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«Bankruptcy Prediction and its Advantages Empirical Evidence from SMEs in the French Hospitality Industry Author Joseph Janer * Academic Supervisor ...»

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The MSc Programme in Economics and Business Administration

(Applied Economics and Finance)

Bankruptcy Prediction

and its Advantages

Empirical Evidence from SMEs in the French

Hospitality Industry


Joseph Janer *

Academic Supervisor

Cédric Schneider

Master’s Thesis

Department of Economics

Copenhagen Business School

December, 2011


The author can be contacted at: joseph.janer@gmail.com

No. of effective pages: 80; No. of characters with spaces: 185,957


This study is about bankruptcy prediction modeling and explores the benefits from its application. Bankruptcies affect all stakeholders: from employees to regulators, investors or managers. Therefore, it is very interesting to understand the phenomenon that leads to bankrupt in order to take advantage of it.

The study begins with an exhaustive literature review with the purpose of understanding well the topic of bankruptcy prediction. Most of the models and techniques of bankruptcy prediction modeling up to this date are covered here.

The main research questions that define this study are: (i) How to predict bankruptcies on a specific industry? (ii) How to attribute probabilities of bankruptcy and classes of risk to these predictions? (iii) How to determine the contributing variables to a predicted bankrupt and to benefit from it?

Linear discriminant analysis (LDA) method is used to answer these questions.

Empirical evidence supports the developed model and study. The rate of good classification is equal to 86.36% of the holdout sample. Type I and II errors are in equivalent proportions after being rebalanced with a cut-off modification achieved by nonlinear programming optimization. Various testing of the model robustness are performed, such as logistic regression, which confirms the significance of the most of the explanatory variables. In order to refine the classification output of the model (either bankrupt or non-bankrupt firms), five classes of risks are developed – from the most to the least risky. In addition, probabilities of default and confidence intervals of the results are presented.

Finally, a deeper examination of the results’ outputs is conducted and contributions from the different ratios that influence the model are analyzed.

i Contents


1. Introduction

2. Research process

2.1. Motivations

2.2. Research Questions

2.3. Limitations

2.4. Contributions

3. Literature review

3.1. Background and history

3.2. Earlier techniques

3.3. Evolution of statistical techniques

3.4. Alternative modeling techniques

3.5. Evolution and empirical applications in France

3.6. Focused models

4. Theoretical model

4.1. Geometrical approach

4.2. Probabilistic approach

5. Data

5.1. Data specificities

5.2. Data reprocessing

6. Model development

6.1. Selection of discriminant variables

6.2. Combination of variables to form the discriminatory model

7. Empirical results

7.1. Validation of a function estimate

7.2. Validation of the final function

7.3. Optimizing the cut-off value through nonlinear programming

7.4. Optimized results

ii 8. Robustness analysis

8.1. Tests of the assumptions

8.2. Complementary tests of robustness

9. Probabilities of bankruptcy and risk classes

9.1. Probability of bankruptcy

9.2. Risk classes and probabilities of bankruptcy of the score

9.3. Uncertainty associated with probability of failure by risk class and its risk coefficient........... 67 10. Analysis of the contributions

10.1. Contributing variables to a score or predicted outcome

10.2. Different contributions and their meanings

10.3. Contributions of the sector

10.4. Contributions for firms

10.5. Analysis of the scores through the period studied

11. Discussion

11.1. Modeling technique used

11.2. Preparation of the discriminatory function

11.3. Model application

11.4. Later and other issues

12. Conclusion and future direction


Appendix A – Initially selected ratios for the study

Appendix B – Shortlisted ratios for the LDA

Appendix C – BvD (Orbis) definition of a company’s status

Appendix D – Ratio reprocessing

Appendix E – SAS coding

Appendix F – Data selection

Appendix G – Estimates of the final model

Appendix H – Model assumptions

Appendix I – Q-Q plots

Appendix J – Classes of risk and scores

Appendix K – Contributions

–  –  –

The purpose of this study is to assess this issue. This is attempted by studying small and medium sized enterprises (SMEs) in the French Hospitality Industry. This study combines both theoretical and empirical interest. From a theoretical perspective this study applies well-known theories, and from an empirical perspective it provides elements for concrete utilization.

The particularity of the topic of firms’ bankruptcy is that it affects all stakeholders: employees, stockholders, managers, investors, and regulators. This study provides benefits for everyone interested to learn about modeling and bankruptcy prediction application.

Predicting bankruptcy is a difficult exercise and many challenges have to be faced. The first challenge starts with the selection of the technique to be used. For this reason, after initiating the research process, two sections are dedicated on the modeling techniques: one on the literature and the other – on the methodology. They are developed in order to determine the most appropriate technique to help answering the research questions raised. Mostly of the bankruptcy prediction techniques are covered in the literature review. Then, the specific theoretical methodology of the technique chosen – the Linear Discriminant Analysis, is presented.

Once the model technique is understood, appropriate data are gathered. However, data often need to be reprocessed according to appropriate techniques. This last step is very important for the rest of the study because the better the incoming data, the better the results of the study. This step is very long in the model development and can take up to 4/5th of the time dedicated to the study (Bardos, 2001). Thus, obtaining good quality data is a must.

Once data are gathered and reprocessed, they are ready and appropriate to be used in the modeling technique. The model development is composed of two steps: univariate and multivariate. First, overall selected ratios are tested. The most appropriate and discriminatory 1 ones are selected for the second phase. Second, ratios are assembled in a multivariate model according to their combined discriminatory abilities.

