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Pacific Accounting ReviewEmerald Article: The Efficacy of Auditors' Going-Concern Opinions Compared with a Temporal and an Atemporal Bankruptcy Risk Model: Analysing U.S Trade and Service Industry Failures 1974 - 1988Patti Cybinski, Carolyn Windsor

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Pacific Accounting Review – Vol. 17, No. 1, June 2005 3

The Efficacy of Auditors’ Going-Concern Opinions Compared with a Temporal and an Atemporal Bankruptcy Risk Model: Analysing U.S Trade and Service Industry Failures 1974 – 1988

PATTI CYBINSKI*CAROLYN WINDSOR*

Conflicting results have emerged from several past studies as to whether bankruptcy prediction models are able to forecast corporate failure more accurately than auditors’ going-concern opinions. Nevertheless, the last decade has seen improved modelling of the path-to-failure of financially distressed firms over earlier static models of bankruptcy. In the light of the current crisis facing the auditing profession, this study evaluates the efficacy of auditors’ going-concern opinions in comparison to two bankruptcy prediction models. Bankrupt firms in the U.S. service and trade industry sectors were used to compare model predictions against the auditors’ going-concern opinion for two years prior to firm failure. The two models are the well-known Altman (1968) Multiple Discriminant Analysis (MDA) model that includes only financial ratio variables in its formulation and the newer, temporal logit model of Cybinski (2000, 2003) that includes explicit factors of the business cycles in addition to variables internal to the firm. The results show overall better bankruptcy classification rates for the temporal model than for the Altman model or audit opinion.

* Patti Cybinski and Carolyn Windsor are Senior Lecturers at the Department of Accounting, Finance and Economics, The Griffith Business School, Griffith University, Nathan Campus, Brisbane.

The authors would like to acknowledge the helpful suggestions of Dr. John Forster as well as the useful feedback of the many members of the School of Accounting, Banking and Finance and the School of Economics who attended the ABF Seminar Series presentation of this work.

4 Pacific Accounting Review

(1) INTRODUCTION

An auditor must issue an alert by way of an audit opinion to investors and the public when a firm’s ability to operate as a going-concern is impaired. A number of studies have shown that in only half the cases where companies ultimately went bankrupt was a going concern opinion ever issued before their filing for bankruptcy (Altman and McGough 1974; Altman 1982; Menon and Schwartz 1986; Chen and Church 1992; Johnson and Khurana 1993). Although auditor evaluations are not intended to be predictors of bankruptcy, users of financial statements still treat the evaluation as an early warning of impending failure, and hence treat an unmodified audit opinion as a “clean bill of health”. Not surprisingly then, the issuance of unmodified opinions to firms that subsequently file for bankruptcy can be viewed as failures of the financial reporting process (Casterella et al. 2000, p. 510).

The magnitude of recent corporate collapses and the economic losses suffered by the community has again raised the issue of public confidence in the auditing profession’s ability to warn investors and the public about a firm’s future viability (Pearlstein and Behr 2001; Day and Crenshaw 2002). As a result, some governments have introduced new regulations affecting the audit profession’s self regulated monopoly franchise. For example, the U.S. Congress responded to the wave of corporate scandals with the landmark Sarbanes-Oxley Act of 2002. The broad corporate governance reforms and antifraud provisions of the act have been felt in boardrooms across the nation (Labaton 2003). Further, the Act has also affected auditors who are now much more risk averse when assessing client risk, with the top audit firms dropping their risky corporate clients in droves (Browning 2005). An implication of the Act is that auditors are now forced to scrutinize the nature and extent of client risk to ensure the veracity of the auditor’s opinion.

Since, for many users, the early warning function is one of the most useful and important deliverables provided by auditors (Casterella et al. 2002, p. 508), the purpose of this study is to reconsider the issue of whether auditors’ going-concern opinions, based on professional judgements, are less precise and less reliable compared with statistically produced bankruptcy models in their predictions.

The literature examining why auditors allegedly “miss” soon-to-be-bankrupt filers is extensive and some insights have been gained from the research. For example, in many cases, soon-to-be-bankrupt companies do not “present” as financially distressed in that they do not have the distress characteristics that are expected from such companies (see McKeown et al. 1991). The results of Mutchler et al. (1997) are also consistent with


the view that the auditor is often not presented with enough cues to trigger an adverse going-concern opinion. In addition, businesses operate in an increasingly complex and changing macro-economic environment that challenges auditor judgment. But these same difficulties and challenges also face the statistical modeler who can only rely on the available data when formulating a bankruptcy prediction model. Hence, a comparison of the two is not unreasonable given they are using similar information.

A problem facing auditors is that the current compliance-oriented standards that guide audit judgments have been less responsive to the complexity of business and stakeholders’ demands for a more reliable analysis of a client’s performance. The current auditing standards maintain simplistic procedures, reductionist static measures and a “rule of thumb” approach (for example, adverse key financial ratios, possible financial difficulties, internal work stoppages, legal proceedings and so on, as outlined in AU Section 341.06 (Georgiades 2001)). Moreover, the standards provide little guidance for a more sophisticated analysis of the client’s audit risk including the entity’s macro-economic context that affects the client’s future viability. In fact, the auditing standards require evaluating mainly historical cost accounting for judgments about going concern decisions that may be unrepresentative of the current financial position.

This study compares the bankruptcy predictions of two very different bankruptcy models against the auditors’ going-concern opinion for a group of bankrupt firms in the U.S. service industry and trade industry sectors. We conduct the comparison for each of the two years prior to failure. First, predictions are made using the well-known Altman (1968) Multiple Discriminant Analysis (MDA) model that includes only financial ratio variables in its formulation. Second, predictions are also made using a more recent temporal logit model of Cybinski (2000, 2003), which includes explicit factors of the business cycles in addition to the variables internal to the firm, thus making it more representative of the complex business environment.

(2) BANKRUPTCY MODEL FORECASTS VS. AUDITORS’ OPINIONS

More than two decades ago, the Cohen Commission (AICPA 1978) voiced concern about evidence that bankruptcy prediction models forecast company failures more accurately than auditors’ going-concern opinions. Furthermore the international auditing standards require the auditor to be alert to the possibility that the going-concern assumption may be subject to question (International Federation of Accountants 1989). While auditors often look to financial distress models as decision aids1 , the auditors’ accuracy in predicting imminent client insolvency does not appear

1 See Kida (1984), Mahzin (1988), Dugan and Zavgren (1989), Koh and Killough (1990), Koh and Oliga (1990), and Graham et al. (1991) for evidence that auditors use financial distress models.


to approach the levels achieved by the “premier” bankruptcy prediction models (Louwers 1998, p. 144).

