corporate budgeting

Tests of the generalizability of Altman’s bankruptcy prediction model

John Stephen Gricea,*, Robert W. Ingramb

aSorrell College of Business, Troy State University, 131 Bibb Graves, Troy, AL 36082, USAbThe University of Alabama, USA

Abstract

Though developed in 1968 using a small sample of firms from the 1950s and 1960s, Altman’s Z-score model remains a commonly used

tool for evaluating the financial health of companies. Because of the age of the model and other attributes, such as its small sample of

manufacturing firms and the use of equal group sizes of bankrupt and non-bankrupt firms, it is likely that model is not as effective in

classifying firms in more recent studies as it was when it was developed by Altman. This study examines three research questions using

recent sample data: (1) Is Altman’s original model as useful for predicting bankruptcy in recent periods as it was for the periods in which it

was developed and tested by Altman? (2) Is the model as useful for predicting bankruptcy of non-manufacturing firms as it is for predicting

bankruptcy of manufacturing firms? (3) Is the model as useful for predicting financial stress conditions other than bankruptcy as it is for

predicting bankruptcy? Our results are consistent with negative answers to questions one and two and a positive answer to question three.

D 2001 Elsevier Science Inc. All rights reserved.

Keywords: Generalizability; Bankruptcy; Z-score model

Altman (1968) developed his well-known Z-score

model using a matched sample of 33 bankrupt and 33

non-bankrupt manufacturing firms from 1946–1965.

Though the Z-score model exhibited high accuracy rates

using both estimation and hold-out samples (95% and

84%), the generalizability of this model to industries and

periods outside of those in the original sample has

received little attention. Nevertheless, the original model

has been employed in recent research to evaluate financial

conditions of firms from a variety of industries and

periods (e.g., Chen and Church, 1996; Chen and Wei,

1993; Carcello et al., 1995; Berger et al., 1996; Subra-

manyan and Wild, 1996). Also, it continues to be used in

a variety of business situations involving the prediction of

bankruptcy and other financial stress conditions. Commer-

cial banks use the model as part of the periodic loan

review process, and investment bankers use the model in

security and portfolio analysis. The model has been

employed as a management decision tool and as an

analysis tool by auditors to assess their clients’ abilities

to continue as going concerns (AICPA, 1987; Dugan and

Zavgren, 1988).

The continued use of Altman’s bankruptcy prediction

model by researchers and practitioners leads to three

research questions considered in this paper:1 Is Altman’s

original model as useful for predicting bankruptcy in

recent periods as it was for the periods in which it

was developed and tested by Altman? Is the model as

useful for predicting bankruptcy of non-manufacturing

firms as it is for predicting bankruptcy of manufacturing

firms? Is the model as useful for predicting financial

stress conditions other than bankruptcy as it is for

predicting bankruptcy?

Our results lead us to question current uses of Altman’s

model. Though our results indicate that the model is

useful for predicting financial distress conditions other

than bankruptcy, they also indicate that the model’s

accuracy is significantly lower in recent periods than that

reported in Altman’s (1968) study across all sample

characteristics considered in this study. Additionally, the

magnitude and significance of the model’s coefficients

differ from those reported by Altman. Our results suggest

that better accuracy can be achieved by re-estimating

* Corresponding author. Tel.: +1-334-670-3154; fax: +1-334-670-3154.

E-mail address: [email protected] (J.S. Grice).

1 Though other models have been proposed and examined in the

literature, Altman’s continues to be the one most cited and used. See

Zavgren (1983) and Jones (1987) for detailed discussions of other models

and techniques used in prior bankruptcy prediction studies.

0148-2963/00/$ – see front matter D 2001 Elsevier Science Inc. All rights reserved.

PII: S0148 -2963 (00 )00126 -0

Journal of Business Research 54 (2001) 53–61

model coefficients using estimation samples from periods

close to test periods. Also, the accuracy of the model

decreases significantly when non-manufacturing firms are

included in the sample.

Section 1 discusses Altman’s model and prior research

relevant to this study. Section 2 describes the sample and

tests employed to evaluate Altman’s model. Section 3

examines findings and Section 4 discusses implications for

users of Altman’s model.

1. Contributions to prior research

This section summarizes Altman (1968) and studies that

have examined his bankruptcy prediction model. It explains

the contributions of the present study to solving problems

identified in these earlier studies.

