# THE Z SCORE

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Financial ratios are useful not only to assess the past or present condition of an enterprise, but also to reliably predict its future solvency or bankruptcy. This type of information is of critical importance to present and potential creditors and investors. There are several different methods of analysis for obtaining this predictive information. The best-known and most time-tested is the *z* score, developed for publicly traded manufacturing firms by Professor 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 vulnerable, 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 *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; 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, 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 z score, as have the scores that indicate solvency, bankruptcy, or the gray area. For nonmanufacturing 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 *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.

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