The Altman Z-Score: Predicting Bankruptcy From Five Ratios (With a Worked Example)

A company can look profitable right up to the quarter it files for bankruptcy. Earnings are an opinion; solvency is a fact — and the two do not always move together. The question a careful investor asks about a cheap stock is not only "is it undervalued?" but "will it still be here in two years?".

In 1968, a young finance professor named Edward Altman set out to answer that second question with arithmetic. He took a group of manufacturers that had gone bankrupt, a matched group that had not, and searched for the combination of financial ratios that best told them apart. The result was the Z-Score: five ratios, five weights, one number.

What the Z-Score measures

The Z-Score does not measure value, quality or growth. It measures distance from bankruptcy — the odds that a company will fail within about two years. A high score signals comfortable solvency; a low score signals a balance sheet sending distress signals a flattering income statement can hide.

That makes it the natural companion to a valuation screen. A low P/E says a stock is cheap. The Z-Score says whether cheap means an opportunity or a terminal decline — the same question the Piotroski F-Score asks from a different angle, and the trap the warning signs of a value trap are built to catch.

The five ratios

Each ratio is read from the same statements — the balance sheet and the income statement.

Notice what dominates. X3 — operating profitability — carries the heaviest weight, because a business that cannot earn on its assets eventually cannot pay for them. X2 quietly penalizes young companies, which have had little time to accumulate retained earnings: a feature when you are judging survival, a flaw when the company is simply new.

The formula and its zones

For a publicly traded manufacturer, Altman's original formula is:

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

The single number lands in one of three zones:

• Z above 2.99 — the safe zone. Bankruptcy within two years is unlikely.
• Z between 1.81 and 2.99 — the grey zone. Neither clearly safe nor clearly failing; watch closely.
• Z below 1.81 — the distress zone. A meaningfully elevated risk of failure.

The thresholds are not laws of nature. They are the lines that best separated Altman's 1968 sample, and he has noted since that they drift over time as accounting and leverage norms change.

A worked example

Take a manufacturer with these figures. All numbers are illustrative, chosen to show the calculation.

The five ratios:

• X1 = 300 / 1,000 = 0.30
• X2 = 400 / 1,000 = 0.40
• X3 = 120 / 1,000 = 0.12
• X4 = 600 / 500 = 1.20
• X5 = 900 / 1,000 = 0.90

Applying the weights:

Z = (1.2 × 0.30) + (1.4 × 0.40) + (3.3 × 0.12) + (0.6 × 1.20) + (1.0 × 0.90) Z = 0.36 + 0.56 + 0.40 + 0.72 + 0.90 = 2.94

At 2.94, the company sits in the grey zone — just below the 2.99 safety line. Not condemned, not in the clear. That in-between result is the honest one for many real businesses, and it is exactly where the score earns its keep: it refuses to call safe a company that is one bad year from trouble.

Two variants worth knowing

The original formula assumes a listed manufacturer. Altman published adaptations for the cases it does not fit:

• Z' (Z-prime), for private companies. X4 uses the book value of equity instead of market value, with re-estimated weights — because a private firm has no share price.
• Z'' for non-manufacturers and emerging markets. X5 (sales / assets) is dropped entirely, because asset intensity varies wildly across service industries and would otherwise distort the score, and the weights are recalibrated.

Running the manufacturing formula on a software company or a bank does not produce a conservative estimate — it produces a meaningless one.

What the Z-Score does not see

• It was built for asset-heavy manufacturers. Asset-light firms, financials and young growth companies break several ratios at once — thin assets distort X5, negative retained earnings sink X2 unfairly.
• X4 moves with the share price. Because it uses market value of equity, a falling stock lowers the Z-Score on its own — which can be circular, since the falling price may be the very fear the score is meant to assess.
• It gives odds, not a date. A distress-zone score is a raised probability, not a claim that failure is imminent. Some low-Z companies recover; some safe-zone companies are undone by a shock no ratio saw coming.
• The thresholds age. Calibrated on one era's bankruptcies, the exact cut-offs drift. The ranking of companies is more durable than the absolute number.

None of this makes it useless. It makes it a screen for fragility, read alongside — never instead of — the business itself.

Where it sits in what we do

Not inside our engine as a literal component — as with the Graham Number and the F-Score, that is deliberate. But the Z-Score asks a question our Health reading takes seriously: could this company fail? Health is where solvency, leverage and the quality of earnings are weighed.

The difference, again, is method. We do not apply one 1968 formula with fixed thresholds; we rank every company against the whole universe, every trading day, because a Z of 2.94 means one thing in a robust market and another in a fragile one. A company in the bottom decile of Health lands on The Avoid List — the list that exists to name the cheap-but-fragile stocks a valuation screen would otherwise hand you as bargains — and is kept out of The Sweet Spot, which opens only to companies whose Health is high. The full rule is on the method page, republished every trading day in the ranking; to run the checks yourself, the stock screener is free.

The Z-Score's lasting lesson is simple: before you ask what a cheap company is worth, ask whether it will live long enough for the question to matter.

This article is information and education. It is not personalized investment advice. Past performance is not a guide to future performance. Investing carries a risk of capital loss.