The Z-Score formula for Predicting Bankruptcy of Edward Altman is a multivariate formula for a measurement of the financial health of a company and a powerful diagnostic tool that forecasts the probability of a company entering bankruptcy within a 2 year period. Studies measuring the effectiveness of the Z-Score have shown the model is often accurate in predicting bankruptcy (72%-80% reliability)

The Z-Score was developed in 1968 by Dr. Edward I. Altman, Ph.D., a financial economist and professor at New York University's Stern School of Business.

The Z-Score bankruptcy predictor combines five common business ratios, using a weighting system calculated by Altman to determine the likelihood of a company going bankrupt. It was derived based on data from manufacturing firms, but has since proven to be effective as well (with some modifications) in determining the risk a service firm will go bankrupt.

How should the results be judged? It depends:

- Original Z-SCORE [For Public Manufacturer] If the score is 3.0 or above - bankruptcy is not likely. If the Score is 1.8 or less - bankruptcy is likely. A score between 1.8 and 3.0 is the gray area. Probabilities of bankruptcy within the above ranges are 95% for one year and 70% within two years. Obviously, a higher score is desirable.

- Model A Z'-Score [For Private Manufacturer] Model A of Altman's Z-Score is appropriate for a private manufacturing firm. Model A should not be applied to other companies. A score of 2.90 or above indicates that bankruptcy is not likely, but a score of 1.23 or below is a strong indicator that bankruptcy is likely. Probabilities of bankruptcy in the above ranges are 95% for one year and 70% within two years. Obviously, a higher score is desirable.

- Model B Z'-Score [For Private General Firm] Edward Altman developed this version of the Altman Z-Score to predict the likelihood of a privately owned non-manufacturing company going bankrupt within one or two years. Model B is appropriate for a private general (non-manufacturing) firm. Model B should not be applied to other companies. A score of 1.10 or lower indicates that bankruptcy is likely, while a score of 2.60 or above can be an indicator that bankruptcy is not likely. A score between the two is the gray area. Probabilities of bankruptcy in the above ranges are 95% for one year and 70% within two years. Again, obviously, a higher score is desirable.  

Note the variations for public and private companies.

Book: John B. Caouette, Edward I. Altman, Paul Narayanan - Managing Credit Risk

Altman Z Score: Definition¶
The Altman Z-Score, 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: 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. 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¶
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

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.

The Z-score formula for predicting bankruptcy was published in 1968 by Edward I. Altman, who was, at the time, an Assistant Professor of Finance at New York University. The formula may be used to predict the probability that a firm will go into bankruptcy within two years. Z-scores are used to predict corporate defaults and an easy-to-calculate control measure for the financial distress status of companies in academic studies. The Z-score uses multiple corporate income and balance sheet values to measure the financial health of a company.

Contents
1 Estimation of the formula
2 Precedents
3 Accuracy and effectiveness
4 Original Z-score Component Definitions Variable Definition Weighting Factor
5 Z-score estimated for private firms
6 Z-score estimated for Non-Manufacturer Industrials & Emerging Market Credits
7 See also
8 References
9 Further reading


[edit] Estimation of the formula
The Z-score is a linear combination of four or five common business ratios, weighted by coefficients. The coefficients were estimated by identifying a set of firms which had declared bankruptcy and then collecting a matched sample of firms which had survived, with matching by industry and approximate size (assets).

Altman applied the statistical method of discriminant analysis to a dataset of publicly held manufacturers. The estimation was originally based on data from publicly held manufacturers, but has since been re-estimated based on other datasets for private manufacturing, non-manufacturing and service companies.

The original data sample consisted of 66 firms, half of which had filed for bankruptcy under Chapter 7. All businesses in the database were manufacturers, and small firms with assets of <$1 million were eliminated.

The original Z-score formula was as follows: Z = 0.012T1 + 0.014T2 + 0.033T3 + 0.006T4 + 0.999T5.

T1 = Working Capital / Total Assets. Measures liquid assets in relation to the size of the company.

T2 = Retained Earnings / Total Assets. Measures profitability that reflects the company's age and earning power.

T3 = Earnings Before Interest and Taxes / Total Assets. Measures operating efficiency apart from tax and leveraging factors. It recognizes operating earnings as being important to long-term viability.

T4 = Market Value of Equity / Book Value of Total Liabilities. Adds market dimension that can show up security price fluctuation as a possible red flag.

