FREE ESSAY ON MODELS FOR PREDICTING CORPORATE FINANCIAL DISTRESS

MODELS FOR PREDICTING CORPORATE FINANCIAL DISTRESS

INTRODUCTION 2
MEASURING FINANCIAL HEALTH 2
FINANCIAL DISTRESS 2
FACTORS AFFECTING FINANCIAL HEALTH 3
Capital Structure and Capital Adequacy 3
Operating Cash Flows and Cost Structure 4
Earnings Capacity 4
Liquidity 4
Asset Conversions - "Growing Broke" 5
Asset Utilisation Efficiency/Turnover 5
Strategic Position 5
PREDICTING FINANCIAL DISTRESS 6
FAILURE PREDICTION MODELS 7
Altman's Z Score 8
Logit Analysis: The Model 9
Other Statistical Failure Prediction Models 10
The Gambler's Ruin Models 10
Alternative Models - Artificial Neural Networks 12
CONCLUSION 12
REFERENCES 13
Introduction
A company trying to achieve its business plan faces problems similar to those faced by a
driver embarking on a long trip. The likelihood that car and driver will reach their
destination is dependent on: 
1) how much fuel is in the car's tank upon starting out, 
2) the car's fuel efficiency, 
3) how many service stations will be available to refill the car's fuel tank along the
way and 
4) whether the car's fuel tank is large enough to cover unexpected accidents, delays, and
detours along the way.
Similarly, whether or not a company survives in a highly competitive business environment
is dependent upon: 
1) how financially healthy the corporation is at its inception, 
2) the company's ability (and relative flexibility and efficiency) in creating cash from
its continuing operations, 
3) the company's access to capital markets, and 
4) the company's financial capacity and staying power when faced with unplanned cash
shortfalls.
Measuring Financial Health
There is no single measure of financial health. Ideally, solvency could be measured along
a continuum in the same way that fuel sufficiency can be measured using a car's petrol
gauge. Full health would equate with having a full tank of fuel. Poor health would be
equivalent to showing an empty tank. As healthiness progressively decreased, the solvency
gauge would register movement in the direction of relative insolvency. Ultimately, as
healthiness continues to decline, the solvency gauge would hopefully flash a warning
light.
Since, in the real world, no single measure of financial health exists, proxies that
measure various aspects of solvency are often combined to estimate a company's
healthiness at a point in time. 
Financial Distress
As a financially healthy company becomes more and more financially distressed, it
ultimately enters an area of great danger. Changes to the company's operations and
capital structure (ie. restructuring) must be made to remain healthy. Apple Computers'
attempts in recent years to restructure its operations to survive in the highly
competitive computer hardware business is a good example of a company trying to
dramatically restructure itself in order to maintain solvency. Continued decreases in
financial health ultimately lead to insolvency and then potentially, bankruptcy.
Available evidence suggests many companies do not adequately attempt to resolve their
financial health problems until it is too late to avoid bankruptcy.
Factors Affecting Financial Health
Capital Structure and Capital Adequacy
Companies finance their long-term operations primarily through two sources of capital -
debt and equity. One of the most important financing decisions a company makes is the
proportion of debt to owner's equity in the company's capital structure. Summary measures
of a company's capital structure include the company's debt to equity ratio (D/E) and
debt to total capital ratio (D/(D+E)).
Interest and principal payments on debt must be paid from operations before any payments
can be distributed to equity holders (in the form of dividends or share buy-backs).
Therefore, the interest and principal, which must be paid on debt, are considered
fixed-costs of operations. From an operational point-of-view, the extent of the burden of
these fixed obligations can be measured relative to the company's continuing ability to
pay the fixed obligations. A frequently used measure of a company's ability to cover its
interest payments is its earnings before interest and taxes and before depreciation and
amortisation (EBITDA) to its interest expense. A company is financially distressed
whenever its EBITDA is less than its interest expense. 
