We discussed how analysts require this information to reach competent, educated decisions about a firm’s financial strength and how it is also useful to note the trends in such information over the past few years to gain some insight into the probable direction of these trends in the near future. Recall also that we grouped these ratios into four categories: liquidity, solvency or leverage, efficiency, and return.

In this installment, we discuss applying these ratios or financial metrics to a question discussed in any corporate finance department, and certainly among bankruptcy and litigation counsel as well as corporate restructuring professionals: Can financial failure be predicted and, if so, avoided?

## Univariate Models

Imagine that we could look at a set of financial statements—any set of financials for any company—and pull one key financial metric that would reliably tell us whether or not the company would fail within the next 12 to 24 months. Many macroeconomic, microeconomic, market, and industry circumstances, none of which can be reliably predicted, often contribute to the financial ruin of a company, but setting those items aside, imagine that we could look at the financial condition of a company through some single ratio and, to some acceptable measure of statistical significance, reliably predict insolvency. This is the basis of research performed by William H. Beaver in an article entitled “Financial Ratios as Predictors of Failure,” published in the *Journal of Accounting Research *in 1966. Beaver compared a group of failed firms with a control group of firms that did not fail. To his sample of firms, he applied 29 different financial ratios over the five years preceding failure and determined that cash flow/total liabilities correctly predicted firm failure 85 percent of the time one year prior to bankruptcy. The prediction rate was only slightly lower, 76 percent of the time, for up to five years prior to bankruptcy. There was, however, a nonuniform distribution between false positives (misclassifying a bankrupt firm as solvent) and false negatives (misclassifying a solvent as bankrupt). In statistical tests, false positives are referred to as Type 1 errors, and false negatives are referred to as Type 2 errors. The main advantage of this univariate model is, of course, its simplicity.

There are several disadvantages, a significant one being the assumption that the complexity of a firm’s financial status can be captured effectively in a single ratio. The ratio itself—cash flow/total liabilities—is basically an activity or an efficiency ratio, measuring the minimum level of regular cash flows needed to maintain a solvent business for a given set of total liabilities. However, given two different businesses with the same amount of total liabilities but different liability payment terms, a single cash flow measure could prove adequate for one business while causing liquidity problems in the other. Nonetheless, the point of interest here is that the Beaver research showed that this relationship among different data, readily available on financial statements and easily computed, is useful in identifying a financial condition that could lead to financial failure.

## Multiple Discriminate Analysis

Probably the best-known insolvency prediction model is the Altman Z-score, developed by Edward I. Altman and presented in the article “Financial Ratios, Discriminant Analysis and the Prediction of Corporate Bankruptcy” published in the *Journal of Finance* in September 1968, when Altman was an assistant professor of finance at New York University (today he is the Max L. Heine Professor of Finance at the Stern School of Business at New York University). Altman described multiple discriminant analysis (MDA) as “a statistical technique used to classify an observation into one of several *a priori* groups dependent upon the observation’s individual characteristics.” It therefore attempts to derive a linear combination of these characteristics that best discriminates between the groups. His characteristics were various combinations of financial ratios that he used to assign a firm to the failing or non-failing group based on its discriminant score. In his original model, Altman selected 66 corporations, 33 of which failed and 33 of which did not, and analyzed various financial ratios from these companies in year t-1 to determine the combination that best discriminates between these two groups a year later.

The original model was defined as follows:

Z-score = 1.2X_{1} + 1.4X_{2} + 3.3X_{3} + 0.6X_{4} + .999X_{5}

Where X_{1} through X_{5} are key financial ratios, as follows:

X_{1} = Working capital/Total assets

X_{2} = Retained earnings/Total assets

X_{3} = Earnings before interest and taxes (EBIT)/Total assets

X_{4} = Market value of equity/Total liabilities

X_{5} = Sales/Total assets

Let’s assess what Altman found to be crucial in predicting insolvency.

X_{1} (working capital/total assets) looks at liquidity. Working capital is usually defined as current assets (cash or those assets that are expected to be converted to cash within one operating year) minus current liabilities (liabilities that must be paid within one operating year). Working capital is closely related to the current ratio, which is determined simply by dividing current assets by current liabilities. Comparing working capital to total assets is an indication of how efficiently stakeholders’ investment in total assets is being utilized.

X_{2} (retained earnings/total assets) looks at profitability. Retained earnings reflects accumulated net profits maintained within the firm (i.e., not withdrawn or distributed). Therefore, on the whole, older firms are typically at an advantage because they have a longer time to accumulate earnings. Again, the comparison to total assets indicates how efficiently stakeholders’ investment in total assets are being used to generate consistent profits.

X_{3} (EBIT/total assets) also compares total assets to a profitability measure. But EBIT (again, earnings before interest and taxes) is a measure of current (i.e.,this year’s) profitability as opposed to the historic accumulated profitability represented by retained earnings. An interesting use of this ratio is as a comparison with the firm’s interest rate on its debt. That interest rate shows the firm’s cost to borrow funds used to acquire assets. EBIT/total assets represents the return that investment in assets creates. An interest rate on debt that exceeds EBIT/total assets can be indicative of deteriorating financial condition.

X_{4} (market value of equity/total liabilities) is a leverage ratio, a different form of the better-known “debt-to-equity” ratio. Because the original Z-score model was based on public corporations, the market value of equity (or market cap) was easily determined. Altman later issued another version of the Z-score model for private firms, which replaces this ratio with book value of equity/total liabilities.

X_{5} (sales/total assets) is another efficiency ratio. It measures how effectively stakeholders’ investment in total assets is being utilized to generate business activity.

