Corporate Bankruptcy Prediction
Ms. Julie Slater
April 11, 2017
Table of Contents
Definition of bankruptcy prediction 4
Breif history and Types of Bankruptcy techniques 4
Financial Covenants 5
Negative Covenants - Why Lenders Use Them 6
The Altman Z-Score – Introduction 7
Breaking Down Altman Z-Score 7
Working Capital to Total Assets 8
Retained Earnings to Total Assets 8
Earnings Before Interest & Taxes to Total Assets 8
Market Value of Equity to Total Liabilities 8
Sales to Total Assets 9
Limitations and Critiquing Altman Z-Score 10
Ohlson O-Score Model - Introduction 10
Breaking Down Ohlson O-Score 11
Definition of bankruptcy prediction
Corporate bankruptcy prediction is an analysis that serves to predict bankruptcy and financial distress of corporations. Thorough finance and accounting knowledge is essential in order to conduct this analysis this space serves to help creditors whether or not a firm is vulnerable to become bankrupt. In financial literature there are different definitions on bankruptcy. According to Altman (1996), bankruptcy occurs when companies are not capable of paying off their debts and they are not able to keep on with their activities.
Bankruptcy prediction is essential for different groups of people in the society, especially during the financial crisis period. Numerous companies failed at a global level and had caused a large amount of losses for not only investors but also financial institutions such as banks and investment corporations. The accurate prediction of potential bankrupt companies is able to warn all investors in advance to avoid significant losses. In many bankruptcy literatures, different methodologies were created for modeling prediction. In general, researchers classified companies into two groups: “Healthy” companies and companies with financial problems.
Brief history and Types of Bankruptcy techniques
In fact, the formal analysis of bankruptcy prediction can trace back to the1930s. Fitzpatrick first conducted research and compared 20 pairs of firms between failed and healthy ones. He thoroughly analyzed and interpreted the ratios as well as several trends in the ratios. Bankruptcy techniques can be divided into two major types in general, which are accounting-based, bankruptcy prediction models and market-based bankruptcy prediction models.
In the accounting-based models, information, especially in the form of ratios, from the financial statements is used to measure the risk of the company. The first researcher to predict bankruptcy in financial ratios was Beaver (1966), who analyzed a sample of 79 failed companies, including both bankrupt and healthy companies in a univariate method. In his research, he mentioned that cash flow/total debt and net income/total assets were the two best predictors of failure. The most famous multivariate model of bankruptcy prediction was called Altman’s Z-score model, which was based on a statistical method called multiple discriminant analysis (MDA). Afterwards, Dr. James Ohlson developed another accounting-based multivariate model on the basis of Altman Z-score model in 1980.
The other category is called market-based models, which is a relatively more recent model. It mainly relies on theoretical foundation and option-pricing theory to value the situation of the company. The most well-known models in these category are The Merton model, developed by Merton (1974) and Hazard Models. In this report, we will mainly focus on the accounting-based models.
In its most simple form, corporate bankruptcy is a product of a company failing to meet a financial obligation, such as an interest or principal payment, which results in the company defaulting and entering bankruptcy. This occurs primarily when a company will take on substantial debt, through borrowing money for the business from lenders. This in-flow of cash in the near-term can allow for a company to grow its operations or acquire another company, and if used wisely and in moderation, can increase the overall value of the firm. However, this source of funding is not without potential downside, as when a company increases its financial leverage, it becomes riskier as it must meet scheduled interest and principal payments. When the firm is prospering and growing its cash flows, having some debt on the balance sheet is manageable, unless the business chooses to be greedy and increase the amount of debt beyond reason.
