# Altman Z-score

In a previous article on this website (What is the risk of investing?) it was mentioned that the largest risk for a company is bankruptcy. But how big is the risk of bankruptcy? And how can that risk be determined for a specific company? To answer these questions, the model of the Altman Z-score can be used.

The Altman Z-score is a mathematical model for the creditworthiness of a company, both public and private. The model of the Altman Z-score is the result of a scientific investigation into the prediction of the possibility of a bankruptcy of a company. Within the model, figures are used that are easy to find, for example on this website. First, there was only one version of the Altman Z-score model, but later on several variations on this model came into existence. All these variants are discussed in this article.

## Altman Z-score users

The Altman Z-score is used by different stakeholders interested in determining the creditworthiness of a company. This credit risk is used, for example, to determine in which company to invest in or the risk of lending money to a company.

The Altman Z-score is most commonly used by banks to determine the risk in issuing loans. In addition, the Altman Z-score an important tool for institutional investors to determine the risk of a company going bankrupt. Also private investors can easily use this model. It is simple and the required data are easy to obtain.

Besides the above two industries, the Altman Z-score model is used by companies in mergers and acquisitions and by turnaround managers. They use the model to determine the risks of the company and to create a strategy in order to get the company out of the danger of bankruptcy.

The Altman Z-score is also used within the insurance industry for the reinsurance of large amounts. If large amounts are insured, an insurer generally is not willing to bear the risk alone. But to determine to which fellow insurers a part of the risk can be reinsured, the creditworthiness of the other insurer is of great importance. To determine this credit risk, the Altman Z-score model is used.

Another example for which the Altman Z-score model is used, is for corporate governance. The outcome of the Altman Z-score model is used to explore the business risks and determine a strategy for hedging.

## Variables Altman Z-score

The formula for calculating the Altman Z-score uses different variables. These variables may vary per variant of the formula. As indicated earlier, there are some variants of the Altman Z-score model. These variants are designed to calculate the risk of bankruptcy of different types of businesses. The following options are available:

- Public traded manufacturing companies.
- Private companies.
- Public non-traded manufacturing companies.
- Companies in emerging developing countries.

The parameters which are used in the Altman Z-score, are discussed below.

- Book value of total liabilities: The amount of the debt can be gathered from the balance sheet. Both long term and short term debt are part of this parameter. The reserves, which is also on the credit side of the balance sheet, is no part of this parameter.
- Market value of the company: The market value is the total price of all outstanding shares. For unlisted companies, this variable will not apply. For these companies, the book value of total assets should be put in place. This book value can be found on the balance sheets of a company.
- Turnover: Turnover is the total sales of the company within a year. This turnover should be the recorded in the same book year as the used profit before tax and interest (EBIT).
- Total retained earnings: The retained earnings is the sum of all profits earned in the past, that was available to reinvest in the company. This refers to the total profits minus dividends and taxes. For young companies, this figure is relatively low, because they had fewer years to build up their retained earnings. Also companies in emerging markets will usually have less retained earnings, just because most companies in these markets will be young companies.
- Total assets: Total assets are all assets on the balance sheet of a company. This concerns both the cash and the properties for which a longer-term investment was needed.
- Working capital: Working capital is the money available at short notice to fund the activities of the company. Working capital is calculated by subtracting the current short-term debts from the cash and cash equivalents. A company with a positive working capital can immediately pay their short term debts, when the creditors want the company to pay. If a company generates profits, working capital will grow, unless they give away all profits (for example, to their shareholders).
- Profit before tax and interest: The profit of the company in a certain book year, before settlement of the tax and interest. Since both taxes and interest can affect the earnings positively or negatively and may result in one-time benefits, they should be ignored in the Altman Z-score model.

## Altman Z-score formula

As indicated earlier, there are four different variations of the Altman Z-score formula. For each formula, boundary values have been determined to indicate whether a company is in the risk of bankruptcy.

## Public manufacturing companies

The results of the Altman Z-score for public production consists of 5 aggregations of the parameters discussed earlier.

Altman Z-Score =

- 1.2 x Working Capital / Total assets +
- 1.4 x Total retained earnings / total assets +
- 3.3 x Profit before tax and interest / total assets +
- 0.6 x Market value of the company / Book value of debt +
- 1.0 x Sales / Total assets.