Bankruptcy model research began with Beaver’s (1966) univariate model while later research turned to multivariate models. Among the most common methods are those of Altman (1968), Deakin (1972), and Ohlson (1980), and in their literature reviews, Zavgren (1983) and Jones (1987) proposed various bankruptcy prediction models that may be useful to auditors. The Altman and McGough (1974) study provided the link between bankruptcy prediction models and auditors’ independent judgements. They compared Altman’s (1968) “Z-score” bankruptcy prediction model with the accuracy of auditors’ going-concern decisions one-year prior to the event for a sample of 34 corporate bankruptcies between 1970 and 1973. The model predicted bankruptcy for 82 percent of the cases while auditors issued going concern opinions for less than half of these failed companies.

Several other studies also concluded that bankruptcy prediction models forecast corporate failure more accurately than auditors’ opinions (see Altman 1982; Levitan and Knoblett 1985; Koh and Killough 1990). These suggest that auditors can use a bankruptcy prediction model to improve their decision accuracy. However, this implication casts doubt upon auditors’ rationality. Further, it suggests that auditors fail to adequately incorporate readily available information such as ratio-based models into their judgments.

Unlike earlier studies that matched bankrupt firms and non-bankrupt firms equally in the estimation samples for bankruptcy modelling, Hopwood et al. (1994) used a bootstrap procedure and sample partitioning to reflect the true proportion of bankrupt companies experienced by auditors. Their results indicate that auditors were confronted with different decision problems with stressed companies than with non-stressed companies. Notably, they document and analyze two primary failure processes: a relatively rapid and unexpected failure where financial distress is not evident in the accounting numbers, and a second process of relatively long duration in which financial distress is evident. They argued that accounting-based statistical models could only explain the second type of corporate failure. Hence their findings do not support the previous research that auditors’ opinions are inferior predictors of bankruptcy relative to statistical prediction models in general. They do contend, however, that bankruptcy not preceded by financial distress is more likely to be driven by management fraud.

In the context of financial distress prediction, Gadenne and Iselin (1996, p. 45) found that when interested user groups of accounting information, including auditors, were presented with relevant and manageable levels of information, their decision accuracy


was not significantly different from that of the statistical models. However, when the level of information was increased, the statistical model outperformed the user groups. Their findings suggest that higher data load may adversely affect human decision accuracy, further supporting the use of well-formulated models as a decision-support tool for the auditor.

Conflicting results can occur between studies that compare the accuracy of decisions arising from statistical models and from auditors’ deliberations for other reasons than those given above. For instance, research has shown that the time interval between the particular model formulation and its application is important. Where bankruptcy models are estimated using recent data, say one-year prior to bankruptcy, Houghton (1984) and Simnett and Trotman (1989) found higher classification accuracy than when the data were older.

Also, when model formulations employ an inferior or inappropriate statistical technique2 , they would fare badly in any comparison of prediction accuracy with auditor opinions, as would models that are incomplete, in that they are missing important predictors of financial distress. For instance, the inclusion of cash-flow variables in model formulations has been hotly debated as an important discriminator of distressed and non-distressed firms (see Largay and Stickney 1980; Ketz and Kochanek 1982; Mensah 1984; Gentry et al. 1985; Casey and Bartczak 1984,1985; Aziz et al.1988; and Gilbert et al.1990; among others).

(3) IMPROVED MODELLING AND THE TEMPORAL MODEL PROCESS

Much has been written about why the traditional bankruptcy prediction models of the 60s, 70s and 80s have not been entirely satisfactory (see Chen and Shimerda 1981; Zmijewski 1984; and Gilbert et al.1990; among others). As noted by Dimitras et al. (1996, p.487), “a unifying theory of business failure has not been developed...”. Bankruptcy research has been concerned with prediction before proper explanations for the bankruptcy phenomenon have been developed and tested, yet software can be purchased that claims to predict “financial distress” of individual enterprises with near perfect accuracy3. Nevertheless, their validity and applicability are limited, most being based on study designs that have estimation samples that consist of bankrupt versus solvent (usually strong) firms, as the basis for discrimination. Gilbert et al (1990) tested traditional bankruptcy models based only on firms’ financial characteristics and

2 See next section for more on improved modelling techiques.3 Examples of commercially marketed Risk Management/Investment tools are Merv Lincoln’s “STOCKdoctor” by Lincoln Indicators (The Weeknd Australian, May 9/10, 1998) and Richard Taffler’s “PAS-score” by Syspas (Financial Review, October 8, 1993).


demonstrated that “if the objective is to identify likely bankruptcies from a pool of problem companies, these bankruptcy models perform poorly” (p.169). They reiterate Taffler’s (1984) contention that bankruptcy model scores should be interpreted as descriptions of financial distress rather than as predictions of bankruptcy per se.

Research into finding superior bankruptcy model formulations in the 1980s led to replacing the popular multivariate discriminant analysis (MDA) formulation (Altman 1968) with logistic analysis (Ohlson 1980), which until recently has been the most used statistical method for failure prediction purposes. The reason was that the assumption of normality of the financial ratio distributions in the MDA procedure was problematic, whereas the maximum likelihood procedure, on which the logistic/probit model is based, does not require that assumption. It also has the added advantage of allowing qualitative variables (i.e., those with categories rather than continuous data) into its formulation. Also the interpretation of individual coefficients is appropriate in the logit model, which therefore lends itself to broader research applications. This is not the case for the MDA model4.

A major criticism of bankruptcy formulations, in the absence of a generally accepted theoretical basis, is that model construction has necessarily involved selecting financial variables on an empirical basis, according to their ability to increase prediction accuracy. The process is usually by stepwise selection procedures that can lead to biased estimates that are then difficult to interpret, and since the choice of variables is based solely on statistical grounds, it ignores other characteristics of the variables. On the other hand, because of the typically large number of independent variables considered in these models without any compelling theory to guide the choice, the multicollinearity that is inevitably present with accounting data dictates the necessity of such data reduction methods in order to reduce the “non-independence” and increase our ability to make inferences from the model as a whole.

Moreover, most of these models are atemporal and ignore the impact of the external macro-economy, excluding macroeconomic indicators such as GDP, interest rates and unemployment rates in their formulations. In other words, most model formulations in the literature are treated as stationary when they are not. Without these variables included, predictions have been successful only insofar as the conditions of the predictive environment mimicked the economic conditions for the sample of firms used to derive the formula.

4 Press and Wilson (1979) give the reasons why the logistic regression model with maximum likelihood estimators is preferred for both classification and for relating qualitative variables to other variables under non-normality and Martin (1977) gives a comprehensive explanation of maximum likelihood estimation techniques in the context of bank failure predictions.


