubinfeid (1990), p.280.MDoran (1989), p.310.68The logit equivalent of the OLS t-statistic is the likelihoodratio test. This statistic is distributed chi-squared with Kdegrees of freedom. EMPIRICAL RESULTSIn light of the results in Section 4.1, reestimation of theparameters of Ohlson's model using data from the 1980s appearswarranted. The aforementioned sample of 99 bankrupt and 1,980nonbankrupt firms from 1981-1990 is used to reestimate the model.The model is estimated using the same nine variables as in Ohlson'soriginal model. These variables are SIZE, TLTA, WCTA, CLCA, OENEG,NITA, FUTL, INTWO and CHIN.57 A profile analysis of these variablesfor the 1980s sample is reported in Table 4-6.Table 4-6 shows the means and the standard deviations of thenine variables for three different types of firms: bankrupt firmsone year prior to bankruptcy, bankrupt firms two years prior tobankruptcy and nonbankrupt firms. The ratios appear to deteriorateas one moves from nonbankrupt firms to bankrupt firms two yearsprior to bankruptcy to bankrupt firms one year prior to bankruptcy.The bankrupt firms have larger means than the nonbankrupt firms for57As defined in Section 2.2.2, SIZE = ln(total assets/GNPprice-level), TLTA = total liabilities/total assets, WCTA = workingcapital/total assets, CLCA = current liabilities/current assets,OENEG = one if total liabilities exceeds total assets, zerootherwise, NITA = net income/total assets, FUTL = funds provided byoperations/total liabilities, INTWO = one if net income wasnegative for the last two years, zero otherwise, and CHIN = (NI,-NIt_1)/(INId +INI,11), where NI isnet income for the most recent period.69TLTA, CLCA, OENEG and INTWO, and smaller means for SIZE, WCTA,NITA, FUTL and CHIN. This is in accordance with what one wouldexpect. The bankrupt firms are on average smaller than thenonbankrupt firms. The standard deviations of the variables are alllarger among the bankrupt firms, except in the case of FUTL.Ohlson's profile analysis of his 1970s sample reached similarconclusions.Table 4-6Profile Analysis of the Variables Used to Reestimate Ohlson's ModelNonbankruptFirmsBankrupt FirmsTwo Years Prior^One Year Priorto Bankruptcy to BankruptcyVariablea mean std dev mean std dev mean std devSIZE 13.4630 2.0315 12.0560 2.0433 11.8990 2.0766TLTA .5026 .2854 .8873 .5274 1.1068 .7179WCTA .3504 .2631 .0329 .5017 -.0864 .5668CLCA .5512 1.2445 1.4235 3.0260 1.9642 3.7041OENEG .0252 .1569 .2316 .4241 .3838 .4888NITA .0876 .1561 -.2783 .5666 -.3930 .8135FUTL .4076 .7477 -.2005 .6882 -.2197 .5137INTWO .1015 .3021 .5263 .4773 .6566 .5020CHIN .0846 .5334 -.2642 .6242 -.2734 .6351Number of firms^1980^95^ 99aSIZE = ln(total assets/GNP price-level)TLTA = total liabilities/total assetsWCTA = working capital/total assetsCLCA = current liabilities/current assetsOENEG = one if total liabilities exceeds total assets, zero otherwiseNITA = net income /total assetsFUTL = funds provided by operations/total liabilitiesINTWO = one if net income was negative for the last two years, zero otherwiseCHIN = (NI,-NI,1)/(INI,I+INI "1), where NI, is net income70Comparing the 1980s sample to Ohlson's 1970s sample, the meanand standard deviation of the leverage variable (TLTA) are bothlarger in the 1980s sample for all three types of firms. This isconsistent with the assumption that the use of financial leveragehas increased in the 1980s. An F-test is conducted on thedifference in means on TLTA. The result supports the conclusionthat the significant difference exists between the bankrupt andnonbankrupt firms at the 1% level.The correlations between the nine variables are shown in Table4-7. Substantial correlation exists between TLTA, OENEG, CLCA andWCTA. This indicates possible collinearity among these variables.Table 4-8 reports the results of reestimating Ohlson's modelusing the new data. Panel