Models for Predicting Corporate Financial Distress

A company trying to achieve its business plan faces problems similar to those faced by a driver embarking on a long trip. The likelihood that car and driver will reach their destination is dependent on:

  • how much fuel is in the car’s tank upon starting out,
  • how many service stations will be available to refill the car’s fuel tank along the way and
  • whether the car’s fuel tank is large enough to cover unexpected accidents, delays, and detours along the way.

Similarly, whether or not a company survives in a highly competitive business environment is dependent upon:

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  • how financially healthy the corporation is at its inception,
  • the company’s ability (and relative flexibility and efficiency) in creating cash from its continuing operations,
  • the company’s access to capital markets, and
  • the company’s financial capacity and staying power when faced with unplanned cash shortfalls.

There is no single measure of financial health. Ideally, solvency could be measured along a continuum in the same way that fuel sufficiency can be measured using a car’s petrol gauge. Full health would equate with having a full tank of fuel. Poor health would be equivalent to showing an empty tank. As healthiness progressively decreased, the solvency gauge would register movement in the direction of relative insolvency.

Ultimately, as healthiness continues to decline, the solvency gauge would hopefully flash a warning light. Since, in the real world, no single measure of financial health exists, proxies that measure various aspects of solvency are often combined to estimate a company’s healthiness at a point in time.

As a financially healthy company becomes more and more financially distressed, it ultimately enters an area of great danger. Changes to the company’s operations and capital structure (ie. restructuring) must be made to remain healthy. Apple Computers’ attempts in recent years to restructure its operations to survive in the highly competitive computer hardware business is a good example of a company trying to dramatically restructure itself in order to maintain solvency. Continued decreases in financial health ultimately lead to insolvency and then potentially, bankruptcy. Available evidence suggests many companies do not adequately attempt to resolve their financial health problems until it is too late to avoid bankruptcy.

Capital Structure and Capital Adequacy

Companies finance their long-term operations primarily through two sources of capital – debt and equity. One of the most important financing decisions a company makes is the proportion of debt to owner’s equity in the company’s capital structure. Summary measures of a company’s capital structure include the company’s debt to equity ratio (D/E) and debt to total capital ratio (D/(D+E)).

Interest and principal payments on debt must be paid from operations before any payments can be distributed to equity holders (in the form of dividends or share buy-backs). Therefore, the interest and principal, which must be paid on debt, are considered fixed-costs of operations. From an operational point-of-view, the extent of the burden of these fixed obligations can be measured relative to the company’s continuing ability to pay the fixed obligations. A frequently used measure of a company’s ability to cover its interest payments is its earnings before interest and taxes and before depreciation and amortisation (EBITDA) to its interest expense. A company is financially distressed whenever its EBITDA is less than its interest expense.

Financial leverage involves the substitution of fixed-cost debt for owner’s equity in the hope of increasing equity returns. As demonstrated by Higgins and others, financial leverage improves financial performance when things are going well but worsens financial performance when things are going poorly. Therefore, increasing the ratio of debt to equity in a company’s capital structure implicitly makes the company relatively less solvent (on the downside) and more financially risky than a company without debt.

The amount of debt a company can successfully absorb and repay from its continuing operations is normally referred to as the company’s debt capacity. Capital adequacy is normally evaluated by looking at the company’s operational cash flow projections and its projections of capital needs.

When companies undertake major new projects or undergo a significant financial restructuring they often perform financial feasibility studies to determine whether the company has the financial capacity to undertake the project and whether the company will be able to repay all future debt payments once the project is built.

Operating Cash Flows and Cost Structure

All other factors being equal, companies that can consistently generate positive cash flows from operations will remain relatively more solvent than those that cannot. This requires that operating cash inflows (collections or sales) consistently exceed operating cash outflows (costs).

Companies which experience erratic cash outflows and inflows are relatively more risky because they are less likely, in one or more time periods, to be able to cover fixed expenses/outflows. Companies which have a higher proportion of fixed costs to variable costs are also relatively more risky and relatively less solvent than companies with a relatively lower proportion of fixed costs in their operating cost structure.

All other things being equal, companies with higher relative earnings and higher relative returns on investment will remain more solvent than their less fortunate competitors. The most commonly used financial measures of earnings capacity are earnings before interest and taxes (EBIT) and net income.

Adequate liquidity is a further necessary component of solvency. Frequently used liquidity measures include:

  • working capital (current assets minus current liabilities),
  • current ratio (current assets divided by current liabilities), and
  • quick ratio (cash, marketable securities and accounts receivable divided by current liabilities).

To evaluate liquidity, each of the assets and liabilities on a company’s balance sheet should be evaluated for liquidity. Current assets are those which will likely be converted to cash within one year or less. Current liabilities are those which must be paid within one year. However, when a company becomes financially distressed, even assets which are normally considered current assets (accounts receivable and stock, for example) may become relatively “illiquid”.