-  Financial leverage involves the substitution of fixed-cost debt for owner's equity in
the hope of increasing equity returns. As demonstrated by Higgins and others, financial
leverage improves financial performance when things are going well but worsens financial
performance when things are going poorly. Therefore, increasing the ratio of debt to
equity in a company's capital structure implicitly makes the company relatively less
solvent (on the downside) and more financially risky than a company without debt. 
-  Capital adequacy relates to whether a company has enough capital to finance its
planned future operations. If the company's capital is inadequate, then it must either be
able to: 
1) successfully issue new equity, or 
2) arrange new debt. 
The amount of debt a company can successfully absorb and repay from its continuing
operations is normally referred to as the company's debt capacity. Capital adequacy is
normally evaluated by looking at the company's operational cash flow projections and its
projections of capital needs. 
When companies undertake major new projects or undergo a significant financial
restructuring they often perform financial feasibility studies to determine whether the
company has the financial capacity to undertake the project and whether the company will
be able to repay all future debt payments once the project is built. 
Operating Cash Flows and Cost Structure
All other factors being equal, companies that can consistently generate positive cash
flows from operations will remain relatively more solvent than those that cannot. This
requires that operating cash inflows (collections or sales) consistently exceed operating
cash outflows (costs). Companies which experience erratic cash outflows and inflows are
relatively more risky because they are less likely, in one or more time periods, to be
able to cover fixed expenses/outflows. Companies which have a higher proportion of fixed
costs to variable costs are also relatively more risky and relatively less solvent than
companies with a relatively lower proportion of fixed costs in their operating cost
structure.
Earnings Capacity
All other things being equal, companies with higher relative earnings and higher relative
returns on investment will remain more solvent than their less fortunate competitors. The
most commonly used financial measures of earnings capacity are earnings before interest
and taxes (EBIT) and net income.
Liquidity
Adequate liquidity is a further necessary component of solvency. Frequently used
liquidity measures include: 
a) working capital (current assets minus current liabilities), 
b) current ratio (current assets divided by current liabilities), and 
c) quick ratio (cash, marketable securities and accounts receivable divided by current
liabilities).
To evaluate liquidity, each of the assets and liabilities on a company's balance sheet
should be evaluated for liquidity. Current assets are those which will likely be
converted to cash within one year or less. Current liabilities are those which must be
paid within one year. However, when a company becomes financially distressed, even assets
which are normally considered current assets (accounts receivable and stock, for example)
may become relatively "illiquid". Long-term assets, in general, are far less liquid than
current assets. Some longer-term assets may be very "illiquid". Also, as stated above,
often a company's long-term liabilities can become immediately due and payable if the
company violates contractual debt covenants or other obligations.
Wilcox (1976) argues that net liquidation value provides a solid conceptual basis for
evaluating a company's liquidity. Net liquidation value is defined as total asset
liquidation value less total liabilities. Wilcox (1976) applies what he calls typical
(not definitive) valuation multipliers to balance sheet assets to arrive at
representative asset liquidation values:
-  Cash Equivalents 100%
-  Other Current Assets 70%
-  Long Term Assets 50%
Wilcox (1976) shows that a company becomes bankrupt when net liquidation value is reduced
to zero.
Asset Conversions - "Growing Broke"
Asset and liability conversions are continuously ongoing in any dynamic business.
Operationally, the company is selling its products thereby creating cash inflows.
Alternatively, sales may be made on credit, increasing the company's accounts receivable.
Concurrently, inventories are produced and sold and production and operating expenses are
incurred to continue operations. If a company's inventories and accounts receivable grow
faster than the corresponding growth in the company's sales and accounts payable,
liquidity will be negatively affected.
Strategic asset conversions are also ongoing, but with less regularity. Decisions to
invest in 'bricks and mortar' and other long-term investments are made and debt and
equity are obtained to supply the capital needed to pay for them.
Slowly but surely, companies can 'go broke' when assets are converted to less liquid
forms over a sustained time period. This can happen when the company's assets grow faster
than the company's sales (often the case for many start-up companies). When this happens,
the company becomes more highly leveraged and less solvent.