The majority of lenders, unless they are primarily focused on restructuring companies and distressed debt, aim to receive their coupon payments throughout the term of the loan and the eventual return of the principal. When approached by a company seeking debt funding who may have a history of putting the company’s debt holders in a jeopardizing situation where it may not be able to fulfill its debt obligations or has made capital allocation decisions in the past that were not in the best interests of debt holders, they may choose to set certain conditions on the debt. These conditions are called covenants and can either be treated as positive or negative. A positive covenant requires the company to maintain certain assets on their balance sheet, an example of this being protective insurance or prepaying operating expenses such as rent. The other type of covenant is a negative or restrictive covenant. These are used more often than positive covenants and will be discussed further in this report in detail. From the borrower’s perspective, if they believe the covenants to be reasonable and achievable, they allow to negotiate a lower cost of debt as the lender’s are prepared to offer better terms if they are guaranteed the peace of mind with the conditions they set on the debt.
Negative Covenants - Why Lenders Use Them
The majority of corporate bankruptcy cases are the end product of a management team seeking to aggressively grow their business through the use of debt funding above that of the firm’s sustainable growth rate. In industries such as oil & gas, if a company chooses to make acquisitions on the basis that they believe the price of oil will remain at a certain price for the foreseeable future and the price declines substantially all of a sudden, the company may risk defaulting on their debt. This is where restrictive covenants come into play, they are responsible for two primary functions. First being, for the company not to go beyond certain leverage ratios:
Debt / EBITDA (Earnings before Tax, Interest, Depreciation and Amortization)
This ratio is used in negative covenants as the lenders are concerned with how many years of cash flow the company needs to cover their outstanding debt. Earnings before tax, interest, depreciation and amortization is used as it is a proxy for a company’s cash flow. Depreciation and amortization are added back to operating income as they are non-cash charges that are susceptible to a company’s accountants altering in order to reduce what the company is required to pay in taxes. Taxes and interest are also added back to operating income as once added back, this EBITDA figure represents the available cash flow that a company can use to pay its debt holders (operating cash flow proxy), as they are above equity holders in a firm’s capital structure. Having a negative covenant imposed on this ratio would prevent the company from going beyond a certain multiple of Debt / EBITDA or else would automatically default on its debt.
EBITDA / Interest
This ratio with EBITDA, similar to the Debt / EBITDA ratio above, calculates how many times a company can meet its annual interest obligations with its operating cash flow. Although not as effective and indicative of a firm’s leverage as the previous ratio, it helps a lender observe how many years of interest payments a firm can satisfy with its cash flow. It is more of a short-term ratio as it does not account for the principal amounts of the debt.
The second component of negative covenants are with respect to a firm’s capital allocation decisions, whether this is choosing to issue dividends or acquire another company, the covenant can limit these actions in order to protect the cash flow available to satisfy the debt holders.
With respect to corporate bankruptcy prediction, companies that are required to have covenants in their debt are firms that are riskier to begin with. However, this is not to say that all firms that incorporate covenants within their debt issuances are at risk of going bankrupt, in some cases imposing a series of covenants can in fact increase the overall value of the firm as the covenants prevent companies from making decisions that will put the company at risk of bankruptcy. Covenants help company management to reduce agency risk, as they increase the likelihood that management will act in the best interests of all stakeholders, not only the equity holders but the debt holders as well.
In Mansi, Qi and Wald’s report on “Debt Covenants and Bankruptcy Risk”, they find that companies that are required to impose covenants on their debt issuance are at higher risk of going bankrupt even with the positive benefits from having stricter regulations for management and lowered agency costs (2012).
The Altman Z-Score – Introduction
To recall, in statistics, a Z-Score refers to how many standard deviations a particular data point is from the mean of the data.
A Z-score of 1 means the data point is one standard deviation away from the mean. A Z-Score of 2 - two standard deviations away from the mean - etc. Z-Score is useful when comparing data points from different sets of data. Z-scores also reveal to statisticians and traders if a score is typical for a specified data set or if it is atypical. In addition to this, Z-scores also make it possible for analysts to adapt scores from various data sets to make scores that can be compared to one another accurately. Usability testing is one example of a real-life application of Z-scores.
