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J ECO BUSN 2691994; 46:269-286 Predicting Corporate Bankruptcy and Financial Distress: Information Value Added by Multinomial Logit Models Thomajean Johnsen and Ronald W. Melicher Efforts to explain a nd/ or predict corporate bankruptcy continues to be of interest from finance, economics, and accounting perspectives. Corporate failure prediction models have generally progressed from univariate financial ratio analysis to multi- variate models, and from discriminant models to logit models that offer an opportunity to estimate directly the probability of failure under less restrictive statistical assumptions. This study examines the added value of two types of information provided by multinomial logit models used to explain and predict corporate bankruptcy: (i) the information obtained by expanding the outcome space by including a third state of financial distress and (ii) secondary classification information. Samples of nonbankrupt, financially weak, and bankrupt firms are identified. Multinomial logit models, reflecting the reformulation of two traditional bankruptcy prediction models, then are used to classify firms during the 1970-1983 period. The status of each financially weak and bankrupt firm is monitored for five years after its initial classification. Significant reductions in misclassification error rates for the multinomial model are documented. Results also suggest that sec- ondary classification information can be used to augment primary classifications to improve the ability to correctly predict bankrupt firms, as well as predict financially weak firms that will suffer severe financial distress in the future. I . I n t r o d u c t i o n Models of corporate bankruptcy have been developed that predict the probability of business failure with a high degree of accuracy. During the decade prior to 1977, several failure prediction studies were conducted for both large and small nonfi- nancial finns. Beginning with Beaver' s (1966) univariate analysis of 30 ratios and culminating with the multiple discriminant analysis (MDA) Zet a model developed College of Business Administration, University of Denver, Denver, Colorado (TJ); College of Business, University of Colorado, Boulder, Colorado (RM). Address reprint requests to Professor Ronald Melicher, College of Business/Finance Division, University of Colorado at Boulder, Campus Box 419, Boulder, Colorado 80309-0419. Journal of Economics and Business 0148-6195/94/$07.00 © 1994 Temple University 270 I..h)hnsc~l and R, W. Mclichc~ by Altman et al. (1977), researchers attempted to improve the accuracy c)f mul t mi tio predictive models by optimizing the set of predictor w~riablcs. After the mid-1970s, researchers focused increasingly on the difficulties associ- ated with the then-prevailing methodological approaches [e.g., sce Eisenbeis (1977). Moyer (1977), Mensah (1984), and Zmijewski (1984)]. Despite the criticisms ex- plored in these later studies, the overriding conclusion from the body of research conducted to date is that financial ratios provide significant indication of the likelihood of financial distress. However, efforts to overcome the methodological difficulties associated with MDA resulted in a shift to logit analysis [e.g., see Ohlson (1980) and Zavgren (1985)], which produces an estimate of the probability of failure under less restrictive statistical assumptions relative to MDA. Of course, all firms in financial distress do not end in business failure. Bankruptcy after all, represents only an extreme result. Thus, financial distress is best depicted as a continuum ranging from being "financially weak" to bankrupt, with thc possibility of various degrees of financial weakness. For example, Lau (1987) extends the traditional fai l ure/ nonfai l ure dichotomy to a financially stable state and four states of financial distress? Although Lau successfully demonstrates the applicability of multistate models to failure prediction, comparisons between multi- state models and two-state models used in other studies are lacking. -~ A multistate classification scheme such as Lau' s permits many more types of classification errors than are possible in the earlier two-state models. Analysis of the performance results should account for such a difference. Therefore, the first objective of this study is to replicate previous research utilizing similar sampling techniques and a two-state model of bankruptcy prediction. The ability to discrimi- nate between bankrupt and nonbankrupt firms will then be compared to that of a multistate model in which an explicit category of "financially weak" firms is defined and included in the sample. The second objective is to determine the added value of the secondary classifi- cation information in the prediction of changes in financial condition and the reliability of primary classifications. Multistate logit models provide J probabilities of entering into J possible states of financial distress. The parameters that describe the distance between these various probabilities may provide additional informa- tion pertaining to impending changes in financial condition as well as the degree of confidence that may be placed in the model' s prediction. For example, consider firms that are accurately cl assi fi ed--t he larger the distance bet ween the highest probability state (primary classification) and the second highest probability state (secondary classification), the greater the confidence in the accuracy of the primary classification. 