# The Altman Z-Score in Edward Altman’s Own Words

*This is the first installment of Edward Altman’s interview series with Larry Cao, CFA. For additional details of their conversation, please check out the two follow-up installments in the series.*

The Altman Z-score is a famous formula for measuring a company’s financial worthiness devised by Edward Altman. I sat down with Altman in Hong Kong recently to discuss the Z-score, its original inspiration, evolution over the years, use and misuse, as well as the current credit situation around the world. In this first installment, Altman discusses how the model was initially developed and what has changed since then.

**Larry Cao, CFA: Can you start by giving us some background on how you came across the problem and how you developed the formula as a solution?**

**Edward Altman:** When I was a graduate student at UCLA in the mid-1960s, one of my mentors, Professor J. Fred Weston, knew that I was looking for a topic for research, and he wrote me a one-word note one day: “bankruptcy.” In those days, bankruptcy was not a very popular research area, although there had been some work done using individual measures to look at the financial risk of companies. I decided I had to look at the subject of predicting financial distress of companies using a multivariate approach.

You know, sometimes breakthroughs are not so much a function of the brilliance of the people but the timing and the luck. And I was very lucky to be a PhD student at the right time in the right place. If I had thought about this subject two years earlier, I would not have had the computer firepower that was just beginning to come on campuses in the United States. If I had been on the scene two years later, someone else would have already done the work.

I combined a number of financial indicators with a technique for statistical classification known as discriminant analysis to predict bankruptcy. That was written in 1967, published in 1968, [and] known as the Z-score model or the Altman Z-score. And this model originally was built and still is mainly relevant for manufacturing companies. I had no idea that, almost 50 years later, people would still be using it and, indeed, using it more than ever.

**In your paper, you used five categories of variables — liquidity, profitability, leverage, solvency, and activity — to predict insolvency. How did you end up choosing the specific variables in the model?**

At that time, there were a lot of variables in the literature that you could choose to predict insolvency. But I decided there are two variables that were potentially very powerful but had not been used yet. One was the retained earnings: The argument there being a firm that has grown its assets mainly by reinvesting earnings is healthier than a firm that has grown the assets by using “other people’s money.” Retained earnings is also a measure of the age of the company and leverage. So that one measure combined leverage, profitability over the life of the company minus dividends, and also the age or experience of the company.

**You would think it makes a lot of sense because it does go back to the history of the companies and says, “Hey, how much money have you made and how much of that have you reinvested rather than paid out to your owners?” Yet you don’t come across models that use retained earnings very much these days.**

That’s true. It’s funny. Retained earnings/total assets is so powerful in my model, but you don’t find them very much taught in the classroom or found in the literature. I found it extremely important and helpful in almost every model I built over the years, for different industries and countries.

**What’s the other new variable you identified?**

The other new variable then — even though now it’s quite commonly understood — was the market value of the equity relative to the book value of the debt, as opposed to the book value of equity. It was the first study that — even before the Merton model, which was 1973, 1974 on risky debt — anticipated the importance of market equity relative to book debt as a very important indicator where it represents the ability of the company to raise money from the capital markets to pay down the debt or to expand the company. So market equity is now a fundamental part of many so-called structural models provided by Merton, KMV, and a number of other providers.

**So Z-score is a statistical model, with all the parameters driven by the particular sample.** [Exactly] **For a different sample, should users get new estimates for the parameters?**

The original sample was manufacturers. Rather than updating the original model for, say, more recent bankruptcies, which we can do, what we prefer to do is build new models. I developed the Z’’-score model in 1995 mainly for emerging market and non-manufacturing industrial companies. We also decided to take out the fifth variable, sales to assets. And we re-estimated the coefficients.

**So you took out an activity ratio?**

Exactly. It was very sensitive to the industry and, to some extent, the country. There was a new breed of corporate debt coming from emerging markets in the mid-90s, such as from Mexican, Brazilian, and Argentinian companies. And we tried to get a model which was more appropriate for that segment of the world and for manufacturers and non-manufacturers. We find that Z’’ is far more robust across sector and countries than Z-score, although both do a good job in classifying companies as to their bankruptcy potential with the same further modifications.

**How did the five variables rank in terms of importance?**

We look at the relative contribution and its statistical test. It turns out return on assets is number one. Retained earnings to total assets is number two. Market equity to total liabilities, three. Sales to assets, four. And the least important one, surprisingly, is the liquidity ratio, net working capital to total sales.

**Has the ranking changed from Z to Z”?**

No, it has not changed, except that sales/total assets is no longer a factor in the revised Z-score model.

**Fascinating. **

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*All posts are the opinion of the author. As such, they should not be construed as investment advice, nor do the opinions expressed necessarily reflect the views of CFA Institute or the author’s employer.*

Image credit: ©iStockphoto.com/suricoma

As per Prof. Altman’s Z score model, Z = 1.2X1 + 1.4X2 + 3.3X3 + 0.6X4 + .999X5; wherein X1, X2, X3, X4 and X5 are related to Working Capital, Retained Earnings, Earnings Before Interest and Taxes (Return on asset), Market Value of Equity and Sales respectively. This indicates ranking in order of importance as Return on asset, Retained earnings, Working capital, Sales and Equity market value, however, as per the interview, the order is Return on assets, Retained earnings, Market value equity, Sales and then working capital. Is there any change in the scoring model?

That’s a great question. What contribute to the Z-score are not only the coefficients but also the variables themselves. Just imagine changing the unit of the variables and the coefficients will change in response. So the proper way to rank the importance of a variable is to compare “coefficient X variable” for each variable.

Warm regards,

Larry

Hi Larry, thank you very much for the interesting interview. Do you know where I can find updated bond rating equivalent tables for z, z’ & z”?

thank you very much and best regards,

Alberto

So the discussion about Altman Z score for manufacturing versus other types of companies was mentioned. I noticed that the Altman Z Score coefficients I learned in Financial Analysis Class are different from those used by GuruFocus, those used by readyratios.com, and those used by the blogger here named AtulSave. Why don’t we have generally accepted Altman Z-score coefficients for specific industries? Or is one of the reasons why some people call Z-score irrelevant is that you can get the answers you want if you just change the coefficients?…Which defeats the purpose of an objective comparison tool.

I please to know about the Altman Z-score model. I want to know how to know the parameters of the model is 1.2, 1.4, 3.3, 0.6 and 0.999? I want to know it because my Bachelor course’s Final Year Project need to discribe about it. Thank you

I am korean.

I want to know Z’-score for private firm and

what is 0.717, 0.847, 3.107, 0.42, 0.998 ?

and it’s meaning.

I want to know how to know the parameters of the model is 1.2, 1.4, 3.3, 0.6 and 0.999? I want to know how prof. Altman create those score, the reason behind those score. I want to know it because my Bachelor course’s Final Year Project need to discribe about it. I need a help please

Thank you