Last Updated 07 Jul 2020

Analysis Of The Three Financial Models

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Bankruptcy refers to the state of an individual who is unable to pay his or her debts and against whom a bankruptcy order has been made by a court. Such orders deprive bankrupts of their property, which is then used to pay their debts. Bankruptcy proceedings are started by a petition, which may be presented to the court by (1) a creditor or creditors; (2) a person affected by a voluntary arrangement to pay debts set up by the debtor under the Insolvency Act 1986; (3) the Director of Public Prosecutions; or (4) the debtor. (Smullen and Hand, 2003).

If we assume that a corporation is a separate legal entity thus qualifying as a legal person, we can adopt the above definition to define bankruptcy in the context of the corporation or corporate bankruptcy as the state of a corporation that is unable to pay its debts and against which bankruptcy order has been made by a court. (Smullen and Hand, 2003).

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Analysis of the models for predicting bankruptcy.

There are three main approaches to predicting bankruptcy which include: accounting analytical approach, option theoretical approach and the statistical approach. Becchetti and Sierra (2002: p. 2100).  Under the statistical approach corporate failure risk is analyzed through four widely known methods which make use of balance sheet ratios: linear or quadratic discriminate analysis, logistic regression analysis, probit regression analysis and neural network analysis.

For the purposes of this paper we will limit our analysis to three basic financial models, which include the Z-Score model, the discriminant model and the Black-Scholes-Merton Probability. We also describe the application of these models in corporations.

1. The Z-Score Bankruptcy Prediction Model

The Z-score prediction model was developed by Altman in 1968. (Grice and Ingram, 2001: p. 53). The Z-score model applies multivariate discriminant analysis (MDA) and employs financial ratios as input variables to predict financial distress. (Tzeng et al, 2007: p. 297). According to Grice and Ingram (2001: p. 53), Altman (1968) used a sample of 33 non-bankrupt manufacturing firms from 1946-1965. Grice and Ingram (2001) assert that despite the fact that the z-score model exhibit high accuracy rates using both estimation and hold-out samples, (95% and 84%), its generalizability to industries and periods outside of those in the original sample has received little attention.

This model has be widely used in a variety of industries to evaluate financial conditions of firms and it is continuously being used in many business situations including bankruptcy prediction and other financial stress conditions. Grice and Ingram (2001) carried out a test on the z-score model based three basic tests which include the model’s ability to predict bankruptcy today as opposed to periods in which it was developed, the usefulness of the model in predicting bankruptcy in non-manufacturing as well as manufacturing firms and its ability to predict bankruptcy in financial stress conditions other than bankruptcy.

Their findings show that although the model is useful in predicting bankruptcy as well as other financial conditions, the models accuracy is significantly lower in recent periods than that reported in the original work by Altman (1968).Grice and Ingram (2001) also find significant differences in the model’s coefficients from those reported by Altman. Based on these findings, Grice and Ingram (2001) suggest that better accuracy can be achieved by re-estimating the model coefficients using estimation from periods close to test periods. In addition Grice and Altman (2001) find that the including non-manufacturing firms in the sample, further weakens the accuracy of the model.

1.1 Application of the Z-Score model

Commercial banks use the model as part of the periodic loan review process; investment bankers use the model in security and portfolio analysis. It 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 (Grice and Ingram, 2001: p. 53).

2. The Black-Scholes-Merton Model.

According to Reisz and Perlich (2007) following from Black and Scholes (1973) and Merton (1974), the common stock of a firm can be seen as a standard call option on the underlying assets of the firm. It is assumed that shareholders have sold the corporation to creditors, and hold the option of buying it back by paying face value (plus interest) of their debt obligations. (Reisz and Perlich, 2007: p. 2). On the other hand, using put/call parity, we can see shareholders as holding the firm’s assets (bought after borrowing money from creditors) as well as a put option with exercise price equal to the face value equal to value of debt.

(Reisz and Perlich, 2007: p. 2). In the event where the where the firm value is below the exercise price, that is, where the price of the firm is below the face value of the debt at maturity, shareholders can freely work walk away without repaying their debt obligations. (Reisz and Perlich, 2007: p. 2). This is similar to selling the firm to the bondholers at the face value of the debt. (Reisz and Perlich, 2007: p. 2). Reisz and Perlich, (2007: p. 2) asserts that such an equity-based valuation model can lead to better bankruptcy predictions.

In a study by Hillegeist et al. (2004), it was found that the probabilities of bankruptcy backed out from the a Black-Scholes-Merton structural model are up to 14 times more informative that ones inferred from accounting-based statistics such as the Altman (1968) Z-score. (Reisz and Perlich, 2007: p. 2). However despite the merits of this Black-Scholes-Merton model, it does not provide any rationale for observed managerial (bounded) risk choices. (Reisz and Perlich, 2007: p. 3). In addition, probabilities of default (PDs) coming from this framework are miscalibrated. (Reisz and Perlich, 2007: p. 3).

3. The Mutiple Discriminant Model

Multiple discriminant analysis (MDA) is a statistical technique employed in the classification of an observation into one of several a priori groupings, dependent upon the observation’s individual characteristics. It is primarily useful in the classification and/or prediction in problems where the dependent variable appears in qualitative form for example, male or female, bankrupt or non-bankrupt. Therefore the first step is to establish explicit group classifications. The number of original groupings may be two or more.

The MDA model is advantageous in that it considers the entire profile of characteristics common to the relevant firms, as well as the interaction of these properties. Conversely, a univariate study can only consider the measurement used for grouping assignments one at a time. Another important advantage of the MDA model is the reduction of the analyst’s space dimensionality.  When analysing a comprehensive list of financial ratios in assessing a firm’s bankruptcy potential, there is reason to believe that some of the measurements will have a high degree of collinearity or correlation with each other. (Altman, 1968).

3.1 Application of Multiple Discriminant Model

Following its first application in the 1930s, the MDA model has been used in many studies and disciplines. In its earlier days it was used only in Biology and behavioural sciences. Today, the model has been applied successfully in financial problems such as credit evaluation and investment classification. For example, Walter made use of the model to classify high and low price earnings ratio firms, and Smith applied the model in the classification of firms into standard investment categories.


A market-based framework for bankruptcy prediction. Alexander S. Reisz and Claudia Perlich. Journal of Financial Stability, 2007, Pages 1-47. A real-valued genetic algorithm to optimize the parameters of support vector machine for predicting bankruptcy. Chih-Hung Wu Gwo-Hshiung Tzeng Yeong-Jia Goo  Wen-Chang Fang. Expert Systems with Applications Volume 32, 2007 Pages 397–408 "Bankruptcy"  A Dictionary of Finance and Banking. John Smullen and Nicholas Hand. Oxford University Press 2005. Oxford Reference Online. Oxford University Press.

Bankruptcy risk and productive efficiency in manufacturing firms. Leonardo Becchetti and Jaime Sierra Journal of Banking & Finance, Volume 27, Issue 11, November 2003, Pages 2099-2120

Tests of the generalizability of Altman’s bankruptcy prediction model. John Stephen Grice and Robert W. Ingram. Journal of Business Research Volume 54, 2001 Pages 53-61.

Financial Ratios, Discriminant Analysis and the Prediction of Corporate Bankruptcy. Edward I Altman. Journal of Finance, Volume 27, Issue 4, September 1968, Pages 589-689.

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