The Portable MBA in Finance and Accounting, 3rd Edition

32 Understanding the Numbers

Edward Altman of New York University. Its reliability can be expressed in
terms of the two types of errors to which all predictive methods are vulner-
able, namely:

1. Type I error: predicting solvency when in fact a firm becomes bankrupt
   (a false positive).


2. Type II error: predicting bankruptcy when in fact a firm remains solvent
   (a false negative).

The predictive error rates for the Altman zscore have been found to be as
follows:

Years Prior to % False % False

Bankruptcy Positives Negatives

163

2186

Given the inherent difficulty of predicting future events, these error rates are
relatively low, and therefore the Altman zscore is generally regarded as a rea-
sonably reliable bankruptcy predictor. The zscore is calculated from financial
ratios in the following manner:

Azscore above 2.99 predicts solvency; a zscore below 1.81 predicts bank-
ruptcy; zscores between 1.81 and 2.99 are in a gray area, with scores above
2.675 suggesting solvency and scores below 2.675 suggesting bankruptcy.
Since the zscore uses equity at market value, it is not applicable to pri-
vate firms, which do not issue marketable securities. A variation of the zscore
for private firms, known as the z′score, has been developed that uses the book
value of equity rather than the market value. Because of this modification, the
multipliers in the formula have changed from those in the original zscore, as
have the scores that indicate solvency, bankruptcy, or the gray area. For non-
manufacturing service-sector firms, a further variation in the formula has
been developed. It omits the variable for asset turnover and is known as the z′′
score. Once again, the multipliers in the formula have changed from those in
the z′score, and so have the scores that indicate solvency, bankruptcy, or the
gray area.
Professor Altman later developed a bankruptcy predictor more refined
than the zscore and named it ZETA. ZETA uses financial ratios for times in-
terest earned, return on assets (the average and the standard deviation), and
debt to equity. Other details of ZETA have not been made public. ZETA is
proprietary and is made available to users for a fee.

z= × +× +×

+× +×

12 14 33

06 10

...
..

Working Capital

Total Assets

Retained Earnings

Total Assets

EBIT

Total Assets

Equity at Market Value

Debt

Sales

Total Assets