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Bankruptcy prediction

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Bankruptcy prediction

Bankruptcy prediction


Attempts to develop bankruptcy prediction models began seriously

sometime in the late 1960’s and continue through today. At least three

distinct types of models have been used to predict bankruptcy:

• statistical models (primarily, multiple discriminate analyses-

MDA), and conditional logit regression analyses,

• gambler’s ruin-mathematical/statistical models,

• artificial neural network models.

Most of the publicly available information regarding prediction

models is based on research published by university professors. Commercial

banks, public accounting firms and other institutional entities (bond

ratings agencies, for eexample) appear to be the primary beneficiaries of

this research, since they can use the information to minimize their

exposure to potential client failures.

While continuing research has been ongoing for almost thirty years,

it is interesting to note that no unified well-specified theory of how and

why corporations fail has yet been developed. The available statistical

models derive merely from the statistical optimization of a set of ratios.

As stated by Wilcox, the „lack of conceptual framework results in the

limited amount of available data on bankrupt firms being statistically

‘used up’ by the search before a useful generalization emerges.“

How useful are these models? Almost universally, the decision

criterion used to evaluate the usefulness of the models has been how well

they classify a company as bankrupt or non-bankrupt compared to the

company’s actual status known after-the-fact (that is ex post). Most of the

studies consider a type I error as the classification of a failed company

as healthy, and consider a type II error as the classification of a healthy

company as failed. In general type I errors are considered more costly to

most users than type II errors. The usefulness of fail/nonfail prediction

models is suggested by Ohlson (Ohlson, J.A., „Financial Ratios and the

Probabilistic Prediction of Bankruptcy,“ Journal of Accounting Research,

Spring 1980.):

“.real world problems concern themselves with choices which have

a richer set of possible outcomes. No decision problem I can think of has a

payoff space which is partitioned naturally into the binary status

bankruptcy versus non-bankruptcy.I have also refrained from making

inferences regarding tthe relative usefulness of alternative models, ratios

and predictive systems. Most of the analysis should simply be viewed as

descriptive statistics – which may, to some extent, include estimated

prediction error-rates – and no „theories“ of bankruptcy or usefulness of

financial ratios are tested.”

Subject to the qualifications expressed above, bankruptcy

prediction models continue to be used to predict failure.

The early history of researchers’ attempts to classify and predict

business failure (and bankruptcy) is well documented in Edward Altman’s

seminal 1983 book, Corporate Financial Distress. There appears to be no

consensus on what constitutes business failure. However, most businesses

are considered to have failed once they have entered formal bankruptcy


A Short Z-Score History

In 1966 Altman selected a sample of 66 corporations, 33 of which

had filed for bankruptcy in the past 20 years, and 33 of which were

randomly selected from those that had not. The asset size of all

corporations ranged from $1 million to $26 million.approximately $5

million to $130 million in 2005 dollars.

Altman calculated 22 common financial ratios for all 66

corporations. (For the bankrupt firms, he used the financial statements

issued one year prior to bankruptcy.) His goal was to choose a small number

of those ratios that could best distinguish between a bankrupt firm and a

healthy one.

To make his selection Altman used the statistical technique of

multiple discriminant analysis. This approach shows which characteristics

in which proportions can best be used for determining to which of several

categories a subject belongs: bankrupt versus nonbankrupt, rich versus

poor, young versus old, and so on.

The advantage to MDA is that many characteristics can be combined

into a single score. A low score implies membership in one group, a high

score implies membership in the other group, and a middling score causes

uncertainty as to wwhich group the subject belongs.

Finally, to test the model, Altman calculated the Z Scores for new

groups of bankrupt and nonbankrupt firms. For the nonbankrupt firms,

however, he chose corporations that had reported deficits during earlier

years. His goal was to discover how well the Z Score model could

distinguish between sick firms and the terminally ill.

Altman found that about 95% of the bankrupt firms were correctly

classified as bankrupt. And roughly 80% of the sick, nonbankrupt firms were

correctly classified as nonbankrupt. Of the misclassified nonbankrupt

firms, the scores of nearly three fourths of these fell into the gray area.

The Z Score Ingredients

The Z Score is calculated by multiplying each of several financial

ratios by an appropriate coefficient and then summing the results. The

ratios rely on these financial measures:

• Working Capital is equal to Current Assets minus Current Liabilities.

• Total Assets is the total of the Assets section of the Balance Sheet.

• Retained Earnings is found in the Equity section of the Balance Sheet.

• EBIT (Earnings Before Interest and Taxes) includes the income or loss

from operations and from any unusual or extraordinary items but not

the tax effects of these items. It can be calculated as follows: Find

Net Income; add back any income tax expenses and subtract any income

tax benefits; then add back any interest expenses.

• Market Value of Equity is the total value of all shares of common and

preferred stock. The dates these values are chosen need not correspond

exactly with the dates of the financial statements to which the market

value is compared.

• Net Worth is also known as Shareholders’ Equity or, simply, Equity. It

is equal to Total Assets minus Total Liabilities.

• Book Value of Total Liabilities is the sum of all current and long-

term liabilities from the Balance Sheet.

• Sales includes other income normally categorized as revenues in the

firm’s Income Statement.

Use balance sheet figures from the end of the reporting period for

all Z Score calculations.

The following table shows how these measures are used to calculate

the three versions of the Z Score. The table is explained below.


In other words, the three Z Score versions (described below) are

calculated as follows:

• Z = 1.2*X1 + 1.4*X2 + 3.3*X3 + .6*X4 + X5


• Z1 = .717*X1 + .847*X2 + 3.107*X3 + .42*X4A + .998*X5


• Z2 = 6.56*X1 + 3.26*X2 +

6.72*X3 + 1.05*X4A

Reasons for Multiple Versions

Two of the ratios shown in the figure have tended to limit the

usefulness of the original Z Score measure.

One of these ratios is X4, the Market Value of Equity divided by

Total Liabilities. Obviously, if a firm is not publicly traded, its equity

has no market value. So private firms can’t use the Z Score.

The other problem is X5, Assets Turnover. This ratio varies

significantly by industry. Jewelry stores, for example, have a low asset

turnover while grocery stores have a high turnover. But since the Z Score

expects a value that is common to manufacturing, it could be biased in such

a way that a healthy jewelry store looks sick and a sickly grocery store

looks healthy.

To deal with these problems, Altman used his original data to

calculate two modified versions of the Z Score, shown above. The Z Score is

for public manufacturing companies; the Z1 Score is for private

manufacturing ...

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