Altman Z-score

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Example of an Excel spreadsheet that uses Altman Z-score to predict the probability that a firm will go into bankruptcy within two years Zscore.JPG
Example of an Excel spreadsheet that uses Altman Z-score to predict the probability that a firm will go into bankruptcy within two years

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

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: [1]

Z = 1.2X1 + 1.4X2 + 3.3X3 + 0.6X4 + 1.0X5.
X1 = ratio of working capital to total assets. Measures liquid assets in relation to the size of the company.
X2 = ratio of retained earnings to total assets. Measures profitability that reflects the company's age and earning power.
X3 = ratio of earnings before interest and taxes to total assets. Measures operating efficiency apart from tax and leveraging factors. It recognizes operating earnings as being important to long-term viability.
X4 = ratio of market value of equity to book value of total liabilities. Adds market dimension that can show up security price fluctuation as a possible red flag.
X5 = ratio of sales to 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.

Precedents

Altman's work built upon research by accounting researcher William Beaver and others. In the 1930s and on, Mervyn[ who? ] and others[ who? ] had collected matched samples and assessed that various accounting ratios appeared to be valuable in predicting bankruptcy.[ citation needed ] Altman 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). [2]

This overstates the predictive ability of the Altman Z-score, however. Scholars have long criticized the Altman Z-score for being “largely descriptive statements devoid of predictive content ... Altman demonstrates that failed and non-failed firms have dissimilar ratios, not that ratios have predictive power. But the crucial problem is to make an inference in the reverse direction, i.e., from ratios to failures.” [3] 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.

Modern academic default and bankruptcy prediction models rely heavily on market-based data rather than the accounting ratios predominant in the Altman Z-score. [4]

Original Z-score component definitions

X1 = working capital / total assets
X2 = retained earnings / total assets
X3 = earnings before interest and taxes / total assets
X4 = market value of equity / total liabilities
X5 = sales / total assets

Z-score bankruptcy model:

Z = 1.2X1 + 1.4X2 + 3.3X3 + 0.6X4 + 1X5

Zones of discrimination:

Z > 2.99 – "safe" zone
1.81 < Z < 2.99 – "grey" zone
Z < 1.81 – "distress" zone

Z-score estimated for non-manufacturers and emerging markets

X1 = (current assets current liabilities) / total assets
X2 = retained earnings / total assets
X3 = earnings before interest and taxes / total assets
X4 = book value of equity / total liabilities

Z-score bankruptcy model (non-manufacturers):

Z = 6.56X1 + 3.26X2 + 6.72X3 + 1.05X4 [5]

Z-score bankruptcy model (emerging markets):

Z = 3.25 + 6.56X1 + 3.26X2 + 6.72X3 + 1.05X4

Zones of discrimination:

Z > 2.6 – "safe" zone
1.1 < Z < 2.6 – "grey" zone
Z < 1.1 – "distress" zone

Examples

Altman's Z-score for International Credit Rating Agencies
DefaulterAmount of LiabilitiesDate of DefaultZ-ScoreRating at the time of defaultThe Consequences
(in $ billion)In year of default1 year prior2 years prior3 years prior4 years priorS&PMoody'sFitch
Bear Stearns 38731-July-20070.29−0.790.450.40.36AA a AA1 a A2Acquired by JP Morgan Chase
AIG 80716-Sep-2008−1.03−0.07−0.020.420.23AA− a A−A1 a A2AA− a A−Bailed out by US Government
Lehman Brothers 39223-Sep-20080.060.090.03-0.030.29AA, A1P1 & A1AA− & F1+Bankrupt
Washington Mutual Bank 30325-Sep-2008−0.35−0.3−0.07−0.13-0.3A− & A2Baa1 & P2A− & F2Acquired by JP Morgan Chase
Ford Motors 1326-Apr-20091.321.031.2311.29CCCaa1, B3CCC, BBRevived
MF Global 5131-Oct-20110.230.470.370.410.46Baa2 a CaaBBB a BB+Bankrupt

[6]

