Data Envelopment Analysis of Corporate Failure for Non- Manufacturing Firms using a Slacks-Based Model

Transcription

1 Data Envelopment Analysis of Corporate Failure for Non Manufacturing Firms using a SlacksBased Model By D Andre Wilson Supervised by Dr. Joseph C. Paradi A thesis submitted in conformity with the requirements for the degree of Masters of Applied Science The Centre for Management of Technology and Entrepreneurship Graduate Department of Chemical Engineering and Applied Chemistry University of Toronto Copyright 2012

2 Data Envelopment Analysis of NonManufacturing Firms Data Envelopment Analysis of Corporate Failure for NonManufacturing Firms using a SlacksBased Model Abstract D Andre Wilson Masters of Applied Science Department of Chemical Engineering and Applied Chemistry University of Toronto 2012 The purpose of this work was to study the ability of the SlacksBased Model of Data Envelopment Analysis in the prediction of corporate failure of nonmanufacturing companies as compared to Altman s Z score model. This research looks at nonmanufacturing firms specifically and attempts to classify companies without looking at the asset size of the firm. A DEA model based on the Altman s Z score financial ratios was created as well as a revised DEA model. The overall accuracy of the models showed the revised DEA model to be more accurate than the original DEA model as well as the Altman Z score. This indicated that bankruptcy could be predicted without the use of total assets or liabilities as variables. This also showed the ability of an SBM DEA model to predict bankruptcy. ii

3 Abstract The purpose of this work was to study the ability of the SlacksBased Model of Data Envelopment Analysis in the prediction of corporate failure of nonmanufacturing companies as compared to Altman s Z score model. DEA had been tested for corporate failure before, however the DEA model used was a BCC model and this was tested against Altman s original Z score model, which is an assetdominated model. This research looks at nonmanufacturing firms specifically and attempts to classify companies without looking at the asset size of the firm. Data was collected on nonmanufacturing companies that filed for bankruptcy between 2000 and 2006 for up to five years before bankruptcy. Nonbankrupt companies were found to match these, based on the SIC codes of the companies. The following data was collected for each company from the financial statements: Current Assets, Current Liabilities, Working Capital, Retained Earnings, Operating Income, Book Value of Equity, Total Assets, Total Liabilities, Number of Employees, and Number of Shareholders. The means of these variables were compared and this showed that the nonbankrupt companies had larger averages for all of these variables, except for the number of employees. The data was split into two groups, one to create the DEA model and determine a cutoff point and the other to test that cutoff point. The Altman Z model used the following formula. iii

4 The EBIT was replaced with Operating Income for this study due to lack of data. The first DEA model utilised the ratios from the Z score and made all numerators outputs and all denominators inputs. A second DEA model was created to exclude total assets and liabilities, to show that bankruptcy can be determined without the total asset size of the firm. The working capital was split into current assets and current liabilities for this second model and two new variables were also added, the total number of employees as an input and the total number of shareholders as an output. Altman s model classified more companies as bankrupt than DEA, whereas DEA classified more as nonbankrupt. Altman had a lower type I error in the first and second years before bankruptcy but DEA had lower type I error in the preceding years. DEA had a lower type II error overall. The overall accuracy of the models showed the revised DEA model to be more accurate than the original DEA model as well as the Altman Z score. This indicated that bankruptcy could be predicted without the use of total assets or liabilities as variables. This also showed the ability of an SBM DEA model to predict bankruptcy. All models had an increase in accuracy as the time before bankruptcy increased, though the revised DEA model had the highest accuracy in the th year before bankruptcy, showing it as a better model for predicting bankruptcy further before the date of bankruptcy. iv

5 Acknowledgements I would first and foremost like to thank Dr. Joseph Paradi, for all of his guidance and advice, as well as for doing everything possible to help me succeed. I truly could not have completed this without him and I am very grateful to him for sticking with me through the ups and downs of this past year and a half. I would like to thank all of the members of CMTE who helped me along the way and for all being so supportive when I needed them, in particular Angela Tran for making herself available when I needed her, as well as Haiyan Zhu for her advice. I would like to thank my family at the National Society of Black Engineers, the Engineering Outreach Office, and the Leaders of Tomorrow for helping to enrich my time at the University of Toronto. I would especially like to thank Nnaziri Ihejirika, for his constant support throughout my journey, for putting up with all of my mood swings and for always being there for me when I needed him. I would like to thank my parents, Larry Wilson and Fran DilletWilson, as well as my siblings Chauntez, Chadeau and Jazz for always supporting me no matter what. Most of all, I would like to thank God, because through Him all things are possible. v

6 Table of Contents Abstract... iii Acknowledgements... v Table of Contents... vi Table of Figures... ix List of Tables... x List of Symbols... xi Chapter 1: Introduction... 1 Thesis Structure... 2 Chapter 2: Literature Review... 4 Beaver s Univariate Study... 4 Altman s Multivariate Model... 6 Subsequent models... 8 Data Envelopment Analysis in Bankruptcy prediction Summary of Literature Review Chapter 3: Data Envelopment Analysis Charnes Cooper Rhodes model BankerCharnesCooper model SlacksBased Model... 2 Advantages/Disadvantages of DEA Chapter 4: Model Development Dealing with Negative Values Model Revision Chapter : Data Acquisition Chapter 6: Results and Discussion Univariate Analysis Second dataset Altman Z results Second group vi