The result is an outcome of the Altman Z-score for publicly-traded manufacturing companies. To determine the risk of bankruptcy, the following bandwidths should be taken into account:

- The company goes bankrupt with an Altman Z-score of below 1.81.
- There is a gray area between 1.81 and 2.99. Studies have shown that with an Altman Z-score below 2.675, there is a 95% chance of a company going bankrupt.
- If the Altman Z-score is 3.0 or higher, then the risk is low that the company goes bankrupt.

## Private enterprises

The parameters used to calculate the Altman Z-score for non-publicly traded companies are slightly different than the other formulas. This is because the value of a company not listed on the stock exchange cannot be determined in the same way as for publicly traded companies.

Altman Z-Score =

- 0.717 x Working Capital / Total assets +
- 0.847 x Total retained earnings / total assets +
- 3107 x Profit before tax and interest / total assets +
- 0.420 x book value of assets / Book value of debt +
- 0.998 x Sales / Total assets.

Besides the other variables, also the ranges of the various risks are different. The boundaries are the following:

- The risk that a private company goes bankrupt is a very large when the Altman Z-score is below 1.23.
- The gray area for this specific formula exists with a result between 1.23 and 2.9.
- The risk that a private company goes bankrupt is almost zero for an Altman Z-score above 2.9.

## Public non-manufacturing companies

The variables that are used for calculating the Altman Z-score for non-manufacturing companies which are listed on the stock exchange, are not the same as those for manufacturing companies. This is because a part of the formula is not used to avoid sector-specific abnormalities in the outcome. In addition, the multiplication factors are different from the Altman Z-score formula for manufacturing companies. The Altman Z-score for public non-manufacturing companies can be calculated as follows:

Altman Z-score =

- 6.56 x Working Capital / Total assets +
- 3.26 x Total retained earnings / total assets +
- 6.72 x Profit before tax and interest / total assets +
- 1.05 x Market value of the company / Book value of debt.

The various risk areas are different from those for non-listed companies, namely:

- The risk of failure is very high with an Altman Z-score below 1.22.
- The gray area in this formula is between 1.22 and 2.9.
- The risk of bankruptcy is very low with and outcome of the Altman Z-score formula above 2.9.

## Companies from emerging markets

The formula of the Altman Z-score for firms from emerging countries is almost exactly the same as the formula for listed non-manufacturing companies. There is only one constant value added at the end of the formula. The Altman Z-score can be calculated as follows:

Altman Z-score =

- 6.56 x Working Capital / Total assets +
- 3.26 x Total retained earnings / total assets +
- 6.72 x Profit before tax and interest / total assets +
- 1.05 x Market value of the company / Book value of debt +
- 3.25.

The bandwidths of the risks of bankruptcy are the same as the Altman Z-score formula for exchange-traded non-manufacturing companies.

## Altman Z-score points of attention

As with any standard formula or model, the Altman Z-score model has some important attention points. These points should attract the attention of the user of the Altman Z-score model, since the conclusions that can be drawn from the results of the model will be influenced by these points.

The first consideration is the volatility of the results of the Altman Z-score. The results of the model may vary over time. This has as main reason that the price of a company’s share is uncertain, because is subject to the opinion of the market. Also, during periods when the stock market is high, the Altman Z-score outcomes will be higher than in times when stocks are low. Because the share price is part of the formula this should be taken into account when calculating the Altman Z-score.

The share price determines a part of the credit risk and the risk of bankruptcy of a company. In a market where sentiment on the stock market is good, it will be easier for a company to borrow money or attract cash on the stock exchange, even if the company has a poor credit history This allows a company to extend their life.

In addition, a standard model as the Altman Z-score never has a 100% success ratio. There will always be some situations where an unexpected event can draw a company to the edge of bankruptcy, even if the company had a very good rating. The other way will be less frequent, but it can of course happen that a company from the brink of collapse is saved by some event.

The Altman Z-score model is a good model for determining the risk of failure of a company. Research comes in around 70 to 80% of bankruptcy cases can be predicted in advance. As a result above a certain score (usually above 3.0) the certainty of the outcome is even greater, so there is a low change that a company will go bankrupt within a few years.