Long-term assets, in general, are far less liquid than current assets. Some longer-term assets may be very “illiquid”. Also, as stated above, often a company’s long-term liabilities can become immediately due and payable if the company violates contractual debt covenants or other obligations.

Wilcox (1976) argues that “net liquidation value” provides a solid conceptual basis for evaluating a company’s liquidity. Net liquidation value is defined as total asset liquidation value less total liabilities. Wilcox (1976) applies what he calls typical (not definitive) valuation multipliers to balance sheet assets to arrive at representative asset liquidation values:

Wilcox (1976) shows that a company becomes bankrupt when net liquidation value is reduced to zero. Asset and liability conversions are continuously ongoing in any dynamic business. Operationally, the company is selling its products thereby creating cash inflows. Alternatively, sales may be made on credit, increasing the company’s accounts receivable. Concurrently, inventories are produced and sold and production and operating expenses are incurred to continue operations. If a company’s inventories and accounts receivable grow faster than the corresponding growth in the company’s sales and accounts payable, liquidity will be negatively affected.

Strategic asset conversions are also ongoing, but with less regularity. Decisions to invest in ‘bricks and mortar’ and other long-term investments are made and debt and equity are obtained to supply the capital needed to pay for them. Slowly but surely, companies can ‘go broke’ when assets are converted to less liquid forms over a sustained time period. This can happen when the company’s assets grow faster than the company’s sales (often the case for many start-up companies). When this happens, the company becomes more highly leveraged and less solvent.

Similarly, a company whose long term investment decisions do not pay off in terms of planned operating returns (thus increasing fixed cost structures and decreasing operating cash flows), will become less solvent.

Asset Utilisation Efficiency/Turnover

Those companies, which survive, use their human and capital assets relatively efficiently. That is, they have relatively higher returns on investment (ROI) and higher returns per employee than less successful competitors. They achieve relatively higher returns through superior asset management (capital and human assets) and through superior strategic positioning. In the absence of aggressive asset management, companies must usually resort to wholesale asset divestitures and/or are forced to restructure to fund their continuing operations. Schoffler (Buzzell and Gale, 1987) and others have documented the high correlation between positive returns on investment and such factors as:

Companies that have strong strategic market positions are more likely to experience higher relative returns on investment than their competitors. These positive returns, in turn, increase the solvency of the market leaders. Those competitors that have lower market shares or lower product quality are less likely to achieve industry average returns and are thus more likely to become less solvent in the future.

In America, each year approximately one percent of all firms required to file with the Securities and Exchange Commission file for bankruptcy. The American Bankruptcy Institute reports that around 50,000 businesses filed for bankruptcy in 1997. Attempts to develop bankruptcy prediction models began seriously sometime in the late 1960’s and continue through today. At least three distinct types of models have been used to predict bankruptcy:

  • statistical models (univariate analysis, multiple discriminate analyses [MDA]), and conditional logit regression analyses,
  • gambler’s ruin-mathematical/statistical models, and
  • artificial neural network models.

Each of these models is discussed below

Most of the publicly available information regarding prediction models is based on research published by academics. Commercial banks, public accounting firms and other institutional entities (ratings agencies, for example) appear to be the primary beneficiaries of this research, since they can use the information to minimise their exposure to potential client failures.

While continuing research has been ongoing for almost thirty years, it is interesting to note that no unified well-specified theory of how and why corporations fail has yet been developed. The available statistical models derive merely from the statistical optimisation of a set of ratios. As stated by Wilcox (1973) the “lack of conceptual framework results in the limited amount of available data on bankrupt firms being statistically ‘used up’ by the search before a useful generalisation emerges.”

Almost universally, the decision criterion used to evaluate the usefulness of the models has been how well they classify a company as solvent or non-solvent compared to the company’s actual status known after-the-fact. Most of the studies consider a type I error as the classification of a failed company as healthy, and consider a type II error as the classification of a healthy company as failed. In general, type I errors are considered more costly to most users than type II errors. The usefulness of fail/non-fail prediction models is suggested by Ohlson (1980)

“…real world problems concern themselves with choices which have a richer set of possible outcomes. No decision problem I can think of has a payoff space which is partitioned naturally into the binary status bankruptcy versus non-bankruptcy…I have also refrained from making inferences regarding the relative usefulness of alternative models, ratios and predictive systems… Most of the analysis should simply be viewed as descriptive statistics – which may, to some extent, include estimated prediction error-rates – and no “theories” of bankruptcy or usefulness of financial ratios are tested.”

