# Altman Z-Score

The Altman Z-Score is an empirical model that predicts the probability of corporate bankruptcy. This article introduces this valuable predictor of financial distress, and offers a calculation spreadsheet.

The Altman Z-Score was published in 1968 by Edward Altman, and measures a company’s financial heatlth. He chose 66 publicly-traded manufacturing companies (half of which had declared bankruptcy, and half of which had not). Altman then examined several common financial ratios based on data retrieved from annual financial reports. After linearly combining these ratios, Altman arrived at an empirical equation (called the the Z-Score) that predicted the risk of corporate failure within two years with an accuracy of 72%, and false-positives at 6%

This equation was also tested against companies not in the initial sample. The equation predicted bankruptcy or non-bankruptcy to within a high degree of accuracy.

Altman later published modification called the Z1-Score, which can be applied to privately-held manufacturing companies, and Z2-score for non-manufacturing companies.

The value of the Z-Score indicates the health of a company, with a higher value being better. The equations use the following financial information.

- Working Capital
- Total Assets
- Retained Earnings
- Earnings Before Tax and Interest, or EBIT
- Market Value of Equity (for publicly-traded companies
- Book Value or Net Worth (for privately-end companies)
- Total Liabilities
- Sales

These quantities are combined into the follows ratios

- X
_{1}= Working Capital / Total Assets (measures liquidity) - X
_{2}= Retained Assets / Total Assets - X
_{3}= Earnings Before Tax and Interest / Total Assets (measures how effectively the company uses its assets to get return) - X
_{4}= Market Value of Equity / Total Liabilities (measures the market’s view of the company’s health) - X
_{4A}= Book Value / Total Liabilties - X
_{5}= Sales / Total Assets (indicated asset turnover)

The Z-score is then a linear combination of these ratios as follows

- Z = 1.2 X
_{1}+ 1.4 X_{2}+ 3.3 X_{3}+ 0.6 X_{4 + 1.0 X5} - Z
_{1}= 0.717 X_{1}+ 0.847 X_{2}+ 3.107 X_{3}+ 0.42 X_{4A + 0.998 X5} - Z
_{2}= 6.56 X_{1}+ 3.26 X_{2}+ 6.72 X_{3}+ 1.05 X_{4A}

The latter two equations are often referred to as Altman model A (for private manufacturing firms) and model B (for general firms). The bands and typical values for the Z-Score are as follows.

These equations are implemented in a spreadsheet available at the bottom of this article

The Z-Score is still widely used primarily because of its simplicity and the ease with which the financial data is obtained. However, Shumway (2001) demonstrated than several of the parameters use in the Z-score equations now do not adequately predict bankruptcy, and identified a better predictive model. Chava and Jarrow (2004) confirmed that the Shumway (2001) model is a better predictor of financial distress.