A Look at Altman's Z-Score

Jun 23, 2011
In 1968, a financial economist from NYU named Edward Altman developed a model for assessing and probabilistically predicting corporate bankruptcy. The formula, known as the Z-score model, was partly unique because it used a previously questionable methodology: multivariate analysis. As Altman notes in his July 2000 paper revisiting the model, the questions to ask once we accept this reasoning are as such: â€ś(1) which ratios are most important in detecting bankruptcy potential, (2) what weights should be attached to those selected ratios, and (3) how should the weights be objectively established.â€ť

Rather than bogging down in the methodology (interested parties can read the paper in the link at the bottom of this article for an in-depth explanation), letâ€™s move forward to the conclusion of the research, and how it set the basis for the Z-score. After evaluating the selected companies, the model Altman developed was as such (in Altmanâ€™s original analysis, this included â€ś66 corporations with 33 firms in each of two group. The bankrupt (distressed) group (Group 1) is manufacturers that filed a bankruptcy petition under Chapter X of the National Bankruptcy Act from 1946 through 1965â€¦ Group 2 consists of a paired sample of manufacturing firms chosen on a stratified random basis.â€ť):

Z = 0.012X1 + 0.014X2 + 0.033X3 + 0.006X4+0.999X5

Where X1 = working capital/total assets, X2 = retained earnings/total assets, X3 = earnings before interest and taxes/total assets, X4 = market value equity/book value of total liabilities, X5 = sales/total assets and Z = overall index; the zones of discrimination were as such:

â€śDistressâ€ť Zones - 1.81< â€śGreyâ€ť Zones< 2.99 - â€śSafeâ€ť Zones

The explanation (and accompanying notes from Altman) for the variables are as follows:

X1 â€“ â€śmeasure of the net liquid assets of the firm relative to the total capitalization. Working capital is defined as the difference between current assets and current liabilities. Liquidity and size characteristics are explicitly considered. Ordinarily, a firm experiencing consistent operating losses will have shrinking current assets in relation to total assets. Of the three liquidity ratios evaluated, this one proved to be the most valuable. Two other liquidity ratios tested were the current ratio and the quick ratio. There were found to be less helpful and subject to perverse trends for some failing firms.â€ť

An important side note here is to watch out for inventory's impact on current assets; a low, quick ratio and inventory with slow turn is a bad combination.

X2 â€“ â€śIt should be noted that the retained earnings account is subject to 'manipulation' via corporate quasi-reorganizations and stock dividend declarations. While these occurrences are not evident in this study, it is conceivable that a bias would be created by a substantial reorganization or stock dividend and appropriate readjustments should be made to the accounts. The age of a firm is implicitly considered in this ratio. For example, a relatively young firm will probably show a low RE/TA ratio because it has not had time to build up its cumulative profits. Therefore, it may be argued that the young firm is somewhat discriminated against in this analysis, and its chance of being classified as bankrupt is relatively higher than that of another older firm. But, this is precisely the situation in the real world. The incidence of failure is much higher in a firmâ€™s earlier years. In 1993, approximately 50% of all firms that failed did so in the first five years of their existence. In addition, the RE/TA ratio measures the leverage of a firm. Those firms with high RE, relative to TA, have financed their assets through retention of profits and have not utilized as much debt.â€ť

The â€śmanipulationâ€ť of retained earnings can generate misleading results, with the classic example being Microsoftâ€™s (MSFT) negative retained earnings due to dividend payouts. Make sure to note when these instances appear and adjust your data accordingly.

X3 â€“ â€śThis ratio is a measure of the true productivity of the firmâ€™s assets, independent of any tax or leverage factors. Since a firmâ€™s ultimate existence is based on the earning power of its assets, this ratio appears to be particularly appropriate for studies dealing with corporate failure. Furthermore, insolvency in a bankrupt sense occurs when the total liabilities exceed a fair valuation of the firmâ€™s assets with value determined by the earning power of the assets. As we will show, this ratio continually outperforms other profitability measures, including cash flow.â€ť

From my perspective, X3 is the only stand-alone operating measure in the model, and shows the capacity to which a firm can â€śescapeâ€ť the trappings of X1, X2, and X3, which are balance sheet items; a strong performance in X3 figures will often be how the remaining variables are improved over time.

X4 â€“ â€śThe measure shows how much the firmâ€™s assets can decline in value (measured by market value of equity plus debt) before the liabilities exceed the assets and the firm becomes insolvent. It appears to be a more effective predictor of bankruptcy than a similar, more commonly used ratio; net worth/total debt (book values).â€ť

X5 â€“ â€śThis final ratio is quite important because it is the least significant ratio on an individual basis. In fact, based on the univariate statistical significance test, it would not have appeared at all. However, because of its unique relationship to other variables in the model, the sales/total assets ratio ranks second in its contribution to the overall discriminating ability of the model.â€ť

As Altman notes, â€śOver the years many individuals have found that a more convenient specification of the model is of the form: Z = 1.2X1 + 1.4X2 + 3.3X3 + 0.6X4 + 1.0X5â€ť. The reason is due to screwy input methodology for the original model, which could easily cause user error and result in inaccurate and useless outputs.

To date, the model has proven successful at indicating potential issues; at the time of writing, Altman had this to say: â€śIn repeated tests up to the present (1999), the accuracy of the Z-Score model on samples of distressed firms has been in the vicinity of 80-90%, based on data from one financial reporting period prior to bankruptcy.â€ť However, there is one glaring problem with the results â€“ â€śit is suggested that the Z-Score model is an accurate forecaster of failure up to two years prior to distress and that accuracy diminishes substantially as the lead time increases.â€ť

Personally, I think the applicability of the model extends beyond the output and (as a corollary) the â€śzoneâ€ť the firm falls into. I believe that by breaking down the model into its individual parts, you are given a picture of what is creating the financial distress at the company (if any); when you chart the results over a couple of quarters/years, you are also given a timeline of how the variables have transformed over time. With these pieces in hand, you can assess how the firm must adjust their capital structure or operating results to continue as a going concern.

Link to paper: http://pages.stern.nyu.edu/~ealtman/Zscores.pdf