Subject to the qualifications expressed above, bankruptcy prediction models continue to be used to predict failure. The early history of researchers’ attempts to classify and predict business failure (and bankruptcy) is well documented in Edward Altman’s 1983 book, Corporate Financial Distress. Statistical prediction models are more generally better known as measures of financial distress. Three stages in the development of statistical financial distress models exist:

Univariate analysis assumes “that a single variable can be used for predictive purposes” (Cook and Nelson 1998). The univariate model as proposed by William Beaver achieved a “moderate level of predictive accuracy” (Sheppard 1994). Univariate analysis identified factors related to financial distress, however, it did not provide a measure of the relevant risk (Stickney 1996).

In the next stage of financial distress measurement, multivariate analysis (also known as multiple discriminant analysis or MDA) attempted to “overcome the potentially conflicting indications that may result from using single variables” (Cook and Nelson 1998). The best-known, and most-widely used, multiple discriminant analysis method is the one proposed by Edward Altman.

Altman’s z-score, or zeta model, combined various measures of profitability or risk. The resulting model was one that demonstrated a company’s risk of bankruptcy relative to a standard. Altman’s initial study proved his model to be very accurate; it correctly predicted bankruptcy in 94% of the initial sample (Altman 1968).

Despite the positive results of his study, Altman’s model had a key weakness; it assumed variables in the sample data to be normally distributed. “If all variables are not normally distributed, the methods employed may result in selection of an inappropriate set of predictors” (Sheppard 1994).

Chistine Zavgren developed a model that corrected for this problem. Her model used logit analysis to predict bankruptcy. Due to its use of logit analysis, her model is considered “more robust” (Lo 1986). Further, logit analysis actually provides a probability (in terms of a percentage) of bankruptcy. Also, the probability calculated might be considered a measure of the effectiveness of management (ie. effective management will not lead a company to the verge of bankruptcy).

During the 1980s and 1990s, the trend has been to use logit analysis in favour of multiple discriminant analysis (Stickney 1996). More recently, logit analysis has been compared to a more advanced analytical tool, neural networks. Research has found that the approaches perform similarly and should be used in combination (Altman, Marco, and Varetto 1994).

Based on multiple discriminate analysis (MDA), the model predicts a company’s financial health based on a discriminant function of the form:

  • Z=0.012X1+0.014X2+0.033X3+0.006X4+0.999X5
  • X3=earnings before interest and taxes/total assets
  • X4=market value of equity/book value of total liabilities

The Z-Score model (developed in 1968) was based on a sample composed of 66 manufacturing companies with 33 firms in each of two matched-pair groups. The bankruptcy group consisted of companies that filed a bankruptcy petition under Chapter 11 of the United States bankruptcy act from 1946 through 1965. Based on the sample, all firms having a Z-Score greater than 2.99 clearly fell into the non-bankruptcy sector, while those firms having a Z-Score below 1.81 were bankrupt.

Altman subsequently developed a revised Z-Score model (with revised coefficients and Z-Score cut-offs) which dropped variables X4 and X5 (above) and replaced them with a new variable X4 = net worth (book value)/total liabilities. The X5 variable was dropped to minimise potential industry effects related to asset turnover.

Around 1977, Altman developed jointly with a private financial firm (ZETA Services, Inc.) a revised seven-variable ZETA model based on a combined sample of 113 manufacturers and retailers. The ZETA model is allegedly “far more accurate in bankruptcy classification in years 2 through 5 with the initial year’s accuracy about equal.” However, the coefficients of the model are not specified (without retaining ZETA Services). The ZETA model is based on the following variables:

  •  capitalisation (five year average of total market value)
  •  size (total tangible assets)

Application of the logit model requires four steps.

  • a series of seven financial ratios are calculated.
  • each ratio is multiplied by a coefficient unique to that ratio. This coefficient can be either positive or negative.
  • the resulting values are summed together (y).
  • the probability of bankruptcy for a firm is calculated as the inverse of (1 + ey).

“Explanatory variables with a negative coefficient increase the probability of bankruptcy because they reduce ey toward zero, with the result that the bankruptcy probability function approaches 1/1, or 100 percent. Likewise, independent variables with a positive coefficient decrease the probability of bankruptcy” (Stickney 1996).

Other Statistical Failure Prediction Models

Many additional bankruptcy prediction models have been developed since the work of Beaver and Altman. Lev (1974), Deakin (1977), Ohlson (1980), Taffler (1980), Platt & Platt (1990), Gilbert, Menon, and Schwartz (1990), and Koh and Killough (1990) amongst others have continued to refine the development of multivariate statistical models. Almost all of these traditional models have been either matched-pair multi-discriminate models or logit models. A 1997 study by Begley, Ming and Watts concludes:

“Given that Ohlson’s original model is frequently used in academic research as an indicator of financial distress, its strong performance in this study supports its use as a preferred model.”