Since the totality of a firm’s business environment impacts enormously upon its success and future viability, models can logically only be expected to be useful to auditors if they include the relevant macroeconomic measures. The firm’s product market, its creditors, its suppliers and its business partners are all affected by the macro-economy.

It has long been established that the rate of corporate failures rises sharply during economic recessions (Lev 1974, pp.134-139). Rose et al. (1982) suggest a complex relationship between overall business failure rates and business cycle indicators. While this means any temporal modelling of firm failure risk calls for the inclusion of macro-economic variables, this remains a relatively unexplored dimension of financial distress modelling. While the bankruptcies and closures engendered by the economic downturn of the seventies led to a surge in studies concerned with business failure, few of them took explicit account of business cycles.

Zavgren (1983) noted that in boom periods when failures are relatively rare, the empirical link between certain otherwise important indicators and the actual occurrence of failure would be weak. So most failure studies that have included macroeconomic conditions measure the asymmetric impacts of the expansion and contraction stages of the cycle upon failure rates (Lev 1974; Mensah 1984; Kane et al. 1996). This helps explain the lack of consistency among studies relying solely on firm-specific information as explanatory variables of failure risk. This lack of consistency arises in relation to (a) the empirically estimated values of the similarly defined coefficients reported in different studies, and (b) differences in the relative contributions of various financial ratios to failure between studies. Such inconsistencies necessarily cast doubt on the empirical methodological framework of financial distress modelling and suggest only limited use of models as a support for auditors’ decisions.

Users of bankruptcy models often judge and choose models on the basis of their reported Type I (misclassifying a bankrupt firm) and Type II (misclassifying a nonbankrupt firm) errors. Unfortunately, these errors may reflect only the difficulty of the discrimination task on the estimation sample upon which the model was formulated rather than the true errors. If the sample was already well-separated on the “distress continuum” (see Cybinski 2000, p.12-13), in that it consisted of bankrupt versus solvent (usually strong) firms, then the misclassification errors reported would be misleadingly good. More information value would be provided by a model that distinguishes distressed firms filing bankruptcy from others, also at risk, but avoiding it (Gilbert et al 1990).

The temporal model by Cybinski (2000, 2003) was developed from one of the few studies that have analysed bankruptcy as a failure process rather than as an event (among them


Partington et al. 1991; Theodossiou 1993; Hill et al. 1996; Richardson et al. 1998). The firm is modelled over several periods of time as it moves towards failure, given that firms do not instantly fail, but generally experience deterioration towards failure over a period of time. In modelling the distress-to-failure process, each firm acts as its own control; its nonfailing years’ data are compared to its own final year’s data before failure. This is distinct from the usual comparison between different firms featuring a strictly dichotomous failed/non-failed distinction. Rather, the model is based on a more difficult (but realistic) study design akin to a pool of problem companies, with some just surviving while others fail. It presents not only a greater modelling challenge but a stronger case for information value if such a model can discriminate between ‘at risk’ firms that survive and ‘at risk’ firms that fail (see Wood and Piesse 1987).

Additionally, the sample on which the temporal model by Cybinski (2000, 2003) is estimated encompasses firms that fail at different years in calendar time and over a long enough time period to cover at least a full business cycle. This temporal aspect of the business environment was explicitly included in the temporal model with orthogonal factor scores representing the prevailing macroeconomic conditions. See Cybinski and Forster (2002) for more detail on these factor scores and the economic series upon which they are loaded.

Thus, future progress in the field of bankruptcy modelling not only depends on the current preoccupation with the identification of relevant financial variables, but, at the very least, also upon incorporating measures of economic adversity, and appropriate time lag effects. Such developments coupled with an extension of the data base both cross-sectionally and over time will hopefully give more reliable models with smaller standard errors for the parameter estimates.

Details of both the Altman (1968) model and the temporal model by Cybinski (2000, 2003) can be found in Appendix A.

(4) SAMPLE

In this study we compare the risk estimates from a recent logit model (Cybinski 2000, 2003) as well as scores from a multiple discriminant analysis (MDA) model (Altman 1968) with the auditors’ going concern opinions for a group of bankrupt firms. This group consisted of all 54 service industry firms and all 56 trade industry firms recorded in the 1991 Standard and Poor’s Compustat Research5 Files as bankrupt or

5 The Research Companies dataset includes companies for which data is no longer included in the Compustat Industrial Files due to a merger, acquisition, bankruptcy, liquidation, etc. [No Chapter 11 filings are included]. There were approximately 6100 Research companies in 1991.


liquidated6 during the 20 year period back to 19717. Hence, the firms in our sample came under SAS No. 34. This standard required only that the auditor be aware of evidence that might indicate that the going-concern assumption was violated and a qualified opinion was issued. The American Institute of Certified Public Accountants (AICPA) amended the way going-concern opinions are reported in SAS No. 59 in 1989. Under SAS No. 59 a going-concern opinion is expressed as a modification of the standard audit report rather than a qualification to the audit report, as was the case under SAS No. 348. The failed firms were selected from industry groups that were broad enough to yield data for a sufficiently large sample (originally 60) from each industry.

Both Altman’s MDA score and the auditors’ opinion for the set of bankrupt service industry firms were taken from the COMPUSTAT Research files. The temporal model risk estimates were calculated after the model coefficients were estimated from the same dataset. In this respect, one expects the Type I error (misclassified bankrupt firm) to be smaller for the temporal model than for the Altman model (out-of-sample classification) for this dataset. Therefore an extra set of firms was taken from the same Compustat Research database that was out-of-sample for both the temporal model and the Altman model, which was originally formulated on a set of manufacturing firms. The extra set consisted of all 56 Trade Industry firms recorded there as bankrupted or liquidated in the period from 1971 to 1991 and with enough data available for at least one of the three decisions compared.

Tables 1a - 1d show, respectively, the frequency distributions of the auditor’s opinion in the last and second last reporting periods prior to bankruptcy/liquidation for both the industry datasets. For easier comparison between statistical model predictions and the auditor’s decision, the audit opinions were re-coded from the five level Compustat scale into two levels as “unqualified” vs. “not unqualified” as follows: -

6 Only these two “Reasons for Deletion” codes were used here. Other reasons not included were: Aquisition or merger, Reverse acquisition (1983 forward), No longer fits original format, Leveraged buyout (1982 forward), Now a private company, Other reason (e.g. no longer files with SEC).7 This happened to include firms bankrupted or liquidated only in the period 1974-1988. It is expected that the most recent failures may not yet have been recorded onto the Research File by October – November 1991 when data was collected.8 Bryan, Tiras and Wheatley (2001) provide evidence that going concern opinions as modifications under SAS No. 59 may be a less effective warning of distress to external users than was a going concern opinion issued as a qualification under SAS 34.