7 DEA Model Revised DEA Model... Comparison of models... 8 Comments on DEA scores Chapter 7: Conclusion and Recommendations Conclusions Recommendations for Future Work... 6 References Appendix A: List of companies Group Group Appendix B: Financial Data Group year before bankruptcy years before bankruptcy years before bankruptcy years before bankruptcy... 9 years before bankruptcy Group year before bankruptcy years before bankruptcy years before bankruptcy years before bankruptcy years before bankruptcy Appendix C: List of paired companies Appendix D: List of Altman Z Scores Group Group Appendix E: List of DEA Scores for Original Model vii

8 Group Group Appendix F: List of DEA Scores for Revised Model Group Group Appendix G: Tstatistics for comparison of means Group Group viii

9 Table of Figures Figure 1: Simak Model Figure 2: Simak Model Figure 3: Simak Model Figure 4: DEA Example Figure : DEA BCC vs CCR efficient frontier Figure 6: Slacks Based Model Figure 7: Profile Analysis of Variables in first DEA model Figure 8: Profile Analysis of remaining variables for revised DEA model Figure 9: Percent error of Altman Z'' Score Figure 10: Classification accuracy of Altman Z'' Model... 4 Figure 11: Classification accuracy of Altman Z'' model including grey area Figure 12: Total classification within each zone of Altman Z'' model Figure 13: Cutoff point determination on year 1 results Figure 14: Closer look at cutoff point for year Figure 1: Cutoff point on year Figure 16: Cut off point for up to years before bankruptcy... 2 Figure 17: Average DEA scores for group 1 first DEA model... 3 Figure 18: Cutoff points for up to years before bankruptcy for revised model... 6 Figure 19: Average DEA scores for group 1 in model Figure 20: Comparison of overall accuracies... 9 Figure 21: Comparison of bankrupt and nonbankrupt classification accuracies... 9 Figure 22: Comparison of type I and type II error Figure 23: Comparison of percent classifications ix

10 List of Tables Table 1: DEA Example Table 2: Number of companies in group Table 3: Number of companies in group Table 4: Number of companies in group 1 used in revised model Table : Number of companies in group 2 used in revised model Table 6: Profile analysis of group 1 bankrupt companies Table 7: Profile Analysis of group 1 nonbankrupt companies Table 8: Profile Analysis of bankrupt companies in group Table 9: Profile Analysis of Nonbankrupt companies in group Table 10: Results of Altman Z'' Model on group Table 11: Results of Altman Z'' model on group Table 12: Cutoff points for first DEA model... 4 Table 13: Classification accuracies of group 1 used to determine cutoff... 4 Table 14: Classification accuracies of cutoff point for model 1 tested on group 2... Table 1: Intersection points for each year of model Table 16: Cutoff points for revised DEA model... 7 Table 17: Classification accuracies used to determine cutoff points for revised model... 7 Table 18: Classification accuracies of cutoff points for revised model on group x

11 List of Symbols Z Altman's Z Score Z" Altman's Z" Score for nonmanufacturing firms EBIT Earnings before Income and Taxes WC Working Capital RE Retained Earnings OI Operating Income BVE Book Value of Equity TA Total Assets TL Total Liabilities CA Current Assets CL Current Liabilities SH Number of Shareholders EM Number of Employees Efficiency CCR DEA Score Input Oriented CCR DEA Score Output Oriented Coefficient for DEA output Coefficient for DEA input DEA output DEA input BCC DEA Score input oriented DEA Score dual multiplier form Vector of DEA inputs Vector of DEA outputs Row vector with all elements unity BCC DEA Score output oriented Vector of coefficients for DEA inputs and outputs Negative DEA slacks Positive DEA slacks DEA Score for Slacks Based Model xi

12 Chapter 1: Introduction When an individual or group is managing a company or investing in a company, something of great importance is the corporate health of that company. A very valuable piece of information would be if that company is headed for corporate financial stress or failure. In the past, many have attempted to predict corporate failure before it occurs. One of the most prevalent methods is to use financial ratios to determine the health of a company. A number of studies have been done to use the information from financial statements, particularly financial ratios to predict failure [BEAV67]. A prominent method of predicting bankruptcy is the Altman Z score [ALTM68]. Edward Altman used Multiple Discriminant Analysis to create a model that uses basic financial ratios in a linear formula to give a score. This score is used to determine whether a company is at risk of corporate stress or failure, whether they are healthy or whether they are classified in an undetermined zone or grey area. Later, in 1997, Paul Simak and Joseph Paradi attempted to compare this method to another analysis type, DEA or Data Envelopment Analysis [SIMA97]. This method used the BCC version of the DEA model and showed that this model was preferable to Altman ZScore for predicting bankruptcy of companies up to 3 years before the bankruptcy date. The problem with these methods is that they were generalized and in particular, did not look at firms that were nonmanufacturing, i.e. there was a large focus on the assetsize of the firms involved [GRIC01B] [HILL04]. In more recent times, more companies are nonmanufacturing Data Envelopment Analysis of Corporate Failure for NonManufacturing Firms 1

