Bankruptcy prediction

Bankruptcy prediction

Introduction

Attempts to develop bankruptcy prediction models began seriouslysometime in the late 1960’s and continue through today. At least threedistinct 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 predictionmodels is based on research published by university professors. Commercialbanks, public accounting firms and other institutional entities (bondratings agencies, for example) appear to be the primary beneficiaries ofthis research, since they can use the information to minimize theirexposure 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 andwhy corporations fail has yet been developed. The available statisticalmodels derive merely from the statistical optimization of a set of ratios.As stated by Wilcox, the “lack of conceptual framework results in thelimited 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 decisioncriterion used to evaluate the usefulness of the models has been how wellthey classify a company as bankrupt or non-bankrupt compared to thecompany’s actual status known after-the-fact (that is ex post). Most of thestudies consider a type I error as the classification of a failed companyas healthy, and consider a type II error as the classification of a healthycompany as failed. In general type I errors are considered more costly tomost users than type II errors. The usefulness of fail/nonfail predictionmodels is suggested by Ohlson (Ohlson, J.A., “Financial Ratios and theProbabilistic Prediction of Bankruptcy,” Journal of Accounting Research,

Spring 1980.):

“…real world problems concern themselves with choices which havea richer set of possible outcomes. No decision problem I can think of has apayoff space which is partitioned naturally into the binary statusbankruptcy versus non-bankruptcy…I have also refrained from makinginferences regarding the relative usefulness of alternative models, ratiosand predictive systems… Most of the analysis should simply be viewed asdescriptive statistics – which may, to some extent, include estimatedprediction error-rates – and no “theories” of bankruptcy or usefulness offinancial ratios are tested.”

Subject to the qualifications expressed above, bankruptcyprediction models continue to be used to predict failure.

The early history of researchers’ attempts to classify and predictbusiness failure (and bankruptcy) is well documented in Edward Altman’sseminal 1983 book, Corporate Financial Distress. There appears to be noconsensus on what constitutes business failure. However, most businessesare considered to have failed once they have entered formal bankruptcyproceedings.

A Short Z-Score History

In 1966 Altman selected a sample of 66 corporations, 33 of whichhad filed for bankruptcy in the past 20 years, and 33 of which wererandomly selected from those that had not. The asset size of allcorporations ranged from $1 million to $26 million…approximately $5million to $130 million in 2005 dollars. Altman calculated 22 common financial ratios for all 66corporations. (For the bankrupt firms, he used the financial statementsissued one year prior to bankruptcy.) His goal was to choose a small numberof those ratios that could best distinguish between a bankrupt firm and ahealthy one. To make his selection Altman used the statistical technique ofmultiple discriminant analysis. This approach shows which characteristicsin which proportions can best be used for determining to which of severalcategories a subject belongs: bankrupt versus nonbankrupt, rich versuspoor, 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 highscore implies membership in the other group, and a middling score causesuncertainty as to which group the subject belongs. Finally, to test the model, Altman calculated the Z Scores for newgroups of bankrupt and nonbankrupt firms. For the nonbankrupt firms,however, he chose corporations that had reported deficits during earlieryears. His goal was to discover how well the Z Score model coulddistinguish between sick firms and the terminally ill. Altman found that about 95% of the bankrupt firms were correctlyclassified as bankrupt. And roughly 80% of the sick, nonbankrupt firms werecorrectly classified as nonbankrupt. Of the misclassified nonbankruptfirms, 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 financialratios by an appropriate coefficient and then summing the results. Theratios 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 forall Z Score calculations. The following table shows how these measures are used to calculatethe three versions of the Z Score. The table is explained below. [pic]