*Auditor’s Opinion Code (AUOP – Compustat code)0=unaudited =>NA - not compared1=unqualified => code 02=qualified => code 13=no opinion => code 1 4=unqualified with additional explanatory language added => code 05=adverse opinion => code 1


Tables 1a-1dFrequency Distributions of Auditor’s Opinion in the Last and Second Last

Reporting Periods Prior to Bankruptcy/Liquidation for the Service Industry and Trade Industry datasets.

Note: Taken from the Compustat variable AUOP. The final two categories of auditor opinion were collected from 1988 forward. Hence only 7 of the 50 audited firms from the Service Industry set and 4 of the 31 audited firms from the Trade Industry set had the possibility of being coded into these two categories in their last financial reports, but none were.

Table 1aLast Reporting Period (Service Industry)

Unaudited or not available 4Unqualified 26Qualified* 22

No opinion ** 2unqualified with additional

explanatory language added***0

Adverse opinion**** 0

Table 1bSecond Last Reporting Period (Service Industry)


No opinion ** 1Unqualified with additional



Table 1cLast Reporting Period (Trade Industry)


No opinion ** 0Unqualified with additional




For comparison between model predictions and the auditor’s decision, the values from the two statistical models were also re-coded as a dichotomy as follows: -

Altman’s Discriminant Analysis Model (1968) Zscore:

Cybinski’s Temporal Logit Model (1998) Risk of Bankruptcy:

An MDA score >1.8 denotes a nonbankrupt prediction => code 0

Probability less than 0.5 => code 0

An MDA score <1.89 denotes a bankrupt prediction => code 1

Probability greater than 0.5 => code 1

(5) ANALYSIS

The rows of Tables 2a-2d show the binary decisions for each firm by the three entities to be compared within the two sample industries and the two final reporting periods before failure. The extent of agreement between the temporal model, Altman’s model and the auditor’s opinion can thus be ascertained visually and from the sum total of correct predictions for each decision entity.

Hypothesis tests can be applied to the column totals in Tables 2a-2d to compare the three decision entities: Altman model, temporal model, auditor. Because the

Table 1dSecond Last Reporting Period (Trade Industry)


No opinion ** 1Unqualified with additional explanatory

language added***0


* Financial statements reflect the effects of some limitation on the scope of the examination or some unsatisfactory presentation of financial information, but are otherwise presented fairly. SPC assigns this code when a company is in the process of liquidating (even if opinion is not actually qualified).** Auditor refuses to express an opinion regarding the company’s ability to sustain operations as a going concern. *** Auditor has expressed an unqualified opinion regarding the financial statement but has added explanatory language to the auditor’s standard report. **** Auditor has expressed an adverse opinion regarding the financial statements of the company.

9 Note that Altman also identified a “grey” area of “undecideds” with Zscores between 1.8 and 2.99.


data is incomplete with many missing entries, we first treat these as independent decisions and use the simplest possible statistical test for detection of a difference between proportions for more than two entities - the chi-squared test of a multinomial experiment. The null hypothesis is that there is no difference in the proportions of correct decisions between the three decision entities.

H0: p1 = p2 = p3

against the alternative that not all three proportions are equal:

H1: not all pj are equal (where j=1,2,3)

We compute the test statistic for an r x c contingency table (r rows, c columns):

where f0 = observed frequency in a particular cell of a 2x3 contingency table fe = expected frequency in a particular cell of a 2x3 contingency table with (r-1)(c-1) degrees of freedom.

If the null hypothesis: p1 = p2 = p3 is rejected above, further Z-tests for differences in two proportions can then be employed to isolate which particular pair/s of decision entities are different in their proportion of correct decisions and in what direction that difference lies.

with p̂i and pi, respectively, the sample and hypothesized values of the relevant proportions and

where X1 = number of correct decisions by entity 1 X2 = number of correct decisions by entity 2

∑⋅⋅

−=−−

cellsall e

eo

fff

cr

22 )(

)1)(1(χ

)11

)(1(

)()ˆˆ(

21

2121

nnpp

ppppZ

+−

−−−=vv

21

21

nnXX

p++=


Table 2aExtent of Agreement between the Temporal Model, Altman’s Model and Auditor’s Opinion in the Last Reporting Period Prior to Bankruptcy/Liquidation (Service

Industry)Code ‘1’ denotes either a bankrupt prediction or an audit not unqualified (see codes below)

Firm Number

Temporal Altman Auditor Firm Number

Temporal Altman Auditor

Prob>0.5 Zscore<1.8 not unqualified

opinion*


opinion*1 0 28 1 1 02 1 1 1 29 1 03 1 0 0 30 1 1 04 1 0 1 31 1 15 0 1 32 1 1 16 1 1 1 31 1 0 07 1 0 0 34 0 0 08 1 1 1 35 0 0 09 1 1 1 36 1 1 010 0 0 0 37 1 0 011 1 0 38 1 1 012 1 1 0 39 1 0 113 1 0 40 1 114 0 1 1 41 0 0 015 1 1 42 1 016 1 1 43 0 1 117 1 1 1 44 1 1 018 0 1 1 45 1 019 1 1 1 46 1 020 1 1 1 47 1 121 1 1 1 48 0 1 122 1 1 1 49 0 1 023 1 1 0 50 0 1 124 1 0 0 51 0 0 025 1 1 0 52 0 1 126 1 0 0 53 1 127 0 1 54 0 0 0

Number of Bankrupt Predictions/Opinions 38 28 24Total Number of Predictions/Opinions Reported 53 43 50

*Auditor’s Opinion Code (AUOP – Compustat code) 0=unadited => blank 3=no opinion => code 11=unqualified => code 0 4=unqualified with additional explanatory

language added => code 12=qualified => code 1 5=adverse opinion = code 1Altman’s Multiple Discrimination Analysis Model (1968) Zscore:

Cybinski’s Temporal Model (1998) Risk of Bankruptcy:

A Zscore (>1.8) is classified as not bankrupt => code 0


A Zscore (<1.8) is classified as bankrupt => code 1



Table 2b

Extent of Agreement between the Temporal Model, Altman’s Model and Auditor’s Opinion in the Last Reporting Period Prior to Bankruptcy/Liquidation (Trade

Industry)Code ‘1’ denotes either a bankrupt prediction or an audit not unqualified (see codes below)

