What the Z-score measures
Edward Altman published the model in 1968. He took 66 US manufacturers, half of which had filed for bankruptcy, and used a statistical method called discriminant analysis to find the combination of ratios that best separated the two groups. Five ratios, each with its own weight, made the cut.
The score rises with liquidity, with profits kept in the business, with operating earnings, with the cushion of equity over debt and with sales relative to assets. In Altman’s samples, companies that later failed tended to have low scores.
The five ratios
- X1, working capital to total assets. Current assets minus current liabilities, relative to the size of the business. Companies running short of cash tend to see working capital shrink first.
- X2, retained earnings to total assets. How much of the business has been funded by profits it kept. Young companies score lower, because they have had less time to build retained earnings.
- X3, EBIT to total assets. Operating earnings relative to the assets that produce them. It carries the largest weight among the ratios in every version.
- X4, equity to total liabilities. The original model uses the market value of the shares; the private-company and non-manufacturer versions use book equity. Either way, it shows how far the value of the business could fall before its liabilities exceed it.
- X5, sales to total assets. Asset turnover. It varies a lot between industries, which is why the non-manufacturer version leaves it out.
Which version to use
- Original Z. Public manufacturing companies, whose share price gives a market value for X4.
- Z′ (Z prime). Private manufacturing companies. Book equity replaces market value in X4, and the weights are re-estimated.
- Z″ (Z double prime). Non-manufacturers and service companies. It drops X5 and uses book equity.
Choose the version in the calculator above. Each one has its own zones, so a score from one version cannot be read against another version’s zones.
Reading the score
| Version | Distress zone | Grey zone | Safe zone |
|---|---|---|---|
| Original Z | Below 1.81 | 1.81 to 2.99 | Above 2.99 |
| Z′ (private) | Below 1.23 | 1.23 to 2.90 | Above 2.90 |
| Z″ (non-manufacturer) | Below 1.10 | 1.10 to 2.60 | Above 2.60 |
The zones describe where companies that later failed tended to score in Altman’s samples. A score in the distress zone is a reason to look closely at liquidity, debt and cash flow; it is not a prediction that a particular company will fail, and a score in the safe zone is no guarantee.
What the Z-score does not show
- It was built on US manufacturers from earlier decades. Later tests found it still separates failing and healthy companies, but how well depends on the period, the industry and the version used.
- It is not designed for banks, insurers and other financial companies, whose balance sheets do not fit the five ratios.
- It uses one balance sheet date and one year’s earnings, so a seasonal business or a one-off result can move it a long way.
- The original version moves with the share price, which can change faster than the business itself.
Common mistakes
- Using the original formula for a private company or a service business instead of Z′ or Z″.
- Using book equity in the original model, or market value in Z′ or Z″.
- Mixing up two forms of the weights. The 1968 paper printed weights such as 0.012 for ratios written as percentages; the familiar 1.2 form expects ratios as decimals.
- Taking the balance sheet and the earnings from different years.
Related measures
The working capital calculator gives the amount behind X1. For a fuller picture of the same statements, run every ratio at once in the financial statement analyzer. The Piotroski F-score looks at whether financial strength is improving, and the Beneish M-score at whether earnings look manipulated.
To keep the calculation, download the Altman Z-score template for Excel or Google Sheets; it shows all three versions side by side.