1A cont i nuum o f fi nanci al di stress f rom we ak t o severe was represent ed by firms reduci ng or omi t t i ng di vi dend payment s, t echni cal def aul t , or l oan payment defaul t, firms i n Chapt er X or XI o f t he Bankruptcy Act , and firms in bankruptcy or l i qui dati on. : Ftagg e t al. ( 1991) at t empt t o predi ct corporat e bankruptcy usi ng a sampl e o f "failing" firms. Event s that were i dent i f i ed as bei ng i ndi cati ve o f pot ent i al fai l ure i ncl uded reduct i ons i n di vi dend payment s, account i ng qual i fi ed audi t opi ni ons, vi ol at i on o f debt covenant s, and t roubl ed debt restructuring. No at t empt was made t o suggest that t he s e cl assi fi cati ons f el l al ong a cont i nuum o f fi nanci al distress. Rather, al l firms in t hes e cat egori es were grouped t oget her and cont rast ed wi t h bankrupt firms (firms havi ng fi l ed f or Chapt er X or XI bankruptcy prot ect i on) usi ng l ogi st i c regressi on analysis. Corporate Bankruptcy 271 II. Mo d e l s o f Qua l i t a t i v e Cho i c e T wo - S t a t e L o g i t Mo d e l Models of qualitative choice apply to cases in which observations of the dependent variable are limited in some sense. In the case of bankruptcy prediction the dependent variable Y, represents a discrete "choice" or state that takes on the value of one if the firm is bankrupt or zero if it is nonbankrupt. The logit model is based on the cumulative logistic probability function in which the probability that Yt = l (Pt ) is given as 1 e~ = 1 + e x p ( - ( a + f l x t ) ) ' where t = 1, 2 . . . . , T firms. Now, solving for (o~ + 13xt), we derive the estimation form of the equation Pt l o g ~ = a + f l x t, 1 - 8 where all logs are natural logarithms. Not e that the ratio of the probability that Yt = 1 to the probability that Yt = 0, is a rather convenient transformation and has intuitive appeal in the context of bankruptcy prediction. The slope of the cumula- tive logistic probability function is greatest where Pt = 0.50, where changes in the independent variables will have their greatest impact. The low slopes at the ends of the distribution suggest that only small changes in probabilities will occur at those points on the distribution, given the same unit change in the independent variable. That is, a firm with a very low or very high initial probability of bankruptcy will be much less influenced by the same one unit change in a predictor variable, when compared to a firm whose initial probability is very close to 0.50. Ex t e n s i o n t o t he Thr e e - St at e L o g i t Mo d e l The multinomial model generalizes the previously discussed case where the depen- dent variable involves only two qualitative states. In general, for J states the probabilities are specified as e x p ( a j + f l j x , ) e ' J = E e x p ( a j + / 3 i x , ) ' where a 1 = J ~ l = 0 and state 1 is the benchmark for comparison [Theil (1969)]. The multinomial model has been used to study a variety of problems, and numerous illustrations appear in the literature. Significant examples include the Boskin (1974) and Schmidt and Strauss (1975) studies of the determinants of occupational choice, the Uhl er and Cragg (1971) study of the structure of house- hold assets, the Theil (1969) study of modes of transportation, and the Lau (1987) study of financial distress. McFadden (1974, 1976) discusses the theory underlying models of discrete choice, with specific focus on the logit model, and he also 272 I Johnson and R. W'. Melichc~ der i ves a ppr opr i a t e me t h o d s of es t i mat i on and devel ops a ppr opr i a t e i nf er ence pr oc e dur e s . Mc Fa d d e n (1981) devel ops a n o n i n d e p e n d e n t logit model , and var i ous ot he r s exami ne t he ef f ect s of mi sspeci f i cat i on in t he k)git model i ncl udi ng Par ks (1980), Lee (1982), and Ru n d (1983). To ext end t he bi nomi al choi ce mode l t o t he case of t hr ee st at es f or this st udy, let Y,i = l, if t he t t h fi rm is cl assi fi ed as t he j t h st at e [ j = 0 ( bankr upt ) , I ( nonba nkr upt ) , or 2 (fi nanci al l y weak)]. As s umi ng no par t i cul ar or de r i ng of t he choi ces and Pri - 1, t he mul t i nomi al Iogit b e c o me s 3 I o g ( PI 2 / PI , ) = oe + [3,.v,. (1) l o g ( Pl 3 / Pt l ) = a 3 + /3~X t. (2) P,~ = 1 - P,2 - P,.~. (3) I n e a c h case, Pt r epr es ent s t he pr obabi l i t y t hat t he j t h st at e will occur . Th e l og o f t he odds o f one st at e in r at i o t o t he s e c ond r e ma i ns a l i near f unc t i on o f t he mat r i x of i n d e p e n d e n t var i abl es. The s e i ndi vi dual odds ar e not d e p e n d e n t on t he odds as s oci at ed wi t h any o t h e r st at e, except t hat t he s ys t em o f e qua t i ons mus t be c ons t r a i ne d so t hat t he sum o f t he i ndi vi dual pr obabi l i t i es equal s 1. Eval uat i on o f Bi nomi al and Mul t i nomi al Choi ce Model s A n u mb e r o f poi nt s ar e i mpor t a nt t o cons i der whe n eval uat i ng t he r esul t s obt a i ne d f r om a l ogi t model . Fi rst , t he es t i mat es o f t he coef f i ci ent s r ef l ect t he ef f ect o f a one uni t c ha nge in an i n d e p e n d e n t var i abl e u p o n l o g [ P J ( 1 - Pt)] and not u p o n t he pr obabi l i t y Pt. I n fact , t he ef f ect u p o n t he pr obabi l i t y Pt d e p e n d s u p o n t he or i gi nal pr obabi l i t y ( t he initial val ues o f t he i n d e p e n d e n t var i abl es) as well as t he coeffi - ci ent s. An addi t i onal c ons i de r a t i on c onc e r ns t he i mpl i cat i ons o f t he r est r i ct i ve as s ump- t i on of i n d e p e n d e n c e pr es ent in t he mul t i nomi a l l ogi t model . Thi s a s s umpt i on hol ds t hat t he odds o f any speci fi c st at e will not be i nf l uenced by t he exi st ence of ot he r al t er nat i ve st at es. Al t h o u g h t hi s a s s umpt i on is o f no c o n s e q u e n c e f or mul t i nomi al pr obi t , t hi s r est r i ct i on in t he cont ext o f a l ogi t e s t i ma t i on ma y ser ve t o be a ser i ous we a kne s s whe n at l east t wo o f t he st at es ar e cl ose subst i t ut es [ J udge et al. (11985); Kme n t a (1986); Ha u s ma n and Mc F a d d e n (1984)]. For exampl e, La u (1987) descr i bes t he five st at es as fol l ows: st at e ~ = fi nanci al stability; st at e 1 = omi t t i ng or r e duc i ng di vi dend pa yme nt s ; st at e 2 = t echni cal def aul t and def aul t on l oan payment s ; st at e 3 = pr ot e c t i on u n d e r Ch a p t e r X or XI 3It may be argued that our nonbankrupt, financially weak, and bankrupt "choices" represent ordered states of financial distress and therefore demand