Wilcox (1971 and 1976), Santomero (1977), Vinso (1979) and others have adapted a gambler’s ruin approach to bankruptcy prediction. Under this approach, bankruptcy is probable when a company’s net liquidation value (NLV) becomes negative. Net liquidation value is defined as total asset liquidation value less total liabilities. From one period to the next, a company’s NLV is increased by cash inflows and decreased by cash outflows during the period.

Wilcox combined the cash inflows and outflows and defined them as “adjusted cash flow.” All other things being equal, the probability of a company’s failure increases, the smaller the company’s beginning NLV, the smaller the company’s adjusted (net) cash flow, and the larger the variation of the company’s adjusted cash flow over time. Wilcox uses the gambler’s ruin formula (Feller, 1968) to show that a company’s risk of failure is dependent on;

Using a more robust statistical technique, Vinso (1979) extended Wilcox’s gambler’s ruin model to develop a safety index. Based on input concerning the variability of “expected contribution margin amounts,” the index can be used to predict the point in time when a company’s ruin is most likely to occur (called first passage time).

The statistics used in gambler’s ruin approaches are somewhat formidable (especially to the average reader). However, both Wilcox and Vinso richly describe some of the factors which most affect business failure. For example, Wilcox states: “The (cash) inflow rate … can be increased through higher average return on investment. However, having a major impact here usually requires long-term changes in strategic position. This is difficult to control over a short time period except by divestitures of peripheral unprofitable businesses…The average outflow rate is controlled by managing the average growth rate of corporate assets. Effective capital budgeting … requires resource allocation emphasising those business units, which have the highest future payoff.

The size of the bet is the least understood factor in financial risk. Yet management has substantial control over it. Variability in liquidity flows governs the size of the bet. This variability can be managed through dividend policy, through limiting earning variability and investment variability, and through controlling the co-variation between profits and investments…True earnings smoothing is attained by control of exposure to volatile industries, diversification, and improved strategic position.”

Vinso supports Wilcox’s emphasis on cash flow processes and stresses the importance of debt capacity: “Before deriving a mathematical model for determining the risk of ruin, it is necessary to describe the process. First, a firm has some pool of resources at time = 0 of some size U0, which are available to prevent ruin (similar to Wilcox’s beginning NAV). Then, earnings come to the firm from revenue(s)…less the costs incurred in producing the revenues.

There are two types of costs to be considered: variable, which change according to the stochastic nature of the revenue sources, and fixed costs, which do not vary with revenue but are a function of the period. So, revenue less variable costs…can be defined as variable profit (which is available to pay fixed costs).

If Ut is less than zero, ruin occurs because no funds are available to meet unpaid fixed costs…These definitions, however, ignore debt capacity, if available, which must be included as the firm can use this source without being forced to confront shareholders, creditors or bankruptcy,…debt holders or other creditors will force reorganisation if a firm is unable to meet contractual obligations because working capital is too low and the firm cannot obtain more debt.”

Alternative Models – Artificial Neural Networks

Since 1990, another promising approach to bankruptcy prediction, based on the use of neural networks, has evolved. Artificial Neural Networks (ANN) are computers constructed to process information, in parallel, similar to the human brain. ANN’s store information in the form of patterns and are able to learn from their processing experience.

Unlike MDA and logit analyses, ANN’s impose less restrictive data requirements (the requirement for linearity, for example) and are especially useful in recognising and learning complex data relationships.

Recent ANN bankruptcy prediction studies include those of Bell, et al. (1990), Hansen & Messier (1991), Chung & Tam (1992), Liang, et al. (1992), Tam & Kiang (1992), Salchenberger (1993), Coats & Fant (1993), Fanning & Cogger (1994), Brockett, et al. (1994), Boritz, et al. (1995), and Etheridge & Siriam (1995 and 1997).

Research has shown that ANN’s offer a viable alternative to other more traditional methods of bankruptcy prediction. The ability of the model to learn allows for the constant re-calibration and validation of the model, which helps increase classification rates. From a theoretical perspective, ANN’s are more desirable because they make fewer assumptions about the data normality and linear separability. One of the main disadvantages of ANN’s is the inability to assign intuition the network weights. Another disadvantage is that the model might simply memorise the data as opposed to forming a general set of classification rules, which can cause estimates on future samples to be less reliable.

Future research in bankruptcy prediction should analyse the economic and institutional factors that can impact the reasons for bankruptcy. Jones (1987) indicated that the lack of homogeneity in the motivation for a bankruptcy filing might complicate the modelling effort. Although normally motivated by an effort to resolve severe financial problems, a firm may file for bankruptcy primarily to void a union contract or for other legal reasons (Jones 1987).

Another area where models can be improved is in catering for predictor variables other than financial ratios may prove beneficial. For example, measures of management experience, management expertise, or other behavioural aspects that impact the operations of the firm could be significant in a bankruptcy prediction model. Additionally, including variables that control for a changing economic environment may provide valuable insights for predicting bankruptcy.


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