To develop the Z-score model, Altman (1968) compiled

a list of 22 financial ratios and classified each into one of

five categories (liquidity, profitability, leverage, solvency,

and activity). The ratios were not selected on a theoretical

basis, but rather, on the basis of their popularity in the

literature and Altman’s belief about their potential rele-

vancy to bankruptcy. He estimated the model using multi-

ple discriminant analysis to derive a linear combination of

variables that discriminated between bankrupt and non-

bankrupt firms. After numerous tests, the linear function

that best discriminated between the 33 bankrupt and 33

non-bankrupt manufacturing firms was:

Z ¼ 1:2X1 þ 1:4X2 þ 3:3X3 þ 0:6X4 þ 0:999X5 ð1Þwhere, X1 is the working capital/total assets, X2 is the

retained earnings/total assets, X3 is the earnings before

interest and taxes/total assets, X4 is the market value equity/

book value of total debt, X5 is the sales/total assets, and Z is

the overall Z-score index. The lower a company’s Z-score,

the higher its probability of bankruptcy.

Scott (1981) noted potential search bias in the variable

selection technique used by Altman. The lack of a theory

of bankruptcy invites the researcher to consider a multi-

tude of variables and then to reduce the original set to

the most accurate subset. The resulting subset of vari-

ables often proves ineffective when applied to a sample

of firms or periods other than those used in developing

the model.

Hold-out sample accuracy rates in Altman’s and other

studies are potentially upwardly biased (Bias here means

that the hold-out sample accuracy rates are higher than the

rates users should expect when they apply the models) for

three reasons: (1) the estimation and hold-out sample

periods are not substantially different, (2) the hold-out

sample consists of firms from the same restricted set of

industries as those in the estimation sample, and (3) the

hold-out samples are small (the largest sample was 111 in

studies we examined) and are not proportional to actual

bankruptcy rates.

Other studies that directly tested the Z-score model

include Moyer (1977), Zmijewski (1983), Holmen (1988),

and Begley et al. (1996). The most relevant of these to our

study is Begley et al. (1996). They applied the Z-score

model to a prediction sample that included 65 bankrupt and

1300 non-bankrupt industrial firms from 1980–1989 and

reported a 78% accuracy rate. They also re-estimated the

Altman (1968) coefficients using a matched sample of 100

bankrupt and 100 non-bankrupt companies. Their re-esti-

mated coefficients exhibited a 78% classification accuracy

using their prediction sample.

The accuracy rates reported in these studies also are

potentially upwardly biased because they suffer from one, or

a combination, of the limitations of the hold-out samples

described above. For example, all prior tests of the Z-score

model used samples that included restricted sets of indus-

tries. Also, except for the Begley et al. (1996) study, the

results of prior research are dated because the samples were

primarily for companies from the 1960s and 1970s. Another

limitation of the test samples is that the samples were small

and not proportional to actual bankruptcy rates.2 Though

Begley et al. (1996) used a proportional sample to test the

Z-score model, they imposed a size restriction on firms

included in their sample, limiting the study to larger

firms. Begley et al. (1996) also used matched samples

of bankrupt and non-bankrupt companies to re-estimate

their models, thus ignoring the effects of proportionate

sampling in developing these models.

When a model is applied to periods other than those used

to develop and test the model, researchers assume the model

is stable across economic conditions that change over time,

such as inflation, interest rates, and credit availability.3 The

effect of changing economic factors on the accuracy,

magnitude, and significance of model coefficients was

evaluated by Mensah (1984) who developed four models

using samples from the 1972–1973, 1974–1975, 1976–

1977, and 1978–1980 periods, each period representing a

different economic environment. He reported that the accu-

racy and structure of the models changed over the four time

periods. Accordingly, it is unlikely that Altman’s model

performs equally well in all financial periods. Tests in the

current study compare both the accuracy rates and estimated

coefficients of the original Z-score model to those derived

using recent proportional samples.

Another limitation of the hold-out samples of prior

studies is that the samples were small. Altman tested his

2 Zmijewski (1983) used a proportionate sample; however, he did not

report the Z-score model’s accuracy rate.3 Begley et al. (1996) also briefly discussed the concerns of using dated

bankruptcy prediction models on recent data. They indicated that the

merger and takeover activity of the 1980s changed the likelihood of

bankruptcy associated with high corporate debt levels. Additionally, they

suggested that the changes in the bankruptcy laws during the 1970s allowed

companies to strategically use bankruptcy. To the extent the reasons for

strategic use are associated with financial variables, models developed prior

to the changes in the law may result in greater classification errors.

J.S. Grice, R.W. Ingram / Journal of Business Research 54 (2001) 53–6154

model on two different independent samples consisting of

91 (25 bankrupt and 66 non-bankrupt) and 111 (53 bankrupt

and 58 non-bankrupt) firms. Also, the hold-out samples

were not proportionately representative of the population of

bankrupt and non-bankrupt firms. The average business

failure rate is less than 1%,4 while the proportion of bank-

rupt to non-bankrupt firms included in previous hold-out

samples ranges from 24% to 50%.

