# Altman Z-Score – Definition

### Altman Z-Score Definition

The Altman Z-score (or simply, “Z-Score”) is a statistical measurement of one variables relationship to the mean (average) of a group of values. More specifcally, the Z-score states the number of standard deviations a variable lies from the mean of the group of values. A zero  Z-score indicates that the mean of the group and the value being tested is identical. A one or negative one Z-score indicates that the value is one standard deviation from the mean.  A positive one indicates that it is one standard deviation above, while a negative one indicaes that it is one standard deviation below the mean.

Z-scores are measures of an observation’s variability and can be put to use by traders in determining market volatility. The Z-score is more commonly known as the Altman Z-score.

The Altman Z-Score is the formula, consisting of five fundamental ratios, used to determine the financial condition of the company and probability for bankruptcy.  The Altman Z-Score formula helps the investors to evaluate the business’s financial strength. This Formula also helps predicting the business’s bankruptcy.

### A Little More on the Altman Z-Score

The Altman Z-Score determines the company’s strength by calculating its financial risk. It highlights the bankruptcy probabilities using various financial indices. The Altman Z-Score was introduced by Edward Altman, a professor at the University of New York, in 1960.

The Altman Z-Score is a valuable tool to evaluate the company’s operations. This fundamental tool measures the company’s viability in the long term, which is helpful for the capital investors to determine the company’s bankruptcy. The poor assessment of the company’s financial viability may cause investor huge lauses. The Altman Z-Score models uses multivariate statistical technique called discriminant analysis. It is used to assess the credit studies or project the movement of the treasury of a potential client.

### The formula Altman Z-score

The Altman Z-score formula calculation is as follows:

Altman Z-score = 1.2 * T 1 + 1.4 * T 2 + 3.3 * T 3 + 0.6 * T 4 + 1.0 * T 5

Where:

T 1 : (Working Capital / Total Assets)

T 2 : (Undistributed profits / Total Assets)

T 3 : (EBITDA / Total Assets)

T 4 : (Stock Market Capitalization / Total Debt)

T 5 : (Net Sales / Total Assets)

### How to use the Altman z-score to predict bankruptcies

The result of the Altman Z-score formula determines if the company is in the safe zone, gray zone or in danger zone.

Z-score more than 2.99 means Safe area.

Z-score between 1.81 and 2.99 means a gray area, specifying that the company may go bankrupt in the following two years.

Z-score less than 1.81 means the danger zone; i.e.  Imminent bankruptcy.

The accuracy of the Altman Z-score in the prediction of bankruptcies

The Altman Z-score formula is 72% accurate two years in advance concerning the bankruptcy, with a false negative rate of 6%.

In its trial era of 31 years, the accurate rate was in between 80% and 90%, one year in advance concerning the bankruptcy, with a false negative rate in between 15% and 20%.

Hence, it can be said that the Altman Z-score formula predictions are considerably accurate. However, it is not an absolute formula, thus, must be used in parallel with a qualitative analysis of the business for more accurate predictions.

### References for Altman Z Score

Predicting financial distress of companies: revisiting the Z-score and ZETA models, Altman, E. I. (2000). Stern School of Business, New York University, 9-12.

Financial ratios, discriminant analysis and the prediction of corporate bankruptcy, Altman, E. I. (1968). The journal of finance, 23(4), 589-609.

Considering the utility of Altman’s Z-score as a strategic assessment and performance management tool, Calandro Jr, J. (2007). Strategy & Leadership, 35(5), 37-43. – The analysis defines the Carton and Hofer’s findings regarding the utility of the Z‐score being a strategic analysis and performance management tool.

CAN ALTMAN Ζ-SCORE MODEL PREDICT BUSINESS FAILURES IN GREECE?, Gerantonis, N., Vergos, K., & Christopoulos, A. (2009). In Proceedings of the 2nd International Conference: Quantitative and Qualitative Methodologies in the Economic and Administrative Sciences(p. 149). Christos Frangos.