Altman Z-Score is a financial model published in 1968 and created by NYU Stern Finance business professor Edward Altman in 1967. The mathematical formula from the model attempts to express a publicly traded manufacturing company’s likelihood of declaring bankruptcy within a two-year time period. Throughout the years, Altman developed other models to fit with different types of companies. In 1983, the Model “A” Z-Score was developed for use with private manufacturing companies. Model “B” was developed for non-public traded general firms and included the service sector.
In 2012, Edward Altman released an updated version called the Altman Z-Score Plus that can be used to evaluate public and private companies, manufacturing and nonmanufacturing companies, and U.S. and non-U.S. companies. It is used to evaluate corporate credit risk. Different models have different variables, weighting and overall predictability scoring systems but have the same roots. Thus I will not fall into detail for the advanced models and will only focus on the original model which will later be derived into Model A, Model B, and Model Plus.
Breaking Down Altman Z-Score
The Altman Z-Score is based on five financial ratios that can be calculated from data found on a company’s annual 10k report. It uses profitability, leverage, liquidity, solvency, and activity to predict whether a company has a high degree of probability of being insolvent. Recall that there is no real mathematical formula to prevent bankruptcy which means that the model only produces a probability of going bankrupt or not.
The number produced by the model is referred to as the company\'s Z-score, which is a reasonably accurate predictor of future bankruptcy. The model is specified as:
Z-Score = 1.2A + 1.4B + 3.3C + 0.6D + 1.0E
A = working capital / total assets
It measures the net liquid asset of a company relative to the total assets.
B = retained earnings / total assets
It measures the financial leverage level of a company.
C = earnings before interest and tax / total assets
It measures productivity of a company’s total assets.
D = market value of equity / total liabilities
It measures what portion of a company’s assets can decline in value before the liabilities exceed the assets.
E = Asset Turnover Ratio = Net sales /Average total assets
It measures revenue generating ability of a company’s assets.
The formula weighs the various business ratios used in the formula and then sums then. This number is the compared to a graded scale.
Working Capital to Total Assets
Working capital is a company’s current assets less its current liabilities and measures a company’s efficiency and its short-term financial health. Positive working capital means that the company is able to meet its short-term obligations. Negative working capital means that a company’s current assets cannot meet its short-term liabilities; it could have problems paying back creditors in the short term, ultimately forcing it into bankruptcy. Companies with healthy, positive working capital shouldn’t have problems paying their bills.
Retained Earnings to Total Assets
The retained earnings of a company are the percentage of net earnings not paid out as dividends; they are “retained” to be reinvested in the firm or used to pay down debt. Retained earnings are calculated as follows:
Beginning retained earnings + net income (net loss) – dividends paid
The ratio of retained earnings to total assets helps measure the extent to which a company relies on debt, or leverage. The lower the ratio, the more a company is funding assets by borrowing instead of through retained earnings which, again, increases the risk of bankruptcy if the firm cannot meet its debt obligations.
Earnings Before Interest & Taxes to Total Assets
This is a variation on return on assets, which is net income divided by total assets. This ratio assesses a firm’s ability to generate profits from its assets before deducting interest and taxes.
Market Value of Equity to Total Liabilities
The ratio of market value of equity to total liabilities shows how much a company’s market value (as measured by market capitalization, or share price times shares outstanding) could decline before liabilities exceed assets.
Unlike the other ratio components used by the Z-Score, market value isn’t based purely on fundamentals—the market capitalization of a firm is an indication of the market’s confidence in a company’s financial position. Generally speaking, the higher the market capitalization of a company, the higher the likelihood that the firm can survive going forward.
Sales to Total Assets
The ratio of sales to total assets, more commonly referred to as asset turnover, measures the amount of sales generated by a company for every dollar’s worth of its assets.
In other words, asset turnover is an indication of how efficiently a company is as using its assets to generate sales. The higher the number the better, while low or falling asset turnover can signal a failure by the company to expand its market share.
A Z-score below 1.8 is indicative of pending bankruptcy. A Z-score of 1.8 to 3 indicates a company that might be headed for bankruptcy. A Z-score above 3 means a company is financially stable.
