How To Calculate A Z-Score

By Ben McClure AAA

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. (For background reading, check out An Overview Of Corporate Bankruptcy.)

Tutorial: Financial Ratios

In a bid to resolve this conundrum, NYU Professor Edward Altman introduced the 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. Here we look at how to calculate the Z-score and how investors can use it to help make buy and sell decisions.

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

Z-Score = 1.2A + 1.4B + 3.3C + 0.6D + 1.0E


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

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

Breaking Down the Z
Now that we know the formula, it's helpful to examine why these particular ratios are included. Let's take a look at the significance of each one:

  • 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 simply is not enough current assets to cover those obligations. By contrast, a firm with significantly positive working capital rarely has trouble paying its bills. (For background reading, see Working Capital Works.)
  • 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 )
    This is a version of return on assets (ROA), an effective way of assessing a firm's ability to squeeze profits from its assets before factors like interest and tax are deducted.
  • Market Value of Equity/Total Liabilities (ME/TL)
    This is a ratio that shows - 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 Z-score, let's look at how it holds up with a tricky test case. Consider the infamous collapse of telecommunications giant WorldCom in 2002. WorldCom's bankruptcy created $100 billion in losses for its investors after management falsely recorded billions of dollars as capital expenditures rather than operating costs.

Here we calculate Z-scores for WorldCom using annual 10-K financial reports for years ending December 31, 1999, 2000 and 2001. Indeed, 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 declaring bankruptcy in 2002.

Input Financial Ratio 1999 2000 2001
X1 Working capital/ Total Assets -0.09 -0.08 0
X2 Retained earnings/Total Assets -0.02 0.03 0.04
X3 EBIT/Total Assets .09 .08 .02
X4 Market Value/Total Liabilities 3.7 1.2 .50
X5 Sales/Total Assets 0.51 0.42 0.3
Z-score 2.5 1.4 .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 actually 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. (For more on corporate accounting gone wrong, see Cooking The Books 101.)

Where Z-Score Falls Short

Alas, the Z-score is not perfect 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 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 net working capital-to-asset ratio. After all, it takes cash to pay the bills.

Finally, 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 really not at risk is on the brink of bankruptcy.

To keep an eye on their investments, investors should consider checking their companies' Z-score on a regular basis. A deteriorating Z-score can signal trouble ahead and provide a simpler conclusion than the 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 financial health, but if the score indicates a problem, it's a good idea to conduct a more detailed analysis.

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