Does Altman Z-Score model accurately predict bankruptcy?

Prof. Dr. Seema Sharma
Associate Professor (Finance)

Contextual discussion:-

There are various ways to assess financial condition of a firm. Choice of financial technique depends upon the purpose for which the assessment activity is done. It aims at achieving right level of complexity to decipher right kind of information for firm’s stakeholders. It may be for any of the stakeholders of the firm – business and corporate manager; sponsors and financial institution; investors; and prospective employees.

Financial ratios are the most extensively used tools for trend analysis, cross-sectional analysis and comparative analysis; and are categorised under various indicators. They also work as input data of more complex mathematical models, such as Du Pont model for decomposition, diagnostic model for creditworthiness and predictive models for bankruptcy.

In the Indian context also, many researchers have developed various models to predict bankruptcy in various sectors. These analyses are still evolving and due to lack of availability of data of the distressed companies, the empirical study and its analysis is still a challenge.

There are many univariate methods pioneered by Beaver (1966) and Multi Discriminant Analysis (MDA) techniques by Altman (1968) to assess the firm, but MDA has the advantage of considering an entire profile of characteristics common to the relevant firms, as well as interaction of these properties. A univariate study, on the other hand, can only focus on measurements of one set of assignments at a time. Another advantage of MDA is the reduction of analyst’s space dimensionally. Therefore the analysis later transforms into its simple one dimension.

The discriminant function, of the form Z = V1X1 + V2X2 + V3X3 + ……… + VnXn transforms the individual values to a single discriminate score or Z value.

Where, Vn = discriminant coefficient and Xn = independent variables.

Hence combination of ratios can be analysed together in order to remove possible ambiguities and misclassifications observed in traditional ratio studies.

Components used in the model:-

Original Z-Score model (Altman, 1968) for public firms classified the variables into five standard categories: liquidity, profitability, leverage, solvency and activity. From initial list of 22 indicators, Altman chose 5 because they could predict corporate health very well.

Z = 0.012 X1 + 0.014 X2 + 0.033 X3 + 0.006 X4 + 0.999 X5


X1 – working capital over total assets (WC/ TA)

Working capital to total assets ratio measures firm’s liquid assets compared to its size.

X2 ­– retained earnings over total assets (RE/ TA)

Retained earnings is a measure that represents a firm’s total reinvestment earnings for its entire life cycle. Here, firm’s age is implicitly a part of this ratio. A newer firm might not reflect a positive ratio as time for accumulating profit would be lesser.

X3 – earnings before interest and tax over total assets (EBIT/ TA)

This ratio is a measure of the productivity of firm’s assets, eliminating factors such as taxes and leverages, because the firm bases its whole existence on return on its assets. This ratio is particularly suited to analyse corporate bankruptcy.

X4 – market capitalisation over total liabilities (MVC/ TL)

This ratio indicates how much firm’s assets may be impaired if value of debt exceeds the value of assets. For listed companies, market value of ordinary and preferred share or market capitalisation is used, but for private enterprises, accounting value of share capital is used. This ratio considers market price, which is neglected by most bankruptcy research models.

X5 – sales over total assets (S/ TA)

Sales over total assets is a standard financial ratio illustrating the ability of firm’s assets to generate sales. This measures firm’s ability to cope with competitive conditions.

Over the years, many researchers have found their own convenient changes in formula suggested by Altman. Researchers have suggested their own reason to change the weights given to each variable using discriminate function, based on individual measurements for firms.

Adapting the model for private firm:-

Altman’s formula was limited in use for public enterprises only, however, auditors could replace market value of a share to book value of share and recalculate the value in case of X4. But in 1983, Altman himself suggested the new formulae with changed coefficients. Hence the result of the revalued Z- Score model with new X4 variable is:

Z’ = 0.717 X1 + 0.847 X2 + 3.107 X3 + 0.42 X4 + 0.998 X5

Where, X4 = book value of equity/ book value of total liabilities. Here, the other variables remained the same as those in original (1968) Z-Score.

Adapting the model for Non-Manufacturing organisations:-

The modification of Z-score model was suggested by Altman. The results were identical to the revised five- variable model. This modified Z”-score model analysed the characteristics and accuracy of a model without sales/ total assets.

Z” = 6.56 X1 + 3.26 X2 + 6.72 X3 + 1.05 X4

This revised Z” – score model is also useful within an industry where provisions of finances differ greatly among firms and adjustments like lease capitalisation are not made.

Adapting the model for firms in emerging markets:-

Altman, Hatzell and Peck applied this expanded Z’-score model to Mexican companies holding euro bonds denominated in US dollars, in 1995. To deal with this problem in 1995, Altman, Hartzell, and Peck changed the original Z score model to create an emerging market model (EMM). Altman et al, reported that modified system have proven accuracy in anticipating both downgrades and defaults and upgrades too. In this model a constant value of + 3.25 was added for standardisation.

Z (EMM) = 3.25 + 6.56 X1 + 3.26 X2 + 6.72 X3 + 1.05 X4

In the Indian context, Bandopadhyay (2006) has developed bankruptcy prediction model based upon MDA and logistic regression technique for Indian corporate bonds sector. This model can predict corporate bankruptcy two years prior to financial distress with an accuracy of more than 95%.


Emerging markets are trying to positively transform into a sustainable economic growth economies through trade, technology transfers and foreign direct investments. Use of various forms of Z- Scores can early warn banks and investors about financial status of a firm. It can forewarn investors and lenders to reassess magnitude of default premium they require for bearing the risk of being attached to risky and distressed firms and help them secure their investment.

Suggested further readings:-

Altman, E. I. (1968), “Financial ratios, discriminant analysis and the prediction of corporate bankruptcy”, Journal of Finance, September, pp. 189-209.

Altman, E.I. (1993), Corporate Financial Distress and Bankruptcy, 2nd edition, John Wiley and sons, New York, NY.

Altman, E.I., Haldemann, R.G. and Narayan, P. (1977), “ZETA analysis a new model to identify bankruptcy risk of corporation”, Journal of Banking and Finance, Vol. 1, PP. 29-54 June.

Altman, E.I., Hartzell, J. and Peck, M. (1995), Emerging Markets Corporate Bonds: A scoring System, Salomon Brothers, and New York, NY.

Altman, E.I., (May 2002), “Revisiting Credit Scoring Models in a Basel II environment prepared for, Credit Rating: Methodology Rationale and Default Risk” London Risk Bonds 2002.