13 and are more service oriented and thus have less focus on the overall assetsize of the company [WORL09]. In response to the focus on manufacturing companies in his original model, Altman created another model, the Altman Z score [ALTM02]. With this score he tested nonmanufacturing firms and redeveloped the coefficients and cutoff points of the original model to suit. This model however, is still substantially based on assets, though more companies are becoming focused on service, are people driven, and do not have a large asset base [WORL09]. Thus an investigation of the Altman Z score for nonmanufacturing firms was done here. This research tests the following: The feasibility/accuracy of DEA as a predictor of bankruptcy in nonmanufacturing firms as compared to the Altman Z model The effectiveness of a SlacksBased DEA model as opposed to a BCC DEA model for bankruptcy prediction The accuracy of bankruptcy prediction without regard to the total asset size of a company and to add a 'human capital' value that focuses on the serviceoriented side of nonmanufacturing firms. The effectiveness of both Altman and DEA in the prediction of bankruptcy for up to five years before the bankruptcy date. Thesis Structure This thesis is structured as follows: Data Envelopment Analysis of Corporate Failure for NonManufacturing Firms 2

14 o Chapter 2 outlines key papers that have contributed to bankruptcy prediction literature with the use of financial statements. o Chapter 3 outlines Data Envelopment Analysis as an efficiency measurement technique, giving an overview of different DEA models as well as mathematical formulas, key terminology and appropriate examples. o Chapter 4 outlines the method for developing the model and the reasoning behind the innovations that were made to the model. o Chapter outlines the method for data acquisition and summarizes the quality of the data used. o Chapter 6 presents the results of the analysis and comments on the findings. o Chapter 7 summarizes the key findings and suggests recommendations and potential areas for further research. Data Envelopment Analysis of Corporate Failure for NonManufacturing Firms 3

15 Chapter 2: Literature Review Having an understanding of the studies related to bankruptcy prediction and analysis techniques are imperative to create a model that is not redundant in literature and that can contribute to the existing knowledge of analysis of corporate failure. This section outlines some of the most relevant findings with bankruptcy prediction and summarizes the implications of this research based on those findings. Beaver s Univariate Study One of the first attempts to predict insolvency or bankruptcy was done by William Beaver in 1967 [BEAV67]. Beaver defined failure as the inability of a firm to pay its financial obligations as they mature and a financial ratio as a quotient of two numbers, where both numbers consist of financial statement items. He also introduced a third term predictive ability which is essentially the usefulness of a data item in identifying an event before it occurs [BEAV67]. Beaver collected data from Moody s industrial manual between 194 and 1964, inclusive. Each failed firm from Moody s was compared to a nonfailed firm in the same industry of the same asset size. At the time there was statistical reason to believe that a larger of two firms will have less probability of failure even if they have identical financial ratios. Therefore he believed that firms of different assetsizes could not be accurately compared [ALEX49]. Beaver compiled 30 ratios and showed 14 to be the most effective: Cash flow/total debt Net income/total assets Total debt/total assets Data Envelopment Analysis of Corporate Failure for NonManufacturing Firms 4

16 Current assets/total assets Quick assets/total assets Working capital/total assets Cash/total assets Current assets/current liabilities Quick assets/current liabilities Cash/current liabilities Current assets/sales Quick assets/sales Working capital/sales Cash/sales Beaver s results ultimately showed cashflow to total debt ratio as the best predictor, with total debt to total assets as second best. He noted that the most crucial factor was the net liquid asset flow supplied to the reservoir while the size of the reservoir was the least important factor. Beaver also visited the concept of likelihood ratios. The likelihood ratio (LR) is the ratio of these to values. ( ) ( ) (1.1) Data Envelopment Analysis of Corporate Failure for NonManufacturing Firms

17 ( ) ( ) A likelihood ratio could be found for every interval for each of the financial ratios in each year before bankruptcy. However, Beaver was inconclusive in his analysis of the likelihood ratios. He stated that in the year before failure the likelihood ratio mirrored the financial ratio, however in years before that the results varied greatly [BEAV67]. He also stated that though his work was univariate, it would be valuable to consider a multivariate approach. This is where Altman stepped in [ALTM68]. Altman s Multivariate Model In 1968, Edward Altman attempted the first multivariate approach to bankruptcy prediction. The analysis technique that he adopted was MDA, multiple discriminant analysis. In Altman s time, MDA was not as popular as regression analysis and was used mainly in biological and behavioural sciences [ALTM68]. MDA is a statistical technique used to classify an observation into one of several a priori groupings dependent upon the observation s individual characteristics. [ALTM68]. It is usually used to classify the variable into a qualitative group e.g. male or female, bankrupt or nonbankrupt [ALTM68]. The process used for MDA was first to establish groups, which could be more than two, and then collect data for objects within each of those groups. Then a linear combination is created from the data collected that will best discriminate between the groups. This is done by assigning coefficients to each piece of data. For the case of bankruptcy, a coefficient is assigned Data Envelopment Analysis of Corporate Failure for NonManufacturing Firms 6

