# Altman Z-score

## What is the Altman Z-Score?

Definition: The Altman Z-score is a financial formula used by investors and creditors to to estimate the likelihood of the company going bankrupt by taking into account a firm’s core activities, liquidity, solvency, profitability and leverage.

## What Does Altman Z Score Mean?

Altman Z-score is a type of Z score, which was published by Edward I. Altman in 1968 as a Z score formula, used to predict the chances of bankruptcy. This methodology can be used to predict the chance of a business organization to move into bankruptcy within a given time, which is mostly about 2 years.

This method is successful in predicting the status of financial distress in any firm. Altman Z score can help in measuring the financial health of a business organization by the use of multiple balance sheet values and corporate income.

By evaluating a firm’s working capital, total assets, total liabilities, retained earnings, operating earnings, and revenues, the Altman Z-score is a reliable predictor of a firm’s solvency. Analysts often equate the this score with corresponding bond ratings because if a firm has a bond rating of BBB, it will have a score that will signify bankruptcy.

Also, Z score is one of the most accurate credit models because a change in a firm’s score suggests that, most likely, the firm’s fundamentals have changed. The Altman Z-score formula is calculated like this:

`Altman Z-score = 1.2A + 1.4B + 3.3C + 0.6D + 1.0E`

Here are each of the components broken down.

`A = WC / TA = Working Capital / Total Assets`
`B = RE / TA = Retained Earnings / Total Assets`
`C = EBIT / TA = EBIT / Total Assets`
`D = MC / TL = Market Cap / Total Liabilities`
`E = S / TA = Sales / Total Assets`
• In this model, if the Z value is greater than 2.99, then the firm is said to be in the “safe zone” and has a negligible probability of filing bankruptcy.
• If the Z value is between 2.99 and 1.81, then the firm is said to be in the “grey zone” and has a moderate probability for bankruptcy.
• And finally, if the Z value is below 1.81, then it is said to be in the “distress zone” and has a very high probability of reaching the stage of bankruptcy.

## Example

Michael is a financial analyst at a boutique securities firm. He is asked to calculate the score for a manufacturing company that has released relatively weak results over the past two quarters. Michael collects information from the following balance sheet and income statement:

Z-Score = ((WC/TA) x 1.2) + ((RE/TA) x 1.4) + ((EBIT/TA) x 3.3) + ((MC/TL) x 0.6) + ((S/TA) x 1.0) = 0.053 + 0.656 + 1.907 + 0.759 + 1.648 = 5.023.

Since the firm has a Z-score higher than 3.0, it is financially strong, and the likelihood of bankruptcy is low. The company has a positive working capital, suggesting that it can meet its short-term obligations with its current assets. Its retained earnings indicate that the company has a relatively low leverage, which allows it to finance its core operations with equity.

Furthermore, the company has strong EBIT, suggesting strong efficiency, and high revenues, suggesting an efficient use of its assets.

## Precedents

Altman’s work built upon research by accounting researcher William Beaver and others. In the 1930s and on, Mervyn and others had collected matched samples and assessed that various accounting ratios appeared to be valuable in predicting bankruptcy. Altman’s Z-score is a customized version of the discriminant analysis technique of R. A. Fisher (1936).

William Beaver’s work, published in 1966 and 1968, was the first to apply a statistical method, t-tests to predict bankruptcy for a pair-matched sample of firms. Beaver applied this method to evaluate the importance of each of several accounting ratios based on univariate analysis, using each accounting ratio one at a time. Altman’s primary improvement was to apply a statistical method, discriminant analysis, which could take into account multiple variables simultaneously.

## Accuracy and Effectiveness

In its initial test, the Altman Z-Score was found to be 72% accurate in predicting bankruptcy two years before the event, with a Type II error (false negatives) of 6% (Altman, 1968). In a series of subsequent tests covering three periods over the next 31 years (up until 1999), the model was found to be approximately 80%–90% accurate in predicting bankruptcy one year before the event, with a Type II error (classifying the firm as bankrupt when it does not go bankrupt) of approximately 15%–20% (Altman, 2000).

From about 1985 onwards, the Z-scores gained wide acceptance by auditors, management accountants, courts, and database systems used for loan evaluation (Eidleman). The formula’s approach has been used in a variety of contexts and countries, although it was designed originally for publicly held manufacturing companies with assets of more than \$1 million. Later variations by Altman were designed to be applicable to privately held companies (the Altman Z’-Score) and non-manufacturing companies (the Altman Z”-Score).

Neither the Altman models nor other balance sheet-based models are recommended for use with financial companies. This is because of the opacity of financial companies’ balance sheets and their frequent use of off-balance sheet items. There are market-based formulas used to predict the default of financial firms (such as the Merton Model), but these have limited predictive value because they rely on market data (fluctuations of share and options prices to imply fluctuations in asset values) to predict a market event (default, i.e., the decline in asset values below the value of a firm’s liabilities).

## Special Considerations

In 2007, the credit ratings of specific asset-related securities had been rated higher than they should have been. The Altman Z-score indicated that the companies’ risks were increasing significantly and may have been heading for bankruptcy.

