A distress indicator for the going concern file
Edward Altman's 1968 Z-score combines five financial ratios into one number intended to separate firms heading for bankruptcy from firms that are not. It is a screening aid. In an audit or review, a low score is one of the conditions and events to weigh in the evaluation under AU-C 570 and ASC 205-40, next to the cash flow forecast, debt maturities and covenant compliance. See going concern under AU-C 570 and the going concern checklist.
The three models
- Z (public manufacturers): 1.2, 1.4, 3.3, 0.6 and 1.0 on X1 to X5, with market value of equity in X4. Distress below 1.81, safe above 2.99.
- Z' (private manufacturers): 0.717, 0.847, 3.107, 0.420 and 0.998, with book value of equity in X4. Distress below 1.23, safe above 2.90.
- Z'' (non-manufacturers and private firms): 6.56, 3.26, 6.72 and 1.05 on X1 to X4, with no sales ratio and book equity. Distress below 1.1, safe above 2.6.
Ratios: X1 = (current assets − current liabilities) ÷ total assets; X2 = retained earnings ÷ total assets; X3 = EBIT ÷ total assets; X4 = equity ÷ total liabilities; X5 = sales ÷ total assets. Ratios are used as decimals. Worked check, labelled illustrative: with X1 = 0.1333, X2 = 0.2667, X3 = 0.1333, X4 = 1.5 and X5 = 1.0, Z' = 0.0956 + 0.2259 + 0.4143 + 0.6300 + 0.9980 = 2.364 (terms rounded), which is in the grey zone.
When to use it, and limits
- Pick the model that fits the entity. Applying Z to a private company with a book-value equity figure, or to a service firm, gives a score the cut-offs were not built for.
- Use figures from the same balance sheet date, with EBIT and sales for the full year. A short or distorted period gives a distorted score.
- The cut-offs reflect the samples the models were fitted to. Treat a score near a cut-off as inconclusive and do not rely on it alone.
- It cannot see liquidity that does not show on the balance sheet, such as an undrawn line of credit or a committed equity injection, or a covenant breach waiting to be called.
Illustrative figures only. Check the result against your firm's methodology before relying on it.
Common questions
What is the Altman Z-score formula?
For public manufacturers, Z = 1.2 X1 + 1.4 X2 + 3.3 X3 + 0.6 X4 + 1.0 X5. X1 is working capital over total assets, X2 retained earnings over total assets, X3 EBIT over total assets, X4 market value of equity over total liabilities and X5 sales over total assets. Scores below 1.81 are the distress zone and above 2.99 the safe zone.
Which Altman model should I use for a private company?
Use Z', which swaps book value of equity for market value in X4 and refits the coefficients: Z' = 0.717 X1 + 0.847 X2 + 3.107 X3 + 0.420 X4 + 0.998 X5, with distress below 1.23 and safe above 2.90. For non-manufacturers and many service businesses, Z'' drops the sales ratio: Z'' = 6.56 X1 + 3.26 X2 + 6.72 X3 + 1.05 X4, with distress below 1.1 and safe above 2.6.
Can the Z-score replace the going concern evaluation?
No. AU-C 570 asks the auditor to evaluate whether conditions and events, considered in the aggregate, raise substantial doubt about the entity's ability to continue as a going concern, including management's plans. It does not prescribe a scoring model. A score is one analytical indicator to put next to cash flow, covenants and debt maturities.
What does the grey zone mean?
It is the range between the distress and safe cut-offs, where the model did not separate failed from surviving firms in its sample. A grey score gives no answer either way, so look at which ratios pull the score down and at liquidity and debt service directly.
Why would the model misjudge a company?
It was fitted to historical samples of failed and surviving firms, so it fits best where the entity looks like the sample. Start-ups, firms with large intangible assets, real estate, financial institutions, recent restructurings and unusual capital structures can score badly or well for reasons unrelated to failure risk. Negative equity is allowed but makes X4 negative.
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