In other words, the three Z Score versions (described below) arecalculated 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 theusefulness of the original Z Score measure. One of these ratios is X4, the Market Value of Equity divided byTotal Liabilities. Obviously, if a firm is not publicly traded, its equityhas no market value. So private firms can’t use the Z Score. The other problem is X5, Assets Turnover. This ratio variessignificantly by industry. Jewelry stores, for example, have a low assetturnover while grocery stores have a high turnover. But since the Z Scoreexpects a value that is common to manufacturing, it could be biased in sucha way that a healthy jewelry store looks sick and a sickly grocery storelooks healthy. To deal with these problems, Altman used his original data tocalculate two modified versions of the Z Score, shown above. The Z Score isfor public manufacturing companies; the Z1 Score is for privatemanufacturing companies; and the Z2 is for general use. Therefore, according to the table, if a company’s Z2 score isgreater 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 aformal declaration of bankruptcy in a federal district court. It is insteada measure of how closely a firm resembles other firms that have filed forbankruptcy. It is a measure of corporate financial distress, a measure ofeconomic bankruptcy. How accurately does the Z Score measure economic bankruptcy? Theoriginal model has drawn several statistical objections over the years. Themodel uses unadjusted accounting data; it uses data from relatively smallfirms; and it uses data that today is nearly 60 years old. And yet, despite these concerns, the original Z Score model is thebest-known and most widely used measure of its kind. This measure is farfrom perfect, but it’s easy to calculate in Excel and many users continueto find it useful. At last count, for example, Google offered 308,000 linksto the phrase, “Z Score”. The Z Score model is a tool that can complement your otheranalytical tools. Seldom, however, should you use any of the Z Scoremeasures 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 developedsince the work of Beaver and Altman. Lev (Lev, B. “Financial StatementAnalysis, 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., andHouston, “How to Identify Failing Companies Before It Is Too Late,”Professional Administration, April 1980.), Platt & Platt (Platt, J.D. andPlatt, M.B., “Development of a Class of Stable Predictive Variables: TheCase of Bankruptcy Prediction,” Journal of Business Finance and Accounting,Spring 1990.), Gilbert, Menon, and Schwartz (Gilbert, L.R., Menon, K., andSchwartz, K.B., “Predicting Bankruptcy for Firms in Financial Distress,”Journal of Business Finance and Accounting, Spring 1990), and Koh andKillough (Koh, H.C. and Killough, L.N., “The Use of Multiple DiscriminantAnalysis in the Assessment of the Going-concern Status of an Audit Client,”Journal of Business Finance and Accounting. Spring 1990) among others havecontinued 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 researchas an indicator of financial distress, its strong performance in this studysupports 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 ruinapproach to bankruptcy prediction. Under this approach, bankruptcy isprobable when a company’s net liquidation value (NLV) becomes negative. Netliquidation value is defined as total asset liquidation value less totalliabilities. From one period to the next, a company’s NLV is increased bycash inflows and decreased by cash outflows during the period. Wilcoxcombined the cash inflows and outflows and defined them as “adjusted cashflow.” All other things being equal, the probability of a company’s failure

increases, the smaller the company’s beginning NLV, the smaller thecompany’s adjusted (net) cash flow, and the larger the variation of thecompany’s adjusted cash flow over time. Wilcox uses the gambler’s ruinformula (Feller, 1968) to show that a company’s risk of failure isdependent on 1) the above factors plus 2) the size of the company’sadjusted cash flow “at risk” each period (i.e., the size of the company’sbet).

Using an alleged more robust statistical technique, Vinso extended Wilcox’sgambler’s ruin model to develop a safety index. Based on input concerningthe variability of “expected contribution margin amounts,” the index can beused to predict the point in time when a company’s ruin is most likely tooccur (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 Vinsorichly describe some of the factors which most affect business failure. Forexample, Wilcox states: The (cash) inflow rate … can be increased through higher averagereturn on investment. However, having a major impact here usually requireslong-term changes in strategic position. This is difficult to control overa short time period except by divestitures of peripheral unprofitablebusinesses…The average outflow rate is controlled by managing theaverage growth rate of corporate assets. Effective capital budgeting …requires resource allocation emphasizing those business units which havethe highest future payoff.

The size of the bet is the least understood factor in financial risk. Yetmanagement has substantial control over it. Variability in liquidity flowsgoverns the size of the bet. This variability can be managed throughdividend policy, through limiting earning variability and investmentvariability, and through controlling the co-variation between profits andinvestments…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 andstresses the importance of debt capacity: Before deriving a mathematical model for determining the risk ofruin, it is necessary to describe the process. (First), a firm has somepool of resources at time = 0 of some size U0, which are available toprevent ruin (similar to Wilcox’s beginning NAV). (Then), earnings come to(the) firm from revenue(s)…less the costs incurred in producing (therevenues). There are two types of costs to be considered: variable, whichchange according to the stochastic nature of the revenue sources, and fixedcosts, 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 isavailable to pay fixed costs). If Ut is less than zero, ruin occurs becauseno funds are available to meet unpaid fixed costs…These definitions,however, ignore debt capacity, if available, which must be included as thefirm can use this source without being forced to confront shareholders,creditors, a third party or a bankruptcy court…debt holders or othercreditors will force reorganization if a firm is unable to meet contractualobligations because working capital is too low and the firm cannot obtainmore debt. (Emphasis added) While Wilcox and the other gambler’s ruin researchers have made asubstantial contribution to business failure prediction, they do not appearto have developed the generally accepted conceptual framework of businessfailure 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 NeuralNetworks (ANN) are computers constructed to process information, inparallel, similar to the human brain. ANN’s store information in the form

of patterns and are able to learn from their processing experience. UnlikeMDA and logit analyses, ANN’s impose less restrictive data requirements(the requirement for linearity, for example) and are especially useful inrecognizing and learning complex data relationships. However, ANN’s are“black boxes” in that they do not reveal how they weigh independentvariables. Thus, the individual role each of the various variables playscannot be determined.

In general, the classification accuracy of ANN’s is considered comparableto 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 thetopic updates and expands its discussion of corporate distress andbankruptcy, as well as the related markets dealing with high-yield anddistressed debt, and offers state-of-the-art analysis and research on thecosts of bankruptcy, credit default prediction, the post-emergence periodperformance 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/