an ordered assumption within the estimation. If so, we recognize the loss of efficiency resulting from the use of an unordered model under those conditions. However, an index of economic failure is a complex construct and difficult to justify in terms of a single variable. Firms may or may not proceed through an ordered sequence of financial distress. We err on the side of caution in using an unordered model, recognizing the bias in estimation of probabilities that may occur if the underlying index of failure is truly unordered and an ordered model is assumed. The trade-off of efficiency, although not consistency, for potential estimation bias seems a reasonable solution. For further discussion, see Amemiya (1985) and Maddala (1983). Corporate Bankruptcy 273 of the Bankruptcy Act; state 4 = bankruptcy and liquidation. If any state is considered a close substitute (e.g., 3 and 4 or 2 and 3), in the context of the multinomial logit, the estimated probabilities will be in error. Therefore, we collapse the intermediate states of financial distress into one category defined as "financially weak firms" to eliminate this possibility. Consequently, we assume that the alternative classifications of financial distress examined here are distinct enough to negate this factor. 4 III. Desi gn of Sampl es and Choice of Prediction Model s Nonbankrupt, Financially Weak, and Bankrupt Firm Samples The sample of bankrupt firms was developed as follows. 5 First, firms reported in the Wall Street Journal Index or in the F and S Index of Corporate Changes that filed for either Chapter X or XI of the U.S. Bankruptcy Courts during the 1970-1983 period were identified. Second, to be included in the final sample, each bankrupt firm had to have a Standard Industrial Classification (SIC) code of less than 6000 and be included on either the Compustat standard or research tapes with a minimum of five years of financial data. Thus, financial and service firms along with "new" firms (i.e., those with less than five years of available financial data) were excluded from the sample. In addition, no bankrupt public utilities were included. The result was an initial sample, before screening for adequate financial data to calculate financial ratios, of 157 bankrupt firms. Two additional samples were constructed for analysis purposes. First, all firms on the Compustat tapes with at least five years of financial data and SIC codes of less than 6000 were identified. Each firm then was "assigned" a year, for purposes of selecting financial data, from 1970 through 1983 using a random number generator. Then, again using a random number generator, 300 firms with randomly assigned "event" years were selected to comprise the nonbankrupt sample. 6 The third sample consists of nonbankrupt but financially "weak" firms. Rather than using the classification processes employed by Lau (1987) or Flagg et al. (1991), we rely on the stock quality rankings prepared by the Standard & Poor's Corporation in its Security Owner's Stock Guide. S & P analyzes past growth and stability of dividends and earnings, as well as other factors, in arriving at its rankings. Thus, a reduction in dividends (an indication of financial distress in both the Lau and Flagg et al. studies) likely would result in a lower S & P ranking, which ranges from A + (highest) to D (in reorganization). A B + ranking is considered to be average. Our operational definition of financially weak includes firms whose common stock rankings are B (below average), B - (lower), or C (lowest). 4Hausman and Wise (1978) provide a comparison of t he logit and i ndependent probit models in which each model produces similar results. 5We wish to acknowledge t he efforts of Al an J. Kritzer in initially developing t he sample of bankrupt firms, as well as t he nonbankr upt and financially weak firm samples used in this study. 6Due t o our sampling met hod, 8 firms with two-digit SIC codes of 49 were included in t he nonbankr upt group and one firm was included in t he financially weak group. The breakdown among t he ni ne firms w a s a s follows: five nat ural gas transmission firms, two combi nat i on gas transmission and di st ri but i on firms, and two sanitary services firms. Preliminary results indicated no differences in classification accuracy for t hese regulated firms relative t o t he unregul at ed firms. 2 7 4 1. , I o h n s c r ~ ~md I~. W. Me l i c h c ~ Three hundred of these financially weak firms were randomly selected from the Compustat tapes with the constraints of SIC codes below 6(100 and live years ~H financial data. These firms were approximately equally distributed over the 1970-1983 period. In addition to identifying the specific year of the S& P ranking for each financially weak firm, we track the common stock ranking for the financially weak and bankrupt firms for five years afterwards. For example, a financially weak firm with an initial below average ranking in 197[) is followed over the 1971-1975 period. Likewise, a firm with a 1983 initial ranking is tracked over the 1984-1988 period. Thus, we study the sample of financially distressed firms over the 1970-1988 period. Bankruptcy Prediction Models Prior bankruptcy studies have examined a large set of diverse financial ratios for purposes of predicting corporate bankruptcies. Rather than trying to develop an independent prediction model based on the relative importance of variables in prior studies, we chose to examine two models (i.e., sets of variables) that have survived the test of time as predictors of corporate bankruptcy. Beaver (1966) identified six variables and Altman et al. (1977) identified seven variables that were important in predicting corporate bankruptcy. These variables form the basis for two independent multivariate logit models used in this study and are identified in Table 1. Both of these basic models reflect the importance of liquidity/cash flow, profitability/rates of return, and financial leverage variables. While the only common variable is the current ratio (current assets divided by current liabilities), there