A of Table 4-8 reports the modelpredicting bankruptcy one year prior. Panel B is the modelpredicting bankruptcy two years prior." In Panel A, while thesigns of the parameters are the same as in Ohlson's original study,the magnitudes have changed. In particular, the coefficient on TLTAfor the new sample is much smaller than in Ohlson's study. Thisimplies that, for the same level of leverage, the estimatedprobability of bankruptcy is less in the 1980s than in the 1970s.A decrease in the coefficient on TLTA is expected given theincreased use of financial leverage in the 1980s. The chi-squarestatistics for SIZE, TLTA, MITA, FUTL, INTWO and CHIN are allsignificant at the 5% level. WCTA is statistically significant at"Ohlson's original parameter estimates are reported in Table2-1 of Section 4-7Correlation Matrix of the Independent Variables Usedto Reestimate Ohlson's Modelvariable° SIZE TLTA WCTA CLCA OENEG NITA FUTL INTWO CHINSIZE:Rb 1.00 -.021 -.015 -.072 -.056 .114 -.051 -.198 .038SL° .00% 34.4% 49.3% .09% 1.00% .01% 2.05% .01% 8.53%TLTA:1.00 -.639 .286 .628 -.362 -.331 .228 -.102SL .00% .01% .01% .01% .01% .01% .01% .01%WCTA:1.00 -.512 -.444 .197 .211 -.206 .115SL .00% .01% .01% .01% .01% .01% .01%CLCA:1.00 .227 -.077 -.081 .127 -.030SL .00% .01% .05% .02% .01% 16.7%OENEG:1.00 -.231 -.079 .277 -.072SL .00% .01% .03% .01% .10%NITA:1.00 .365 -.436 .203SL .00% .01% .01% .01%FUTL:1.00 -.223 .082SL .00% .01% .02%INTWO:1.00 -.047SL .00% 3.07%CHIN:1.00SL^ .00%°SIZE = ln(total assets/GNP price-level)TLTA = total liabilities/total assetsWCTA = working capital/total assetsCLCA = current liabilities/current assetsOENEG = one if total liabilities exceeds total assets, zero otherwiseNITA = net income /total assetsFUTL = funds provided by operations/total liabilitiesINTWO = one if net income is negative for the last two years, zero otherwiseCHIN = (NI,-NI,I)/(INI,I+INI1), where NI, is net incomebR = Correlation coefficient.°SL = Significant level.72Table 4-8Results of Reestimating Ohlson's ModelPanel A:^Model 1: One Year Prior to BankruptcyVariable'^Estimates Chi-square P-valueINTERCEPT^-2.2473 4.93 0.0263SIZE^-0.1659 5.52 0.0188TLTA 1.7518 11.14 0.0008WCTA -0.8496 2.69 0.1012CLCA^0.0350 0.20 0.6537OENEG -0.2911 0.32 0.5744NITA -2.5018 7.11 0.0076FUTL^-2.3620 12.33 0.0004INTWO 0.9512 6.70 0.0096CHIN -0.5192 3.85 0.0498Likelihood Ratio 364.61Overall Correct RateR-Square96.8%0.660Panel B:^Model 2: Two Years Prior to BankruptcyVariable'^Estimates Chi-square P-valueINTERCEPT^-0.7325 0.54 0.4629SIZE^-0.1639 5.89 0.0152TLTA 0.8749 2.77 0.0961WCTA -2.0623 10.88 0.0010CLCA^-0.2224 3.08 0.0792OENEG -0.0916 0.03 0.8680NITA -6.1045 22.45 0.0000FUTL^-1.6608 7.12 0.0076INTWO -0.1286 0.11 0.7414CHIN -0.3576 2.16 0.1418Likelihood Ratio 282.99Overall Correct Rate^96.4%R-Square^ 0.586aSIZE = ln(total assets/GNP price-level)TLTA = total liabilities/total assetsWCTA = working capital/total assetsCLCA = current liabilities/current assetsOENEG = one if total liabilities exceeds total assets, zero otherwiseNITA = net income /total assetsFUTL = funds provided by operations/total liabilitiesINTWO = one if net income was negative for the last two years, zero otherwiseCHIN = (NI,-NI1)/(INI,I+INI,1), where NI, is net income73the 10% level. The chi-square statistics for CLCA and OENEG areinsignificant. These significance levels are similar to Ohlson'sresults except in the cases of OENEG and INTWO. In Panel B, theestimates of the intercept and the coefficient on CHIN have changedsigns from what they were in Ohlson's original study. Thecoefficient on TLTA in Model 2 is lower than in Ohlson's originalstudy and its significance level is reduced to the 10% level. Thechi-square statistics for SIZE, WCTA, NITA and FUTL aresignificant at the 5% level, while CLCA is significant at the 10%level. OENEG, INTWO and CHIN are not significant at the 10% level.The likelihood ratio statistic for Model 1 is 364.61 with 9degrees of freedom, which is significant at the 1% level ofsignificance. This indicates that Model 1 does have power todistinguish bankrupt from nonbankrupt firms. Similar results applyfor Model 2.Table 4-9 tests for a significant difference between theparameter estimates in Ohlson's model and those in the reestimatedmodel. The Z-values in the table are computed by the followingformula"A A- gi2[ SE( iii1)2+ SE( i 12)2 ]1/2where Oa is the ith estimate from Ohlson's model. 