Altman's Z-scores of largest Indian Defaulters during April 2005 to March 2013
DefaulterAmount of Liabilities (in Rs cr)Date of defaultZ-ScoreRating at the time of defaultThe Consequences
in Crore In the Year of default1 yr prior to default2 yr prior to default3 yr prior to default4 yr prior to default
Arvind Products251.810-Feb-20091.581.932.141.611.73CRSIL BBBRestructured
Ansal Properties & Infraestructure13595-Oct-20092.33.214.224.853.06Fitch BBBRestructured
Kingfisher Airlines Limited4105.881-Dec-2011−2.361.850.610.791.93CRISIL DNon Operational
Royal Orchid Hotel Limited22031-Mar-20120.771.061.171.622.17ICRA BBB+Restructured
Deccan Chronicle Holdings39022-Jul-2012−0.122.743.012.542.77Care A1Assets sold by banks
Suzlon Energy Limited1094817-Jun-2012−0.111.231.281.191.24ICRA BBB− a DRestructured

[6]

See also

Related Research Articles

In finance, default is failure to meet the legal obligations of a loan, for example when a home buyer fails to make a mortgage payment, or when a corporation or government fails to pay a bond which has reached maturity. A national or sovereign default is the failure or refusal of a government to repay its national debt.

<span class="mw-page-title-main">Equity (finance)</span> Ownership of property reduced by its liabilities

In finance, equity is an ownership interest in property that may be offset by debts or other liabilities. Equity is measured for accounting purposes by subtracting liabilities from the value of the assets owned. For example, if someone owns a car worth $24,000 and owes $10,000 on the loan used to buy the car, the difference of $14,000 is equity. Equity can apply to a single asset, such as a car or house, or to an entire business. A business that needs to start up or expand its operations can sell its equity in order to raise cash that does not have to be repaid on a set schedule.

<span class="mw-page-title-main">Valuation (finance)</span> Process of estimating what something is worth, used in the finance industry

In finance, valuation is the process of determining the value of a (potential) investment, asset, or security. Generally, there are three approaches taken, namely discounted cashflow valuation, relative valuation, and contingent claim valuation.

Credit risk is the possibility of losing a lender holds due to a risk of default on a debt that may arise from a borrower failing to make required payments. In the first resort, the risk is that of the lender and includes lost principal and interest, disruption to cash flows, and increased collection costs. The loss may be complete or partial. In an efficient market, higher levels of credit risk will be associated with higher borrowing costs. Because of this, measures of borrowing costs such as yield spreads can be used to infer credit risk levels based on assessments by market participants.

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Edward I. Altman is a Professor of Finance, Emeritus, at New York University's Stern School of Business. He is best known for the development of the Altman Z-score for predicting bankruptcy which he published in 1968. Professor Altman is a leading academic on the High-Yield and Distressed Debt markets and is the pioneer in the building of models for credit risk management and bankruptcy prediction.

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Bankruptcy prediction is the art of predicting bankruptcy and various measures of financial distress of public firms. It is a vast area of finance and accounting research. The importance of the area is due in part to the relevance for creditors and investors in evaluating the likelihood that a firm may go bankrupt.

A period of financial distress occurs when the price of a company or an asset or an index of a set of assets in a market is declining with the danger of a sudden crash of value occurring, either because the company is experiencing increasing problems of cash flow or a deteriorating credit balance or because the price had become too high as a result of a speculative bubble that has now peaked.

<span class="mw-page-title-main">Financial ratio</span> Numerical value to determine the financial condition of a company

A financial ratio or accounting ratio is a relative magnitude of two selected numerical values taken from an enterprise's financial statements. Often used in accounting, there are many standard ratios used to try to evaluate the overall financial condition of a corporation or other organization. Financial ratios may be used by managers within a firm, by current and potential shareholders (owners) of a firm, and by a firm's creditors. Financial analysts use financial ratios to compare the strengths and weaknesses in various companies. If shares in a company are traded in a financial market, the market price of the shares is used in certain financial ratios.