18 to each financial ratio chosen and the output of the linear combination is a number that can assign a firm into bankrupt or nonbankrupt. MDA allowed for the entire profile of variables to be analyzed simultaneously rather than individually [ALTM02]. To develop the model Altman took a sample of 66 corporations with 33 firms in the bankrupt group and 33 in the nonbankrupt group. All bankrupt firms were manufacturers that filed a bankruptcy petition under Chapter 11 of the National Bankruptcy Act between 1946 and 196. The nonbankrupt firms were selected by a paired sample method (similar to Beaver) [BEAV67]. A list of 22 potential ratios was compiled which were split into five standard ratio categories: liquidity, profitability, leverage, solvency and activity ratios. From the list of 22, five ratios were selected to be able to do the best overall job at collectively predicting bankruptcy. These were selected based on: (1) statistical significance of various potential functions while determining the relative contribution of each individual variable, (2) the intercorrelation between the variables, (3) the predictive accuracy of various profiles and (4) judgement of the analysis. [ALTM68] The final model was: (1.2) Where: (1.2a) (1.2b) Data Envelopment Analysis of Corporate Failure for NonManufacturing Firms 7

19 (1.2d) (1.2e) With cutoff zones: Altman found a classification accuracy of 83.% for his model and he showed that his model could predict bankruptcy up to three years before the bankruptcy date. Subsequent models Later in 1972, Edward Deakin revisited Beaver s analysis. [DEAK72] He used the 14 ratios that Beaver found to be most effective and attempted to use a discriminant analysis similar to Altman s. Deakin also attempted to look at data up to years before the date of bankruptcy. In his analysis he found that the significance for each ratio changed across the years. And he found that he was only able to get significant prediction result for up to 3 years before the date of bankruptcy. Data Envelopment Analysis of Corporate Failure for NonManufacturing Firms 8

20 In 1980, James Ohlson attempted an alternative method of bankruptcy prediction using a probabilistic approach [OHLS80]. Ohlson looked at data between 1970 and Essentially for this method he looked at the vector of financial ratios and determined a vector of parameters for those ratios and looked at the probability of bankruptcy for those ratios and parameters. He then attempted to find a cutoff probability point between zero and one for bankruptcy and nonbankruptcy. The ratios that Ohlson employed were: Size = log(total assets/gnp pricelevel index) TLTA = Total liabilities divided by total assets WCTA = Working capital divided by total assets CLCA = Current liabilities divided by current assets ONENEG = One if total liabilities exceeds total assets, zero otherwise NITA = Net income divided by total assets FUTL = Funds provided by operations divided by total liabilities INTWO = One if net income was negative for the last two years, zero otherwise CHIN (NIt NIti)/(INItI + INItil), where NIt is net income for the most recent period. The denominator acts as a level indicator. The variable is thus intended to measure change in net income. Ohlson, however did not find promising results with this model as compared to Altman s model and thus is not commonly used today. In 1984, Zmijewski explored the potential methodological drawbacks of the previous bankruptcy prediction techniques [ZMIJ84]. His main issue was that previous studies that had used nonrandom samples, i.e. bankrupt and nonbankrupt groups had predelineated before modeling. Zmijewski attempted to use random sampling and incorporated a probit model to Data Envelopment Analysis of Corporate Failure for NonManufacturing Firms 9

21 test bankruptcy. The firms chosen for this study were from the American and New York Stock Exchanges with SIC codes of less than 6000 and were obtained between 1972 through What Zmijewski did was to create a variable B where if B>0 then the company is at risk of bankruptcy. His model is below: ( ) ( ) (1.3b) Where : o ROA = Net Income to Total Assets (Return on Assets) o FINL = Total Debt to Total Assets (Financial Leverage) o LIQ = Current Assets to Current Liabilities (Liquidity) o u = Normally Distributed Error term. However, Zmijewski found that his results were qualitatively similar to those that use nonrandom sampling and that there was no apparent improvement on the overall classification rates [ZMIJ84]. In the 90s there were many critiques of bankruptcy prediction. In 1993, SuJane Hsieh, criticized methods for determining the cutoff point of bankruptcy [HSIE93]. Some issues that were pointed out were the fact that the cutoff point is determined by trial and error not by statistics and that the cutoff point is determined without considering the relative loss for Type I and Type II errors. Hsieh derived a modified Bayesian decision model to estimate an optimal cutoff point for bankruptcy prediction models. A function was added in this model to account for the error costs of Type I and Type II errors and attempted to minimize these costs and not simply the probability of the error. However though Hsieh came up with this method for determining Data Envelopment Analysis of Corporate Failure for NonManufacturing Firms 10

22 the cutoff point, it has never actually been applied to previous bankruptcy models to determine its effectiveness vs. the common trial and error approach. In 2001, John Grice and Michael Dugan noted another drawback that models may not be as effective outside of the time period in which that model was created [GRIC01A]. That same year Tyler Shumway attempted to create a bankruptcy prediction method using a hazard model to account for changes over time [SHUM01]. He collected data for over 31 years and used the same ratios that Altman had used in his ZScore model. Shumway model, though it showed results better than Altman s in the first year before bankruptcy, had a significant decline in accuracy before the second year before bankruptcy. It can be seen that many bankruptcy models have used Altman s model as a benchmark for bankruptcy prediction. In 2001 another study was done by John Grice, along with Robert Ingram to look at the generalizability of the Altman Z score model [GRIC01B]. Grice looked at data between 1988 and 1991 and again showed that Altman s model was not as accurate during that time as it was on the time that it was developed. It was also shown that Altman s model was significantly more effective at predicting bankruptcy at a sample of specifically manufacturing firms than for a general dataset of companies. In 2004, a study was then done by Sudheer Chava and Robert Jarrow to look at the industry effects in bankruptcy prediction [CHAV04]. Data was collected from 1962 to 1999 and firms were taken from the AMEX, NYSE and NASDAQ listings. This study looked at both yearly and monthly intervals and showed that monthly intervals had the potential of being better predictors of failure if the data can be collected. A hazard model was run on the variables from Data Envelopment Analysis of Corporate Failure for NonManufacturing Firms 11

