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The predictive error rates for the Altman Z-Score have been found to be as follows:
Given the inherent difficulty of predicting future events, these error rates are relatively low, and
therefore the Altman Z-Score is generally regarded as a reasonably reliable bankruptcy predictor. The
Z-Score is calculated from financial ratios in the following manner:
A Z-Score above 2.99 predicts solvency, and a Z-Score below 1.81 predicts bankruptcy. Z-Scores
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 Z-Score uses equity at market value, it is not applicable to private firms, which do not
issue marketable securities. A variation of the Z-Score for private firms has been developed. It is
known as the Z‟ Score, and uses the book value of equity rather than the market value. Due to this
modification, the multipliers in the formula have changed from those in the original Z-Score, and so
have the scores that indicate solvency, bankruptcy, or the gray area. For firms that are not
manufacturers but are in the service sector, 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 the original Z-Score, and so have the scores that
indicate solvency, bankruptcy, or the gray area.
Professor Altman later developed a more refined bankruptcy predictor than the Z-Score and named
it ZETA. ZETA uses financial ratios for times interest 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.
Summary and Conclusions
Financial ratios contain critically important business information and are used for many different
purposes by many different parties inside the business and outside of the business. Clearly all