Results of oversampling bankrupt firms include mis-

statement of Type I and Type II errors. Altman (1968)

used an equal number of bankrupt and non-bankrupt

companies for his estimation sample. Altman et al.

(1977) reported classification accuracy under assumptions

of equal prior probabilities as well as under different

probabilities.5 The overall accuracy rate (92%) of their

model was not affected when prior probabilities more

representative of the average business failure rate were

incorporated. However, the number of bankrupt (non-

bankrupt) firms misclassified increased (decreased) under

the more representative prior probabilities. The Z-score

model understated Type I errors and overstated Type II

errors. Zmijewski (1984) also tested the effect of dispro-

portionate sampling in bankruptcy prediction studies and

reported similar findings.

Hold-out sample tests in prior studies included firms

from the same industries as those in the estimation sample.6

The test samples used in prior studies that directly tested the

Z-score model also included restricted sets of industries.

Platt and Platt (1991) demonstrated that a bankruptcy

prediction model that included industry-relative ratios pro-

duced improved prediction accuracy relative to a model that

included only unadjusted ratios. Industry-relative ratios

were adjusted for the average ratio for a specific industry.

Their results suggest that a bankruptcy estimation model

developed using firms from one set of industries may not be

highly accurate in predicting bankruptcies for firms in other

industries. Tests in the current study evaluate results of

applying Altman’s model to industries other than manufac-

turing firms.

Even though the Z-score model was developed to predict

bankruptcy, this event is only one of several indicators (or

consequences) of financial distress. It is not clear whether

Altman’s model is specifically useful for identifying firms

that are likely to go bankrupt or whether it is more

generally a model for identifying firms experiencing finan-

cial distress, though the model is commonly used for this

purpose. While firms that experience financial distress are

more likely to declare bankruptcy than other firms, most

financially distressed firms do not declare bankruptcy.

Gilbert et al. (1990) suggested that financial dimensions

that distinguish bankrupt from healthy firms are different

from those that separate bankrupt from distressed firms.

Bankruptcy is a joint result of financial distress and other

events that precipitate legal action.7

This study considers the Z-score model’s ability to assess

financial distress conditions other than bankruptcy. If Alt-

man’s model is better suited for predicting bankruptcy than

for predicting other financial distress problems, it may not

be appropriate for some of the applications for which it has

been used.

2. Research design

This section describes the sample selection criteria.

Also, it explains the methodology employed to test the

Altman model.

2.1. Sample

The analyses in this study used a 1985–1987 estimation

sample and a 1988–1991 prediction sample from Compus-

tat’s annual industrial and research files. 1985 was the first

year of the study because certain variables were unavailable

prior to this year. The final year in the prediction sample was

1991 because the number of bankrupt firms identified on

Compustat was minimal in years following 1991 and we

wanted to ensure that sufficient data were available to

determine whether a firm declared bankruptcy subsequent

to the test period. Distressed companies were defined as

those reported by Compustat as meeting one or more of the

following conditions: (1) Chapter 11 bankruptcy, (2) Chap-

ter 7 liquidation, (3) bonds vulnerable to default, or (4) low

4 The average business failure rate between 1970 and 1991 ranged from

.038% to 1.19% (Gentry et al., 1985).5 Altman et al. (1977) adjusted the model’s cutoff score to simulate the

effect of using unequal prior probabilities. The adjustment factor was

calculated as ln( p1/p2) where p1 and p2 represent the prior probabilities of

the bankrupt and non-bankrupt groups. If their sample violated the

assumptions of equal variance–covariance matrices between the groups

and multivariate normality, then this adjustment factor may be inappropri-

ate. Though Altman et al. did not report information related to these

assumptions, prior research suggests the assumptions are typically violated

for the estimation samples used to develop bankruptcy prediction models

(Jones, 1987).6 Altman et al. (1977) used a hold-out sample that included 61

manufacturing and 50 retail firms to test the Z-score model; however, they

did not report the model’s accuracy by industry classification. The model

exhibited an 84% classification accuracy for the entire hold-out sample.