Similarly, a company whose long term investment decisions do not pay off in terms of
planned operating returns (thus increasing fixed cost structures and decreasing operating
cash flows), will become less solvent.
Asset Utilisation Efficiency/Turnover
Those companies, which survive, use their human and capital assets relatively
efficiently. That is, they have relatively higher returns on investment (ROI) and higher
returns per employee than less successful competitors. They achieve relatively higher
returns through superior asset management (capital and human assets) and through superior
strategic positioning. In the absence of aggressive asset management, companies must
usually resort to wholesale asset divestitures and/or are forced to restructure to fund
their continuing operations. 
Strategic Position
Schoffler (Buzzell and Gale, 1987) and others have documented the high correlation
between positive returns on investment and such factors as: 
1) higher relative market shares, 
2) relative product quality and 
3) lower relative capital intensity. 
Companies that have strong strategic market positions are more likely to experience
higher relative returns on investment than their competitors. These positive returns, in
turn, increase the solvency of the market leaders. Those competitors that have lower
market shares or lower product quality are less likely to achieve industry average
returns and are thus more likely to become less solvent in the future.
Predicting Financial Distress
In America, each year approximately one percent of all firms required to file with the
Securities and Exchange Commission file for bankruptcy. The American Bankruptcy Institute
reports that around 50,000 businesses filed for bankruptcy in 1997. 
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: 
a) statistical models (univariate analysis, multiple discriminate analyses [MDA]), and
conditional logit regression analyses, 
b) gambler's ruin-mathematical/statistical models, and 
c) artificial neural network models. 
Each of these models is discussed below.
Most of the publicly available information regarding prediction models is based on
research published by academics. Commercial banks, public accounting firms and other
institutional entities (ratings agencies, for example) appear to be the primary
beneficiaries of this research, since they can use the information to minimise 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
optimisation of a set of ratios. As stated by Wilcox (1973) 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 generalisation 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 solvent or non-solvent compared to the
company's actual status known after-the-fact. 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/non-fail prediction
models is suggested by Ohlson (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 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. 
Failure Prediction Models
The early history of researchers' attempts to classify and predict business failure (and
bankruptcy) is well documented in Edward Altman's 1983 book, Corporate Financial
Distress. 
Statistical prediction models are more generally better known as measures of financial
distress. Three stages in the development of statistical financial distress models exist:

1. univariate analysis, 
2. multivariate (or multi-discriminate [MDA]) analysis, and 
3. logit analysis. 
Univariate analysis assumes that a single variable can be used for predictive purposes
(Cook and Nelson 1998). The univariate model as proposed by William Beaver achieved a
moderate level of predictive accuracy (Sheppard 1994). Univariate analysis identified
factors related to financial distress, however, it did not provide a measure of the
relevant risk (Stickney 1996). 
In the next stage of financial distress measurement, multivariate analysis (also known as
multiple discriminant analysis or MDA) attempted to overcome the potentially conflicting
indications that may result from using single variables (Cook and Nelson 1998). The
best-known, and most-widely used, multiple discriminant analysis method is the one
proposed by Edward Altman. 
Altman's z-score, or zeta model, combined various measures of profitability or risk. The
resulting model was one that demonstrated a company's risk of bankruptcy relative to a
standard. Altman's initial study proved his model to be very accurate; it correctly
predicted bankruptcy in 94% of the initial sample (Altman 1968). 
Despite the positive results of his study, Altman's model had a key weakness; it assumed
variables in the sample data to be normally distributed. If all variables are not
normally distributed, the methods employed may result in selection of an inappropriate
set of predictors (Sheppard 1994). 
Chistine Zavgren developed a model that corrected for this problem. Her model used logit
analysis to predict bankruptcy. Due to its use of logit analysis, her model is considered
more robust (Lo 1986). Further, logit analysis actually provides a probability (in terms
of a percentage) of bankruptcy. Also, the probability calculated might be considered a
measure of the effectiveness of management (ie. effective management will not lead a
company to the verge of bankruptcy). 
