How to Calculate a 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.

Tutorial: Financial Ratios

In a bid to resolve this conundrum, New York University 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.

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

$\begin{aligned} &\text{Z-Score} = (1.2 \times A) + (1.4 \times B) + (3.3 \times C) + (0.6 \times D) + (1.0 \times E)\\ &\textbf{where:}\\ &A = \text{Working Capital} \div \text{Total Assets} \\ &B = \text{Retained Earnings} \div \text{Total Assets} \\ &C = \text{Earnings Before Interest \& Tax} \div \text{Total Assets} \\ &D = \text{Market Value of Equity} \div \text{Total Liabilities} \\ &E = \text{Sales} \div \text{Total Assets} \\ \end{aligned}$​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. A 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.

It's helpful to examine why these particular ratios are part of the 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)

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.

To demonstrate the power of the 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 created $100 billion in losses for its investors 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 December 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.

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.

The 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 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.

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.