is similarity in terms of profitability and financial leverage variables. At the same time, the two models differ in that the Beaver model Table 1. Summary of Explanatory Variables a Used in the Binomial and Multinomial Logit Models Zeta Variables [ Al t ma n e t al . ( 1977) ] Z1 = S t a n d a r d d e v i a t i o n ( E B I T / t o t a l a s s e t s ) Z 2 = E B I T / t o t a l a s s e t s Z 3 = E B I T / t o t a l i n t e r e s t Z 4 = R e t a i n e d e a r n i n g s / t o t a l a s s e t s Z 5 = C u r r e n t a s s e t s / c u r r e n t l i a bi l i t i e s Z 6 = C o mmo n e q u i t y / t o t a l c a p i t a l Z 7 = T o t a l a s s e t s Beaver Variables [ Be a v e r ( 1966) ] B1 = C a s h f l o w/ t o t a l d e b t B2 = Ne t i n c o me / t o t a l a s s e t s B3 = T o t a l d e b t / t o t a l a s s e t s B4 = Wo r k i n g c a p i t a l / t o t a l a s s e t s B5 = C u r r e n t a s s e t s / c u r r e n t l i a bi l i t i e s B6 = ND c r e d i t i n t e r v a l ( ND = n e t d e f e n s i v e a s s e t s ) a E BI T = e a r n i n g s b e f o r e i nt e r e s t a n d t axes; t ot al c a pi t a l = l o n g - t e r m de bt pl us c o mmo n equi t y; c a s h f l ow = ne t i n c o me pl us d e p r e c i a t i o n , de pl e t i on, a n d a mo r t i z a t i o n ; wo r k i n g c a pi t a l = c u r r e n t as s et s mi nus c u r r e n t l i abi l i t i es; ND c r e di t i nt er val = [ ( cash + ma r k e t a b l e s e c ur i t i e s - c u r r e n t l i a b i l i t i e s ) / ( o p e r a t i n g ex- p e n s e s - d e p r e c i a t i o n - de pl e t i on - a mor t i z a t i on) ] . Corporate Bankruptcy 275 contains a unique "ND (net defensive assets) credit interval" variable, whereas the Zeta model (terminology used by Altman et al.) includes a measure of variability (i.e., standard deviation) of the return on assets. Consequently, we chose to examine the primary and secondary classification abilities of each model when viewed in a multinomial logit framework. In order to avoid using financial data for firms already in bankruptcy (since our interest is in bankruptcy prediction abilities), financial ratio data for bankrupt firms are taken from the last financial statement prior to the bankruptcy. Thus, financial data are at least 12 months prior to bankruptcy (and could be as much as 23 months prior). For example, a firm with a December fiscal year might file for bankruptcy in January 1982. The financial data for this firm would come from the December 1980 financial statements. Likewise, a firm with a December fiscal year might file for bankruptcy in November 1983. The financial statements used to predict bankruptcy for this firm would be dated December 1981. Search of the Compustat tapes for all data necessary to calculate the variables in the Beaver and Zeta models resulted in a reduction of the initial sample sizes. The final sample sizes included in this study were: Number Percent Bankrupt firms 112 17.0 Nonbankrupt firms 293 44.4 Financially weak firms 7 255 38.6 Total 660 100.0 While the bankrupt firms are overrepresented in this study relative to their proportion in terms of the overall population of firms, choice-based sample bias [e.g., see Zmijewski (1984)] is much less problematic than when bankrupt firms are matched equally with nonbankrupt firms. IV. Bankruptcy Prediction Results Addi ng Financially Weak Fi rms as a Classification Category If the binomial (BN) approach is less efficient, then total misclassification errors from the estimation of the three functions from the BN model would be greater than the total misclassification errors from the three functions estimated simulta- neously by the multinomial model (MN). Three BN functions are estimated separately (bankrupt versus nonbankrupt; bankrupt versus weak; nonbankrupt versus weak), producing a total of six possible types of misclassification errors. The three functions were estimated in this manner in order to standardize a compari- son to the MN results. For the MN model, these three functions also are estimated, producing the same types of errors; however, the classification results are produced 7Firms included in t he financially weak sample were checked against t he firms in t he nonbankr upt sample to avoid specific represent at i on in bot h samples. Of course, ot her financially weak firms were likely t o have been a part of t he nonbankr upt sample. 2 7 6 1 Iohnsen and R. W. Mctichc~ Table 2. Total Number of Misclassilication Errors for the Beaver and Zeta Variables Mi s c t a s s i f i c a t i o n s / Va r i a b l e s t ot a l s a mp l e '~; Ch a n g e Bi n o mi a l mo d e l Be a v e r 3 0 l ) / 6 6 0 Ze t a 2 9 5 / 6 6 0 Mu l t i n o mi a l mo d e l Be a v e r 2 5 7 / 6 6 0 14.3c/~ Z e t a 2 5 3 / 6 6 0 - 14.2~f Note: Tot al mi scl assi f i cat i on er r or is def i ned as t he sum of ba nkr upt firms mi scl assi f i ed as nonba nkr upt or weak, pl us nonba nkr upt fi rms mi scl assi f i ed as b a n k r u p t or weak, pl us weak fi rms mi scl assi f i ed as ba nkr upt or nonba nkr upt . The pe r c e nt change in mi scl assi f i cat i on is c a l c ul a t e d as t he r educt i on in t ot al mi scl assi f i cat i on er r or s be t we e n t he BN a nd MN mo d e l s f r om a single est i mat i on. The probabi l i t i es f r om t he MN and BN model s are used to cat egori ze each firm into st at e J using t he highest pr edi ct ed probabi l i t y as an i ndi cat i on of state. A firm is misclassified if it in fact di d not actually ent er into t hat state. Tabl e 2 present s t he t ot al number of misclassification er r or s f or t he basic Beaver and Zet a vari abl es when est i mat ed using t he BN and MN approaches. The basic model f or t he Zet a and Beaver variables pr oduces an i mpr ovement in t ot al misclassification rat es on t he or der of 14% (43 firms f or t he Beaver variables and 42 firms f or t he Zet a vari abl es) f or t he MN model when compar ed to t he BN model results. In or der to det er mi ne t he source of i mpr ovement , we now t urn our at t ent i on to t he individual component s of t he t ot al misclassification