23 Altman s model [ALTM68], Zmijewski s model [ZMIJ84] and Shumway s model [SHUM01] and showed that industry groupings had a significant effect on the slope and intercept coefficients in these models. In 2004, Stephen Hillegeist, Elizabeth Keating, Donald Cram and Kyle Lundstedt attempted to use an options pricing model to look at the probability of bankruptcy [HILL04]. However again this model looked only at manufacturing firms to compare to Altman s Z score [ALTM68] and Ohlson s model [OHLS80] and it was suggested by the authors that the coefficients should be updated for industry adjustments. From the literature review it can be seen that industry is a factor in bankruptcy prediction. One of the most wellknown authors of bankruptcy prediction, Edward Altman also made another model based from his Altman Z score, specifically for nonmanufacturing firms [ALTM02]. This model is shown below. (1.4) Where: (1.4a) (1.4b) (1.4c) (1.4d) With cutoff zones: Data Envelopment Analysis of Corporate Failure for NonManufacturing Firms 12

24 As shown in studies such as the 2001 study by Grice [GRIC01B], Altman s original model is very much focused on manufacturing firms as are other models. Altman model for nonmanufacturing firms, called the attempts to look at an alternate industry set, but has not been studied much in subsequent papers and should be explored further. Data Envelopment Analysis in Bankruptcy prediction Comparing Altman Z score model to results from Data Envelopment Analysis (DEA) was done in 1997 by Simak and Paradi. The idea was to show that DEA would also be a valid model in the prediction of corporate failure [SIMA97]. Simak stated that when planning to invest in a company, most would like to know if the risk is acceptable for the return [SIMA97]. This is one of the main reasons why early warning indicators for corporate distress are widely researched. One of the more common methods is regression based multivariate ratio analysis, however it has many shortcomings associated with it so there are needs to explore other methods. Simak chose to use Data Envelopment Analysis (DEA) for several reasons. The advantages of DEA are outlined in the following chapter. Data Envelopment Analysis of Corporate Failure for NonManufacturing Firms 13

25 In Simak s model, the focus was on the Z score model. He split this model into a DEA model by making all of the denominators into DEA inputs and all of the numerators into outputs. He had the following model: Figure 1: Simak Model 1 Simak made two revisions to this model. First he changed the market value of equity to the book value. This allowed for his DEA model to be applied to private companies whose shares did not have market values, and also that the book value was more readily available on the balance sheet of a company [SIMA97]. This gave the model shown in Figure 2. Figure 2: Simak Model 2 Data Envelopment Analysis of Corporate Failure for NonManufacturing Firms 14

26 Simak also changed the EBIT, Earnings before Interest and Tax, with Operating Income [SIMA97]. The EBIT is defined as follows: Whereas the operating Income is defined as: The NonOperating Income is mostly miscellaneous income such as interests on notes receivable, capital gains/losses etc. Replacing EBIT with Operating Income, the model focuses more on the management s competence at running the normal operations of the firm. This model is shown in Figure 3. Figure 3: Simak's Model 3 Simak collected data from New Generation Research Inc. [NEWG11] for companies that applied for bankruptcy between 1991 and 199, which included 426 companies with assets between $1 million and $1 billion. From these a random sample of 43 companies was selected. These 43 companies were matched with nonbankrupt counterparts based on their SIC numbers. The companies had to have the first 3 digits of the SIC number match. Data was classified into January 1993, January 1994 and January 199, and each company s data was allocated to these groups based on the closest proximity to their fiscal year end. Three groups were created from Data Envelopment Analysis of Corporate Failure for NonManufacturing Firms 1

27 that dataset, one year before bankruptcy, two years before bankruptcy and 3+ years before bankruptcy. The Jan 1993 data was used to determine a cutoff point for the models and this was tested on the other years. Trial and Error determined 0.66 as a cutoff point and Simak found 7% accuracy at classifying bankrupt firms, 6% accuracy at classifying nonbankrupt firms and an overall accuracy of 63%. Simak commented on the low classification accuracy of nonbankrupt firms and that the walking wounded should be considered, i.e. companies that were near bankruptcy but still survived [SIMA97]. He also noted that narrowing down to more specific industries could likely increase the accuracy of the results. Simak used the BCC Inputoriented DEA model for all of his analyses. He noted that he tried some studies using the outputoriented BCC and obtained similar results, however he stated that perhaps using different DEA models for analysis could be of interest [SIMA97]. Another study was done in 2004 by Anja Cielen, Ludo Peeters, and Koen Vanhoof on bankruptcy prediction using DEA [CIEL04]. This study compared a linear programming approach, a customized data envelopment analysis model and a rule induction/decision tree model. This study looked specifically at companies in Belgium that declared bankruptcy between 1994 and 1996, inclusive. These authors selected 11 ratios that they had found from previous literature. These ratios were: Equity ratio Equity/total assets Retained earnings/total assets Retained earnings/total assets Data Envelopment Analysis of Corporate Failure for NonManufacturing Firms 16