7 A limitation of the Z-score model is that the variable set does not

incorporate proxies for non-financial events that precipitate bankruptcy. For

example, a bank’s refusal to extend credit, lawsuits, and union problems are

three factors associated with bankruptcies. Arguably, a bank’s refusal to

extend credit is typically attributable to firms’ poor financial performances

or high debt levels. However, union problems and lawsuits could result in

firms filing bankruptcy as a result of strategic management decisions. That

is, management may deem it necessary to file bankruptcy to secure a

favorable outcome in negotiations or court proceedings, even though the

firm is not experiencing serious financial problems. The lack of

homogeneity in the motivation for bankruptcy filings complicates the

modeling effort, and users should recognize that the Z-score model does not

capture all events that may cause, or precede, bankruptcy.

J.S. Grice, R.W. Ingram / Journal of Business Research 54 (2001) 53–61 55

stock ratings.8 The non-distressed firms were selected

randomly from the population of Compustat firms for which

S&P ratings were available.9

The 1985–1987 estimation sample included 972 compa-

nies (148 distressed and 824 non-distressed). This sample

was used to re-estimate coefficients in Eq. (1). The 1988–

1991 prediction sample included 1002 companies (148

distressed and 854 non-distressed). This sample was used

to evaluate the predictive accuracies of both Altman’s

original and the re-estimated (1985–1987) Z-score models.

These samples included bankrupt and other financially

distressed firms and included non-manufacturing as well

as manufacturing firms. Subsamples were used to address

the various research questions examined in this study.

Table 1 reports descriptive statistics by distressed and

non-distressed groups for the estimation and prediction

samples. A comparison of the 1985–1987 distressed and

non-distressed variable means indicates that working capi-

tal/total assets (X1), retained earnings/total assets (X2), and

earnings before interest and taxes/total assets (X3) were

lower in the distressed than in the non-distressed group.

The p-values for the test of mean differences between

distressed and non-distressed companies were significant

for each of these variables. The means for market value of

equity/book value of total debt (X4) and sales/total assets

(X5) were not significantly different between the distressed

and non-distressed groups, however. The descriptive statis-

tics for Altman’s variables using the 1985–1987 sample

were similar to those reported by Altman for his estimation

sample except for the market value variable, which was

significantly different between his bankrupt and non-bank-

rupt groups.

The descriptive statistics for the 1988–1991 predic-

tion sample in Table 1 are similar to those of the

1985–1987 sample except for sales/total assets. The

means for sales/total assets were significantly different

between the distressed and non-distressed firms in the

1988–1991 sample.10 The means for the market value

variable were not significantly different between the

distressed and non-distressed groups for the 1988–

1991 prediction sample.

Our sample included firms from all two-digit SIC codes

for which data were available to calculate model variables.

Financial institutions were excluded because Compustat

does not include current asset and liability data for these

firms. The 1985–1987 sample included 79 distressed and

435 non-distressed manufacturing firms (SIC code 2000–

3999) and 69 distressed and 389 non-distressed non-manu-

facturing firms. The 1988–1991 sample included 78 dis-

tressed and 452 non-distressed manufacturing firms and 70

distressed and 402 non-distressed non-manufacturing firms.

The 1985–1987 sample included 86 bankrupt companies

and 62 companies that were financially distressed but that

Table 1

Descriptive statistics for 1985–1987 and 1988–1991 samples

1985–1987

sample Statistic X1 X2 X3 X4 X5

Non-distresseda Mean 0.229 0.283 0.107 2.264 1.235

(n=824) Standard

deviation

0.199 0.241 0.081 3.156 0.812

Minimum �0.266 �1.690 �0.406 0.040 0.033

Maximum 0.858 1.384 0.508 28.705 7.283

Distresseda Mean 0.092 �0.565 �0.176 3.166 1.213

(n=148) Standard

deviation

0.389 1.056 0.409 13.992 0.988

Minimum �2.410 �6.203 �2.042 0.014 0.000

Maximum 0.841 0.550 0.038 161.918 6.593

p-valueb 0.000 0.000 0.000 0.436 0.799

1988–1991 Sample

Non-distresseda Mean 0.200 0.182 0.090 2.267 1.239

(n=854) Standard

deviation

0.208 1.794 0.110 4.058 0.760

Minimum �0.684 �2.427 �1.722 0.361 0.002

Maximum 0.843 1.077 0.351 59.890 5.284

Distresseda Mean 0.061 �0.773 �0.122 2.268 1.622

(n=148) Standard

deviation

0.500 2.152 0.349 9.158 1.173

Minimum �3.442 �19.023 �2.446 0.003 0.001

Maximum 0.861 0.663 0.301 101.802 6.633

p-valueb 0.000 0.000 0.000 0.998 0.000

X1 = working capital/total assets; X2 = retained earnings/total assets;

X3 = earnings before interest and taxes/total assets; X4 = market value of

equity/total assets; X5 = sales/total assets.a The distressed group includes companies that experienced bankruptcy

or liquidation as well as those that received low S&P ratings for their bonds

or stock. The non-distressed group includes companies that were rated by

S&P and did not receive low bond or stock ratings.b p-Value of t-test of differences in variable means between the

distressed and non-distressed groups.

