How to Calculate an Altman Z-Score

How do you know when a company is at risk of corporate collapse? To detect any signs of looming bankruptcy, investors calculate and analyze all kinds of financial ratios: working capital, profitability, debt levels, and liquidity. The trouble is, each ratio is unique and tells a different story about a firm's financial health. At times they can even appear to contradict each other. Having to rely on a bunch of individual ratios, the investor may find it confusing and difficult to know when a stock is going to the wall.

In a bid to resolve this conundrum, New York University professor Edward Altman introduced his Z-score formula in the late 1960s. Rather than search for a single best ratio, Altman built a model that distills five key performance ratios into a single score. As it turns out, the Z-score gives investors a pretty good snapshot of corporate financial health.

Note that the Altman Z-score should not be confused with the z-score determined through a z-test, a test of statistical significance similar to a t-test.

Key Takeaways

  • The Z-score is a heuristic formula developed to estimate the chances of a company going bankrupt.
  • The formula looks at working capital, retained earnings, and EBIT, all relative to a firm's total assets.
  • A Z-score above 3.0 signals good financial health, while a score below 1.8 suggests a high risk of bankruptcy.

Altman Z-Score Formula

The Altman Z-score formula for manufacturing firms, which is built out of the five weighted financial ratios:

Z-score = ( 1.2 × A ) + ( 1.4 × B ) + ( 3.3 × C ) + ( 0.6 × D )   + ( 1.0 × E ) where: A = Working Capital ÷ Total Assets B = Retained Earnings ÷ Total Assets C = Earnings Before Interest & Tax ÷ Total Assets D = Market Value of Equity ÷ Total Liabilities E = Sales ÷ Total Assets \begin{aligned} &\text{Z-score} = (1.2 \times A) + (1.4 \times B) + (3.3 \times C) + (0.6 \times D) \\ &\qquad \qquad \ + (1.0 \times E) \\ &\textbf{where:}\\ &A = \text{Working Capital} \div \text{Total Assets} \\ &B = \text{Retained Earnings} \div \text{Total Assets} \\ &C = \text{Earnings Before Interest \& Tax} \div \text{Total Assets} \\ &D = \text{Market Value of Equity} \div \text{Total Liabilities} \\ &E = \text{Sales} \div \text{Total Assets} \\ \end{aligned} Z-score=(1.2×A)+(1.4×B)+(3.3×C)+(0.6×D) +(1.0×E)where:A=Working Capital÷Total AssetsB=Retained Earnings÷Total AssetsC=Earnings Before Interest & Tax÷Total AssetsD=Market Value of Equity÷Total LiabilitiesE=Sales÷Total Assets

Strictly speaking, the lower the score, the higher the odds are that a company is heading for bankruptcy. An Altman Z-score of lower than 1.8, in particular, indicates that the company is on its way to bankruptcy. Companies with scores above 3 are unlikely to enter bankruptcy. Scores in between 1.8 and 3 define a gray area.

Understanding the Altman Z-Score

It's helpful to examine why these particular ratios are part of the Altman Z-score. Why is each significant?

Working Capital/Total Assets (WC/TA)

This ratio is a good test for corporate distress. A firm with negative working capital is likely to experience problems meeting its short-term obligations because there are simply not enough current assets to cover those obligations. By contrast, a firm with significantly positive working capital rarely has trouble paying its bills.

Retained Earnings/Total Assets (RE/TA)

This ratio measures the amount of reinvested earnings or losses, which reflects the extent of the company's leverage. Companies with low RE/TA are financing capital expenditure through borrowings rather than through retained earnings. Companies with high RE/TA suggest a history of profitability and the ability to stand up to a bad year of losses.

Earnings Before Interest and Tax/Total Assets (EBIT/TA)

The ratio Earnings Before Interest and Tax/Total Assets (EBIT/TA) is a version of return on assets (ROA), an effective way of assessing a firm's ability to squeeze profits from its assets before deducting factors like interest and tax.