During the 1980s and 1990s, the trend has been to use logit analysis in favour of
multiple discriminant analysis (Stickney 1996). More recently, logit analysis has been
compared to a more advanced analytical tool, neural networks. Research has found that the
approaches perform similarly and should be used in combination (Altman, Marco, and
Varetto 1994).
Altman's Z Score
Based on multiple discriminate analysis (MDA), the model predicts a company's financial
health based on a discriminant function of the form:
Z=0.012X1+0.014X2+0.033X3+0.006X4+0.999X5
Where:
X1=working capital/total assets
X2=retained earnings/total assets
X3=earnings before interest and taxes/total assets
X4=market value of equity/book value of total liabilities
X5=sales/total assets 
The Z-Score model (developed in 1968) was based on a sample composed of 66 manufacturing
companies with 33 firms in each of two matched-pair groups. The bankruptcy group
consisted of companies that filed a bankruptcy petition under Chapter 11 of the United
States bankruptcy act from 1946 through 1965. Based on the sample, all firms having a
Z-Score greater than 2.99 clearly fell into the non-bankruptcy sector, while those firms
having a Z-Score below 1.81 were bankrupt. 
Altman subsequently developed a revised Z-Score model (with revised coefficients and
Z-Score cut-offs) which dropped variables X4 and X5 (above) and replaced them with a new
variable X4 = net worth (book value)/total liabilities. The X5 variable was dropped to
minimise potential industry effects related to asset turnover.
Around 1977, Altman developed jointly with a private financial firm (ZETA Services, Inc.)
a revised seven-variable ZETA model based on a combined sample of 113 manufacturers and
retailers. The ZETA model is allegedly far more accurate in bankruptcy classification in
years 2 through 5 with the initial year's accuracy about equal. However, the coefficients
of the model are not specified (without retaining ZETA Services). The ZETA model is based
on the following variables:
-  return on assets 
-  stability of earnings 
-  debt service 
-  cumulative profitability 
-  liquidity/current ratio 
-  capitalisation (five year average of total market value) 
-  size (total tangible assets) 
Logit Analysis: The Model
Application of the logit model requires four steps. 
1. a series of seven financial ratios are calculated. 
2. each ratio is multiplied by a coefficient unique to that ratio. This coefficient can
be either positive or negative. 
3. the resulting values are summed together (y). 
4. the probability of bankruptcy for a firm is calculated as the inverse of (1 + ey). 
Explanatory variables with a negative coefficient increase the probability of bankruptcy
because they reduce ey toward zero, with the result that the bankruptcy probability
function approaches 1/1, or 100 percent. Likewise, independent variables with a positive
coefficient decrease the probability of bankruptcy (Stickney 1996). Table 1 shows the
financial ratios used in the logit model and their respective coefficients.
TABLE 1 - Financial Ratios used in Logit Model
FINANCIAL RATIO COEFFICIENT
+ 0.23883
Average Inventories/Sales - 0.108
Average Receivables/Average Inventories - 1.583
(Cash + Marketable Securities)/Total Assets - 10.78
Quick Assets/Current Liabilities + 3.074
Income from Continuing Operations/(Total Assets - Current Liabilities) + 0.486
Long-Term Debt/(Total Assets - Current Liabilities) - 4.35
Sales/(Net Working Capital + Fixed Assets) + 0.11
y = Sum of (Coefficient * Ratio)
Probability of Bankruptcy = 1/(1 + ey)
Other Statistical Failure Prediction Models
Many additional bankruptcy prediction models have been developed since the work of Beaver
and Altman. Lev (1974), Deakin (1977), Ohlson (1980), Taffler (1980), Platt & Platt
(1990), Gilbert, Menon, and Schwartz (1990), and Koh and Killough (1990) amongst 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 or
logit models. 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."
The Gambler's Ruin Models
Wilcox (1971 and 1976), Santomero (1977), Vinso (1979) 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 (ie. the size of the
company's bet).
