Altman Z-Score, Explained: Reading Bankruptcy Risk With the Exact Formula

The Altman Z-Score compresses five balance-sheet and market ratios into a single number that flags financial distress. Here is the exact formula, what each ratio measures, the zones, the variants, and where the model quietly stops working.

What the Altman Z-Score is

The Z-Score is a bankruptcy-risk model published in 1968 by Edward Altman, then a finance professor at NYU Stern. Working from a sample of 66 publicly traded manufacturing companies — half of which had filed for bankruptcy — Altman used a statistical technique called multiple discriminant analysis to find the combination of financial ratios that best separated the failed firms from the survivors. The output is a single score that places a company on a continuum from financially healthy to distressed.

It was one of the first models to show that a handful of accounting ratios, weighted correctly, could anticipate corporate failure with meaningful accuracy — Altman reported roughly 72% accuracy in identifying bankruptcies two years before they happened, and higher accuracy in the year immediately prior. Nearly six decades later it remains one of the most cited screens in credit and equity research. It is a descriptive statistic, not a prediction of any specific outcome, and it is one input among many.

The exact formula (five ratios)

The original model — often called the Z-Score for public manufacturers — is:

Z = 1.2·X1 + 1.4·X2 + 3.3·X3 + 0.6·X4 + 1.0·X5

Each term captures a different dimension of financial health. The coefficients are the weights Altman's analysis assigned; the ratios themselves are what you compute from the filings.

Notice that X3 carries the heaviest weight (3.3) and X4 injects live market information, which is why the score moves as a stock re-rates, not only when new financials are filed.

The three zones

Altman mapped the score to three interpretive bands. The thresholds below apply to the original public-manufacturer model:

The grey zone is not a failure of the model — it is the model being honest about uncertainty. A score of 2.4 is a signal to dig into the financials, not a conclusion.

A worked example

Take a hypothetical manufacturer with total assets of 1,000: working capital 300, retained earnings 400, EBIT 120, market capitalisation 800, total liabilities 500, and sales 900. The ratios are X1 = 0.30, X2 = 0.40, X3 = 0.12, X4 = 1.60, X5 = 0.90.

• 1.2 × 0.30 = 0.36
• 1.4 × 0.40 = 0.56
• 3.3 × 0.12 = 0.40
• 0.6 × 1.60 = 0.96
• 1.0 × 0.90 = 0.90

Summed, Z ≈ 3.18 — inside the safe zone. Change one input and the picture shifts: if the market cap fell to 200, X4 drops to 0.40, its contribution falls from 0.96 to 0.24, and the score slides into the grey zone even though the underlying business is unchanged. That sensitivity to the equity-value term is a feature to understand, not a flaw to ignore.

The variants: Z' and Z''

The original model assumes a public manufacturer with a market price and an inventory-heavy balance sheet. Altman later published two re-estimated versions for other cases, each with its own coefficients and its own zone cut-offs.

Z' (private firms). Private companies have no market capitalisation, so X4 is redefined as book value of equity over total liabilities, and every weight is re-fitted:

Z' = 0.717·X1 + 0.847·X2 + 3.107·X3 + 0.420·X4 + 0.998·X5

Z'' (non-manufacturers / emerging markets). To reduce the effect of industry differences in asset turnover, the sales ratio X5 is dropped entirely, leaving four terms:

Z'' = 6.56·X1 + 3.26·X2 + 6.72·X3 + 1.05·X4

Applying the wrong variant — or the wrong thresholds — is one of the most common errors. A retailer or software company scored against the manufacturer thresholds will read as misleadingly distressed, purely because service and retail businesses run different asset-turnover profiles.

Limitations and where it does not apply

The Z-Score is a screen, not a verdict, and it has clear boundaries:

• It does not apply to banks, insurers, or other financial firms. Their balance sheets are leveraged by design, deposits and policy reserves inflate liabilities, and ratios like working capital and asset turnover simply do not carry the same meaning. The correct behaviour for a financial company is to abstain — return no score — rather than print a number that looks precise but is meaningless.
• A low score signals balance-sheet stress, not guaranteed failure. Many firms sit in the distress zone for years, refinance, or recover. The score describes a statistical resemblance to firms that later failed in Altman's sample; it does not forecast that any particular company will.
• It is backward- and market-looking. Ratios come from past filings, and X4 moves with the share price, so a market sell-off can push the score down before anything changes operationally.
• It was fitted decades ago on US manufacturers. Accounting standards, capital structures, and asset-light business models have all shifted since, which is exactly why the variants exist and why the score is best read alongside cash-flow, coverage, and qualitative analysis.

Used properly, it is a fast, transparent triage tool: a way to rank a universe and decide where deeper reading is worth your time.

How Quintarthai helps

Quintarthai computes the Altman Z-Score deterministically across the screener and inside each company deep-dive, drawing the underlying ratios from public filings (SEDAR+ / EDGAR) so you can see the inputs behind the number, the zone it falls in, and which variant applies. Banks, insurers, and other financials are correctly flagged to abstain rather than shown a misleading score, and the same calculation runs identically every time you load it.