Firm Number




opinion*


opinion*1 1 29 0 1 02 1 30 13 1 31 0 1 04 0 32 1 15 1 33 1 16 0 0 34 0 07 1 35 0 08 1 36 1 0 09 1 37 1 010 1 38 1 0 011 1 39 1 1 012 1 0 0 40 0 013 1 0 0 41 014 0 0 42 0 015 0 0 43 1 016 1 1 44 1 117 0 0 45 1 1 118 0 0 0 46 019 0 0 47 0 020 1 48 1 021 0 49 1 1 122 1 50 1 123 0 51 0 1 024 0 52 1 0 025 1 53 1 1 026 1 1 0 54 0 127 1 0 55 0 128 1 0 0










Table 2c

Extent of Agreement between the Temporal Model, Altman’s Model and Auditor’s Opinion in the Second Last Reporting Period Prior to Bankruptcy/Liquidation

(Service Industry)Code ‘1’ denotes either a bankrupt prediction or an audit not unqualified (see codes below)

Firm Number




opinion*


opinion*1 1 0 28 0 0 02 0 1 1 29 03 0 0 0 30 1 0 04 0 31 05 0 1 32 06 1 0 1 33 1 1 07 0 0 0 34 0 0 08 1 35 0 0 09 0 36 1 1 010 1 0 0 37 1 1 011 1 0 0 38 1 1 012 1 39 0 0 013 0 0 40 0 1 014 0 1 1 41 015 1 1 42 1 0 116 0 1 1 43 0 1 117 1 1 44 1 1 118 1 1 1 45 0 019 0 0 0 46 1 0 020 0 0 0 47 021 0 0 1 48 022 1 1 1 49 0 0 023 0 1 0 50 1 1 024 1 0 0 51 0 0 025 0 0 0 52 1 0 026 1 0 0 53 1 1 027 0 1 1 54 0










Table 2d

Extent of Agreement between the Temporal Model, Altman’s Model and Auditor’s Opinion in the Second Last Reporting Period Prior to Bankruptcy/ Liquidation

(Trade Industry)Code ‘1’ denotes either a bankrupt prediction or an audit not unqualified (see codes below)

Firm Number




opinion*


opinion*1 0 30 0 12 1 31 1 1 03 0 32 04 0 33 0 0 05 0 1 34 1 1 16 1 0 0 35 0 17 0 36 08 0 37 0 0 09 0 0 38 0 010 0 39 1 0 011 1 40 112 1 0 0 41 1 0 013 0 0 0 42 0 014 0 1 43 0 015 0 1 44 016 0 1 45 0 0 017 0 0 46 118 0 0 0 47 0 1 119 0 0 48 020 0 1 0 49 021 0 0 50 1 0 022 1 51 1 1 123 1 1 0 52 124 0 53 0 0 025 1 54 0 0 026 1 0 0 55 0 0 027 0 1 0 56 128 0 0 57 1 0 129 1










Next, pairwise comparisons of the three decision entities can be made as shown in Tables 3a-3d by cross-tabulating the binary decision outcome and applying the chi-square test for independence (or non-agreement) for each pair of decision-makers10. Note the data is reduced here to just those firms for which complete data exists for both decisions.

As a test of independence now, the null and alternative hypotheses are:

H0: The two categorical variables (binary decision sets for each entity) are independent (ie. there is no relationship between them).11

against the alternative:

H1: The two categorical variables are dependent (ie. they are related in that they predominately agree or predominately disagree).12

Note that the rule of five applies for both a chi-squared test of a multinomial experiment in Tables 2a-2d, as well as for a chi-squared test of independence (contingency table) in Tables 3a-3d. The expected values should be at least five to ensure that the (continuous) chi-squared distribution provides an adequate approximation of the (discrete) sampling distribution. Note that if an observed value is less than five it is possible that the expected value may be five or greater and the rule is still satisfied. Where possible, cells can be combined in order to satisfy this rule.13 The rule of five is satisfied here for all of the cells in Tables 3a-3b (i.e. for the Service Industry data) but not for all cells of the Trade Industry tables in Tables 3c-3d where Fisher’s Exact Test may be applied using the hypergeometric distribution, or a Mantel-Haenszel Chi-Squared Test is applied (see Conover 3rd ed. 1999, pp.188-193).

10 Note that the two extreme cases that would result in rejection of the null hypothesis of independance is actually that either all of the decisions agree (+ve agreement) or all disagree (–ve agreement).11 This implies that their joint probability is equal to the product of their marginal probabilities of occurrence and conditional probabilities do not enter the formula. If the null hypothesis cannot be rejected, this means that the data shows no evidence of any relationship (either +ve or –ve agreement) between the decision entities.12 Hence it is a two-tailed test of independence. If significant, one gauges whether the direction of agreement is positive or negative by the ratio of agreements: disagreements in the table.13 Note that the rule of five is somewhat conservative. A discussion of alternatives to the rule of five can be found in Conover (1971, p.152) and in Siegel (1956, p.178).


Table 3aChi-Squared Tests for Independence of Two Categories/Variables in the Last

Reporting Period before Bankruptcy/Liquidation (Service Industry).In each case H0: The two categories are independent (ie. not generally related) vs. H1: the two categories are not independent (ie. they are related - the predictions/opinions either predominantly agree or predominantly disagree).

Contingency TablesData taken from financial reports tendered in the last reporting period prior to bankruptcy/liquidationTemporal model predictions vs Auditors’ opinion

Auditor OpinionUnqualified Not Unqualified

TotalTemporal Not bankrupt 7 8 15Model Bankrupt 18 16 34Predictions Total 25 24 49

Test Statistic Chi-Squared = 0.16P-Value = 0.69

Ratio of Agreements: Disagreements 23:26Conclusion: Independent. Neither the number of agreements or disagreements are significantly large enough to reject the hypothesis that the outcomes of the two decision entities are unrelated.

Temporal model predictions vs Altman model predictionsAltman Model PredictionsNot bankrupt Bankrupt

TotalTemporal Not Bankrupt 6 7 13Model Bankrupt 9 21 30Predictions Total 15 28 43

Test Statistic Chi-Squared = 1.04.P-Value = 0.31


Altman model predictions vs Auditors’ opinion Auditor OpinionUnqualified Not Unqualified

TotalAltman Model Not bankrupt 12 2* 14Predictions Bankrupt 9 16 25

Total 21 18 39Test Statistic Chi-Squared = 8.9P-Value = 0.003

Ratio of Agreements: Disagreements 28:11Conclusion: Not Independent/Predominant Agreement – the outcomes of the two decision entities are related.

* Note: the expected value of this cell is 6.5 > 5 so Chi-Squared is valid under the Rule of Five.


Table 3bChi-Squared Tests for Independence of Two Categories/Variables in the Second

Last Reporting Period before Bankruptcy/Liquidation (Service Industry).In each case H0: The two categories are independent (ie. not generally related) vs. H1: the two categories are not independent (ie. they are related - the predictions/opinions either predominantly agree or predominantly disagree).