28 Expired taxes Tax and social security charges/short term debt Cash ratio Cash/restricted current assets Inventories Work in progress, finished goods and contracts in progress/ current assets Financial debtratio Amounts payable within one year at credit institutions/short term debt Gross return Operating cash flow before taxes/total assets Coverage of debt Cash flow before dividends/total debts Net return Operating profit/loss after depreciation before financial charges and taxes/total assets Current ratio Current assets/short term debts Quick ratio Amounts receivable within one year + Investments + cash/ amounts payable within one year Leverage or debt ratio External liabilities/total assets Ratios that were found to have a positive correlation with bankruptcy were inputs to the model and ratios that with a positive correlation were made to be outputs to the model. This study also showed DEA to be a better predictor of bankruptcy than the LP model or the decision tree model. DEA has not been studied extensively as a predictor of bankruptcy but from the studies that have been done there seems to be potential for this analysis technique. Summary of Literature Review There is a rich literature on bankruptcy prediction using financial data and we included here only the most relevant to our work. Some have included many different models, from univariate analysis [BEAV67] [MERW42] to MDA [ALTM68][DEAK72], to DEA [SIMA97] [CIEL04] Data Envelopment Analysis of Corporate Failure for NonManufacturing Firms 17

29 as well as with other forms such as neural networks [BACK94], and hazard models [SHUM01], yet Altman seems to be referenced the most frequently [SIMA97][DEAK72][CIEL04][SHUM01]. Though Altman s original model has been modified to apply to different areas of industry, i.e. the Altman Z model [ALTM77] [ALTM02] this model has not been studied in much detail. Similarly with DEA, the few papers using this technique for bankruptcy prediction has shown it to be a promising method [SIMA97] [CIEL04] but not much has been done in this aspect particularly with respect to nonmanufacturing firms. This paper attempts to look at that niche of bankruptcy prediction for nonmanufacturing firms using data envelopment analysis. It also attempts to focus less on asset size, as do many other models [ALEX49] and attempt to incorporate the human capital [WEAT03]. Data Envelopment Analysis of Corporate Failure for NonManufacturing Firms 18

30 Chapter 3: Data Envelopment Analysis The purpose of this section is to give brief overview of DEA and to provide a description of the main DEA models used as well as the model that will be used in this research. Data envelopment Analysis, DEA, is a fractional linearprogramming model used to measure the relative efficiency of different DecisionMaking Units (DMUs) [COOP78]. Efficiency in the most simplistic sense is just the measure of the output of a certain thing (DMU) relative to the input to that DMU. It is calculated with equation (3.1). (3.1) This calculation can be used to measure different DMUs against each other. These DMUs can be anything that has certain characteristics that can be used as inputs and outputs to determine the efficiency of said DMU. For example, we can look at the efficiency of a hospital, it might measure its efficiency by the number of patients it treats per number of doctors. The hospital is the DMU, the number of patients treated is the output and the number of doctors is the input. If we had data for a number of different hospitals we could compare them using theirs efficiency. For example: Table 1: DEA Example Hospital Doctors Patients Efficiency (Patients/Doctors) Data Envelopment Analysis of Corporate Failure for NonManufacturing Firms 19

31 Patients By comparing these institutions we can see that Hospital or DMU 3 is the most efficient. In DEA, this DMU would be the most efficient and apparently would have nothing to improve. The other DMUs would be compared to this one in terms of efficiency i.e. all other DMUs would want to reach an efficiency of 1 to be similar to DMU 3. If we plot this on a graph we can visualize this [COOP07] Doctors Figure 4: DEA Example The line passing through the point (3,3 and 0,0) corresponds to the efficiency of 1 which is what DMU 3 has. This line is known as the efficient frontier. All other DMUs are enveloped by this frontier. DEA states that all DMUs that fall on the efficiency frontier are said to be efficient whereas all others below it are inefficient. But DEA takes this a step further. Suppose you have more than one input or more than one output. You would have to come up with another way to measure efficiency. DEA does this by making a virtual input and virtual output, keeping the equation for efficiency similar [COOP07]. Data Envelopment Analysis of Corporate Failure for NonManufacturing Firms 20

32 (3.2) We can take the virtual input as a sum of the inputs and the virtual output would be defined similarly. Going back to the hospital example, suppose another input was the number of nurses. The efficiency would then be: However there is a flaw in this. One could argue that a doctor would be a more important input than a nurse. Perhaps for this hospital a nurse can only treat 1 in every 4 patients that comes in, and a doctor must be present to treat the other 3. Thus the doctor should be treated as a more important input. We could say that the importance or weight of the doctor is three times that of the nurse. Therefore the efficiency becomes: The virtual input now depends upon the weighted sum of the inputs. This is the case in DEA. The virtual input is defined as a weighted sum of the inputs and likewise the virtual output is defined as a weighted sum of the inputs. (3.3) (3.4) Where v and u are the weights for the inputs and outputs respectively. Data Envelopment Analysis of Corporate Failure for NonManufacturing Firms 21