8 The Compustat research file contains companies that were deleted

from the annual industrial file because of bankruptcy (liquidation) and

identifies bankrupt (liquidated) firms with a 02 (03) code for footnote 35.

The files report S&P bond and stock ratings (data items 280 and 282).

Companies whose bonds were rated CCC or below or whose stock was

rated ‘‘lower B’’ or below were included in the distressed sample.9 Companies that maintained codes for data item 280 (282) that were

less than 19 (18) were included in the non-distressed sample. A random

number generator was used to select the companies for the non-distressed

group. Approximately 25% (18%) of the companies for each year in the

1985–1987 (1988–1991) sample were selected. These proportions were

used to: (1) closely equate the number of non-distressed firms in each

sample, and (2) reduce the opportunity for a firm to be selected in multiple

years. Including firms in the non-distressed population that were not rated

by S&P increased the non-distressed group by approximately 500

companies. These firms were not included in the results reported in this

study because we could not assume firms were non-distressed just because

they were not rated by S&P. The accuracy rates of the re-estimated models

using the larger estimation sample were not significantly different from

those reported in this study, however.

10 Minimum and maximum values for certain variables indicated

outliers in the sample. The results reported in this study did not change

when the outliers were omitted, however. Specifically, the p-value for the

X4 variable was affected by outliers, but the coefficients and explanatory

power of the models were not affected when the outliers were removed.

Details of these results are available from the authors.


had not declared bankruptcy. Of the distressed companies,

26 eventually declared bankruptcy after 1987 and prior to

1997. The 1988–1991 sample included 92 bankrupt com-

panies and 56 companies that were financially distressed but

that had not declared bankruptcy. Of the distressed compa-

nies, 18 declared bankruptcy subsequent to 1991 and prior

to 1997. The bankrupt firms were unique for the 1985–1987

and 1988–1991 samples. Twenty-two of the firms that were

distressed in the 1985–1987 sample also appeared in the

distressed group in the 1988–1991 sample.

2.2. Test procedures

We evaluated the classification accuracy of Altman’s Z-

score model using the full 1988–1991 sample, a subset of

the sample containing only bankrupt firms in the distressed

group, and a subset of the sample containing only manu-

facturing firms in both distressed and non-distressed

groups. The Z-scores were derived for each of these

samples using Altman’s coefficients from Eq. (1).11 The

accuracy of the Z-score model was calculated by dividing

the number of firms correctly predicted by the total number

of firms in the sample.

Binomial tests of proportions were used to test the

significance of differences between the accuracies reported

by Altman and those reported in the current study using the

1988–1991 sample. For the binomial test, p1 and p2 are

defined as the proportion of successes (correct predictions)

for two samples, n1 and n2. The test statistic is calculated as

(p1�p2)/sp1�p2, where s is defined as the standard devia-

tion of the binomial probability distribution. The binomial

test is appropriate if nipi and ni(1�pi) are greater than 5.

The classification accuracy of Altman’s model using a

subset of the 1988–1991 sample containing only bankrupt

firms was used to evaluate the model’s ability to assess

financial distress other than bankruptcy. Binomial tests

compared the model’s classification accuracy using the

full 1988–1991 sample to the accuracy using the bank-

ruptcy subset.

The Z-score model’s classification accuracy using a

subset of the 1988–1991 sample containing only manufac-

turing firms was used to evaluate the sensitivity of the

model to non-manufacturing industries. Binomial tests

compared the model’s classification accuracy using the full

1988–1991 sample to the accuracy using the manufacturing

subset of the sample.

To compare results from Altman’s original model with

those from a more recent period, the Z-score model’s

coefficients were re-estimated using the 1985–1987 esti-

mation sample. The coefficients were re-estimated using

the methodology Altman originally employed to derive

his model, discriminant analysis (DA). Arguably, DA is

no longer the prevalent statistical methodology used by

bankruptcy prediction researchers to develop prediction

models.12 The use of DA was necessary in this study so

direct comparisons could be made between the coeffi-

cients in the original and re-estimated Z-score score

models.13

We compared the coefficients of the 1985–1987 model

to those shown in Eq. (1) to test the stationarity of the

model. Also, we compared the magnitude and significance

of the coefficients for the manufacturing-only and bank-

ruptcy-only models to those for the 1985–1987 model to

evaluate whether re-estimations of Altman’s model were

sensitive to industry classifications or financial conditions.