Notice that the denominator in four of these five ratios is total assets, meaning the fewer assets carried, the higher the ratio and, therefore, the Z-score. Regarding the coefficients (i.e., the number that each ratio is multiplied by in the Z-score formula shown above), these are the result of Altman’s research and are fixed, meaning they are the same for each Z-score application. The results of the research show that firms with a Z-score > 2.99 are in the “safe zone,” meaning there is a low expectation of financial failure within the next year, all else being equal. For firms with a Z-score < 1.81, there is a high expectation of financial failure. Scores between 1.81 and 2.99 are in a gray zone. This is built into the scoring process to allow for subjectivity in corporate finance decision making.

Companies using the Z-score process to aid in corporate finance initiatives must also consider the cost of Type 1 and Type 2 errors. The cost of a Type 1 error (misclassifying failed firms as solvent) can often be much larger than the cost of a Type 2 (false negative) error. Because of these cost asymmetries, it made sense to fudge the optimal cutoff point in the scoring process a little. Further, MDA is a statistical process that is similar to regression analysis, but it is computationally different from regression analysis. For instance, the ordinary least squares regression methodology is not suitable when estimating a linear relationship with a binary (i.e., failed/non-failed) dependent variable. As a result, the standardized coefficients cannot be interpreted like the β-coefficients of a regression. Therefore, they do not indicate the relative importance of the different variables. Sofie Balcien & Herbert Ooghe, *35 Years of Studies on Business Failure: An Overview of the Classic Statistical Methodologies and their Related Problems* (2004 working paper).

It should be noted that the MDA Z-score process is not intended as a predictor of financial failure. It simply allows for the application of the Altman research to the stated financial ratios of any given subject business, and then identifies the extent to which the subject business resembles other businesses in either the failed or non-failed groups.

## Conditional Probability Models

James A. Ohlson published “Financial Ratios and the Probabilistic Prediction of Bankruptcy” in the *Journal of Accounting Research* in 1980. He used an econometric methodology known as a logit regression analysis. While it may not be obvious from its name, this method can be a less demanding statistical technique than MDA (specifically with regard to MDA’s statistical requirements imposed on the distributional properties of the predictors). A logistical (or logit) regression is a type of probabilistic classification model. While the nature of the logistic function is interesting, it is not relevant to this discussion. What is relevant is that logit regression is used to model how the probability of an event may be affected by one or more explanatory variables. Ohlson describes his application of conditional logit analysis as follows: “The fundamental estimation problem can be reduced simply to the following statement: given that a firm belongs to some prespecified population, what is the probability that the firm fails within some prespecified time period?”

The output of a logit analysis is a score between 0 and 1, which translates to a failure probability. While the model specification itself is irrelevant to our discussion here, it uses nine independent variables as predictors, all of which are based on financial statement data:

**Size**—total assets/GNP price level index. In Ohlson’s 1980 model, the price index assumed a base of 100 for 1968, and the variable is the log of the ratio.

**Debt-to-assets**—a leverage ratio and the corollary of debt-to-equity

**Working capital/total assets**—a ratio measuring the efficiency of stakeholders’ investment in assets to generate liquidity

**Current liabilities/current assets**—a liquidity measure and the inverse of the current ratio (current assets/current liabilities)

A qualitative variable that takes on a value of 1 if total liabilities exceed total assets, and zero otherwise. Such variables (sometimes referred to as “dummy” variables) are often used to indicate the presence or absence of a specific condition.

**Net income/total assets**—a ratio indicating the efficiency with which stakeholders’ investment in total assets generates profits

**Funds provided by operations/total** **liabilities**—a liquidity measure comparing total liabilities with funds provided by operations as opposed to funds provided by either the firm’s investing or financing activities

Another qualitative variable that takes on a value of 1 if net income was negative for the past two years, or a zero otherwise

**(NI**_{t} – NI_{t-1})/(|NI_{t}| + |NI_{t-1}|), where NI_{t} is net income for the most recent period. This variable is intended to measure change in net income.

All of these ratios and financial data are easily computed from current and historical financial statement data. Each tells a story of its own, but the research discussed here shows how they can be used in combinations to elicit further insight into the overall financial condition of the firm. Many banks track similar information (Z-scores and other statistical data indicating financial strength or weakness) over periods of time, noting changes and determining whether extension of further credit should be based on adjusted loan covenants. This type of analysis is designed for ex ante monitoring of financial condition and creditworthiness. However, it can be used ex post, after an insolvency occurs, to determine what was known or reasonably knowable about the company’s financial condition before the insolvency. It is important to note that these models only reflect possibilities of future financial failure. In other words, no financial failure prediction model on its own is sufficient to be able to predict financial failure with certainty 100 percent of the time.

## Summary

The quest for a statistical or econometric model to predict bankruptcy reliably is a natural outgrowth of basic ratio analysis. The models outlined here merely scratch the surface of the extensive research and literature in this area since the 1960s. Obviously, financial failure prediction is a complex, multidimensional analysis, which must incorporate the specific facts and circumstances of each case. To add to the research complexity, there is much discussion and dispute over the definition of financial failure itself. It can range from the time of legal filing for protection under the Bankruptcy Code to the moment in time that actual economic insolvency occurs (these two conditions rarely coincide). In turn, actual economic insolvency can include liquidity insolvency (the point beyond which bills cannot be paid as they come due) to balance sheet insolvency (where the stated value of all liabilities exceeds the fair value of the assets). Financial failure can also be defined as financial distress, such as loan failure. Regardless of all these complexities, financial statement information provides significant input to calibrating these models through the key financial metrics or ratios derived therefrom.