0i2 is theA^ Aith estimate from the reestimated model. SE(011) and SE(012) are"This formula is based on the assumption that the two samplesare independent.74the standard errors of Oa and 012, respectively.The Z-values indicate whether there is a significant change inthe parameters. In Panel A, the coefficient on TLTA for thereestimated model 1 is significantly less than in Ohlson's model atthe 1% level. The coefficient on SIZE is significantly lessnegative than in Ohlson's model at the 10% level. For othercoefficients, there is no significant change. Similar to theresults for model 1, the coefficient on TLTA for the reestimatedmodel 2 is significantly less than in Ohlson's model 2 at the 1%level. The coefficient on SIZE is again less negative, this time atthe 1% level of significance. The reestimated coefficient on CHINis significantly less than in Ohlson's model 2 at the 5% level. Thecoefficient on OENEG is significantly less negative and thecoefficient on NITA is significantly more negative than in Ohlson'smodel 2, at the 10% level. There is no significant change for thecoefficients on CONST, WCTA, CLCA, FUTL and INTWO. These resultssupport the Leverage Hypothesis, that the coefficient on TLTA hasdecreased in the 1980s, but they reject the Intercept Hypothesis,that the intercept has increased. It appears , therefore, that theincreased rate of bankruptcies in the 1980s is related to thevariables that are included in Ohlson's model and not to an overallincrease in the probability of bankruptcy for all firms. Based onthe analysis presented here, it is not possible to determinewhether the increased rate of bankruptcies in the 1980s is due tothe change in the bankruptcy law changing the coefficients inOhlson's model, or not.75Table 4-9Test for a Significant Change in the Parameters of Ohlson's ModelWhen Reestimated Using the 1980s Datavariable'Panel A:Ohlson's ModelModel 1Reestimated Model Z-valueestimate std err estimate std errINTERCEPT -1.320 1.361 -2.247 1.012 0.547SIZE -0.407 0.108 -0.166 0.071 -1.869*TLTA 6.030 0.912 1.752 0.525 4.064-*WCTA -1.430 0.757 -0.850 0.518 -0.633CLCA 0.076 0.099 0.035 0.078 0.322OENEG -1.720 0.702 -0.291 0.518 -1.638NITA -2.370 1.281 -2.502 0.938 0.083FUTL -1.830 0.775 -2.362 0.673 0.518INTWO 0.285 0.351 0.951 0.368 -1.310CHIN -0.521 0.236 -0.519 0.265 -0.006Panel B:Ohlson's ModelModel 2Reestimated Model Z-valuevariable' estimate std err estimate std errINTERCEPT 1.840 1.333 -0.732^0.998 1.544SIZE -0.519 0.097 -0.164^0.068 -2.993***TLTA 4.760 0.872 0.875^0.526 3.816-*WCTA -1.710 0.961 -2.062^0.625 0.307CLCA -0.297 0.405 -0.222^0.127 -0.177OENEG -1.980 0.818 -0.092^0.551 -1.914*NITA -2.740 1.522 -6.104^1.288 1.687*FUTL -2.180 0.799 -1.661^0.623 -0.512INTWO -0.780 0.406 -0.129^0.390 -1.156CHIN 0.422 0.201 -0.358^0.243 2.473-Significant at the 1% level based on a two-tailed test of significance.***Significant at the 5% level based on a two-tailed test of significance.