Temporal model predictions vs Auditors’ opinionAuditor OpinionUnqualified Not Unqualified

TotalTemporal Not bankrupt 16 7 23Model Bankrupt 14 6 20Predictions Total 30 13 43




TotalTemporal Not Bankrupt 12 7 19Model Bankrupt 9 10 19Predictions Total 21 17 38




TotalAltman Model Not bankrupt 18 3* 21Predictions Bankrupt 8 8 16

Total 26 11 37Test Statistic Chi-Squared = 5.54P-Value = 0.02


* Note: the expected value of this cell is 6.5 > 5 so Chi-Squared is valid under the Rule of Five.


Table 3cChi-Squared Tests for Independence of Two Categories/Variables in the Last

Reporting Period before Bankruptcy/Liquidation (Trade Industry).In each case H0: The two categories are independent (ie. not generally related) vs. H1: the two categories are not independent (ie. they are related - the predictions/opinions either predominantly agree or predominantly disagree).


TotalTemporal Not bankrupt 4* 0* 4Model Bankrupt 12 3* 15Predictions Total 16 3 19

Test Statistic Fisher’s Mantel-Haentszel Chi-Exact Test Squared = 0.9P-Value ≈ 0.98 P-Value = 0.34



TotalTemporal Not Bankrupt 3* 1* 4Model Bankrupt 10 3* 13Predictions Total 13 4 17




TotalAltman Model Not bankrupt 21 1* 22Predictions Bankrupt 2* 4 6

Total 23 5 28Test Statistic Fisher’s Mantel-Haentszel Chi-Exact Test Squared = 11.96P-Value ≈ 0.003 P-Value = 0.0005


* Note: the expected values of the asterisked cells are <5 so a Chi-Squared Test of Independence is not valid. Both a Fisher’s Exact Test and a Mantel-Haenszel Chi-Sqaured Test are valid.


Table 3dChi-Squared Tests for Independence of Two Categories/Variables in the Second

Last Reporting Period before Bankruptcy/Liquidation (Trade Industry).In each case H0: The two categories are independent (ie. not generally related) vs. H1: the two categories are not independent (ie. they are related - the predictions/opinions either predominantly agree or predominantly disagree).


TotalTemporal Not bankrupt 11 3* 14Model Bankrupt 8 3* 11Predictions Total 19 6 25




TotalTemporal Not Bankrupt 8 3* 11Model Bankrupt 7 4* 11Predictions Total 11 7 22




TotalAltman Model Not bankrupt 21 4 25Predictions Bankrupt 5 3* 8

Total 26 7 33Test Statistic Fisher’s Mantel-Haentszel Chi-Exact Test Squared = 1.63P-Value ≈ 0.32 P-Value = 0.20


* Note: the expected values of the asterisked cells are <5 so a Chi-Squared Test of Independence is not valid. Both a Fisher’s Exact Test and a Mantel-Haenszel Chi-Sqaured Test are valid.


(6) RESULTS

For both industry datasets in the last reporting period before bankruptcy/liquidation, the binary decision outcomes are summarized in Table 4a below.

Table 4aSummary of binary decision outcomes in the last reporting period before

bankruptcy/liquidation

SERVICE INDUSTRY DATASETTemporal

ModelAltman Model

Auditor's Opinion

Number of Bankrupt Predictions/Not Unqualified Opinions 38 72% 28 65% 24 48%Number of Nonbankrupt Predictions/Unqualified Opinions 15 15 26Total Number of Predictions/Opinions Reported 53 43 50

TRADE INDUSTRY DATASETTemporal

ModelAltman Model

Auditor's Opinion


For both industry datasets in the second-last reporting period before bankruptcy/liquidation, the binary decision outcomes are summarized in Table 4b below.

Table 4bSummary of binary decision outcomes in the second last reporting period before

bankruptcy/liquidation

SERVICE INDUSTRY DATASETTemporal

ModelAltman Model

Auditor's Opinion


TRADE INDUSTRY DATASETTemporal

ModelAltman Model

Auditor's Opinion


Tables 2a and 2b show the extent of agreement between the temporal model, Altman’s model and the auditor’s opinion for individual firms in the last reporting period prior to bankruptcy/liquidation for the service industry and the trade industry datasets respectively. Table 4a shows that the temporal model identified 72% of the service industry bankrupt firms as distressed14 at this time compared with 65% for the Altman model, whilst only 48% of the audited bankrupt firms were denied an unqualified going concern opinion by the auditor.

14 The definition of “distressed” here is “having a bankruptcy risk estimate greater than 0.5”.


With regards to the last comparison, it is worth pointing out that the auditor is given an advantageous position (as explained next) and nevertheless, still showed the lowest percentage of correct decisions. Firstly, if a company is in the process of liquidation at the time of submitting their financial reports, Standard and Poor’s assigns a “qualified” code regardless, even if the opinion is not actually qualified. The authors are not able to know to what extent this occurred for the companies in the datasets used here. Secondly, if the auditor refuses to express an opinion regarding the company’s ability to sustain operations as a going concern, it is also regarded as “not unqualified” (i.e. code 1 in this study) as the authors have regarded ‘non-commital’ as a denial, to some extent, of an unqualified report. So, in both instances, since we are dealing with just bankrupt firms, the auditor would have been coded with a ‘correct decision’ without actually having made a decision.

Notwithstanding the above, the null hypothesis of equal proportions of correct decisions by the three decision entities is rejected at the .04 level of significance [χ2

2 = 6.42, p=0.040]. The follow-up Z-tests, for paired differences in the overall proportion of correct decisions made, show that outcomes from the temporal model and Altman’s model are not statistically significantly different from each other [Z=0.69, p=0.49] and that both give significantly higher correct classifications than the auditors [p=0.007, p= 0.049 respectively].

Tables 2c and 2d show the figures for the second last reporting period before failure for the service industry and trade industry datasets respectively. The accuracy of the decision is not as straightforward here as in the final year before failure since the firms all survived another reporting period. Note that the temporal model is based on discriminations between firms in their previous surviving years against their final year before bankruptcy so a “not bankrupt” decision is a correct classification at this time within that model structure. A “bankrupt” decision therefore signals that the firm is already in trouble despite its continued survival. Altman (1968), on the other hand, used his model to ascertain whether a firm would fail for up to 5 periods into the future (though he noted it was accurate for up to only two periods, p. 604).

Table 4b shows that, for the service industry dataset, Altman’s model signalled bankruptcy for 45% of the bankrupt firms two reporting periods prior to bankruptcy, whereas the temporal model figure was 43%, and only 30% of the audited firms were denied an unqualified going concern opinion. Whether such comparisons are meaningful or not, there was not enough evidence in the data to reject the null hypothesis of equal proportions of “bankrupt/not unqualified” decisions made by the three decision entities [χ2

2=2.2, p=0.33].