In the initial stages, the Altman Z-score was found to be 72% exact in predicting bankruptcy two years preceding the event, including a Type II error (false positives) of 6%. However, the model was found to be about 80-90% accurate in the process of predicting bankruptcy one year preceding the event, in a series of ensuing tests including three distinctive time periods over the next 31 years. However, a type II error, classifying the company as bankrupt while it is not going so, of 15-20% was also included in these tests.
Investors can use Altman Z-scores to determine whether they should buy or sell a particular stock if they are concerned about the underlying company’s financial strength. Investors may consider purchasing a stock if its Altman Z-score value is closer to 3 and selling or shorting a stock if the value is closer to 1.8.
The approach of Altman’s Z-Score formula has achieved ample acceptance by management accountants, auditors, database systems, and courts used for loan evaluation. Besides the approach of this formula has been used in an assortment of countries and contexts, although it had been initially designed for publicly held manufacturing firms featuring assets of more than $1 million.
The strength of the Z-score as a predictive tool of financial distress is derived from its empirical roots. First of all, it can be calculated quickly, based on standard financial ratios that have an intuitive interpretation. Secondly it provides clear distress and finds out grey and safe zones of a company that can be used as milestones. They can also be used as an indicator of the urgency of required actions. Finally, it simply works. Although it is a simple model derived 40 years ago, used in the right instances for the right industries, it has been shown to provide relatively accurate predictions for the first two years.
Altman Z-Scores and the Financial Crisis
In 2007, the credit ratings of specific asset-related securities had been rated higher than they should have been. The Altman Z-score indicated that the companies\' risks were increasing significantly and may have been heading for bankruptcy.
Altman calculated that the median Altman Z-score of companies in 2007 was 1.81. These companies\' credit ratings were equivalent to B. This indicated that 50% of the firms should have been rated lower, and they were highly distressed and had a high probability of becoming bankrupt.
Altman\'s calculations led him to believe that a crisis would occur and there would be a meltdown in the credit market. Altman believed the crisis would stem from corporate defaults, but the meltdown began with mortgage-backed securities (MBS). However, corporations soon defaulted in 2009 at the second-highest rate in history.
Limitations and Critiquing Altman Z-Score
The main problem with Altman Z-score with the formulation of solvency risk is that the formula is not suited for many industries. Indeed, the original model was formulated for operating industrial companies. For example, highly regulated utilities show up having very high bankruptcy risk no matter their financial strength. For instance, low or negative working capital doesn’t score well on Altman Z but some industries can operate with zero or negative working capital. For example, a restaurant gets paid in cash, but their suppliers will generally give them net 30 on their payables and the inventory (food) turns over very quickly. Thus, the first ratio of the formula (working capital / total assets) will mislead the results of the model.
Altman Z-score also does not analyze the financial sector properly. Indeed, companies like banks do not have clear sales. Financial firms tend to be highly levered and their operating risks and exposures are not well disclosed. Thus the model made up by Edward Altman does not fit for these types of companies and industries because the last ratio of the model will provide wrong insights.
Z-score do not work for new companies, as their low earnings will always render a low Z-score. In addition, the Z-score does not directly account for cash flow. A company may have a high Z-score but be unable to pay its bills, and thus have to declare bankruptcy.
Ohlson O-Score Model - Introduction
The Ohlson O-Score bankruptcy prediction model is a financial formula published in 1980 by Dr. James Ohlson of the New York University. As an alternative method to the Altman Z-score, it is also an accounting-based model, which includes financial statements analysis and ratio analysis. However, there are few major difference between the two models. First of all, compared with Altman Z-score model, the Ohlson O-score model includes more factors (nine) to describe all aspects of public-traded companies. More importantly, 105 bankrupt companies to 2058 non-bankrupt companies were analyzed by Dr. Ohlson, while only fifty-three failed firms and non-failed firms were analyzed in the Z-score model. As a result, the overall accuracy rate for the estimation sample was 96% and for the hold-out sample 85%. (Mareike Kira Kleinert, 2014). One essential advantage is that the observer is able to tell whether the selected company went bankruptcy before or after the date of release, given that the 10-K reports indicate the exact releasing time.
