Predicting financial distress
In 1968 Edward Altman, a professor at New York University, used a statistical technique called discriminant analysis on 66 US manufacturers, half of which had gone bankrupt. He found that five ratios, weighted and added together, separated the two groups remarkably well. The resulting Z-score is still one of the best-known tools in credit analysis.
The original formula
Z = 1.2 X1 + 1.4 X2 + 3.3 X3 + 0.6 X4 + 1.0 X5
| Ratio | Measures |
|---|---|
| X1 = working capital ÷ total assets | Liquidity |
| X2 = retained earnings ÷ total assets | Accumulated profitability and age |
| X3 = EBIT ÷ total assets | Operating profitability |
| X4 = market value of equity ÷ total liabilities | Solvency cushion |
| X5 = sales ÷ total assets | Asset turnover |
| Z | Zone |
|---|---|
| Above 2.99 | Safe |
| 1.81 to 2.99 | Grey |
| Below 1.81 | Distress |
Worked example
A listed manufacturer with $10 million of total assets, $1.5 million of working capital, $3 million of retained earnings, $1.2 million of EBIT, a market capitalization of $6 million, $4 million of liabilities and $12 million of sales:
| Ratio | Value | Weighted |
|---|---|---|
| X1 | 0.150 | 0.18 |
| X2 | 0.300 | 0.42 |
| X3 | 0.120 | 0.40 |
| X4 | 1.500 | 0.90 |
| X5 | 1.200 | 1.20 |
| Z | 3.10, safe zone |
Variants
- Z′ (private companies): uses the book value of equity instead of market value. Z′ = 0.717 X1 + 0.847 X2 + 3.107 X3 + 0.420 X4 + 0.998 X5, with a distress zone below 1.23 and a safe zone above 2.90.
- Z″ (non-manufacturers and emerging markets): drops X5, which varies widely across industries. Z″ = 6.56 X1 + 3.26 X2 + 6.72 X3 + 1.05 X4, with zones at 1.10 and 2.60.
How to use it
The Z-score is a screening tool. It flags companies whose balance sheet and profitability look like those of firms that failed in the past. Track it over several years: a steady decline matters more than one value. Combine it with cash flow analysis, debt maturities and interest coverage.
Limits
The weights were estimated on 1960s US manufacturers. They are less reliable for very different businesses, such as software companies with few tangible assets. The score is not meaningful for banks, insurers or other financial firms, and accounting choices can move the ratios.
This calculator gives estimates for education and planning. It is not investment, tax or legal advice; for decisions about your own situation, talk to a qualified financial professional.