*Significant at the 10% level based on a two-tailed test of significance.aSIZE = ln(total assets/GNP price-level)TLTA = total liabilities/total assetsWCTA = working capital/total assetsCLCA = current liabilities/current assetsOENEG = one if total liabilities exceeds total assets, zero otherwiseNITA = net income /total assetsFUTL = funds provided by operations/total liabilitiesINTWO = one if net income was negative for the last two years, zero otherwiseCHIN = (NIc-NI,)/(INLI+INI,1), where NI, is net income76Using a cutoff point of 0.5, the percentage of firms correctlyclassified is 96.8 percent for Model 1, and 96.4 percent for Model2. This is higher than for Ohlson's model which correctlyclassified 96.12 percent of firms using Model 1 and 95.55 percentof firms using Model 2.A naive model which classifies all firms as nonbankruptcorrectly classifies 95.24 percent (1980/(99+1980)) of firms oneyear prior to bankruptcy and 95.47 percent (1980/(95+1980)) twoyears prior. Compared to the naive model, the reestimated modelsperform better.The Type-I and Type-II errors are computed for selected cutoffpoints with respect to the reestimated models. The results arelisted in Table 4-10. The cutoff point which minimizes the sum oferrors is 0.06 for both Models.Comparing Table 4-10 to Table 4-2, the Type-II error rates arelower and Type-I error rates are higher for the reestimated model1 than for Ohlson's original model 1 applied to the 1981-1990 data.In comparing the reestimated model 1 with Ohlson's originalresults, the Type-I and Type-II errors are all lower for anyselected cutoff point. In contrast to the poor performance ofAltman's model, when Ohlson's model is reestimated with 1980's datait appears to outperform his original model one year prior tobankruptcy. It is not possible to test the predictive ability ofthe reestimated model 2 to Ohlson's original model 2 for firms twoyears prior to bankruptcy as Ohlson does not report this analysisfor his sample.77Table 4-10Type-I and Type-II Errors for Selected Cutoff PointsCutoff PointsReestimated Model 1Type-I^Type-IIReestimated ModelType-I^Type-II0.00 0% 100% 0% 100%0.02 7.08 25.91 2.02 34.650.04 10.10 15.35 10.10 18.030.06 13.13 10.51 14.14 12.530.08 21.21 7.53 20.20 9.290.10 22.22 6.01 25.25 7.070.20 38.38 2.93 40.40 2.470.30 47.47 1.36 48.48 1.360.40 52.52 0.76 55.55 0.610.50 59.59 0.40 58.58 0.300.60 67.67 0.25 66.66 0.250.70 69.69 0.15 69.69 0.250.80 74.74 0.15 74.74 0.200.90 78.78 0.15 77.77 01.00 100 0 100 0278CHAPTER 5CONCLUSIONSThis study has examined two bankruptcy prediction modelsexisting in the literature. The first one is Altman's Z-scoremodel. Altman's model uses multiple discriminant analysis todistinguish between bankrupt and nonbankrupt firms. The secondmodel is Ohlson's probabilistic model. Ohlson's model uses a logitfunction to estimate the probability that bankruptcy will occur fora firm. Although a number of studies have constructed statisticalmodels to predict the potential bankruptcy of corporate firms,Altman's and Ohlson's models are the two models most commonlymentioned in the literature.Altman's and Ohlson's models with their originally estimatedparameters have been widely used in the literature since they weredeveloped. There is considerable evidence that these models arestill used today. However, there is reason to expect that the modelparameters have changed from what they were when Altman and Ohlsonoriginally estimated their models. Therefore, the reexamination ofAltman's and Ohlson's models appears justified.There are two major reasons to expect that the model parametershave changed since the 1970s. The first reason is that thebankruptcy law in the U.S. changed dramatically in the late 1970s.The change in bankruptcy law is expected to increase the number offirms filing for bankruptcy. The evidence provided in this papersupports this expectation. The second reason for expecting a change79in the model parameters is the increased use of financial leveragein the 1980s. The statistical data given in this study indicatesthat the financial leverage follows an upward trend from the 1970sto the 1980s.In this study, the predictive abilities of Altman's