# Altman Z Score Model Definition

The Altman Z Score model, defined as a financial model to predict the likelihood of bankruptcy in a company, was created by Edward I. Altman. Altman was a professor at the Leonard N. Stern School of Business of New York University. His aim at predicting bankruptcy began around the time of the great depression, in response to a sharp rise in the incidence of default.

## Altman Z Score Model Explanation

To Dr. Altman, z score explained an important issue of the time. For this, he used a weighting system combined with a set of four or five financial ratios to predict a company’s probability of failure. Altman created three different Z Score Models that each serve unique purposes. The original Z Score Model was developed in 1968. It was made from the basis of statistical data from public manufacturing companies and eliminated all companies with assets less than \$1 million. However, this original model was not intended for small, non-manufacturing, or private companies. Later, Dr. Altman developed two additional models to the original Z Score Model. In 1983, the Model “A” Z-Score was developed for use with private manufacturing companies. Model “B” was developed for non-public traded general firms and included the service sector. Different models have different variables, weighting and overall predictability scoring systems.

### Altman Z Score Purpose

The purpose of the Z Score Model is to measure a company’s financial health and to predict the probability that a company will collapse within 2 years. It is proven to be very accurate to forecast bankruptcy in a wide variety of contexts and markets. Studies show that the model has 72% – 80% reliability of predicting bankruptcy. However, the Z-Score does not apply to every situation. It can only be used for forecasting if a company being analyzed can be compared to the database.

### Altman Z Score Analysis

In general analysis, the lower the Z-Score, the higher risk of bankruptcy a company has, and vice visa. Different models have different overall predictability scoring. Probabilities of bankruptcy in the above ranges are 95% for one year and 70% within two years.

1. Original Z-Score for public manufacturing companies:

```Z-Score	        Forecast
Above 3.0        Bankruptcy is not likely
1.8 to 3.0       Bankruptcy can not be predicted-Gray area
Below 1.8        Bankruptcy is likely```

2. Model A Z-Score for private manufacturing companies:

```Z-Score	         Forecast
Above 2.9         Bankruptcy is not likely
1.23 to 2.9       Bankruptcy can not be predicted-Gray area
Below 1.23        Bankruptcy is likely```

3. Model B Z-Score for private general companies:

```Z-Score	         Forecast
Above 2.60	Bankruptcy is not likely
1.10 to 2.60	Bankruptcy can not be predicted-Gray area
Below 1.10	Bankruptcy is likely```

### Altman Z Score Formula

1. Original Z-Score formula for public manufacturing companies:

Original Z-Score = 1.2X1 + 1.4X2 + 3.3X3 + 0.6X4 + 0.999X5

2. Model A Z-Score for private manufacturing companies: this model substitutes the book values of equity for the Market value in X4 compared to original model.

Model A Z-Score = 0.717X1 + 0.847X2 + 3.107X3 +0.420X4 +0.998X5

3. Model B Z-Score for private general companies: this model analyzed the characteristics and accuracy of a model without X5 – sales/total assets.

Model B Z-Score = 6.56X1 + 3.26X2 +6.72X3 +1.05X4

X1 = working capital/total Assets. It measures the net liquid asset of a company relative to the total assets.

X2 = retained earnings/total Assets. It measures the financial leverage level of a company.

X3 = earnings before interests and taxes/total Assets. It measures productivity of a company’s total assets.

X4 = market value of equity/book value of total liabilities. It measures what portion of a company’s assets can decline in value before the liabilities exceed the assets.

X5 = sales/total Assets. It measures revenue generating ability of a company’s assets.

### Altman Z Score Calculation

If:
Working Capital = \$5,000,000
Retained Earnings = \$1,000,000
Operating Income = \$10,000,000
Market Value of Equity = \$2,000,000
Book Value of Total Liabilities = \$500,000
Sales = \$15,000,000
Total Assets = \$3,000,000

Working Capital / Total Assets = \$5,000,000 / \$3,000,000 = 1.67
Retained Earnings / Total Assets = \$1,000,000 / \$3,000,000 = .33
Operating Income / Total Assets = \$10,000,000 / \$3,000,000 = 3.33
Market Value of Equity / Book Value of Total Liabilities = \$2,000,000 / \$500,000 = 4
Sales / Total Assets = \$15,000,000 / \$3,000,000 = 5

Model A Z-Score = 0.717X1 + 0.847X2 + 3.107X3 +0.420X4 +0.998X5 = .717(1.67) + .847(.33) + 3.107(3.33) + .420(4) + .998(5) = 18.49321

### Altman Z Score Example

For example, Benny is the CFO of a company which manufactures custom car parts. The company, which started as a local car shop, has evolved into a regional product provider. Benny has been part of the team since he gained his CPA license and has helped the company manage the success it acquired.

With the recent credit market situation, Benny wants to make sure his company will be able to meet the financial obligations it has committed to. Benny decides to calculate for the Altman Z Score; manufacturing has been hit hard enough that he feels he has to. With this decision, he begins assembling company financial reports to find the factors of the Altman Z Score equation as they relate to his company.

Benny performs this calculation:

If:
Working Capital = \$5,000,000
Retained Earnings = \$1,000,000
Operating Income = \$10,000,000
Market Value of Equity = \$2,000,000
Book Value of Total Liabilities = \$500,000
Sales = \$15,000,000
Total Assets = \$3,000,000

Working Capital / Total Assets = \$5,000,000 / \$3,000,000 = 1.67
Retained Earnings / Total Assets = \$1,000,000 / \$3,000,000 = .33
Operating Income / Total Assets = \$10,000,000 / \$3,000,000 = 3.33
Market Value of Equity / Book Value of Total Liabilities = \$2,000,000 / \$500,000 = 4
Sales / Total Assets = \$15,000,000 / \$3,000,000 = 5

Model A Z-Score = 0.717X1 + 0.847X2 + 3.107X3 +0.420X4 +0.998X5 = .717(1.67) + .847(.33) + 3.107(3.33) + .420(4) + .998(5) = 18.49321

### Altman Z Score Example Conclusion

Benny’s employer has a z score well over 2.9, making bankruptcy very unlikely. This is just as Benny expected. Still, he is happy to do the work. He knows that if he continues to pay attention to the finances of the company he can control them. In this way Benny knows he can direct the finances of the company, turning inefficiency into profit.

Next, Benny does research and finds the Altman Z Score for private companies in his industry. He can use this information to compare his company to common best practices. If he is below the standard, he can find how others have solved the problem. If he is above the standard, he can expand projects which differentiate his company from the average firm.

Benny presents his work in true fashion of Altman; Z-Score tables are made, manufacturing competitive analysis is done, and the project is completed to excellent standards. The effort finally pays off when Benny is offered a bonus of stock options. He feels even closer to the company he has developed his abilities in.

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