33 It is not always straightforward to determine the weight of a particular input or output, especially when there are a large number of inputs/outputs. Linear programming is used to solve this. DEA has two main models using a fractional LP to calculate the frontiers, the CCR and the BCC model. Charnes Cooper Rhodes model The CCR model or Charnes Cooper Rhodes model, used a constant returnstoscale (CRS) approach [COOP07]. It is designed to find the optimal weights for each input and output for each DMU. If we take the equation for the efficiency that was shown above we can solve with the following formula. Subject to: ( ) (3.) We can change this into a linear programming model by simply splitting the efficiency ratio into the following: Subject to: ( ) (3.6) Data Envelopment Analysis of Corporate Failure for NonManufacturing Firms 22

34 Patients This would be an outputoriented model. This can also be done in another way, called an input oriented model [COOP07]. As shown in Equation (3.7). Subject to: ( ) (3.7) BankerCharnesCooper model The BCC or BankerCharnesCooper model uses a variable returnstoscale (VRS) approach [BANK84]. To visualize the difference between CRS and VRS let us go back to the hospital example. The efficient frontier outlined in Figure 4 would be a CRS efficient frontier. However for a VRS model, the efficient frontier would be as shown in Figure Doctors Figure : DEA BCC vs. CCR efficient frontier Data Envelopment Analysis of Corporate Failure for NonManufacturing Firms 23

35 Notice now there are three points on the efficient frontier rather than DMU3 only. Portions of the VRS frontier shows different returnstoscale behaviour, which is variable depending of the size of the DMU's scale, and allows for more efficient DMUs and also that the inefficient DMUS are now closer to the frontier and are thus more efficient. In CRS there is a constant returns to scale and the frontier is simply a straight line this means that for a unit of input the output production is always the same while the VRS frontier is piecewise linear and has different returns to scale depending on the DMU's scale. The BCC model also has output and input oriented models. The input model is shown below: Subject to: (3.8) Where is a scalar. and are the vectors of the inputs and outputs respectively for all DMUs, and and are the vectors for the DMU being optimized.. is a vector of the coefficients for the inputs and outputs with all elements nonnegative and is a row vector with all elements unity [COOP07]. The dual multiplier form is: Subject to: (3.9) Data Envelopment Analysis of Corporate Failure for NonManufacturing Firms 24

36 , free in sign Again and are the vectors of the inputs and outputs respectively, but here rather than, and are the vectors of variables for the inputs and outputs, similar to the example of virtual efficiency above. The output version is: Subject to: (3.10) The dual form is: Subject to: (3.11), free in sign SlacksBased Model Another model is the SlackBased Model, or SBM, which is an Additive DEA model. Additive DEA models, rather than establishing the radial projection onto the efficient frontier (input or output directions), it optimises the positive and negative slacks and with the projection is not radial that is, the suggestion for improvements show both input reductions and output Data Envelopment Analysis of Corporate Failure for NonManufacturing Firms 2

37 Output augmentations thus the nonradial projections. The radial approaches look at the changes that occur proportionally, i.e. a projection from an origin, whereas SBM looks at the nonradial projection, or inputs that change nonproportionally, i.e. looks at each point as its own origin. This is shown in Figure s s Input Figure 6: Slacks Based Model The is the negative slack and the is the positive slack. SBM uses the values of these slacks to calculate the efficiency of the units, unlike the BCC or CCR models which would use a ratio of the distance from the point to the efficient frontier with the distance to the origin. SBM models are units invariant but not translation invariant [COOP07]. The model for SBM is shown below. Input oriented: Subject to: Data Envelopment Analysis of Corporate Failure for NonManufacturing Firms (3.12) 26

38 Output Oriented model: Subject to: (3.13) Advantages/Disadvantages of DEA DEA has several advantages over other analysis techniques, such as regression. DEA does not take an average it looks at an efficient frontier and attempts to project DMU performance onto that. It does not have fixed coefficients for the variables, i.e. it is nonparametric; it varies the coefficients of each DMU to maximize their efficiency. In this way it also focuses on individual inputs/outputs by analyzing the coefficients produced for each one. One of the biggest advantages of DEA is the ability to handle multiple inputs and outputs simultaneously, Data Envelopment Analysis of Corporate Failure for NonManufacturing Firms 27

39 unlike regression, and these inputs and outputs can have different units and still be analyzed together. A disadvantage of most DEA models is that they do not account for random error and assume that all deviations from the frontier are due to lack of efficiency of the DMU [TRAN07]. While there are stochastic and fuzzy DEA models, they are seldom used because the error distribution in the variables for the former and the fuzzy membership functions for the latter are hard to ascertain for real data sets. DEA has decreased accuracy with small sample sizes and must typically have a minimum number of DMUs. The rough rule of thumb is: { ( )} (3.14) Where n, m and s are the number of DMUs, inputs and outputs, respectively [COOP07]. Some DEA models cannot process negative numbers and allowances must be made for that. Also most DEA models, because they assign coefficients based on maximizing efficiency, can end up giving some coefficients zero or near zero values to make the DMU look the best it can be and often this is not acceptable, but there are techniques in DEA that can address this aspect satisfactorily. Lastly, DEA only looks at relative efficiency, comparing DMUs to other DMUs in their set, and does not look at the actual optimal efficiency. Some work has been done on this through the creation of a theoretical frontier [CHAR94]. Data Envelopment Analysis of Corporate Failure for NonManufacturing Firms 28