Market Value of Equity/Total Liabilities (ME/TL)

This ratio shows that if a firm were to become insolvent, how much the company's market value would decline before liabilities exceed assets on the financial statements. This ratio adds a market value dimension to the model that isn't based on pure fundamentals. In other words, a durable market capitalization can be interpreted as the market's confidence in the company's solid financial position.

Sales/Total Assets (S/TA)

This tells investors how well management handles competition and how efficiently the firm uses assets to generate sales. Failure to grow market share translates into a low or falling S/TA.

WorldCom Test

To demonstrate the power of the Altman Z-score, test how it holds up with a tricky test case. Consider the infamous collapse of telecommunications giant WorldCom in 2002. WorldCom's bankruptcy cost investors $200 billion in losses after management falsely recorded billions of dollars as capital expenditures rather than operating costs.

Calculate Z-scores for WorldCom using annual 10-K financial reports for years ending Dec. 31, 1999, 2000, and 2001.You'll find that WorldCom's Z-score suffered a sharp fall. Also note that the Z-score moved from the gray area into the danger zone in 2000 and 2001, before the company declared bankruptcy in 2002.

Input Financial Ratio 1999 2000 2001
X1 Working capital/ Total Assets -0.09 -0.08 0.00
X2 Retained earnings/Total Assets -0.02 0.03 0.04
X3 EBIT/Total Assets 0.09 0.08 0.02
X4 Market Value/Total Liabilities 3.70 1.20 0.50
X5 Sales/Total Assets 0.51 0.42 0.30
Z-score: 2.50 1.40 0.85

But WorldCom management cooked the books, inflating the company's earnings and assets in the financial statements. What impact do these shenanigans have on the Z-score? Overstated earnings likely increase the EBIT/total assets ratio in the Z-score model, but overstated assets would shrink three of the other ratios with total assets in the denominator. So the overall impact of the false accounting on the company's Z-score is likely to be downward.

Altman Z-Score Disadvantages

The Altman Z-score is not a perfect metric and needs to be calculated and interpreted with care. For starters, the Z-score is not immune to false accounting practices. As WorldCom demonstrates, companies in trouble may be tempted to misrepresent financials. The Z-score is only as accurate as the data that goes into it.

The Altman Z-score also isn't much use for new companies with little or no earnings. These companies, regardless of their financial health, will score low. Moreover, the Z-score doesn't address the issue of cash flows directly, only hinting at it through the use of the networking capital-to-asset ratio. After all, it takes cash to pay the bills.

Z-scores can swing from quarter to quarter when a company records one-time write-offs. These can change the final score, suggesting that a company that's not at risk is on the brink of bankruptcy.

To keep an eye on their investments, investors should consider checking their companies' Z-score regularly. A deteriorating Z-score can signal trouble ahead and provide a simpler conclusion than a mass of ratios.

Given its shortcomings, the Z-score is probably better used as a gauge of relative financial health rather than as a predictor. Arguably, it's best to use the model as a quick check of economic health, but if the score indicates a problem, it is a good idea to conduct a more detailed analysis.

Article Sources
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  1. NYU Stern School of Business. "Professor Edward Altman Launches Digital App for Renowned Z-Score, "Altman Z-Score Plus"."

  2. NYU Stern School of Business. "Predicting Financial Distress of Companies: Revisiting the Z-Score and Zeta Models," Page 18, 26.

  3. Govinfo.gov. "The Worldcom Case: Looking at Bankruptcy and Competition Issues."

  4. GetFilings.com "WorldCom 10-K (1999)."

  5. U.S. Securities and Exchange Commission. "WorldCom 10-K (2001)."

  6. U.S. Securities and Exchange Commission. "WorldCom 10-K (2002)."

  7. U.S. Securities and Exchange Commission. "Report of Investigation by the Special Investigative Committee of the Board of Directors of Worldcom, Inc."

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