In short, the major finding of the study is that the size of the company, measures of the financial structure, measures of performance and measures of current liquidity are statistically critical in predicting the probability of bankruptcy.
The Ohlson model chooses to use the conditional logit analysis to replace the well-known multivariate discriminated analysis (short for MDA analysis) that is used in the previous models. Based on Dr. James Ohlson’s theory, there are three key problems associated with the MDA analysis. First of all, many strict unrealistic assumptions were made in the MDA analysis. For example, the model assumes all the explanatory variables and predictors are normally distributed, which rarely make sense in the real life. Secondly, the result of MDA is basically a score, which is a ranking device and has little intuitive interpretation. For decision problems such that a misclassification structure is an inadequate description of the payoff partition, the score is not directly relevant (Ohlson, 1980). Lastly, in the MDA analysis, the procedures to match failed and non-failed firms according to size and industry have proved to be irrational, and it would be more effective to include these factors as the predictors rather than using them as criteria to match different companies.
Instead, the conditional logit analysis that Ohlson applied avoids all the problems above since it is not based on those strict assumptions. A new statistical concept is used in the Ohlson model, “given that a firm belongs to some prespecified population, what is the probability that the firm fails within some prespecified time period?” (Ohlson, 1980). Under this context, no more assumptions are required.
Breaking Down Ohlson O-Score
The Ohlson O-Score is a financial formula which is based on nine independent variables. It depicts a probability between 0 and 1. Among these variables, six financial ratios are consistent with the Altman Z-score model. For example, both models covered leverage ratio, return on assets ratio and working capital ratio. Overall, his results showed that the factors “size” of a company and the “financial structure of a company” as well as the “current liquidity” play a crucial role in detecting bankruptcy (Ohlson, 1980). In fact, there are three sets of models are computed in the Ohlson model. Specifically, Model i predicts bankruptcy in one year; Model ii predicts bankruptcy in two years on condition that the company did not go bankrupt in the previous year; Model iii predicts bankruptcy in one or two years. The model of Ohlson (1980) is as follows:
(i) Ohlson = -1.32 - 0.407 A + 6.03B - 1.43C + 0.0757D - 2.37E - 1.83F + 0.285G - 1.72H - 0.521I
(ii) Ohlson= 1.84 - 0.519A + 4.76B- 1.71C- 0.297D - 2.74E -2.18 F -0.78G -1.98H + 0.4218I
(iii) Ohlson= 1.13 - 0.478A + 5.29B- 0.990C + 0.062D - 4.62E -2.25F -0.521G-1.91H + 0.212I
The specific examination of the nine variables are as followed:
1. A= SIZE = log (total assets/GNP price-level index).
The reason why size is included as a variance is that smaller companies are more likely to go bankrupt and be seen as riskier. Moreover, Ohlson adjusted for inflation using the GNP price level index, which assumed a base value of 100 for 1968. The index year is as of the year prior to the year of the balance sheet date. Total assets are as reported in dollars.
2. B= TL/TA = Total liabilities divided by total assets.
TL/TA is an indicator of financial leverage, it is a percentage meaning how much of total assets are financed by creditors, debts and liabilities. The higher the ratio, the higher levels of liabilities and hence, higher risk of default. It includes both long-term and short-term as well as all tangible and intangible assets.
3. C= WC/TA= Working capital divided by total assets.
WC/TA is an indicator of financial liquidity, which represents the net current assets or working capital of a company as a percentage of its total assets. Working capital measures a company’s efficiency and its short-term financial health. It is calculated as a company’s current assets minus its current liabilities.
4. D= CL/CA= Current liabilities divided by current assets.
CL/CA is an indicator of financial leverage, it is a percentage of current assets (Inventory, asset receivable, etc.) that is financed by current liabilities (accounts payable, notes payable, etc.)