The Ohlson O-score for predicting bankruptcy is a multi-factor financial formula postulated in 1980 by Dr. James Ohlson of the New York University Stern Accounting Department as an alternative to the Altman Z-score for predicting financial distress.

The Beneish model is a statistical model that uses financial ratios calculated with accounting data of a specific company in order to check if it is likely that the reported earnings of the company have been manipulated.

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<span class="mw-page-title-main">Yoshiko Shirata</span> Japanese accounting scholar (born 1952)

"Cindy" Yoshiko Shirata is a Japanese accounting scholar who specialized in corporate bankruptcy prediction. She is best known for her SAF2002 bankruptcy prediction model. Her bankruptcy prediction model has been used by major banks and rating companies in Japan. She is considered one of the most well-known experts to develop bankruptcy prediction models in Japan.

References

Altman, Edward I. (July 2000). "Predicting Financial Distress of Companies" (PDF). Stern.nyu.edu: 15–22.

Altman, Edward I. (September 1968). "Financial Ratios, Discriminant Analysis and the Prediction of Corporate Bankruptcy". Journal of Finance. 23 (4): 189–209. doi:10.1111/j.1540-6261.1968.tb00843.x. S2CID   154437292.

Altman, Edward I. (May 2002). "Revisiting Credit Scoring Models in a Basel II Environment" (PDF). Prepared for "Credit Rating: Methodologies, Rationale, and Default Risk", London Risk Books 2002. Archived from the original (PDF) on 2006-09-18. Retrieved 2007-08-08.

Eidleman, Gregory J. (1995-02-01). "Z-Scores – A Guide to Failure Prediction". The CPA Journal Online.

Fisher, Ronald Aylmer (1936). "The Use of Multiple Measurements in Taxonomic Problems". Annals of Eugenics. 7 (2): 179. doi:10.1111/j.1469-1809.1936.tb02137.x. hdl: 2440/15227 .

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.

  1. realequityresearch.dk/Documents/Z-Score_Altman_1968.pdf
  2. Predicting Financial Distress of Companies: Revisiting the Z-SCORE and ZETA Models
  3. Johnson, C.G. 1970. Ratio Analysis and the Prediction of Firm Failure. Journal of Finance, 25(5), 1166-1168. For additional criticism, see, for example, Moyer, R.C. 1977. Forecasting Financial Failure. Financial Management, 6(1), 11-17.
  4. See, for example, Shumway, T. 2001. Forecasting Bankruptcy More Accurately: A Simple Hazard Model. Journal of Business, 74(1), 101–124.; Campbell, J.Y., J. Hillscher, and J. Szilagyi. 2008. In Search of Distress Risk. Journal of Finance, 63(6), 2899-2939; Li, L. and R. Faff. 2019. Predicting Corporate Bankruptcy: What Matters? International Review of Economics and Finance, 62, 1–19.
  5. Edward I. Altman; et al. (June 2017). "Financial Distress Prediction in an International Context: A Review and Empirical Analysis of Altman's Z-Score Model". Journal of International Financial Management and Accounting . 28 (2): 131–171. doi:10.1111/jifm.12053. S2CID   155302026.
  6. 1 2 Khatkale, Swati (2014). Symbiosis International University (ed.). "An exploratory study to assess the performance of indian credit rating agencies 2005 2013". hdl:10603/38090 . Retrieved 19 December 2021. On the other hand all the defaults in case of Indian rated companies were in non-structured financial products. Defaulters like Arvind Products, Suzlon, Royal Orchid Hotel, Deccan Chronicle Holding & Ansal Properties had investment grade ratings either at the time of default or just a few days before the default. Altman's Z score predicted default in case of Royal Orchid, Arvind Products & Suzlon Energy, which was not reflected in the ratings. This showed that simple model like Altman's Z score was more informative than the ratings given by Credit Rating Agencies. Thus the findings of the case studies support the findings of overall accuracy of Indian Credit Rating Agencies based on default rates. So Indian Credit Rating Agencies have to improve the accuracy & timeliness of the ratings of normal non structured products.

Further reading