# Bankruptcy and the Z-score

The likelihood of a company going bankrupt

A company files for bankruptcy protection when it can no longer pay its expenses since it effectively has no working capital left and cannot raise the funds it needs to continue with its operations.

While there are speculative investing strategies which specifically deal with buying bankruptcy companies, these are best left to the professionals or at least the experienced investor. Famous investors like Benjamin Graham made good use of these hedge fund tactics but they are dangerous for the average investor.

As a general rule, buying while companies under bankruptcy protection is something that is best avoided as the average investor is usually left with nothing or at best very little. Bankruptcy is the end result for a financially distressed company and unfortunately for the stockholders this usually means loss of ownership of the company along with losing their invested capital.

Bankruptcy can result in either the company being liquidated with all its assets sold off to pay its creditors or the company's ownership is effectively handed over to its creditors who allow the company to continue to operate in order to recoup their debts. In the first case once all the creditors are paid and if there are funds left over then the stockholders' receive the balance. If there is no surplus then the stockholders' entire investment is lost. The same applies if the company is handed over to the creditors.

The likelihood of a company ending up in bankruptcy can be determined with a calculation known as the Z-score.

The Z-score was devised by Edward Altman who was a Professor of Finance and the formula utilizes items taken from the income statement and from the balance sheet statement. There are two versions of the Z-score depending on the industry group. The original version was specifically intended for manufacturing companies and a newer version which is more versatile and includes non-manufacturing companies. However neither version is suitable for financial companies.

## Original Z-score

The original Z-score was devised for manufacturing companies with high levels of hard assets. Their revenue is largely dependant on their assets such as plant and machinery.

The Z-score is calculated from five ratios as follows:

Z-score calculation:

X1 = Working Capital / Total Assets

X2 = Retained Earnings / Total Assets

X3 = Earnings Before Interest and Tax / Total Assets

X4 = Market Value of Equity / Total Liabilities

X5 = Revenue / Total Assets

Working Capital = Current Assets - Current Liabilities

Market Value of Equity = Stock price x Diluted shares outstanding

Z-score = (1.2 * X1) + (1.4 * X2) + (3.3 * X3) + (0.6 * X4) + X5

The Z-score provides a probability of a company becoming bankrupt within two years and the bankruptcy risk is broadly classified into three risk categories as follow:

Z-score probability of bankruptcy:

- Low risk: If Z-score greater than 3.0
- Moderate risk: If Z-score between 1.8 and 3.0
- High risk: If Z-score less than 1.8

The Z-score can even be negative and this indicates a very high risk of bankruptcy. Basically the higher the Z-score then the lower the bankruptcy risk. Conversely the lower the Z-score then the higher the bankruptcy risk.

Example: A speculative manufacturing company has a stock price of $10 and 30m diluted shares outstanding and has the following balance sheet items; Current Assets of $60m, Current Liabilities of $40m, Total Assets of $180m, Total Liabilities of $70m and Retained Earnings of $100m. The income statement items are Revenue of $50m and Earnings before Interest and Tax of $15m.

The Z-score is calculated as follows:

Working Capital = 60 - 40 = $20m

Market Value of Equity = 10 * 30m = $300m

X1 = 20 / 180 = 0.11

X2 = 100 / 180 = 0.56

X3 = 15 / 180 = 0.08

X4 = 300 / 70 = 4.29

X5 = 50 / 180 = 0.28

Z-score = (1.2 * 0.11) + (1.4 * 0.56) + (3.3 * 0.08) + (0.6 * 4.29) + 0.28 = 4.0

With a Z-score of 4.0 this company is a low bankruptcy risk since the Z-score is greater than 3.0.

## Revised Z-score

The newer version of the Z-score is used for today's market. It does not use Revenue or Market Value of Equity but instead uses Stockholders' Equity. This version is more general and is intended for the broader market - not just manufactures, but it is not suited to financial companies. The Z-score is calculated from four ratios as follows:

Z-score calculation for general companies:

X1 = Working Capital / Total Assets

X2 = Retained Earnings / Total Assets

X3 = Earnings before Tax and Interest / Total Assets

X4 = Stockholders' Equity / Total Liabilities

Working Capital = Current Assets - Current Liabilities

Z-score = (6.56 * X1) + (3.26 * X2) + (6.72 * X3) + (1.05 * X4)

The Z-score provides a probability of a company becoming bankrupt within two years and the bankruptcy risk is broadly classified into three risk categories as follow:

Z-score probability of bankruptcy for general companies:

- Low risk: If Z-score greater than 2.6
- Moderate risk: If Z-score between 1.1 and 2.6
- High risk: If Z-score less than 1.1

The Z-score can even be negative and this indicates a very high risk of bankruptcy. Basically the higher the Z-score then the lower the bankruptcy risk. Conversely the lower the Z-score then the higher the bankruptcy risk.

Example: A speculative non-manufacturing company has the following balance sheet items; Current Assets of $100m, Current Liabilities of $90m, Total Assets of $200m, Total Liabilities of $180, Retained Earnings of $2m and a Stockholders' Equity of $20m. From the income statement the Earnings before Interest and Tax is $1m.

The Z-score for general companies is calculated as follows:

Working Capital = 100 - 90 = $10m

X1 = 10 / 200 = 0.05

X2 = 2 / 200 = 0.01

X3 = 1 / 200 = 0.005

X4 = 20 / 180 = 0.11

Z-score = (6.56 * 0.05) + (3.26 * 0.01) + (6.72 * 0.005) + (1.05 * 0.11) = 0.5

With a Z-score of 0.5 this company is a high bankruptcy risk since the Z-score is less than 1.1.

## Summary

The Z-score is merely a probability indicator and any company can be a bankruptcy risk in the future even if it is a low probability now. Also some companies end up in bankruptcy will little advanced warning.

The Z-score can also indicate a high probability of bankruptcy, but the company never goes into bankruptcy.

The indicator is especially useful for investing strategies involving speculative stocks which can help investors avoid the high risk stocks. The Z-score is only a probability and not a certainty so there are no guarantees, but at least the probability of a company with a high Z-score not going into bankruptcy is on the side of the speculative investor.

Some high risk speculative trading strategies specifically look for financially distressed stocks that are not under bankruptcy protection. These speculative strategies utilize short selling tactics and the Z-score is a convenient probability indicator for locating stocks with a low or even a negative Z-score as these stocks are a high probability for bankruptcy with two years.

While the Z-score is a useful indicator, it should be used in conjunction with fundamental analysis techniques such as financial ratio analysis in order to determine whether a company is fundamentally sound or not.

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