E= OENEG = Dummy variable
One if total liabilities exceed total assets, zero otherwise.
5. F= NI/TA= Return on Asset (ROA)
NI/TA is an indicator of profitability relative to total assets. It is a percentage that measures the efficiency of how the company generates earnings from the asset. The formula is net income divided by total assets.
6. G= FU/TL = Funds provided by operations divided by total liabilities.
FU/TL is a leverage ratio that indicate financial risk of a company. It is normally used by the credit rating agency or individual investor. Funds provided by operations is calculated as the Net operating income plus depreciation, amortization and deferred income taxes (all the noncash items).
8. H= INTWO = dummy variable= One if net income was negative for the last two years, zero otherwise.
9. I= CHIN= (NIt – Nit-1)/(|Ni t| + |NI t-1|) NIt is net income for the most recent period.
CHIN is a percentage to the measure change in net income. The denominator acts as a level indicator.
In summary, the variables include one liquidity ratios (WC/TA), one profitability ratios (NI/TA), three leverage ratios (TL/TA and CL/CA and FU/TL), two dummy variables (INTWO and OENEG), One Size indicator and one Net income change percentage. Based on Ohlson (1980), the overall accuracy rate is more than 96%. The specific prediction result is shown in appendix 1.
The probability of failure is calculated as P = exp(O-score)/1+exp(O-score). The O-score is transformed into a probability(Percentage) using a logistic transformation. Thus, when P >0.5 indicates potential bankruptcy while company and P <0.5 indicates safe in the following one year.
In order to minimize the Type I and Type II error and get a more useful accuracy rate, Ohlson found that 0.038 is the optimal cutoff point. Type II errors are non-bankrupt firms that are classified as bankrupt, while Type I errors are bankrupt firms that are classified as non-bankrupt. The specific result can be found in appendix 2.
As the alternative method of the Altman Z-score model, Ohlson’s model has a similar functionality and has been used in many studies in the field of bankruptcy forecasting. Individual investors can also use it as a tool to forecast their goal companies. In comparison, Ohlson’s model generate a more obvious result (yes or no) rather than a scoring model like Altman Z-score. Most importantly, its predictive ability and accuracy rate are proved to be superior than the other accounting-based models. In the Pongsgat et al.’s research (2004), Ohlson’s model and Altman’s Z-score model were compared and concluded that Ohlson’s model performed better in terms of the predictive ability in all three phases before bankruptcy. Many researchers also applied various accounting-based methods to their own country, such as Oude Avenhuis (2013) which analyzed Dutch listed and large non-listed firms, and summarized that the model of Ohlson (1980) is the most accurate under the same statistical technique. Wang & Campbell (2005) also found out that Ohlson’s model is “an applicable measure of predicting firm delisting in China.” It is reported the accuracy rate achieved 95%.
There are two major problems exist in the accounting-based single logit model. First of all, the first problem is that bias exist in the sample selection process given the fact that it selected only one and non-randomly observation. Besides, in the model, the time varying changes issue is not considered. To be more exact, as Grice and Dugan stated in their research paper (2003), the relationship between ratios and its effect on bankruptcy changes over industries and time. In Hensher and Jones’s report (2007) research states : “all parameters are fixed and the error structure is treated as white noise, with little behavioral definition”. The models assumes that bankruptcy prediction of various combinations of ratios does not change over different economic conditions. However, it may vary in the real life (Mensah, 1984).
In conclusion, it seems that although the result of Ohlson´s model (1980) shows high accuracy rate, the model itself is inefficient and biased.
The biggest calamity that can befall equity investors is corporate bankruptcy, which wipes out the equity of a firm and knocks the stock’s investment value down to zero. Fundamental analysis attempts to gauge the financial strength of a company using a variety of metrics, many of which we have highlighted in this report. Used in conjunction with one another, financial ratios can often help us to paint a picture of the long-term viability of a firm.
