Altman Z-score
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For the concept of standard score in statistics, often called the z-score, see Standard
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
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
1The formula
2Precedents
3Accuracy and effectiveness
4Original Z-score component definitions
5Z-score estimated for non-manufacturers and emerging markets
6See also
7References
8Further reading
9External links
The formula[edit]
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 = working capital / total assets. Measures liquid assets in relation to the size of
the company.
X2 = retained earnings / total assets. Measures profitability that reflects the
company's age and earning power.
X3 = 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.
X4 = market value of equity / book value of total liabilities. Adds market dimension
that can show up security price fluctuation as a possible red flag.
X5 = 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.
Precedents[edit]
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[edit]
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[edit]
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[edit]
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
discriminat
ion:
Z > 2.6 – "safe" zone
1.1 < Z < 2.6 – "grey" zone
Z < 1.1 – "distress" zone
