# What is a Z-Score?

A Z-score is a number that shows how far one data point stands from the average of all data points in a given group.

## 🤔 Understanding a Z-score

In theory, a Z-score can be calculated using just about any group of data points to compare one point to the group average (aka the mean). For example, you could use a Z-score to compare the wingspan of LeBron James to the average of all NBA players. Or, you could compare a company’s stock price to the average stock price of a collection of companies, like the S&P 500. In mathematical terms, the Z-score tells you how many standard deviations away from the average a particular data point falls. Here’s the formula used to calculate a Z-score:

In the financial and investment world, a Z-score often means the Altman Z-score, which has a more specific purpose. The Altman Z-Score — named after its creator Edward Altman — is commonly used to help you determine how close or far company is from bankruptcy, usually in relation to a group of similar companies. The Altman Z-score is one of many ways to measure a company’s financial health. The Altman Z-score formula is a slightly more complicated variation on the original, using multiple financial measures like working capital and EBIT. Here’s what the Altman Z-score formula looks like:

If a company’s Altman Z-score is greater than 3, it is considered less likely to fall into bankruptcy. A company with a score below 1.8 is considered to be at risk for bankruptcy within two years. Scores between 1.8 and 3 are considered a grey area; a score closer to 1.8 is considered at higher risk of bankruptcy, while those closer to 3 is considered at lower risk. While the Altman Z-score is widely used as an indicator of a company’s health, keep in mind that it doesn’t guarantee whether a company will or won’t declare bankruptcy.

Let’s look at the fictional company, George’s Jungle Excursions, to run an example of the Altman Z-score. Assume George’s Jungle Excursions has the following numbers pulled from its financial statements: Sales: $2M, EBIT: $1M, Total Assets: $4M, Book Value of Total Liabilities: $2M, Retained Earnings: $2M, Market Value of Equity: $6M, and Working Capital: $1M.

Since its resulting Altman Z-score is greater than 3, George’s Jungle Excursions would be considered unlikely to file for bankruptcy.

## Takeaway

The Altman Z-score is like cholesterol…

It’s one among several indicators of your risk of heart disease, along with a variety of other factors, like blood pressure and family history. While it can’t predict heart disease with certainty, people with high cholesterol are considered to be at higher risk of heart disease compared to people with lower levels.

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## What does a Z-score tell you?

A Z-score looks at a data point in a group (think test scores, credit scores, net income, profits, revenue...) and measures how far from the group average that data point falls. A Z-score can help you identify statistical outliers, or a member of a group that stands out from the pack.

As you can see in the formula above, the Altman Z-score is calculated using a specific set of financial numbers that can be found in a company’s income statement and balance sheet. NYU finance professor Edward Altman initially came up with the formula to determine the likelihood of bankruptcy for a manufacturing company with $1M or more in assets. Since its original publishing, Altman revised the formula so that it can be used for companies in a variety of industries and for those with less than $1M in assets.

## How do you calculate an Altman Z-score?

The Altman Z-score may look complicated, but it’s pretty simple to calculate if you have the necessary ingredients on hand. Think of the ingredients as figures reflecting a company’s assets and costs. You can usually find them in a company’s balance sheet or income statement. Here are the ingredients you’ll need to calculate an Altman Z-score, and what each one means:

Working capital: This is the value that remains after subtracting a company’s current liabilities from its current assets.

Retained earnings: This is the amount of net income a company has left after paying out dividends to its shareholders.

Earnings before interest and taxes (EBIT): This is how much a company made in profits before paying for interest and taxes. Market value of equity: This is the total dollar value of a company’s equity (aka market capitalization).

Book value of total liabilities: This is the total dollar value of a company’s liabilities recorded in its financial statements (aka accounting “books”), including its debts and obligations. Sales: This is the dollar value of a company’s total sales in a given period of time.

Total assets: This refers to a company’s combined assets (such as receivables, investments, etc.).

If this is starting to sound too complicated, fear not, the Internet is here to help. Online calculators can help you calculate Z-scores — all you have to do is plug in the numbers. You can also set up a formula in Excel. Here’s an example.

In Excel, the simplest way to set up the Altman Z-score is to set up a cell for each of the variables. Then set up a cell for each of the variable formulas, remembering to link to the data entry cell for each. That is 1.2(working capital/total assets), 1.4(retained earnings/total assets), 3.3(earnings before interest and taxes (EBIT)/total assets), 0.6(market value of equity/book value of total liabilities), and 1.0(sales/total assets). Then set up a last cell to add each of the formula cells together.

## How do you interpret a Z-score?

The Altman Z-score has a set scale by which results are expected to be measured. A score of 3 or greater indicates a company should be safe from filing bankruptcy. A score between 1.81 and 3 indicates that a company is likely to file bankruptcy at some point. A score below 1.81 indicates that a company may file for bankruptcy soon (within 2 years).

For statistical Z-scores, there’s no scale to rely on for interpretation. Instead, Z-scores only tell you how far from the average a chosen data point falls — what that means depends on the dataset you’re analyzing.

## What does a negative Z-score mean?

For standard Z-scores, a negative Z-score simply means that the number being examined fell below the average of the group.

Depending on what you are studying, a negative Z-score could be an encouraging or discouraging sign. For example, if you’re looking at a company’s debt compared to the average of a group, then a negative Z-score would mean the company has less debt than the group average — encouraging. But if you were looking at revenue instead, a negative Z-score would mean the company has less revenue than the average of the pool — discouraging.

## What’s the difference between a Z-score and standard deviation?

While the Z-score shows a particular data point’s the actual distance from the group average (aka mean) value, the standard deviation tells you the average distance from the mean value. More precisely, the Z-score tells you how many standard deviations away from the average a specific data point falls.

## How are Z-scores used in real life?

Z-scores have a wide-range of uses in the real world. A wildlife biologist could use a Z-score to study a pack of zebras. A pathologist could use a Z-score to analyze a collection of blood samples. One common use for Z-scores is in bank loans. For example, a lender might compare your income-to-debt ratio to a group’s average as one way of determining how creditworthy you are.

## What are the limitations of Z-scores?

While a Z-score can be a helpful way to compare one data point to an average, there are several limitations you should know about. Take the Altman Z-score, for example. The primary limitation here is that the Altman Z-score can’t predict with certainty if a company will file for bankruptcy. It can only tell you how a company’s score compares to that of others.

Natural disasters and other unexpected events can skew a company’s Altman Z-score. For example, a large one-time loss due to a fire or sudden political upheaval in a country with a company subsidiary might drastically affect that company’s sales, assets, and book value of liabilities. A Z-score calculated during a period of irregular conditions could make an otherwise stable company appear to be in dire straits.

The Altman Z-score is also susceptible to false accounting. If a company is publishing financial reports with falsified data, the Z-score will provide an inaccurate picture of the company's financial health. The same is true if incorrect numbers are entered through errors in calculations. As the old saying goes, garbage in, garbage out.

Finally, if you’re analyzing the health of a brand new company, the Altman Z-score may not be the most helpful. A new company’s finances may be more volatile, have smaller reserves of funds, and have shorter or longer cycles for credit compared to an established company. The Altman Z-score formula doesn’t necessarily take these unique factors into account.

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