Using a more robust statistical technique, Vinso (1979) 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 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 emphasising 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."
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 or bankruptcy,...debt holders or other creditors will force reorganisation if a
firm is unable to meet contractual obligations because working capital is too low and the
firm cannot obtain more debt."
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 recognising and
learning complex data relationships. 
Recent ANN bankruptcy prediction studies include those of Bell, et al. (1990), Hansen &
Messier (1991), Chung & Tam (1992), Liang, et al. (1992), Tam & Kiang (1992),
Salchenberger (1993), Coats & Fant (1993), Fanning & Cogger (1994), Brockett, et al.
(1994), Boritz, et al. (1995), and Etheridge & Siriam (1995 and 1997). 
Research has shown that ANN's offer a viable alternative to other more traditional
methods of bankruptcy prediction. The ability of the model to learn allows for the
constant re-calibration and validation of the model, which helps increase classification
rates. From a theoretical perspective, ANN's are more desirable because they make fewer
assumptions about the data normality and linear separability. One of the main
disadvantages of ANN's is the inability to assign intuition the network weights. Another
disadvantage is that the model might simply memorise the data as opposed to forming a
general set of classification rules, which can cause estimates on future samples to be
less reliable.
Conclusion
Future research in bankruptcy prediction should analyse the economic and institutional
factors that can impact the reasons for bankruptcy. Jones (1987) indicated that the lack
of homogeneity in the motivation for a bankruptcy filing might complicate the modelling
effort. Although normally motivated by an effort to resolve severe financial problems, a
firm may file for bankruptcy primarily to void a union contract or for other legal
reasons (Jones 1987). 
Another area where models can be improved is in catering for predictor variables other
than financial ratios may prove beneficial. For example, measures of management
experience, management expertise, or other behavioural aspects that impact the operations
of the firm could be significant in a bankruptcy prediction model. Additionally,
including variables that control for a changing economic environment may provide valuable
insights for predicting bankruptcy.
Bibliography
References
Altman, Edward I. Corporate Financial Distress. New York, NY: John Wiley and Sons, 1983.
Altman, Edward I. (1968) Financial Ratios, Discriminate Analysis and the Prediction of
Corporate Bankruptcy, The Journal of Finance.
Altman, Edward I. Homepage of Professor Edward I. Altman, New York, NY: Stern School of
Business. Available at www.stern.nyu/~ealtman. 
Altman, Edward I, Giancarlo Marco, and Franco Varetto (1994) Corporate Distress
Diagnosis: Comparisons Using Linear Discriminant Analysis and Neural Networks (the
Italian Experience), The Journal of Banking and Finance.
Altman, Edward I. and Thomas P. McGough (1974) Evaluation of a Company as a Going
Concern, The Journal of Accountancy.
Beaver, W., 1967, Financial Ratios as Predictors of Failures, in Empirical Research in
Accounting, Journal of Accounting Research.
Begley, J., Ming, J., Watts, S., 1997,Bankruptcy Classification Errors in the 1980s: An
Empirical Analysis of Altman's and Ohlson's Models, Review of Accounting Studies. 
Bell, T.B., G.S. Ribar and J. Verchio, 1990, Neural Nets Versus Logistic Regression: A
Comparison of Each Model's Ability to Predict Commercial Bank Failures,"
Boritz, J.E., D.B. Kennedy and A.M. Albuquerque, 1995, Predicting Corporate Failure Using
a Neural Network Approach, Intelligent Systems in Accounting, Finance and Management.
Brockett, P.L., W.W. Cooper, L.L. Golden and U. Pitaktong, 1994, A Neural Network Method
for Obtaining an Early Warning of Insurer Insolvency. The Journal of Risk and Insurance.

Buzzell, R.D., Gale, B.T., 1987, The PIMS Principles Linking Strategy to Performance, New
York: The Free Press.
Chung, H.M. and K. Y. Tam, 1992, A Comparative Analysis of Inductive-Learning Algorithms,
Intelligent Systems in Accounting, Finance and Management.
