Bankruptcy prediction

Introduction

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 example) appear to be the primary beneficiaries of

this research, since tthey 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 geeneralization 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). Mo

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 the relative usefulness of alternative models, ratios

and predictive systems. Most of the analysis shhould 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 h

proceedings.

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 which 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 e

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 wh

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.

[pic]

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 companies; and the Z2 is for general use.

Therefore, according to the table, if a company’s Z2 score is

greater than 2.60, it’s currently safe from bankruptcy. If the score is

less than 1.10, it’s headed for bankruptcy. Otherwise, it’s in a gray area.

How to Interpret the Z Score

The Z Score is not intended to predict when a firm will file a

formal declaration of bankruptcy in a federal district court. It is instead

a measure of how closely a firm resembles other firms that have filed for

bankruptcy. It is a measure of corporate financial distress, a measure of

economic bankruptcy.

How accurately does the Z Score measure economic bankruptcy? The

original model has drawn several statistical objections over the years. The

model uses unadjusted accounting data; it uses data from relatively small

firms; and it uses data that today is nearly 60 years old.

And yet, despite these concerns, the original Z Score model is the

best-known and most widely used measure of its kind. This measure is far

from perfect, but it’s easy to calculate in Excel and many users continue

to find it useful. At last count, for example, Google offered 308,000 links

to the phrase, “Z Score”.

The Z Score model is a tool that can complement your other

analytical tools. Seldom, however, should you use any of the Z Score

measures as your only means of analysis.

In other words:

• Z-SCORE ABOVE 3.0 – The company is safe based on these

financial figures only.

• Z-SCORE BETWEEN 2.7 and 2.99 – On Alert. This zone is an area

where one should exercise caution.

• Z-SCORE BETWEEN 1.8 and 2.7 – Good chances of the company

going bankrupt within 2 years of operations from the date of

financial figures given.

• Z-SCORE BELOW 1.80- Probability of Financial embarassment is

very high.

Other Statistical Failure Prediction Models

Many additional bankruptcy prediction models have been developed

since the work of Beaver and Altman. Lev (Lev, B. “Financial Statement

Analysis, A New Approach,” Englewood Cliffs, N.J.: Prentice-Hall, 1974.) ,

Deakin (Deakin, E.B., “A Discriminant Analysis of Predictors of Business

Failure,” Journal of Accounting Research, March, 1972.), Ohlson (Ohlson,

J.A., “Financial Ratios and the Probabilistic Prediction of Bankruptcy,”

Journal of Accounting Research, Spring 1980.), Taffler (Taffler, R., and

Houston, “How to Identify Failing Companies Before It Is Too Late,”

Professional Administration, April 1980.), Platt & Platt (Platt, J.D. and

Platt, M.B., “Development of a Class of Stable Predictive Variables: The

Case of Bankruptcy Prediction,” Journal of Business Finance and Accounting,

Spring 1990.), Gilbert, Menon, and Schwartz (Gilbert, L.R., Menon, K., and

Schwartz, K.B., “Predicting Bankruptcy for Firms in Financial Distress,”

Journal of Business Finance and Accounting, Spring 1990), and Koh and

Killough (Koh, H.C. and Killough, L.N., “The Use of Multiple Discriminant

Analysis in the Assessment of the Going-concern Status of an Audit Client,”

Journal of Business Finance and Accounting. Spring 1990) among others have

continued to refine the development of multivariate statistical models.

Almost all of these traditional models have been either matched-pair multi-

discriminate models (such as Altman’s) or logit models (such as Ohlson’s).

A 1997 study by Begley, Ming and Watts concludes:

”Given that Ohlson’s original model is frequently used in academic research

as an indicator of financial distress, its strong performance in this study

supports its use as a preferred model.”

Alternative Failure Prediction Models – The “Gambler’s Ruin” Models

Wilcox, Santomero, Vinso and others have adapted a gambler’s ruin

approach to bankruptcy prediction. Under this approach, bankruptcy is

probable when a company’s net liquidation value (NLV) becomes negative. Net

liquidation value is defined as total asset liquidation value less total

liabilities. From one period to the next, a company’s NLV is increased by

cash inflows and decreased by cash outflows during the period. Wilcox

combined the cash inflows and outflows and defined them as “adjusted cash

flow.” All other things being equal, the probability of a company’s failure

increases, the smaller the company’s beginning NLV, the smaller the

company’s adjusted (net) cash flow, and the larger the variation of the

company’s adjusted cash flow over time. Wilcox uses the gambler’s ruin

formula (Feller, 1968) to show that a company’s risk of failure is

dependent on 1) the above factors plus 2) the size of the company’s

adjusted cash flow “at risk” each period (i.e., the size of the company’s

bet).