Table 4a shows that for the out-of-sample predictions using the trade industry dataset, in the final reporting period before failure, the temporal model still identified 67%


of these bankrupt firms as failing even though the model was formulated specifically for the service industry. This compared with only 21% for the Altman model also formulated on a different sample of manufacturing firms, while just 23% of the audited bankrupt firms were denied an unqualified going-concern opinion by the auditor. There is a statistically significant difference in prediction accuracy here, with the null hypothesis of equal proportions of correct decisions by the three decision entities rejected [χ2

2 = 21.2, p<0.0001], and the temporal model outperforming the other two decision entities [both p<0.0001].

For the trade industry dataset at two reporting periods prior to bankruptcy, the temporal model signalled bankruptcy for 43% of the bankrupt firms, whereas Altman’s model figure was 24%, and 25% of the audited firms were denied an unqualified going-concern opinion at this time. The null hypothesis of equal proportions of “bankrupt/not unqualified” decisions made by the three decision entities can be rejected at the 10% level of significance but not the 5% level [χ2

2 =5, p= 0.08], but the statistically more powerful pairwise Z-test comparisons show that the decisions of the auditor and the Altman model are not statistically significantly different from each other [Z=0.07, p= 0.94] whereas the temporal model again signals more bankruptcies than the other two entities [both p=0.04].

Tables 3a-3d give pairwise cross-tabulations of the binary decisions of the three decision-entities and the respective tests for independence (no relationship) for each pair. For the trade industry dataset, there were too many missing values and too few bankrupt decisions arising from both Altman’s model and the auditors to give valid chi-squared tests of independence with the temporal model for paired contingency tables in both final reporting periods. Consequently other nonparametric tests have been employed here15 as detailed in the Analysis section above.

For pairwise comparisons between the temporal model and the other two decision entities, for both the final reporting periods before failure and for both the service industry and the trade industry datasets, there is not enough evidence to reject the null hypothesis that the decision outcomes are unrelated. In other words, they don’t consistently agree or disagree [all p>0.33]. In contrast, for the comparisons between the auditors’ decisions and Altman’s atemporal model, there is predominant agreement [p<.02]. The only exception occurs in the second last reporting period for the trade industry dataset where the total number of agreements for the sample size of 33 is not significantly large enough to reject the hypothesis that the decision outcomes of

15 The actual distribution of the test statistic is discrete and can be approximated by a continuous chi-squared distribution when the sample size is large. However, the approximation is poor if the expected cell frequencies are small (the “rule of five” convention is that no more than 20% of cell frequencies “less than five”). Fisher’s Exact Test or a Mantel-Haenszel Test is appropriate in these cases.


the auditors and from Altman’s model are unrelated [p=0.32]. Nevertheless, for this comparison, the ratio of agreements:disagreements is 24:9 and agreement does occur predominantly on nonbankrupt/unqualified decisions (21 of the 24 agreements).

(7) DISCUSSION

The macroeconomic environment of firms has largely been excluded from empirical analyses of business failure. This may explain the inconsistencies in the prediction accuracy of the various bankruptcy models when they are applied to more recent data, as well as auditors’ reluctance to rely more on them in a going-concern decision. Based on the findings of this study, we suggest here that the auditors could indeed have benefited from the information supplied by the bankruptcy models. In the final reporting period for the service industry dataset, this study has shown that with respect to the total percentage of accurate decisions, both bankruptcy models outperform the auditor. Moreover, on comparing both models against the auditors’ opinions we find that in the final reporting period before bankruptcy, the temporal model gave superior prediction accuracy on both datasets (i.e. including the holdout dataset).

In the second last reporting period before bankruptcy, we find that the margin of difference in prediction accuracy between the bankruptcy models and the auditors’ opinions is reduced and it is significantly different only for the trade industry dataset and only between the temporal model and the auditors (43% to 25% resp.) .

It is not surprising, then, to find that there is no overall agreement between the temporal model and both the other decision models on individual firm decisions in both reporting periods before failure. They clearly signal different firms as failing.

For the service industry dataset, the Type I (false negative) error rate for the temporal model was 28% in the final reporting period before failure. In other words the model classified slightly more than a quarter of the bankrupt firms as “not distressed” or “able to survive another reporting period”. This compares with 35% of the bankrupt firms predicted as “not bankrupt” by the Altman model and slightly more than half given an unqualified going-concern opinion by the auditors. The differences in Type I errors were even more startling for the trade industry dataset that was out-of-sample for both the Altman model and the temporal model formulations; one third for the temporal model compared to 79% for the Altman model and 77% for the auditors.

The temporal model correctly classified more of the (bankrupt) firms as risking failure in the next year for both its estimation sample (as expected) and for another holdout sample of firms, and the difference was statistically significant in all but one case.


This study also found that the Altman model and the auditors agree more often on individual firms. There is consistently strong agreement across three of the four comparison tables between the auditors and the Altman model [p<.003, p<.003, p<.02 respectively]. Both decision entities predominantly make “nonbankrupt/unqualified” decisions and they both agree on 70-89% of all their decisions. These results could indicate that they both have a “bankrupt/not unqualified” outcome for only the most distressed firms, i.e., those with a very high risk of bankruptcy in the temporal model.

Clearly, the higher bankruptcy classification rates for the temporal model would suggest that, for a sample of distressed or problem companies at least, a more complex failed-firm model including macroeconomic factors in its formulation can perform far better than an atemporal model or the auditors’ decision process, especially in providing support in the form of a risk assessment.

(8) CONCLUSION

Professional audit standards require auditors to understand the client entity and its economic environment by using various operating indicators such as financial indicators and management attributes and/or deficiencies. There is no professional requirement for any more sophisticated analysis of the entity’s business environment using statistical modelling. The problem with using operating indicators is that they provide only a simplistic and static measure of the entity’s business environment when auditors are supposed to give a going-concern opinion that in reality predicts the entity’s viability or otherwise (for 12 months). It is argued that a bankruptcy model that includes a temporal approach can provide a sophisticated tool to assist forming a going-concern opinion and complement the auditor’s professional judgement.

This study has shown that newer models like the temporal model presented by Cybinski (2000, 2003) can improve decision accuracy over the static or atemporal models of the past, when used as an adjunct to the auditor’s tools in the going-concern decision. One reason is simply because they are more sensitive to changing macroeconomic conditions and how they impact on distressed firms. Hence temporal models are more useful for out-of-sample predictions of distress (or bankruptcy risk), although we need always to be mindful of limitations due to external validity concerns when using models for the assessment of a particular firm’s insolvency risk (other than in the industry in which the model was estimated and, in the case of the Cybinski temporal model, for other than failed firms). Nevertheless these limitations do not preclude the application of these models in a practical way when researchers/auditors use them for explanatory purposes rather than for forecasting - as a decision support.