andOhlson's original models are tested on a paired sample of 99bankrupt and 99 nonbankrupt firms and on a sample of 99 bankruptand 1,980 nonbankrupt firms, respectively. The samples are obtainedfrom the firms during the time period of 1981-1990. When Altman'sand Ohlson's models are applied to the samples, an increase in theType-I (classifying bankrupt firms as nonbankrupt) error rate isexpected due to the change in U.S. bankruptcy law in the late 1970sand an increase in the Type-II (classifying nonbankrupt firms asbankrupt) error rate is expected due to the increased use offinancial leverage in the 1980s.For Altman's model, Moyer's 1970s sample is used as a holdoutsample. Comparing Moyer's results with those for the 1980s sample,the Type-I error rate has declined and the Type-II error rate hasincreased in the 1980s period. These results are consistent withthe Type-II Error Hypothesis, that the increased use of leverage inthe 1980s increases the Type-II error rate, but are inconsistentwith the Type-I Error Hypothesis, that the change in U.S.bankruptcy law in the 1970s increases the Type-I error rate.For Ohlson's model, the Type-I error rate is also lower and theType-II error rate is again higher for the 1980s sample than forOhlson's original sample. The increased Type-II error rate is80consistent with the Type-II Error Hypothesis that the increased useof leverage in the 1980s increases the Type-II error rate. Thedecreased Type-I error rate is inconsistent with the Type-I ErrorHypothesis.Ideally, these two hypotheses should be tested by comparing theresults from the 1980s sample with those from a true holdout sampleapplied to Ohlson's original model. Unfortunately, such a holdoutsample is unavailable. Given the lack of a true holdout sample, wewould expect the Type-I and Type-II error rates to increase whenthe model is applied to a sample outside of the original estimationsample. This is an alternative explanation for the observedincreased rate of Type-II errors when Ohlson's model is applied tothe 1980s data.The Altman and Ohlson model parameters are then reestimatedusing the 1980s samples. Altman's model is reestimated on a pairedsample of 99 bankrupt and 99 nonbankrupt firms from the 1981-1990.In comparing the reestimated model with Altman's original study,the magnitudes have changed However, since statistics such asstandard errors are unavailable for individual variables in thediscriminant function, the significance of the parameter changecannot be measured. Therefore, considerably more attention is givento the reestimation of Ohlson's model in this study.Ohlson's model is reestimated on the sample of 99 bankrupt and1,980 nonbankrupt firms. Comparing the 1980s sample to Ohlson's1970s sample, the mean and standard deviation of the leveragevariable (TLTA) are both larger in the 1980s sample for both81bankrupt and nonbankrupt firms. This result is consistent with theassumption that the use of financial leverage has increased in the1980s.In comparing the reestimated model with Ohlson's originalstudy, the magnitudes have changed. The results of the reestimationsupport the Leverage Hypothesis that the increased use of leveragein the 1980s leads to a significant decrease in the coefficient onTLTA in Ohlson's model. However, the results do not support theIntercept Hypothesis that the change in the bankruptcy law in the1970s leads to a significant increase in the intercept in themodel.The reestimated model performs better than a naive model thatclassifies all firms as nonbankrupt. Comparing the reestimatedmodel to Ohlson's original model and sample, the Type-I and Type-IIerror rates for the reestimated model one year prior to bankruptcyare lower for any selected cutoff point. Therefore, for firms veryclose to bankruptcy, the reestimated model appears to outperformOhlson's original model.Because both Altman's and Ohlson's original models make lessType-I errors and more Type-II errors in the 1980s, users of thesemodels may prefer the original model to the reestimated model iftheir cost of a Type-I error is higher than their cost of a Type-IIerror. If the cost savings due to the reduced cost of Type-I errorsmore than offsets the increased cost of Type-II errors, users willprefer the original model. Determining whether this is true or notrequires knowledge of the relative cost of the two types of errors,82which we do not have information on. 