Binomial tests compared the accuracies of the re-estimated

models to those using Altman’s original model.

3. Results

This section reports test results used to evaluate the

generalizability of Altman’s model. These results are di-

vided into two primary categories. The first are those using

coefficients from Altman’s 1968 model. The second are

those using our 1985–1987 estimation sample to recompute

model coefficients.

3.1. Classification accuracy of Altman’s (1968) model

Table 2 reports results of tests of Altman’s (1968)

model. The table contains four panels. Panel A contains

the classification results from Altman’s study. Panel B

contains the classification results using Altman’s model

to predict outcomes for our 1988–1991 sample. The

overall correct classification rate dropped from 83.5% in

Panel A to 57.8% in Panel B, a significant difference at the

0.05 level using the binomial test. Classification rates for

both the distressed and non-distressed groups were sig-

nificantly lower in the 1988–1991 sample than in the

original sample. These results indicate that Altman’s model

is not as useful for predicting financial distress in recent

periods as it was in the 1960s.

11 Firms were classified as distressed if their Z-scores were <2.675

(Altman, 1968). Firms with a 2.675 Z-score had approximately a 50%

chance of being classified as distressed in Altman’s study.

12 See Jones (1987) for detailed discussions of DA and other statistical

methodologies used in bankruptcy prediction research.13 Linear models, such as Eq. (1) derived using DA, assume the

variance–covariance matrices of the distressed and non-distressed groups

are equal. Unequal variance–covariance matrices for the groups suggest

that a quadratic discriminant function may be more suitable for the sample.

Altman’s (1968) study does not report information related to this

assumption. However, prior research suggests that the samples used to

derived bankruptcy prediction models typically violate the equal variance–

covariance matrix assumption (Jones, 1987). The estimation sample used in

this study violated the equal variance–covariance assumption based on

Bartlett’s test of homogeneity. Further analysis indicated no significant

differences between the accuracy rates of the quadratic and linear

discriminant models, however.


The sample used in Panel B includes both bankrupt and

other financially distressed firms, perhaps explaining the

lower classification rates. Panel C includes only bankrupt

firms in the distressed group for the 1988–1991 sample. A

comparison of these results with those in Panel A and Panel

B reveals that the classification rates for the bankrupt firms

were significantly lower in the 1988–1991 sample than in

the original sample. Further, the classification rates for the

bankrupt firm sample were approximately the same as that

for the Panel B sample. These results indicate that Altman’s

model predicts financial distress other than bankruptcy with

the same accuracy as it predicts bankruptcy. Consequently,

the lower accuracy of Altman’s model for the 1988–1991

sample was not due to the inclusion of non-bankrupt firms

in the distressed group.

Panel D of Table 2 reports results for the 1988–1991

sample when the sample is limited to manufacturing firms.

A comparison of these results with those in Panel A reveals

that the prediction accuracy was significantly lower for the

1988–1991 sample than for the original sample. The overall

accuracy for the 1988–1991 sample was 69.1%, compared

to the rate of 83.5% for Altman’s sample. Classification

results for the distressed group were significantly lower for

the 1988–1991 sample. Those for the non-distressed group

were lower for the 1988–1991 sample, but the difference

was not significant at the 0.05 level.

A comparison of Panel D results with those for Panel B

indicates that classification results for the manufacturing

sample were significantly higher than those for the total

1988–1991 sample. These results suggest that Altman’s

model is more useful for predicting financial distress of

manufacturing firms than for predicting financial distress of

non-manufacturing firms.

3.2. Classification accuracy of a re-estimated model

Additional evidence of the stationarity of the Z-score

model was obtained by re-estimating the model’s coeffi-

cients using our 1985–1987 sample. Table 3 reports results

for the re-estimated model. Data are reported for four

models. The first column of coefficients contains those for

Altman’s (1968) model. The second column contains those

for the re-estimation sample from 1985 to 1987. A compar-

ison of these columns reveals several differences in the

coefficients. Most of the coefficients for the 1985–1987

model are lower than those for Altman’s original model, and

most of these changes are quite large, suggesting the model

is not stationary. Differences between the univariate F

statistic for Altman’s original and the 1985–1987 models

reported in Table 3 provide further indication of a statio-

narity problem. The retained earnings/total assets and earn-

ings before interest and taxes/total assets variables exhibit

higher significance levels in the 1985–1987 model than in

Altman’s original model. The market value of equity/book

value of total debt variable has a higher significance level in

the original model, and the working capital/total assets and

sales/total assets variables maintained about the same level

of significance.