rates. The types of classification er r or s can be decomposed i nt o t he following ele- ments: Component 1. The misclassification of bankr upt firms as nonbankr upt plus t he misclassification of nonbankr upt firms as bankrupt . Component 2. The misclassification of bankr upt firms as weak plus t he misclassi- fication of weak firms as bankrupt . Component 3. The misclassification of nonbankr upt firms as weak plus t he misclassification of weak firms as nonbankr upt . Because t he focus of our analysis is on t he pr edi ct i on of financial distress, we confi ne our discussion to component s 1 and 2. However , t he er r or rat es f or component 3 were not substantially di fferent with respect t o t he est i mat i on pr ocedur e. Misclassification of Bankrupt versus Nonbankrupt Firms (Component 1) Tabl e 3 present s t he t ot al number of misclassifications of bankr upt versus non- bankr upt firms f or t he bi nomi al (BN) and mul t i nomi al (MN) met hods. The basic Zet a model results in a t ot al er r or r at e of 41 misclassified firms f or t he BN model . When t he weak firm groupi ng is added in t he MN est i mat i on, t he t ot al er r or rat e dr ops t o 11 f r om 41 ( - 7 3 %) . The basic Beaver model pr oduces a t ot al er r or r at e of 38 firms using t he bi nomi al est i mat i on. When t he weak firms are added in a mul t i nomi al est i mat i on, t he t ot al er r or r at e is r educed t o 16 ( - 58%). Tabl e 4 r epor t s t he results of t he est i mat i on of t he funct i ons discriminating bankr upt f r om nonbankr upt firms using t he bi nomi al and mul t i nomi al approaches. Corporate Bankruptcy Table 3. The Number of Miselassification Errors of Bankrupt versus Nonbankrupt Firms for the Zeta and Beaver Variables 277 Type of error a I II Tot al % Change b Bi nomi al model Zet a vari abl es 26/ 112 15/ 293 41/ 405 - - Beaver vari abl es 25 / 112 13/ 293 38/ 405 - - Mul t i nomi al model Zet a vari abl es 6/ 112 5/ 293 11/ 405 - 73.2% Beaver variables 11/ 112 5/ 293 16/ 405 - 57.9% aError I = misclassification of bankrupt firms as nonbankrupt; Error II = misclassification of nonbankrupt firms as bankrupt. bpercent Change is calculated as the reduction in total errors between the BN and MN models. Both approaches produce similar coefficients with similar levels of significance for the Zeta variables. The coefficients on Z1 [standard deviation of EBIT/ t ot al assets (TA)], Z2 (EBIT/TA), Z4 [retained earnings (RE)/TA], and Z7 (TA) are signifi- cant (a = 0.01) when estimated using a binomial or multinomial approach. Only the standard error on EBI T/ TA declined relative to its coefficient under the MN method. Note, however, for the Beaver variables, there is an increase in signifi- cance for B1 [cash flow (CF)/total debt (TD)], B2 [net income (NI)/TA], and B3 (TD/TA) for the MN method relative to the BN estimation. The standard errors for each of these coefficients are reduced in the MN case. We compare the bankrupt/nonbankrupt misclassification rates for this study to the original Beaver (1966) and Altman et al. (1977) results. Although our study covers a later time period, the misclassification rates for the two-state models are similar. The Beaver (1966) study reports an error rate of 13% compared to 9% for this study. Similarly Altman et al. (1977) report an error rate of 7% compared to 10% here. Error rates from applying the three-state model are much lower at 4% (Beaver variables) and 3% (Zeta variables). Misclassification of Bankrupt versus Weak Firms (Component 2) The numbers of misclassification errors from the binomial models are compared to the error misclassification rates from the MN models are presented in Table 5. The basic Zeta model produces a total error rate of 60 misclassified finns for the binomial estimation. When the weak firm group is added to the classification scheme using a multinomial estimation, total error is reduced from 60 to 56 ( - 7%) . The basic Beaver model produces a total error rate of 59 finns for the binomial case. When the weak finns are added and estimated using the MN method, the error rate is reduced to 51 from 59 (-14%). Finally, it is important to note that the functions that discriminate between bankrupt versus weak finns and bankrupt versus nonbankrupt finns presented in Table 4 are different. The Zeta variables Z1 (the standard deviation of EBIT/TA), Z2 (EBIT/TA), and Z4 (RE/ TA) are significant predictors for both groups. However Z7 (TA), while important in the bankrupt/nonbankrupt distinction, is unimportant in the discrimination of bankrupt versus weak firms. T a b l e 4 . T h e E s t i m a t e d F u n c t i o n s f o r B a n k r u p t v e r s u s N o n b a n k r u p t F i r m s ( B / N B ) a n d B a n k r u p t v c r s u s W e a k F i r m s ( B , / W } f o r t h e Z e t a a n d B e a v e r V a r i a b l e s B i n o m i a l f u n c t i o n M u l t i n o m i a l f u n c t i o n M u l t i n o m i a l f u n c t i o n ( B / N B ) ( B / N B ) ( B / W ) C o e f f . t - R a t i o C o e f f . t - R a t i o C o e f f , t - R a t i o Z e t a V a r i a b l e s Z 1 8 . 5 1 6 1 2 . 9 4 ~ ' 7 . 8 1 6 0 2 , 8 3 ~ 3 . 9 3 2 0 1 , 8 3 Z 2 - 9 . 9 6 9 3 - 4 . 7 4 ~ ' - 1 3 . 3 2 0 0 - 7 . 6 4 ~ - 1 1 . 2 4 0 0 7 . 5 0 ~ ' Z 3 - 0 . 6 0 9 9 E - 0 4 - 0 . 4 3 - 0 , 1 1 5 0 E - 0 3 - 1 . 1 0 0 . 1 8 3 9 E - 0 4 1 . 4 2 Z 4 - 6 . 8 1 9 8 5 . 7 7 ~ ' - 5 . 2 2 2 0 - 4 . 2 9 " - 2 . 6 9 5 0 ~ 4 O ~ Z 5 - 0 . 1 1 6 5 1 . 2 5 0 . 0 4 6 5 0 . 4 2 - 0 . 1 0 6 2 i . 2 4 Z 6 0 . 1 4 9 1 0 . 3 5 - 0 . 3 5 7 3 - 0 . 4 4 0 . 1 9 1 1 2 ~ 8 , ~ Z 7 - 0 . 4 4 6 3 E - 0 2 - 3 . 5 3 ~ ' 0 . 0 4 1 2 E - 0 1 - 3 . 4 9 " 0 . 2 0 5 8 E - 0 2 1 . 7 5 C o n s t a n t 1 . 9 5 0 6 4 . 1 2 " 1 . 6 3 6 0 3 . 9 0 ~ 0 . 2 8 2 0 i ! . S ~ G o o d n e s s o f f i t X ~ = 2 1 8 , 9 8 3 ~ X : = 1 0 1 5 - 6 3 3 ~ B e a v e r V a r i a b l e s B 1 - 6 . 7 0 0 3 1 . 6 8 - 5 . 9 7 8 0 4 . 2 8 ~ - 5 . 7 1 9 ( } i I ? ~ B 2 - 5 . 6 1 9 8 0 . 7 4 1 . 4 5 4 0 - 3 . 2 9 ~ - 0 . 8 7 3 0 2 . 1 I ~ B 3 6 . 1 7 5 4 3 . 9 3 ~ 5 . 1 7 0 0 5 . 9 & 0 . 6 2 5 6 I A 3 B 4 - 2 . 7 4 2 3 1 . 5 9 - 2 , 5 3 8 0 1 . 8 0 - 3 . 