After data are combined, results from different models are interpreted and refined. Specifically, the results’ section is composed of four parts. First, each combination of ratios composing a model is tested on different estimates to select the best estimate from each model. Second, among the different models, the final model is selected. Third, results from this final model are adjusted by nonlinear programming. Lastly, following these adjustments, the final model results are explored.

The next step is to verify the robustness of the model. Different tests on major assumptions and overall goodness of fit are performed. For testing the assumptions, tests on multivariate normality, homoscedasticity and multicollinearity are performed. For the overall goodness of the model, a logistic regression is performed to test the significance of the variables included in the final model. Other tests, such as test on the equality of group means, the Eigenvalues and Wilk’s lambda, are performed.

The analysis of the developed model is further studied more in detail. Probabilities of bankruptcy according to different scores’ intervals are generated. The initial classification, opposing bankrupt to non-bankrupt firms, is refined into five classes of risk. In addition, uncertainty accompanying probabilities of bankruptcy and risk classes is modeled through confidence intervals.

Then, benefits from the model are further explored. Specific variables contributing to the scores are analyzed over time. For example, results from the industrial sector, as well as from particular situations encountered by firms, are analyzed. Finally, more general observations on the performed study are discussed.

The layout of the study is as follow: Section 2 covers the research process; Section 3 presents an exhaustive literature review of prior researches; Section 4 presents the theoretical model; Section 5 describes the data; Section 6 presents the development to the final model; Section 7 presents the empirical results; Section 8 presents the robustness analysis; Section 9 presents the analysis of the risk classes and posterior probabilities; Section 10 presents the analysis of contributions; Section 11 discusses the research study, and section 12 concludes.


2. Research process

2.1. Motivations This subject was chosen because it allows working on both practical and theoretical aspects of a firm’s life. Bankruptcy’s study has recently become a hot topic due to the worldwide economic turmoil. This topic is very interesting and challenging. It concerns many actors of the business world and therefore, once achieved, the results should benefit the whole community. It is a good motivation to attempt to capture and understand the elements and reasons that lead to a corporate default. An additional motivation is to develop and implement a quantitative model to predict bankruptcies on SMEs that are the most present in the economic world 2. Finally, one last motivation is, once the model developed, to benefit from it and to advance in understanding of bankruptcies.

2.2. Research Questions To begin on this thesis, the initial intention was to study the risks of doing business with another firm that might go bankrupt. Therefore, the initial draft research question was: How to predict the bankruptcy of a company and to avoid default on payments? However, this angle of research was restricted to firms interacting with other firms.

As the subject of bankruptcy concerns all stakeholders, it is preferred to study the topic of bankruptcy prediction from a broader perspective, as on industry level, for example. In addition, it would be beneficial to take advantage of the bankruptcy prediction and to determine: (i) the probabilities of bankruptcy of a certain prediction, and (ii) the contributing variables to a predicted outcome.

Consequently, the final research questions that define this thesis are: (i) How to predict bankruptcies on a specific industry? (ii) How to attribute probabilities of bankruptcy and classes of risk to these predictions? (iii) How to determine the contributing variables to a predicted bankrupt and to benefit from it?

2 For example, with 23 million, SMEs in the EU represent 99% of businesses. Source: European Commission’s website, http://ec.europa.eu/enterprise/policies/sme/index_en.htm 3

2.3. Limitations In order to structure this study, three major limitations are set. The first one concerns the model.

It is not possible before starting the literature review of bankruptcy prediction to determine and to identify a model to answer the questions raised. The model will be determined after studying the literature review. However, the model used will apply only quantitative data. Specifically, only financial statement data will be selected as they are available for everyone and should objectively contribute to answer the questions raised.

Second, this limitation concerns the economic impact of the thesis. This study will focus on SMEs 3 because these firms are at the core of any industry and represent its biggest share. They are often well established in their business segment and should be less complex to analyze than multinationals or micro and start-up firms (Stili, 2002).

Finally, the last main limitation concerns the data. In order to satisfy the research questions raised, this study will focus on a specific industry – the French Hospitality Industry. In addition, detailed specificities and limitations of the data are explained in the data section.

2.4. Contributions This study contributes in several aspects to this domain. It starts with an exhaustive literature review of the studies conducted on bankruptcy predictions up-to-date. The study applies a wellknown methodology – the Linear Discriminant Analysis, to an unprecedented targeted population (specific niche of SMEs’ firms of the French hospitality industry). The advantage to focus the model on a specific industry allows tailoring it to the industry’s specific needs for better results. It

provides different perspectives and additional possibilities of analysis and interpretation, such as:

the use of nonlinear programming for cut-off optimization, various tests on the model’s robustness (including a logistic regression), and analysis of risks and variables contributing to the score output.

3 Note that the term SMEs such as used in this study refers to a subjective category of companies, which is detailed in the data section 4

3. Literature review

3.1. Background and history The analysis of corporate distress traces its history back to two centuries ago (E. I. Altman & Edith Hotchkiss, 2006). At first, potential corporate distresses were assessed based on some qualitative information, which were very subjective. In particular, four references were mostly used, such as: (i) the capacity of the manager in charge of the project or company, (ii) the fact that the manager had an important financial involvement in the company as a financial guarantee, (iii) the project and the industry in itself, and (iv) the fact that the firm possessed assets or collateral to back-up in case of a bad situation. Surprisingly, these recommendations could still be considered in many existing investment decisions.

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