Z scores-A Guide to failure prediction, Eidleman, G. J. (1995). The CPA Journal, 65(2), 52.

Business bankruptcy prediction models: A significant study of the Altman’s Z-score model, Siddiqui, S. A. (2012). Financial ratios are the fundamental indicator of the business’s soundness, and operational and financial health. Altman proposed z-score model that combines these ratios, to predict the business’s financial viability/bankruptcy up to 2-3 years in advance. The paper highlights Altman’s studies to predict the business bankruptcy, and summarizes the research carried out by Altman to develop the z-score model. In modern economy, this model can be used to predict the bankruptcy and distress, one, two or three years in advance.

Distressed firm and bankruptcy prediction in an international context: A review and empirical analysis of Altman’s Z-score model, Altman, E., Iwanicz-Drozdowska, M., Laitinen, E., & Suvas, A. (2014). This paper reviews the previous literature on the importance and efficacy of the Altman Z-score bankruptcy prediction model and in its implication in finance and other relevant areas, globally. Analysis of 33 scientific papers published since 2000 in mainstream accounting and financial journals, has been done in the review. The paper also used a sample of international firms (from 31 European and 3 non-European countries) to evaluate the performance of the model for distress and bankruptcy prediction of the firm. Since our sample has firms that primarily belong to private sector and are non-financial, we have used the version of the z-score model developed for manufacturing and non-manufacturing firms, in our testing. The overall literature review shows that z-score performed well in most of the cases.For our most of the sample countries, the accuracy rate was around 75% , while in some cases, more than 90%.

Financial Distress Prediction in an International Context: A Review and Empirical Analysis of Altman’s Z‐Score Model, Altman, E. I., Iwanicz‐Drozdowska, M., Laitinen, E. K., & Suvas, A. (2017). Journal of International Financial Management & Accounting, 28(2), 131-171. This paper evaluates the performance classification of z-score model, especially for the banks that operate globally and must evaluate the failure risks of the firms. The performance of the model is assessed for 31 European and 3 non-European countries. Since our sample has firms that primarily belong to private sector and are non-financial, we have used the version of the z-score model developed for manufacturing and non-manufacturing firms, in our testing. The overall literature review shows that z-score performed well in most of the cases.For our most of the sample countries, the accuracy rate was around 75% , while in some cases, more than 90%.

The Altman z-score revisited, Russ, R., Peffley, W., & Greenfield, A. (2004). This study contains the research on the Altman z-score measure of bankruptcy. To Answer the criticisms of the original study, this study takes into an account a large sample, all the data from recent years, statistical methods, and the elimination of the matched pair design of the original study, for rescaling the z-score, which significantly improves the predictive power of the model in predicting bankruptcy for two years prior in advance..

Altman’s Z-Score models of predicting corporate distress: Evidence from the emerging Sri Lankan stock market, Samarakoon, L., & Hasan, T. (2003). This study evaluates the ability of three variations of the Altman’s Z-Score model (Z, Z’, and Z”) of distress prediction formed in the U.S. to determine the corporate distress in the rising market of Sri Lanka. The findings show that the models are remarkably accuracy in predicting distress using the financial ratios calculated from the  financial statements in the year before the distress. The overall success rate of the z-score was 81%. The paper concludes that Z-Score models bear great potential in assessing the risk of corporate distress in emerging markets as well.

An evaluation of Altman’s Z-score using cash flow ratio to predict corporate failure amid the recent financial crisis: Evidence from the UK, Almamy, J., Aston, J., & Ngwa, L. N. (2016). Journal of Corporate Finance, 36, 278-285. This paper assesses the extension of the Z-score model in determining the viability of the UK companies; using discriminant analysis, and performance ratios to evaluate which ratios are statistically important in predicting the health of the UK companies from 2000 to 2013. The findings show that cash flow when used with the original Z-score variable, is helpful in predicting the health of UK companies. A J-UK model was established to test the health of UK companies. When compared to the Z-score model, the accuracy rate was 82.9%, which is consistent with Taffler’s (1982) UK model.