4 2 4 0 2 , 5 5 ~ ' B 5 0 . 5 1 2 2 1 . 6 2 0 . 3 6 3 2 1 . 2 0 0 . 0 8 4 1 ~ L 2 8 B 6 - 2 . 0 8 3 7 2 . 3 5 a - 1 . 7 9 1 0 - 2 . 3 4 ~ - 2 . 1 7 1 0 2 . ~ 7 ~ ' C o n s t a n t - 4 . 2 9 5 2 - 3 . 2 0 ~ ' - 3 . 2 5 9 0 - 4 . 3 9 ~ - 0 . 2 1 3 2 ( ! 4 1 G o o d n e s s o f f i t ) ¢ : = 2 2 1 . 8 5 7 ~ ' X z = 1 0 4 3 . 3 1 9 ~ ' ~ ' S i g n i f i c a n c e l e v e l , a , 0 . 0 1 . Corporate Bankruptcy Table 5. The Number of Misclassification Errors of Bankrupt versus Weak Firms for the Zeta and Beaver Variables 279 Type of error a I II Total % Change b Binomial model Zeta variables 42/ 112 18/255 60/ 367 - - Beaver variables 43/ 112 16/255 59/ 367 - - Multinomial model Zeta variables 40/ 112 16/255 56/ 367 - 6.7% Beaver variables 28/ 112 23/255 51/ 367 - 13.6% aTotal error = the sum of error I and error II. Error l = the number of bankrupt firms misclassified as weak; error II = the number of weak firms misclassified as bankrupt. bReduction in total errors between the BN and MN models. In a similar fashion, B1 ( CF/ TD) , B2 ( NI / TA) , and B6 (ND credit interval) are factors common to bot h groups. Although B3 ( TD/ TA) is significant for bankrupt versus nonbankrupt firms, it fails to discriminate bet ween bankrupt and weak firms. In addition, B4 [working capital ( WC) / TA] contributes to the ability to distinguish bet ween bankrupt versus weak firms. These differentiating factors support the contention made earlier that the categories of financial health or distress defined in this study do, in fact, represent three independent states. Substantial changes i n federal bankruptcy law occurred during the period studied. The Federal Bankruptcy Reform Act of 1978 was adopt ed effective in January 1979. To assess the influence of the Reform Act, the sample was seg- ment ed by a time period prior to and following the effective year. The classification rates for each of the samples segmented by time period are presented in Table 6. Chi-square tests of association indicate no relationship bet ween classification rates and time period. Reliability of Classification Accuracy We assess the reliability of the classification results for one set of independent variables by examining the secondary choices made for financially weak and Table 6. The Number of Correct and Incorrect Classifications for Firms Prior to 1979 and Post 1978 Observed Sample Incorrect (%) Correct (%) chi-square Bankrupt Prior 26 (41%) 37 (59%) 0.0023 Post 20 (41%) 29 (59%) Nonbankrupt Prior 58 (34%) 114 (66%) 0.0712 Post 39 (32%) 82 (68%) Financially weak Prior 74 (44%) 96 (56%) 0.0318 Post 38 (45%) 47 (55%) 2811 I ,Iohnscn and I~,, W. Mclichc~ bankrupt firms. We define secondary choices as the state indicated by ihe secon~.f highest probability produced bv the Zeta model, s (i) Secondary Analysis of Mischtssified F'irms. All financially weak firms originally misclassified (112 firms) as bankrupt or nonbankrupt were correctly classified on a secondary basis. There were 18 bankrupt and 82 nonbankrupt firms originally misclassified as weak that were correctly classified on a secondary basis. These 212 firms are notable in that if secondary classifications are included in the calculation of total error, then the Zeta model would misclassify only41 firms (in comparison to the original 253 presented in Table 2). On the other hand, there were six bankrupt firms originally misclassified as nonbankrupt that remained misclassified on a secondary basis. These six firms can be considered true outliers in that some bankrupt firms, for example, appear to have ratios that mimic a nonbankrupt firm? ~ These firms are interesting in that they do not represent borderline cases. Given the original classification was as a nonbankrupt firm and the secondary classification was as a weak firm, these cases are suggestive of possible upgrades in financial condition or of successful merger or reorganization candidates. Indeed, at least one firm from this set, Continental Air, was a proposed merger candidate at the time of its initial rating of B - in 1980. However, Continental Air was subsequently downgraded to D five years later. Two other firms from this set also received a rating downgrade by Standard and Poor' s. Saxon Industries was downgraded to D two years after its initial rating of B, and Lafayette Radio was downgraded to C five years later. The remaining three firms were not rated or were dropped by Standard and Poor' s. A separate class of outliers includes 22 bankrupt firms originally misclassified as weak. These 22 cases also were misclassified on a secondary basis. Four firms out of this group received a downgrading to C or D one year following their initial ratings. The remaining 18 firms were not rated or were dropped by Standard and Poor' s from its Securi~ Owner's Stock Guide. (ii) Secondary Analysis of Correctly Classified Firms. In order to determine the reliability of the correct classifications produced by the Zeta model, the difference between the highest and second highest predicted probability was calculated and defined as a distance score. We expect firms with large relative distance scores to be reliably classified, and those with relatively smaller scores to be unreliably classified. In this section, we focus on firms with unreliable classifications and arbitrarily define this group as having a distance score less than or equal to 0.20, or a 20% deviation. ~° Table 7 presents the distance scores for the bankrupt and weak firms. 8The results of the same analysis for the Beaver model were similar and therefore not reported here. 9At least four of these firms may have filed for nonfinancial reasons as permitted by the Bankruptcy Act of 1979. Two of the firms filed in 1981 and two others in 1982. The remaining two outliers filed in 1974 and 1978. 10 While this is an arbitrary cutoff classification for unreliability, we followed through by examining the secondary classifications for each bankrupt and financially weak firm. Corporate Bankruptcy Table 7. Secondary Classification Results for Correctly Classified Firms 281 Bankrupt Weak Mean distance a 0.5547 0.1800 Mi ni mum 0.0160 0.0018 Maxi mum 1.0000 0.4731 n 66 143 Di st ri but i on of distance scores 0. 