40 Chapter 4: Model Development The section outlines the method used to develop the two DEA models used in this study, the first is based on Altman s Z model and the second is a revised model attempting to test the dependence on asset size and the relevance of human capital. The first phase of this model is to compare it with the most popular bankruptcy prediction model, the Altman Zscore. Edward Altman had three main Z score models; the original general Zscore, the Z model and the Z model, the latter of which is the model of interest here [ALTM78]. The Z score was designed for nonmanufacturing firms [ALTM02] and is defined as follows: (4.1) Where: (4.1a) (4.1b) (4.1c) (4.1d) With cutoff zones: Data Envelopment Analysis of Corporate Failure for NonManufacturing Firms 29

41 This Z score was used as the basis to create the first DEA model. The ratios were split and recombined into virtual inputs and outputs for the DEA model. All of the numerators were made to be outputs and the denominators were inputs in the model. The ratios were not inputted directly as it has been shown that ratios used as inputs or outputs in DEA can affect the accuracy of the model [SIGA09]. Due to data availability, EBIT was substituted for operating income. It has been shown that Operating Income is also a valuable indicator of corporate health in DEA [SIMA97]. Therefore the model consisted of: Outputs: Working Capital (WC) Retained Earnings (RE) EBIT or Operating Income (OI) Book Value of Equity (BVE) Inputs: Total Assets (TA) Total Liabilities (TL) And a virtual efficiency of: (4.2) Dealing with Negative Values The DEA model chosen was a SBM, or slacksbasedmodel, due to lack of previous work on corporate failure being done with this DEA model type. However, there is the issue with negative values. Many bankrupt companies will have negative values for their working capital, Data Envelopment Analysis of Corporate Failure for NonManufacturing Firms 30

42 retained earnings, operating income and even equity. However, negative values cannot be computed with this model. Not much research has been done to accommodate negative values in certain DEA models [KERS09], thus some sort of solution would have to be found to accommodate them. Hence the model was revised. Each output was split into a positive and negative measure. For example, Working capital (WC) was split into WC+ and WC, WC+ being the positive values for Working Capital and WC being the negative. The absolute value of the negative variable would be taken but it would then be placed in the model as an input rather than an output, i.e. WC would be an input, whereas WC+ would be an output. This method is essentially saying that Working Capital is an output, and therefore should be made as large as possible to optimize the efficiency. Working Capital is an inflow to the company. However a negative Working Capital can be view as an outflow from the company and therefore should be minimized. Thus it would be defined as an input, as the inputs to the model are minimized. Therefore we get a new visualization of the virtual efficiency. (4.3) Model Revision The model was then revised to accomplish one of its main purposes, to see how accurately bankruptcy can be measured regardless of assetsize. Hence the model was run again without total assets in the model. The total liabilities input variable was also removed and working capital was split into current assets and current liabilities. In an attempt to test the relevance of human capital, which is important to smaller, nonmanufacturing firms to the model, the number of employees and the number of shareholders was added to the model. Number of Data Envelopment Analysis of Corporate Failure for NonManufacturing Firms 31

43 employees was added to introduce the measure of individuals as a contributor to the efficiency of a company. The number of shareholders was added because for many smaller nonmanufacturing firms the shareholders have decisionmaking power and invest both time and money that contribute to the success of a firm. The number of shareholders investing in a business can also be seen as a reflection of the financial wellbeing of a company as viewed by the public. The revised model had the following virtual efficiency. (4.4) Data Envelopment Analysis of Corporate Failure for NonManufacturing Firms 32

44 Chapter : Data Acquisition One of the most critical components of this research is the collection of viable data. This was not an easy task as there are few databases for bankrupt companies. This section will discuss how the data collection was done, how companies were selected and which data was collected on each company. One of the first tasks was to find a list of bankrupt companies. This is difficult as once a company has reached failure it is usually removed from most exchange listings and other databases. However a list of bankrupt companies was found at New Generation Research Inc. [NEWG11], which was also used by Simak [SIMA97]. This site has filings for companies that date back to 1986 listed in alphabetical order of the company name. This list was narrowed down to those that could be classified as nonmanufacturing or servicebased firms. These companies must also have filed for bankruptcy between the years of 2000 and The reason for these dates was that more recent filings would be more easily obtained, and more easily compared to current companies. Bankruptcy filings from 2007 to present were not selected due to the economic recession taking place. During that time, significantly more bankruptcy filings took place than in previous years and it was considered that data from this time period could skew the results. The companies filing bankruptcy during that period would be more so for external reasons, which is not what is being studied in this project. This list consists primarily of companies filing for bankruptcy in the United States. No other extensive list of bankrupt companies was found and thus the focus of this work will be on the United States and Canada. Data Envelopment Analysis of Corporate Failure for NonManufacturing Firms 33