Although exploratory in nature, the formulation of a temporal model for failure risk is informative concerning the possible comparative effects of the internal ratios and the external economy on failure risk and the means of examining these effects together. The fact that reasonable results were obtained when a particular temporal model for the service industry was applied to the trade industry group is an encouraging result for testing external validity of such models in future research.

Improved bankruptcy modelling will also, no doubt, engender greater public confidence in auditor objectivity with the professional use of quantitative decision support. Current audit procedures require the auditor to trust client management for information in an intensive interactive relationship, which has led to standards that focus on prescriptive behavioural parameters for that relationship (Windsor and Ashkanasy 1995). Rather than introducing more of the same in the imminent revision of auditing standards, the inclusion of sophisticated and objective approaches to audit procedures such as statistical modelling should be seriously considered. This would allow for a more impartial analysis of the client firm in a more holistic environment and provide an opportunity for auditors to increase their professional decision-making expertise.


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APPENDIX A

THE ALTMAN MODEL(1968)

Concept Calculation in Standard and Poor’s COMPUSTAT database.ZSCORE=1.2*(WCAP/AT)+1.4*(RE/AT)+3.3*(EBIT/AT)+0.6*(@VALUE(PRCCF*CSHO,CEQ)+PSTK)/(AT-CEQ-PSTK)+.999*(SALE/AT)This concept is a bankruptcy prediction model developed by Edward Altman at New York University in 1968.

Altman’s (1968) Multiple Discriminant Analysis model was written:

Z = .012X1 + .014X2 + .033X3 + .006X4 + .999X5 where

X1 = Working capital/total Assets

X2 = Retained earnings/total assets

X3 = EBIT/total assets

X4 = Market value equity/book value of total debt

X5 = Sales/total assets

Note that in this formulation X1 to X4 must be calculated as absolute % values hence the the coefficients of these ratios are one hundredth those of the COMPUSTAT formulation.The sample on which the model is based was composed of 66 manufacturing corporations with 33 firms in each of two groups; a bankrupt group and a non-bankrupt group.

THE MODEL BY CYBINSKI (2000, 2003)

The path to failure was analyzed using a stepwise logit model of probability of failure in the next reporting period using the dependent variable “1” for “bankrupt” in the final year before failure and “0” for “surviving” in all previous years. The stepwise regression was based on the final four consecutive years of financial statements available in Standard and Poor’s COMPUSTAT database for sixty bankrupt service industry firms.

The parameter estimates for the final logit model of firm failure risk (using goodness of fit criterion) are listed below.

* Extract from SAS output.


The Estimated (Logit) Model: Analysis of Maximum Likelihood Estimates#

Parameter Standard Wald Pr > Variable Estimate Error Chi-Square Chi-Square INTERCEPT 1.4658 0.3972 13.6212 0.0002 PC3 0.9115 0.1818 25.1319 0.0001 PC4 0.4133 0.1404 8.6650 0.0032 PC5 -0.7695 0.2497 9.4930 0.0021 PC2_1 0.4736 0.1327 12.7349 0.0004 PC5_1 -0.8011 0.1790 20.0306 0.0001 INT1 -0.0206 0.00441 21.8895 0.0001 INT2 -0.0166 0.00383 18.8065 0.0001 INT3 -0.0821 0.0533 2.3675 0.1239 INT4 - 0.6916 0.2952 5.4874 0.0192 INT5_1 - 2.2866 0.6560 12.1513 0.0005 INT5_4 1.6171 0.5183 9.7339 0.0018

Model Chi-Square of 120.776 with 11 DF (p=0.0001), Residual Chi-Square = 8.8668 with 4 DF (p=0.0645).Note: the residual chi-square value is nearly significant at 0.05 level - i.e. lack-of-fit is not significant.The overall significance of the above model was p=0.0001 with an overall classification accuracy for predicting a final or surviving year for the 60 service industry firms of 72% in the estimation sample, a type I error rate (probability of misclassifying a final year before bankruptcy) of 29%, and a Type II error rate (probability of misclassifying a surviving year as a final one) of 28%.

#This is a minimum adequate model and was estimated from an original set of variables comprising the current and lagged values of: - (a) Twenty-three financial ratios considered relevant to bankruptcy in the current literature, and (b) Five principal components representing the macro-environment of the U.S. matched by year.

THE INTERNAL VARIABLES IN THE FINAL MODEL: THE FINANCIAL RATIOS.The following are the ratio labels in the model above (bracketed by type) with their definitions and explanation notes (and the formula using COMPUSTAT names).

INT1 (liquidity) working capital/total assets (%) where working capital = (current assets-current liabilities). [(ACT-LCT)/AT x100]

INT2 (leverage) total liabilities/total assets (%) or the debt ratio [LT/AT x 100] This ratio is interpreted as a measure of the firm’s capital structure -the higher the debt ratio, the greater the chance of predicting failure.

INT3 (cash-flow) cash flow from operations**/total current liabilities [(FOPT+WCAPCH)/LCT]

INT4 (leverage) a binary dummy variable taken from interest coverage after tax = (net income before extraordinary items + interest expense)/interest expense [(IB+XINT)/XINT*] or COMPUSTAT ratio, IC.

INT5_1 AND INT5_4 (turnover) are respectively, the lowest and highest dummy variable categories of sales/net plant (property plant and equipment total on balance sheet minus depreciation) [SALE/PPENT*]

** Cash Flow is defined here as Total Funds from Operations plus Working Capital Changes - taken from, the Statement of Changes/Statement of Cash Flows.* The denominator of the ratio is often equal to zero so there was a need to categorize this ratio..


THE EXTERNAL VARIABLES IN THE FINAL MODEL: THE MACROECONOMIC VARIABLES.Refer to Cybinski (2000, 2003) for more detail on these factors and the economic series upon which they are loaded.

PC2_1 Cost of Capital and Borrowing Factor (lagged one year)PC3 Labour Market Tightness FactorPC4 Construction Activities Factor PC5 Expenditures Factor PC5_1 Expenditures Factor (lagged one year)

Three lag periods were initially used in the stepwise regression analysis. Loss of degrees of freedom, and non-orthogonality between lagged variables resulted in only one lag period showing any statistical significance (p<0.05), and then for only two of the five macro-economic variables, shown above.

Note: Both models rated Working capital/total assets as the best indicator of ultimate discontinuance.

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