T5 = Sales/ Total Assets. Standard measure for total asset turnover (varies greatly from industry to industry).

Altman found that the ratio profile for the bankrupt group fell at -0.25 avg, and for the non-bankrupt group at +4.48 avg.

[edit] 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.

[edit] Accuracy and effectiveness
In its initial test, the Altman Z-Score was found to be 72% accurate in predicting bankruptcy two years prior to the event, with a Type II error (false positives) of 6% (Altman, 1968). In a series of subsequent tests covering three different time periods over the next 31 years (up until 1999), the model was found to be approximately 80-90% accurate in predicting bankruptcy one year prior to the event, with a Type II error (classifying the firm as bankrupt when it does not go bankrupt) of approximately 15-20% (Altman, 2000).[1]

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).[2]

[edit] Original Z-score Component Definitions Variable Definition Weighting Factor
T1 = Working Capital / Total Assets

T2 = Retained Earnings / Total Assets

T3 = Earnings Before Interest and Taxes / Total Assets

T4 = Market Value of Equity / Total Liabilities

T5 = Sales/ Total Assets

Z Score Bankruptcy Model:

Z = 1.2T1 + 1.4T2 + 3.3T3 + 0.6T4 + .999T5

Zones of Discrimination:

Z > 2.99 -“Safe” Zones

1.81 < Z < 2.99 -“Grey” Zones

Z < 1.81 -“Distress” Zones

[edit] Z-score estimated for private firms
T1 = (Current Assets-Current Liabilities) / Total Assets

T2 = Retained Earnings / Total Assets

T3 = Earnings Before Interest and Taxes / Total Assets

T4 = Book Value of Equity / Total Liabilities

T5 = Sales/ Total Assets

Z' Score Bankruptcy Model:

Z' = 0.717T1 + 0.847T2 + 3.107T3 + 0.420T4 + 0.998T5

Zones of Discrimination:

Z' > 2.9 -“Safe” Zone

1.23 < Z' < 2. 9 -“Grey” Zone

Z' < 1.23 -“Distress” Zone

[edit] Z-score estimated for Non-Manufacturer Industrials & Emerging Market Credits
T1 = (Current Assets-Current Liabilities) / Total Assets

T2 = Retained Earnings / Total Assets

T3 = Earnings Before Interest and Taxes / Total Assets

T4 = Book Value of Equity / Total Liabilities

Z-Score Bankruptcy Model:

Z = 6.56T1 + 3.26T2 + 6.72T3 + 1.05T4

Zones of Discrimination:

Z > 2.6 -“Safe” Zone

1.1 < Z < 2. 6 -“Grey” Zone

Z < 1.1 -“Distress” Zone

[edit] See also
Standard score
Z-test
Z-factor
Altman Z-Score Classic [3]
[edit] References
Altman, Edward I. (July, 2000). ""Predicting Financial Distress of Companies"". Retrieved on September 4th, 2009 from http://pages.stern.nyu.edu/~ealtman/Zscores.pdf: 15–22.  
Altman, Edward I. (September, 1968). ""Financial Ratios, Discriminant Analysis and the Prediction of Corporate Bankruptcy"". Journal of Finance: 189–209.  
Altman, Edward I. (May, 2002). ""Revisiting Credit Scoring Models in a Basel II Environment"". Prepared for "Credit Rating: Methodologies, Rationale, and Default Risk", London Risk Books 2002. http://www.stern.nyu.edu/fin/wor ... 2/pdf/wpa02041.pdf.  
Eidleman, Gregory J. (1995-02-01). "Z-Scores - A Guide to Failure Prediction". The CPA Journal Online. http://www.nysscpa.org/cpajournal/old/16641866.htm.  
Fisher, Ronald Aylmer (1936). "The Use of Multiple Measurements in Taxonomic Problems". Annals of Eugenics 7:179. http://www.nysscpa.org/cpajournal/old/16641866.htm.  
The Use of Credit Scoring Modules and the Importance of a Credit Culture by Dr. Edward I Altman, Stern School of Business, New York University.
^ Predicting Financial Distress of Companies: Revisiting the Z-SCORE and ZETA Models
^ Predicting Financial Distress of Companies:Revisiting the Z-SCORE and ZETA Models
^ http://altmanzscoreclassic.com

请问这个系数一直是固定不变的吗？是不是随着不同国家不同年代而变化