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Ph.D. dissertation,State University of New York at Buffalo, 1983.88APPENDIX AListing of Bankrupt and Liquidated FirmsCompany Name^ Typea^DateALLIS-CHALMERS CORP^ B^06-29-87AMDORA CORP^ B 04-20-90AMER HEALTHCARE MGMT B^08-10-87AMER MEDICAL ELECTRONICS INC^B 07-16-87AMERICAN MEDICAL BLDGS INC B^08-15-90AMERICAN MONITOR CORP^ B 12-18-85AMES DEPT STORES INC B^04-26-90BANYAN CORP^ B 05-31-91BASIX CORP B^02-29-88BEST BUY DRUGS INC^ B 11-13-87BLUE DOLPHIN ENERGY B^06-01-88BOBBIE BROOKS INC B 01-15-82CANTON INDUSTRIAL CORP B^02-22-88CARDIS CORP^ B 05-25-88CARE ENTERPRISES B^03-28-88CARIBBEAN SELECT INC^ B 12-28-90CF & I STEEL CORP B^11-07-90CHARTER CO^ B 04-20-84CIRCLE K CORP B^05-15-90CISTRON BIOTECHNOLOGY INC^B 05-26-88COMPUTER DEVICES INC -CL B B^10-31-83CONESCO INDUSTRIES LTD B 08-20-85CONSOLIDATED PACKAGING CORP^B^06-20-84DART DRUG STORES INC^ B 08-09-89DIGICON INC^ B^01-31-90ENDOTRONICS INC B 03-27-87EXCALIBUR TECHNOLOGIES B^03-12-85FINEVEST FOODS B 02-04-91FLAME INDUSTRIES INC^ B^05-31-83FLANIGAN'S ENTERPRISES INC^B 11-04-85FORUM GROUP INC B^02-19-91GLOBAL MARINE INC B 01-28-86HALLWOOD HOLDINGS^ B^02-05-87HILLS DEPARTMENT STORES INC^B 02-04-91IMPERIAL INDUSTRIES INC B^10-02-86INTERCO INC^ B 01-24-91INVITRON CORP L^05-29-91ITEL CORP B 01-19-81JAMCO LTD B^10-05-87JG INDUSTRIES INC^ B 06-16-81KENILWORTH SYSTEMS CORP^B^09-01-82KEY CO -CL B B 06-20-88KURZWEIL MUSIC SYSTEMS INC B^05-07-90LA POINTE INDUSTRIES B 02-09-8989APPENDIX A - ContinuedCompany Name^ Type^DateLIONEL CORP^ B^02-19-82LONE STAR INDUSTRIES^ B 12-10-90LOUISIANA-PACIFIC RESOURCES^B^05-04-84MAGIC CIRCLE ENERGY CORP B 04-17-85MANAGEMENT ASSISTANCE LIQ TR B^09-09-86MAXON INDUSTRIES INC^ B 08-17-81MHI GROUP INC^ B^11-xx-84MICHIGAN GENERAL CORP B 04-22-87MUELLER INDUSTRIES B^08-26-82NATIONAL LUMBER & SUPPLY INC^B 04-03-90ND RESOURCES INC^ B^12-03-84NUMEX CORP^ B 02-xx-81OLSON INDUSTRIES INC B^04-04-91OVERMYER CORP B 04-17-90PARTNERS OIL CO B^04-12-83PENGO INDUSTRIES INC^ B 05-24-88PETTIBONE CORP^ B^01-31-86PHOENIX RESOURCE COS B 04-26-88PUBCO CORP B^07-02-82RAMTEK CORP B 09-29-88RESURGENS COMMUNICATIONS GP^B^11-30-88RETAILING CORP OF AMERICA B 01-04-91ROBERTSON COS INC^ B^07-20-90SALANT CORP^ B 02-22-85SHIRT SHED INC B^04-04-85SILK GREENHOUSE INC B 07-31-91SIMETCO INC B^10-30-86SMITH INTERNATIONAL INC^B 03-07-86SOUTHERN HOSPITALITY B^07-01-88STANDARD METALS CORP B 03-07-84STANWICK CORP^ L^02-04-86STORAGE TECHNOLOGY CP -CL A^B 10-31-84STUARTS DEPARTMENT STORES B^12-11-90SUNF INC L 12-14-89SYNTECH INTERNATIONAL INC^B^07-16-90TACOMA BOATBUILDING^ B 09-23-85TEREX CORP^ B^11-04-83TERRANO CORP B 09-xx-85TEXSCAN CORP B^11-25-85TGX CORP B 02-22-90TODD SHIPYARDS CORP^ B^08-17-87TONS OF TOYS INC B 12-08-89TS INDUSTRIES INC B^08-21-89ULTIMAP CORP^ B 12-18-90ULTRAK INC B^03-22-85UMC ELECTRONICS CO^ B 10-23-8590APPENDIX A - ContinuedCompany Name^ Type^DateUNR INDUSTRIES INC B^07-29-82WALL TO WALL SOUND & VIDEO^B 07-20-90WESTAR CORP^ B^11-09-88WESTERN CO OF NO AMER B 02-02-88WHEELING PITTSBURGH CP B^04-16-85WICKES COS INC B 04-24-82WINJAK INC -CL A^ B^12-19-88WTD INDUSTRIES INC B 01-31-91ZENITH LABORATORIES B^05-04-8813 and L indicate bankruptcy and liquidation, respectively.91


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