Multivariate significance tests of the coefficients for the

1985–1987 sample revealed that only the retained earnings/

total assets and earnings before interest and taxes/total assets

coefficients were significant at the 0.05 level. Altman did

not report the multivariate significance of his tests; however,

he indicated that each ratio provided significant information

in the original Z-score model.

Limiting the 1985–1987 sample to bankrupt firms for

the distressed group or to manufacturing firms for both

distressed and non-distressed groups had relatively little

effect on model coefficients or significance tests. The third

column of numbers in Table 3 reports results for the bank-

ruptcy sample, and the fourth column reports results for the

manufacturing sample. A comparison of these numbers with

the second column reveals the results are similar for most

variables. Coefficients for the working capital/total assets

variable were lower for the bankruptcy and manufacturing

samples than for the total sample of 1985–1987 firms. A

comparison of columns three and four with column one

again indicates that the original model is not stationary, even

if only bankrupt or only manufacturing firms are included in

the sample.

Table 2

Comparisons of classification accuracies using coefficients from Altman’s

(1968) model

Sample Statistic Overall

Distressed

group

Non-distressed

group

Panel A

Altman’s (1968) Accuracya 83.5% 96.0% 78.8%

sample n 91 25 66

Panel B

1988–1991 Accuracya 57.8% 70.9% 55.5%

sample n 979 148 831

Test statisticb 4.748* 2.552* 3.668*

Panel C

Bankruptcy Accuracya 56.1% 68.2% 54.9%

samplec n 972 85 887

Test statisticd 0.779 0.439 0.238

Test statisticb 5.045* 2.621* 3.762*

Panel D

Manufacturing Accuracya 69.1% 69.2% 69.1%

samplec n 547 78 469

Test statisticd 4.283* 0.270 4.741*

Test statisticb 2.755* 2.524* 1.597

a Accuracy rates represent correct classifications using Altman’s (1968)

model coefficients.b Test statistic for binomial tests comparing the accuracy rates to those

in Panel A.c The manufacturing and bankruptcy samples are subsets of the 1988–

1991 sample.d Test statistic for binomial tests comparing the accuracy rates to those

in Panel B.

* Significant at the 0.05 level.


Table 4 reports predictive accuracies using coefficients

estimated from the 1985–1987 model. These coefficients

were used to predict outcomes for the 1988–1991 sample

and can be compared to results in Table 2. The four panels

in Table 4 parallel those in Table 2. Panel A reports the

classification accuracies of Altman’s 1968 model when

used to predict outcomes for the 1988–1991 sample. Panel

B reports the classification accuracies using the 1985–

1987 reestimation model to predict outcomes for the

1988–1991 sample. Classification results for the reestima-

tion sample were significantly higher for the reestimation

model than for Altman’s original model. Binomial test

Table 3

Coefficients for Altman’s (1968) and 1985–1987 re-estimated models

Variables and statistics Altman’s (1968) modela 1985–1987 modelb Bankruptcy-only modelc Manufacturing-only modeld

Working capital/total assets 1.200 0.058 �0.301 �0.386

p-Value 0.831 0.307 0.345

Univariate F 32.66* 39.67* 19.573* 9.67*

Retained earnings/total assets 1.400 1.504 1.599 2.067

p-Value 0.000 0.000 0.000

Univariate F 58.86* 387.37* 369.01* 278.84*

Earnings before interest and taxes/total assets 3.300 2.073 2.627 1.385

p-Value 0.000 0.000 0.019

Univariate F 26.56* 289.23* 309.12* 185.33*

Market value equity/book value debt 0.600 �0.014 �0.033 �0.005

p-Value 0.129 0.001 0.607

Univariate F 33.26* 3.025 11.41* 2.815

Sales/total assets 0.990 �0.058 �0.157 �0.069

p-Value 0.396 0.033 0.557

Univariate F 2.840 0.261 1.050 0.249

p-Value: multivariate significance of the coefficient in the full model. Altman did not report the multivariate significance of his coefficients.

Univariate F: individual discriminating ability of each ratio.a Coefficients and significance levels reported in Altman’s (1968) study (N=66, 33 bankrupt and 33 non-bankrupt firms).b Coefficients estimated using the full 1985–1987 sample (N=972, 824 non-distressed and 148 distressed companies).c Coefficients estimated using a subset of the 1985–1987 sample that included only bankrupt companies in the distressed group (N=910, 824 non-

distressed and 86 distressed firms).d Coefficients estimated using a subset of the 1985–1987 sample that included only manufacturing companies (N=555, 476 non-distressed and 79

distressed firms).


