The Altman Z-Score: Formula, Zones, Calculation and Limits

A bank credit officer in Lagos has twenty minutes to decide whether to renew the borrowing facility of a listed manufacturer. He cannot study the board. He has the company’s accounts and one question: is this business moving towards financial distress?

In 1968 the American professor Edward Altman showed that five ratios, combined in one formula, separated companies that went bankrupt from those that did not, correctly for most of the companies he tested up to two years before failure. The result is the Z-score. It is widely used because it needs only published figures, and it is widely criticised for the same reason.

This topic sets out the formula, the meaning of each ratio, the three zones, how to calculate and read a score, the version for private companies, and the limits of the model. It builds on the course so far, especially the work on key performance indicators in information needs at each level of management. The next topic covers the Argenti model and qualitative failure prediction.

The formula and the ratios

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

• X1 = working capital ÷ total assets. Working capital is current assets less current liabilities. It measures liquid assets in relation to the size of the business. A falling or negative X1 shows liquidity trouble.
• X2 = retained earnings ÷ total assets. It measures cumulative profitability and the age of the business: young companies and those that have lost money have low values. It also shows how much of the assets were financed from the company’s own profit.
• X3 = earnings before interest and tax ÷ total assets. It measures the productivity of the assets whatever the financing, and carries the largest weight because earning power is the best guard against failure.
• X4 = market value of equity ÷ total liabilities. It shows how far the value of the business could fall before liabilities exceed assets. It needs a share price, so it applies only to listed companies.
• X5 = sales ÷ total assets. The asset turnover, a measure of how well the assets generate sales.

Use the ratios as decimals, not percentages: 0.15, not 15. The coefficients show how much each ratio contributes to separating failing from sound companies.

The zones

• Safe zone: Z above 2.99. Low chance of failure in the next two years.
• Grey zone: Z from 1.81 to 2.99. Uncertain. Both false alarms and misses are common, so the company needs close monitoring and more analysis.
• Distress zone: Z below 1.81. High chance of failure within about two years.

Other versions

The original model was built for listed manufacturing companies. Altman later produced versions for others. The version for private manufacturing companies is Z′ = 0.717 X1 + 0.847 X2 + 3.107 X3 + 0.420 X4 + 0.998 X5, where X4 uses the book value of equity instead of market value. Its zones are safe above 2.9, grey from 1.23 to 2.9 and distress below 1.23. A version for non-manufacturers and emerging markets drops the sales ratio and has its own constants and zones.

The coefficients and zones always go together, so never mix a version’s coefficients with another’s zones.

Using and judging the score

Advantages

• Objective and quick. It uses published figures, needs no judgement in scoring and can be applied to many companies at once.
• One summary measure that combines liquidity, profitability, leverage and activity.
• Tested. Altman found it classified correctly a high proportion of companies up to two years before failure.
• Can be tracked over time. A falling score is an early warning even if the zone has not changed.
• Pointers to the cause. The five terms show which ratio is dragging the score down.

Limitations

• Historical accounts. It looks backwards and relies on accounting figures, which can be affected by accounting policy and creative accounting.
• Ignores management and governance, the cause of many failures.
• Built on one sample of American listed manufacturers in a certain period, so it may not suit other industries, countries or economic conditions, such as high inflation and exchange rate shocks.
• Needs a share price for the original model, and market values can swing for reasons other than the company’s health.
• The grey zone is wide, so many companies get no clear answer.
• A signal, not a certainty. A low score means higher risk, not that failure is sure.
• Asset-light and service businesses score differently from manufacturers.

For this reason the score should be read with qualitative information about management, governance and the market, and with the trend, not only the level.

Calculating the Z-score

1. Find the five items: working capital, retained earnings, EBIT, market value of equity (or book value for the private version), total liabilities, sales and total assets.
2. Calculate each ratio as a decimal.
3. Multiply each by its coefficient (1.2, 1.4, 3.3, 0.6, 1.0 for the original) and add.
4. Compare with the zone limits (2.99 and 1.81).
5. Comment: which terms are strong or weak, the trend, and what to do.

Money is in ₦ million. Ratios are shown to two decimal places unless a fourth place is needed, and the final score is rounded once, at the end.

Worked examples

1. X1.
   120 ÷ 800 = 0.15.
   X2. 200 ÷ 800 = 0.25.
   X3. 96 ÷ 800 = 0.12.
   X4. 480 ÷ 400 = 1.20.
   X5. 1,040 ÷ 800 = 1.30.
2. Z.
   1.2 × 0.15 = 0.180
   1.4 × 0.25 = 0.350
   3.3 × 0.12 = 0.396
   0.6 × 1.20 = 0.720
   1.0 × 1.30 = 1.300.
   Total 2.95.
3. Zone. 2.95 is between 1.81 and 2.99: the grey zone, just below the safe line.
4. Comment. The company is not in distress, but a small deterioration would take it out of safety. The management should watch working capital and earnings.

1. X1.
   40 ÷ 800 = 0.05.
   X2. 150 ÷ 800 = 0.1875.
   X3. 24 ÷ 800 = 0.03.
   X4. 240 ÷ 480 = 0.50.
   X5. 800 ÷ 800 = 1.00.
2. Z.
   0.060 + 0.2625 + 0.099 + 0.300 + 1.000 = 1.72.
3. Zone. Below 1.81: the distress zone. The score fell by 1.23 in one year.
4. Comment. Every term fell, but earning power (X3) and the market view (X4) fell most. The cause is the collapse in profit and the fall in share price. The company should act on costs and on its borrowing at once, and a lender should review the facility.

Expect variants: the private-company formula, a table of ratios already worked out, a question asking which ratio explains a change, or a request to combine the result with a qualitative review.

Where the multi-ratio approach came from

An early use of ratios to predict failure was William Beaver’s study in the 1960s, which compared failed and non-failed companies one ratio at a time. He found that the ratio of cash flow to total debt was the most significant single indicator.

Its weakness is that one ratio on its own is not a reliable predictor: it is hard to say when a single ratio is at a dangerous level, ratios change over time, and ratios can give contradictory signals (poor liquidity with good profitability). The answer was a model that combines several ratios, each given a weighting, into one score, which is how the Z-score is built.

Common mistakes

• Using percentages instead of decimals. 0.15 is correct, 15 is wrong.
• Mixing the ratio definitions. X4 uses market value of equity over total liabilities, not over total assets.
• Using the wrong zone limits for the version of the model.
• Stopping at the zone. Comment on the terms and the trend.
• Treating the score as certain. It signals risk.
• Ignoring limits. Historical data, no management view and one-sample origin are the usual points.

Quick revision

• Z = 1.2 X1 + 1.4 X2 + 3.3 X3 + 0.6 X4 + 1.0 X5.
• X1 working capital ÷ total assets; X2 retained earnings ÷ total assets; X3 EBIT ÷ total assets; X4 market value of equity ÷ total liabilities; X5 sales ÷ total assets.
• Zones: above 2.99 safe; 1.81 to 2.99 grey; below 1.81 distress.
• Private version: 0.717, 0.847, 3.107, 0.420, 0.998; zones 2.9 and 1.23.
• Strengths: objective, quick, tested. Limits: historical accounts, ignores management, one sample, wide grey zone.

How the marks are earned

• Calculate: each ratio, each weighted term and the total.
• Interpret: the zone and the main contributors.
• Discuss: two advantages, two limits and the case for using a qualitative model as well.

Practice questions

These are original questions, written in the style of the Skills examination. Work each one before you open the answer.

Recall check: multiple choice

Section B style: written questions

Model answers

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