The biggest issue regarding corporate bankruptcy is in the end the fact that it is not 100% predictable. Markets and industries are impacted by external environment components like economic crisis or demographical events that can change the entire operations and management of a company, making it more or less insolvent. Moreover, internal factors, like the quotation on a stock market or the type of sales a company is making, are also influencing corporate bankruptcy in different ways. Thus, predicting companies’ insolvency with the right assumptions and the right models is not easy.
Failure of being 100% accurate, here is what we suggest. First of all, investors should select prediction models according to the type of company they are looking to invest in. As said before, every model is not suited for every company. Then, they should combine the most models they can to eliminate errors and to reduce the number of assumptions they used. Finally, investors should check if the companies they seek to invest in are protected by financial covenants. If they are here to restrain borrowing, they are also a form of risk evaluation. Indeed, only risky companies need negative covenants in case something goes wrong regarding the company’s solvency.
Based on what we developed in this paper, here are our recommendations:
Altman Z-Score Classic Model → public manufacturing companies of at least 5 years
Altman Z-Score Model A → private manufacturing companies of at least 5 years
Altman Z-Score Model B → non-public traded companies of at least 5 years
Ohlson O-Score Model → Excellent for Chinese corporations and when the market is stable
No financial covenants → The company is less protected from bankruptcy but is less risky
Negative covenants → The company is protected but also riskier than other investments
1. Mensah, Y. (1984). An Examination of the Stationarity of Multivariate Bankruptcy Prediction Models: A Methodological Study. Journal of Accounting Research, 22, (1), 380-395.
2. Ohlson, J. (1980). Financial Ratios and the Probabilistic Prediction of Bankruptcy. Journal of Accounting Research, 18(1), 109-131. doi:10.2307/2490395
3. Mani Shehni Karamzadeh (2012). Application and Comparison of Altman and Ohlson Models to Predict Bankruptcy of Companies. Research Journal of Applied Sciences, Engineering and Technology 5(6)
4. Hillegeist, S. A., Keating, E. K., Cram, D. P., & Lundstedt, K. G. (2004). Assessing the probability of bankruptcy. Review of Accounting Studies, 9(1), 5-34. doi: 10.1023/B:RAST.0000013627.90884.b7
5. David Lundqvist, Jakob Strand (2013). Bankruptcy Prediction with Financial Ratios -Examining Differences across Industries and Time. Degree Project Master of Science in Business and Economics, Lund University
6. Mareike Kira Kleinert (2014). Comparison of accounting-based bankruptcy prediction models of Altman (1968), Ohlson (1980), and Zmijewski (1984) to German and Belgian listed companies during 2008 – 2013. Master Thesis Business Administration Tilburg University
7. Patrick Gerritsen (2015). Accuracy rate of bankruptcy prediction models for the Dutch professional football industry. Master Thesis Business Administration-financial management. University of Twente.
8. David A. Hensher, Stewart Jones（2007）. Forecasting Corporate Bankruptcy: Optimizing the Performance of the Mixed Logit Model. Journal of Accounting finance and business studies. DOI: 10.1111/j.1467-6281.2007. 00228.x
9. Ying Wang; Campbell, Michael（2010）. Business Failure Prediction for Publicly Listed Companies in China. Journal of Business & Management;2010, Vol. 16 Issue 1, p75
10. · Some Facts and Figures on Secured Lending by G. Nini and D. C. Smith, University of Pennsylvania (2015)
11. · Corporate Financial Distress and Bankruptcy - Predict and Avoid Bankruptcy, Analyze and Invest in Distressed Debt by E. I. Altman and E. Hotchkiss, John Wiley & Sons (2006)
12. Investment Banking - Valuation, Leveraged Buyouts and Mergers & Acquisitions by Joshua Rosenbaum and Joshua Pearl, John Wiley & Sons (2009)
13. Debt Covenants and Bankruptcy Risk by S. Mansi, Y. Qi and J. Wald (2012) by SSRN Electronic Journal
...(download the rest of the essay above)