Table 4

Comparisons of the classification accuracy of Altman’s (1968) model and the 1985–1987 re-estimation model

Model Statistic Overall Distressed group Non-distressed group

Panel A

Altman’s (1968) Accuracya 57.8% 70.9% 55.5%

Panel B

1985–1987 Re-estimationb Accuracya 88.1% 54.7% 93.8%

Test statisticc 13.657* 3.702* 15.871*

Panel C

Bankrupt firmsd Accuracya 87.6% 48.6% 94.9%

Test statisticc 13.243* 4.225* 15.989*

Panel D

Manufacturing firmse Accuracya 86.4% 55.4% 92.1%

Test statisticc 12.681* 2.945* 14.871*

a Accuracy rates represent the correct classifications for each model using the 1988–1991 sample.b Model coefficients are reported in Table 3.c Test statistic comparing the re-estimated model’s accuracy rates to those of Altman’s (1968) model.d Model estimated using a subset of the 1985–1987 sample that included only bankrupt firms from the distressed group. Model coefficients are reported

in Table 3.e Model estimated using a subset of the 1985–1987 sample that included only manufacturing firms. Model coefficients are reported in Table 3.



results were significant at the 0.05 level. These results also

hold for Panel C that includes only bankrupt firms in the

nondistressed group and for Panel D that includes only

manufacturing firms in the distressed and nondistressed

groups. The overall classification results for Panel B, C,

and D are similar to those reported by Altman in his 1968

study (see Panel A of Table 2).

A comparison of results for the distressed and non-

distressed groups in the re-estimation model in Panel B of

Table 4 with those of Altman’s original model in Panel A

indicates that the Type I and Type II error rates differ

between the models. Accuracy rates for the distressed group

were higher for Altman’s model than for the re-estimation

model, while accuracy rates for the non-distressed group

were lower for Altman’s model. These results demonstrate

the effect of using proportionate samples of distressed and

non-distressed companies in the re-estimation model. Alt-

man used a matched sample of 33 bankrupt and 33 non-

bankrupt firms and, accordingly, ignored the prior pro-

babilities of group membership. The 1985–1987 models

were developed using proportionate samples of distressed

and non-distressed companies. As a result, the Type I (Type

II) errors for the Altman (1968) model were lower (higher)

than those for the re-estimated models.14 These results hold

for the bankrupt only and manufacturing only samples as

well as for the total sample.

4. Summary

This study evaluated the generalizability of Altman’s

(1968) Z-score model using a proportionate sample of

distressed and non-distressed companies from time periods,

industries, and financial conditions other than those used by

Altman to developed his model. The findings indicated that

the accuracy of Altman’s model declined when applied to

our samples. Altman reported an 83.5% overall accuracy for

his model using a sample from 1958 to 1961. The overall

accuracy for the 1988–1991 sample used in this study was

57.8%. Additionally, the coefficients of Altman’s (1968)

model changed dramatically when re-estimated using a

1985–1987 sample. Thus, it appears the relation between

financial ratios and financial distress changes over time.

Altman’s model was sensitive to industry classifications

in the sample used in this study. The overall accuracy of

the model was significantly higher for manufacturing firms

(69.1%) than for the entire sample (57.8%) that included

non-manufacturing firms. Altman’s model was not sensi-

tive to type of financial distress. The overall accuracy of

the model for bankrupt companies (56.1%) in the 1988–

1991 sample was not significantly different from that of

the entire sample (57.8%) that included other financial

distress situations.

Other results of this study indicate that those who employ

Altman’s Z-score model should re-estimate the model’s

coefficients rather than relying on those reported by Altman

(1968). Because the coefficients are not stable, significantly

better classification results were achieved when the model’s

coefficients were re-estimated using 1985–1987 data than

when the original coefficients were used.

Finally, care should be used in applying Altman’s model

because of the potential underestimation of Type I and

overestimation of Type II errors that result from using

non-proportional samples of bankrupt and non-bankrupt

firms. This problem can be overcome by re-estimating

Altman’s model coefficients using a sample of firms that

approximates the proportions of distressed and non-dis-

tressed firms in the population.

In conclusion, our findings suggest that results of recent

studies that have used Altman’s model to estimate financial

distress of sample firms should be interpreted cautiously.

The ability of the model to accurately classify firms as being

financially distressed is likely to differ considerably from

that assumed by those employing the model.

Acknowledgments

We gratefully acknowledge comments from Mike

Dugan, Rich Houston, Mary Stone, Gary Taylor, and an

anonymous reviewer.

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