# Understanding Z Scores

Z-scores are the numbers that are calculated using the Altman z-score mathematical formula. The formula uses corporate financial data to predict whether or not a company will go bankrupt in the next few years. The formula was invented in 1968 by Edward I. Altman, an assistant professor of finance at New York University. Since then, the formula has been able to correctly predict bankruptcies 72 percent of the time. While the formula is not fool-proof, it has become a fairly reliable indicator of a company's financial health.

#### Understanding Z-Scores Formula

The original Z-scores formula was geared towards publicly traded companies. More recently, mathematicians came up with variations of the originals that were specifically tailored to predict bankruptcies of privately held companies and non-manufacturing companies.

It is worth noting that the z-scores are calculated based on the assumption that the financial data used to calculate them is correct. It has no way to determine if the companies falsified their data. However, if companies falsify data to make their finances look better than they really are, they are much more likely to face bankruptcy anyway.

#### Original Z-Scores Formula

This formula is used to calculate the possibility of bankruptcy in publicly held companies--in other words, companies that have stocks on the stock market and publish their financial data. The original formula is Z = 1.2T1 + 1.4T2 + 3.3T3 + .6T4 + .999T5. The variables signify the following:

• T1--working capital divided by total company assets.
• T2--retained earnings divided by total assets.
• T3--earnings sans interest and taxes divided by total assets.
• T4--market value of equity divided by the book value of total liabilities.
• T5--sales divided by total assets.

Once each of those variables are calculated, they must be plugged into the formula to calculate the company's Z-score. If the Z-score is above 2.99, the company is safe from bankruptcy. If the Z-score is between 1.8 and 2.99, the company is potentially in danger of bankruptcy, but its finances are sound enough to allow for it to avoid that fate under the right financial policy. If the Z-score is below 1.8, the company will become bankrupt unless extreme measures are taken to fix its finances.

#### Z-Score Formula for Private Firms

This formula is used to calculate z-scores who don't sell stocks and generally keep their finances private. The formula is Z = 0.717T1 + 0.847T2 + 3.107T3 + 0.420T4 + 0.998T5. T1 signifies the value of current assets (minus current liabilities) divided by the company's total assets, while T4 signifies book value of equity divided by total liability. The rest of the variables are the same as they are in the original formula. The Z-scores are only somewhat different. If the z-score is above 2.9, the company is safe from bankruptcy. If the Z-score is between 1.23 and 2.9, the company faces the potential threat of bankruptcy. And if the Z-score is below 1.23, the private company is in danger of bankruptcy.

#### Z-Score Formula for Non-Manufacturing Companies

This formula is used to calculate z-scores for publicly traded and privately held companies that aren't involved in any manufacturing or manufacturing-related industries. It can also be used to calculate z-scores for companies that operate in emerging markets, developing countries that show some promise of becoming developed. Since developing countries are less financially stable than developing countries, the likelihood of bankruptcy is greater.

The formula is Z = 6.56T1 + 3.26T2 + 6.72T3 + 1.05T4. The variables are the same as they are for private firms, except Tis absent. If the Z-score is above 2.6, the company is safe from bankruptcy, while the Z-score between 1.1 and 2.6 signifies potential risks and a Z-score below 1.1 signifies the danger of going bankrupt.