8-1. 0 22 0 0.6-0.79 8 0 0.4-0.59 10 6 0.2-0.39 15 51 0-0. 19 11 86 b aThe distance score is calculated as the difference between the highest predicted probability and the second highest predicted probability. bTwelve of these firms were classified as bankrupt on a secondary basis. The remaining 131 (6 + 51 + 74) firms were classified as nonbankrupt. Not surprisingly, all bankrupt firms correctly classified, received a weak classifi- cation as a secondary choice. Eleven of those firms were within 0.20 (20%) of being classified as weak, suggesting at least a lack of confidence in the "bankrupt" classification. In contrast, 22 of the correctly classified bankrupt firms have the largest distance scores. For this group, a high degree of confidence exists in the bankrupt classification and a low expectation for improving financial conditions. For the weak firms, the secondary choice for 20 cases was a bankrupt classifica- tion. Eight of the firms were within 0.20 of being classified as bankrupt, suggesting an increased probability of further deterioration in financial coridition. Six of the firms remained at a C rating or were downgraded to C by Standard and Poor's within three to five years following the initial rating. The remaining 121 correctly classified weak firms were classified as nonbankrupt on a secondary basis. Eighty of the firms are within 0.20 of being classified as nonbankrupt, suggesting an in- creased probability of an improvement in financial condition. One-fourth (21 firms) of the 80 firms experienced an upgrade in rating to B or better within three years. The remainder either had no rating change or a slight change in rating (for example, B to B- ) . If this sample is representative, then firms correctly classified as weak and with a distance score of 0.20 or less have approximately a 25% chance of receiving an upgrade to B or better and approximately a 10% chance of receiving a downgrade to C. V. Five-Year Follow-Up Examination of Financially Weak Firms Each of the 255 firms that was classified as being financially weak (i.e., below average in terms of S & P stock ratings) was examined for a period of five years after the initial year in which it was classified. This was done to determine the extent to which they remained financially weak and/ or suffered other indications of worsening financial distress over time. For example, a financially weak firm initially classified in 1970 was monitored over the 1971-1975 period. Likewise, a firm classified as weak in 1983 was tracked over the 1984-1988 period. 282 I', J ohns on and R. Vv Mclichcl Ta b l e 8. Di st r i but i on of Pr i mar y and Secondar y Cl assi fi cat i ons for Fi nanci al l y Weak Fi r ms Panel A: Distribution across Status c~f Ratings 3 Years or 5 Years Following the Initial Rating Total W/ NB NB/ ' W W/ B B/ W I~,ov¢ lotals (i) O~,erall Totals' 3 Years 1 (14 42 13 12 21 I 5 Years 1(18 78 14 I I 21 I (ii) "Upgrade" in Rating Subgroup (rating increased to B or hi gher) 3 Years 32 27 1 (1 60 5 Years 38 37 2 2 79 (iii) "Problem" Subgroup (rating declined to or r e mai ne d at C and/ or the fi rm suffered other i ndi cat i ons of fi nanci al di stress) 3 Years 12 15 6 7 41) 5 Years 22 ! 6 8 5 51 (iv) "No Change" in Rating Subgroup (rating of B or B - remained unchanged) 3 Years 60 4(1 6 5 111 5 Years 48 25 4 4 81 Panel B: Di s t ri but i on across Initial Rat i ngs S & P Rating W/ NB or NB/ W W/ B or B/ W Total B 140 B - 70 C 8 Total 218 Observed X 2 = 72.64 Cri ti cal g 2 = 9.21 (c~ = 0.01) 5 145 15 85 17 25 37 255 Note: Primary classifications are listed first and W = weak, NB = nonbankrupt, and B = bankrupt. Ratings ceased for 44 (255 - 211) firms after the initial ratings. Table 8 contai ns the primary and secondary classification results for the finan- cially weak firms three years and five years after their initial classification year. Panel B shows a strong correlation bet ween the Standard & Poor' s c ommon stock ratings and the pri mary/ secondary classifications for the financially weak firms. A chi-square test of associ ati on bet ween stock rating and initial classification was significant (at = 0.01). That is, the lower the c ommon stock rating, the more likely that the firm will be classified as bankrupt / weak or weak/ bankrupt (with the first classification bei ng the primary one). Focusi ng first on the three-year results from Panel A(i ) in Table 8 in order to establish a benchmark for compari son, 186 o f 211 (88.2%) firms were classified as weak/ nonbankrupt (104 firms) or nonbankrupt / weak (82 firms). Thus, 11.8% (25 of 2 1 1 ) we r e classified as either weak/ bankrupt (13 firms) or bankrupt / weak (12 firms). For firms experiencing an increase in stock rating (either an i mprovement in Corporate Bankruptcy 283 the overall weak category or movement to the average or above categories), the percentage originally classified as weak/ nonbankr upt or nonbankr upt / weak was 98.3% (59 of 60) as presented in Panel A(ii) of Table 8. That is, only one firm (1.7%) that was initially classified as weak/ bankr upt (none was classified as bankr upt / weak) exhibited an upgrade in its stock rating over the following three- year period. Thus, almost all weak firms that showed improved common stock ratings after three years were originally classified as weak/ nonbankr upt or non- bankrupt / weak. Financially weak firms that declined to a C rating or suffered ot her indications of financial distress, such as a trading suspension, being placed in reorganization, or being liquidated, three years after the initial rating year were much more likely to have been initially classified as weak/ bankr upt or bankrupt / weak. Panel A(iii) of Table 8 shows that 13 of 40 (32.5%) firms in this "probl em" subgroup were classified as either weak/ bankr upt or bankrupt / weak. In contrast, 27 of 40 (67.5%) were originally in the weak/ nonbankr upt or nonbankr upt / weak cate- gories. Financially weak firms that had no change in their