Coats, P.K. and L.F. Fant, 1993, Recognizing Financial Distress Patterns Using a Neural
Network Tool, Financial Management.
Cook, Roy A. and Jeryl L. Nelson. A Conspectus of Business Failure Forecasting, Available
at www.sbaer.uca.edu/docs/proceedings/88sbi291.txt
Deakin, E., Business Failure Prediction: An Empirical Analysis,, 1977, in E. Altman and
A. Sametz, eds., Financial Crises: Institutions and Markets in a Fragile Environment, New
York: Wiley.
Etheridge, H.L. and R.S. Sriram, 1995, A Neural Network Approach to Financial Distress
Analysis, Advances in Accounting Information Systems.
Fanning, K. and K.O. Cogger, 1994, A Comparative Analysis of Artificial Neural Networks
Using Financial Distress Prediction, Intelligent Systems in Accounting, Finance and
Management.
Gilbert, L.R., Menon, K., and Schwartz, K.B., 1990, Predicting Bankruptcy for Firms in
Financial Distress, Journal of Business Finance and Accounting.
Hansen, J.V. and W.F. Messier, 1991,Artificial Neural Networks: Foundations and
Application to a Decision Problem, Expert Systems with Applications.
Jones, F. L. 1987. Current Techniques in Bankruptcy Prediction. Journal of Accounting
Literature.
Koh, H.C. and Killough, L.N., 1990, The Use of Multiple Discriminant Analysis in the
Assessment of the Going-concern Status of an Audit Client, Journal of Business Finance
and Accounting. 
Lev, B., 1974, Financial Statement Analysis, A New Approach. Englewood Cliffs, N.J.:
Prentice-Hall.
Liang, T.P., J.S. Chandler, I. Han and J. Roan, 1992, An Empirical Investigation of Some
Data Effects on the Classification Accuracy of Probit, ID3, and Neural Networks,
Contemporary Accounting Research.
Lo, Andrew W.,1986 Logit Versus Discriminant Analysis: A Specification Test and
Application to Corporate Bankruptcies, Journal of Econometrics 
Ohlson, J.A., 1980 Financial Ratios and the Probabilistic Prediction of Bankruptcy,
Journal of Accounting Research.
Platt, J.D. and Platt, M.B., 1990, Development of a Class of Stable Predictive Variables:
The Case of Bankruptcy Prediction, Journal of Business Finance and Accounting.
Salchenberger, L.M., E.M. Cinar and N.A. Lash, 1992 Neural Networks: A New Tool for
Prediction Thrift Failures, Decision Sciences. 
Santomero, A.M. and J.D. Vinso, 1977, Estimating the Probability of Failure for
Commercial Banks and the Banking System, Journal of Banking and Finance.
Sheppard, Jerry Paul.,1994 The Dilemma of Matched Pairs and Diversified Firms in
Bankruptcy Prediction Models, The Mid-Atlantic Journal of Business 
Stickney, Claude P., 1996 Financial Reporting and Statement Analysis. 3rd Edition. Ft.
Worth, TX: The Dryden Press.
Taffler, R., and Houston, 1980, How to Identify Failing Companies Before It Is Too Late,
Professional Administration.
Tam, K.Y. and M.Y. Kiang, July 1992, Managerial Applications of Neural Networks: The Case
of Bank Failure Predictions, Management Science..
Vinso, J.D., 1979, A Determination of the Risk of Ruin, Journal of Financial and
Quantitative Analysis.
Wilcox, J.W., 1971,A Gambler's Ruin Prediction of Business Failure Using Accounting Data,
Sloan Management Review, Vol. 12.
Wilcox, J.W., 1976, The Gambler's Ruin Approach to Business Risk, Sloan Management
Review.
Wilcox, J.W., 1973, A Prediction of Business Failure Using Accounting Data, Journal of
Accounting Research, Vol. 11.
Zavgren, Christine V., 1985 Assessing the Vulnerability to Failure of American Industrial
Firms: A Logistic Analysis, Journal of Business Finance and Accounting.