Using an alleged more robust statistical technique, Vinso extended Wilcox’s

gambler’s ruin model to develop a safety index. Based on input concerning

the variability of “expected contribution margin amounts,” the index can be

used to predict the point in time when a company’s ruin is most likely to

occur (called first passage time).

The statistics used in gambler’s ruin approaches are somewhat formidable

(especially to the average business reader). However, both Wilcox and Vinso

richly describe some of the factors which most affect business failure. For

example, Wilcox states:

The (cash) inflow rate . can be increased through higher average

return on investment. However, having a major impact here usually requires

long-term changes in strategic position. This is difficult to control over

a short time period except by divestitures of peripheral unprofitable

businesses.The average outflow rate is controlled by managing the

average growth rate of corporate assets. Effective capital budgeting .

requires resource allocation emphasizing those business units which have

the highest future payoff.

The size of the bet is the least understood factor in financial risk. Yet

management has substantial control over it. Variability in liquidity flows

governs the size of the bet. This variability can be managed through

dividend policy, through limiting earning variability and investment

variability, and through controlling the co-variation between profits and

investments.True earnings smoothing is attained by control of exposure to

volatile industries, diversification, and improved strategic position.

(Emphasis added)

Vinso supports Wilcox’s emphasis on cash flow processes and

stresses the importance of debt capacity:

Before deriving a mathematical model for determining the risk of

ruin, it is necessary to describe the process. (First), a firm has some

pool of resources at time = 0 of some size U0, which are available to

prevent ruin (similar to Wilcox’s beginning NAV). (Then), earnings come to

(the) firm from revenue(s).less the costs incurred in producing (the

revenues). There are two types of costs to be considered: variable, which

change according to the stochastic nature of the revenue sources, and fixed

costs, which do not vary with revenue but are a function of the period. So,

revenue less variable costs.can be defined as variable profit (which is

available to pay fixed costs). If Ut is less than zero, ruin occurs because

no funds are available to meet unpaid fixed costs.These definitions,

however, ignore debt capacity, if available, which must be included as the

firm can use this source without being forced to confront shareholders,

creditors, a third party or a bankruptcy court.debt holders or other

creditors will force reorganization if a firm is unable to meet contractual

obligations because working capital is too low and the firm cannot obtain

more debt. (Emphasis added)

While Wilcox and the other gambler’s ruin researchers have made a

substantial contribution to business failure prediction, they do not appear

to have developed the generally accepted conceptual framework of business

failure that had been hoped for by Wilcox.

Alternative Models – Artificial Neural Networks

Since 1990, another promising approach to bankruptcy prediction,

based on the use of neural networks, has evolved. Artificial Neural

Networks (ANN) are computers constructed to process information, in

parallel, similar to the human brain. ANN’s store information in the form

of patterns and are able to learn from their processing experience. Unlike

MDA and logit analyses, ANN’s impose less restrictive data requirements

(the requirement for linearity, for example) and are especially useful in

recognizing and learning complex data relationships. However, ANN’s are

“black boxes” in that they do not reveal how they weigh independent

variables. Thus, the individual role each of the various variables plays

cannot be determined.

In general, the classification accuracy of ANN’s is considered comparable

to logit and MDA models.

[pic]

Altman, Edward I. / Hotchkiss, Edith

Corporate Financial Distress and Bankruptcy

Predict and Avoid Bankruptcy, Analyze and Invest in Distressed Debt

Short description:

This Third Edition of the most authoritative finance book on the

topic updates and expands its discussion of corporate distress and

bankruptcy, as well as the related markets dealing with high-yield and

distressed debt, and offers state-of-the-art analysis and research on the

costs of bankruptcy, credit default prediction, the post-emergence period

performance of bankrupt firms, and more.

[pic]Edward I. Altman

Essay

Bankruptcy prediction

Author:

Elvyra Sabaliauskaitė

ĮV-05/1

Content:

• Introduction

A Short Z-Score History

The Z Score Ingredients

Reasons for Multiple Versions

How to Interpret the Z Score

• Other Statistical Failure Prediction Models

• Alternative Failure Prediction Models – The “Gambler’s Ruin”

Models

• Alternative Models – Artificial Neural Networks

Sources:

http://www.solvency.com/

http://www.valuebasedmanagement.net/

http://books.global-investor.com/