ratings as of three years after the initial classification year had 19 of 125 (9.9%) of this subgroup' s firms classified as weak/ bankr upt or bankrupt / weak. Thus, based on financial ratio data available at least 12 months prior to the year of initial classification, a combined pri mary/ secondary classification procedure was able to identify firms that are relatively more likely to have experienced increased financial distress over the next three years. Examination of financially weak firms five years after the year of initial classifi- cation produced similar results as shown in Table 8. Twenty-five of 211 (11.8%) weak firms were initially classified as weak/ bankr upt or bankr upt / weak. The corresponding proportion for the "probl em" subgroup was 13 of 51 (25.5%), compared with 8 of 81 (9.9%) for the "no change" subgroup and 4 of 79 (5.1%) for the "upgrade" subgroup. These results further support the value of a combined pri mary/ secondary classification procedure to identify financially weak firms that are more likely to suffer increased financial distress in the future. Five-Year Follow-Up Examination of Bankrupt Firms Table 9 contains the primary and secondary classification results for the bankrupt firms five years after the initial classification year. Due to the erratic distribution of the follow-up data, we were unable to identify a consistent three- or five-year interval in which ratings were available. Therefore, our follow-up examination focused on identifying any rating change that occurred within a five-year interval following the initial rating. Similar to the financially weak firms, Panel B of Table 9 also shows a strong relationship bet ween Standard & Poor' s common stock ratings and the pri mary/ secondary classifications produced by the Zet a model. A chi-square test of association bet ween stock rating and initial classification was significant (ot = 0.01). Bankrupt firms with lower stock ratings were more likely to be classified as bankr upt / weak or weak/ bankr upt . The five-year results presented in Panel A(i) in Table 9 show that 28 of 112 (25%) firms were classified as weak/ nonbankr upt or nonbankrupt / weak, and 84 284 1, J o h n s c r ~ a n d R. W. Me l i c hc ~ T a b l e 9 . D i s t r i b u t i o n o f P r i t n a ~ ' a n d S e c o n d a r y C l a s s i f i c a t i o n s f o r B a n k r u p t F i r ms Pa ne l A: Di s t r i b u t i o n a c r o s s St at us o f Ra t i ng s 5 Yc a r s F o l l o wi n g t he Ini ti al Rat i ng Tot al W/ NB NB / W W/ B B / W Row t ot al s (i) Ot~erall totals 22 6 i 8 66 I 12 (ii) "Upgrade" in Rating Subgroup ( r at i ng i nc r e a s e d t o B o r h i g h e r ) 0 0 0 0 0 ( i i i ) "Problem" Subgroup ( r at i ng d e c l i n e d t o o r r e ma i n e d at C a n d / o r t he firm s uf f e r e d o t h e r i ndi c a t i o ns o f f i nanci al di s t r e s s ) 4 3 1 7 15 (iv) No Ratings Identified after Initial Rating Year 13 l 11 26 51 (v) Not Rated at Initial or Following Years 5 2 6 33 46 Pa n e l B: Di s t r i b u t i o n a c r o s s I ni t i al Ra t i n g s S & P Ra t i ng W/ NB o r NB / W W/ B o r B / W To t a l B 10 B - 7 C 4 N o t r at e d 7 To t a l Ob s e r v e d )t ,z = 21.97 Cri t i cal g 2 = 16.81 (co = 0.01) 3 13 22 29 19 23 40 47 84 112 Note." Primary cl assi fi cati ons arc l i sted first and W = weak, NB = nonbankrupt , and B = bankrupt. (75%) were classified as weak/bankrupt or bankrupt/weak. Given the extreme state of financial distress, it is not surprising to observe that 51 [45.5% in Panel A(iv)] were dropped by Standard & Poor's after the initial rating year, and 46 [41.1% in Panel A(v)] were not rated at the initial or following years. Further, the remaining 15 firms experienced a rating decline or suffered other indications of financial distress. Panel A(iii) shows that 8 of the 15 (53%) firms experiencing further problems were classified as weak/bankrupt or bankrupt/weak. In contrast, 7 of the 15 (46.7%) with further problems were classified as weak/ non- bankrupt or nonbankrupt/weak. It is notable that none of the firms from this group received an upgrade in rating regardless of classification. VI. S u mma r y a nd Co n c l u s i o n s Three major conclusions emerge from this study. First, misclassification error can be reduced by adding to the outcome space used to predict bankruptcy. The Corporate Bankruptcy 285 el ement of i nf or mat i on added in this case is an addi t i onal st at e of financial distress. The addi t i on of a " weak" st at e of financial distress r educed t he st andar d er r or s associ at ed with a known set of i ndependent vari abl es used t o pr edi ct bankrupt cy. In this case, two sets of general l y accept ed pr edi ct or vari abl es are exami ned, specifically t he Beaver (1966) and Ze t a [Al t man et al. (1977)] variables. Tot al misclassification er r or is r educed by 43 firms f or t he Beaver vari abl es and by 42 firms f or t he Zet a variables. The maj ori t y of t he i mpr ovement is at t r i but ed t o t he bankr upt versus nonbankr upt firm classification. Of t he t ot al misclassification errors, t he misclassification of bankr upt versus nonbankr upt firms was r educed by 22 (using Beaver vari abl es) and 30 (using Zet a vari abl es) firms. The misclassifica- t i on of bankr upt versus weak firms was r educed by 8 ( Beaver vari abl es) and by 4 ( Zet a vari abl es) firms. Of no less i mpor t ance is t he observat i on t hat t he t hr ee st at es of financial heal t h appear t o be i ndependent . They are i ndependent in t he sense t hat significant pr edi ct or s of vari ous states of financial heal t h depend upon t he part i cul ar st at e under consi derat i on. Finally, t her e is significant i nf or mat i on t o be deri ved f r om t he secondar y classification results obt ai ned f r om mul t i st at e logit model s. I nf er ences regardi ng t he i ncreased chance of ei t her i mprovi ng or det er i or at i ng financial condi t i ons f or individual firms can be det er mi ned based on t hei r existing financial condi t i on. 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