Altman calculated that the median Altman Z-score of companies in 2007 was 1.81. These companies’ credit ratings were equivalent to a B. This indicated that 50% of the firms should have had lower ratings, were highly distressed and had a high probability of becoming bankrupt.

Altman’s calculations led him to believe a crisis would occur and there would be a meltdown in the credit market. Altman believed the crisis would stem from corporate defaults, but the meltdown began with mortgage-backed securities. However, corporations soon defaulted in 2009 at the second-highest rate in history.

## Application of Altman Z Score in Predicting Bankruptcy

The value of the Altman Z score is generally around – 0.25 for firms that have the highest probability of going bankrupt. On the other hand, for firms having the least probability of facing a bankruptcy, the value of Altman Z score value is as high as + 4.48.

This formula is helpful for investors to determine if they should consider buying a stock or sell some of the stocks they have. Generally, the Altman Z score below 1.8 denotes that the firm is under the chance of getting into bankruptcy. On the other hand, the firms with Altman Z score above 3 are deemed to be less likely to go bankrupt. So an investor can decide to buy a stock if the Altman Z score is closer to value 3 and similarly they can decide to sell a stock if the value is closer to 1.8.

In 2007, the specific asset-related securities had been given higher credit ratings than they must have been. However, the companies were correctly predicted to be increasing their financial risk and should have been heading for bankruptcy. Altman calculated that the median Altman Z score of firms in 2007 was 1.81. These companies’ credit ratings were the same as that of the financial ratio B, which is used in the formula of Z above. This indicated that almost half of the companies are being rated lower, and they were extremely distressed and had a high likelihood of reaching a stage of bankruptcy.

Therefore, Altman’s Z Score calculations led him to believe that a crisis would occur and there would be a meltdown in the credit market. Altman believed that the crisis would stem from company defaults. However, the meltdown began with mortgage-backed securities (MBS). Still, firms shortly defaulted in 2009 at the second-highest rate in history, as predicted by Altman’s model.

## Altman Z score for private firms

The original formula is modified to fit in case of private firms and the business ratios used in case of this are:

 Financial ratio used Formula for the financial ratio A ( Current Assets − Current Liabilities )/Total Assets B Retained Earnings/Total Assets C Earnings Before Interest and Taxes/Total Assets D Book Value of Equity/Total Liabilities E Sales/Total Assets

The actual Altman Z Score formula for this model for determining the probability for a firm to close bankruptcy is:

`Z’ = (0.717 x A) + (0.847 x B) + (3.107 x C) + (0.420 x D) + (0.998 x E)`
• In this model, if the Z value is greater than 2.99, then the firm is said to be in the “safe zone” and has a negligible probability of filing bankruptcy.
• If the Z value is between 2.99 and 1.23, then the firm is said to be in the “grey zone” and has a moderate chance of bankruptcy.
• And finally, if the Z value is below 1.23, then it is said to be in “distress zone” and has a very high probability of reaching the stage of bankruptcy.

## Altman Z score for Non-manufacturing Firms (Developed and Emerging Markets)

The original formula is slightly modified to be used in case of firms that are non-manufacturing and operating in the emerging markets. We use only four financial ratios in this model. The four ratios are as follows:

 Business ratios used Formula for the business ratio A ( Current Assets − Current Liabilities ) / Total Assets B Retained Earnings / Total Assets C Earnings Before Interest and Taxes / Total Assets D Book Value of Equity / Total Liabilities

The actual Altman Z Score formula for this model for determining the probability for a non-manufacturing firm, operating in developed markets, to file a bankruptcy is as follows:

`Z’’ = (6.56 x A) + (3.26 x B) + (6.72 x C) + (1.05 x D)`

The actual formula Altman Z Score formula for this model for determining the probability for a non-manufacturing firm, operating in emerging markets, to file a bankruptcy is as follows:

`Z’’ = 3.25 + (6.56 x A) + (3.26 x B) + (6.72 x C) + (1.05 x D)`
• In this model, if the Z value is greater than 2.6, then the firm is said to be in the “safe zone” and has a negligible probability of filing a bankruptcy.
• If the Z value is between 2.6 and 1.1, then the firm is said to be in the “grey zone” and has a moderate chance of bankruptcy.
• If the Z value is below 1.1, then it is said to be in the “distress zone” and has a very high probability of reaching the stage of bankruptcy.

## Summary

Define Altman Z-Score: The Altman score is a financial ratio that calculates the liquidity of a company and helps analysts predict the likelihood that the firm will go bankrupt.

• The Altman Z-score is a formula for determining whether a company, notably in the manufacturing space, is headed for bankruptcy.
• The formula takes into account profitability, leverage, liquidity, solvency, and activity ratios.
• An Altman Z-score close to 1.8 suggests a company might be headed for bankruptcy, while a score closer to 3 suggests a company is in solid financial positioning.
• This scoring system was originally designed for manufacturing firms having assets of \$1 million or more. Given the targeted nature of the model, it has since been modified to be applicable to other types of organizations.
• This approach to evaluating organizations is better than using just a single ratio, since it brings together the effects of multiple items – assets, profits, and market value. As such, it is most commonly used by creditors and lenders to determine the risk associated with extending funds to customers and borrowers.