This research only used financial ratios. Other factors such as economy, operation, and management were not considered in this study; therefore, the total relationship between the causes and effects of business failure was not met.
The data used in this thesis are obtained from US stock market in the period of 1970-2006, and concentrate on construction firms which have different characteristics from other industries’. Therefore, this study only concentrates on construction contractor. It means that the results should be cross-checked in data of other industries.
Additionally, the accuracy of any financial ratio-based predictive model largely depends on the reliability of accounting data source. In some real cases, financial data might be manipulated, which leads to failure of model. Besides, the data used in this research are all available data firm years and the bankrupt sample is the data from the last financial statement issued before the firms declared bankruptcy. That is, this model is not able to assure for predicting insolvency more than one year prior to bankruptcy.
1.5 T
6 Chapter 3: Introduce the methodologies of default prediction, Grey System Theory, how to apply Over-sampling technique to resolve imbalance data problem, and how to use ROC curve (Receiver Operating Characteristic curve) to evaluate the prediction power of this model.
Chapter 4: Presents the standard of data collection.
Chapter 5: Analyzing and validating input data.
Chapter 6: Present the conclusions and suggestions.
7
CHAPTER 2: LITERATURE
This chapter presents a brief overview of the development of bankruptcy prediction model in both general industry and construction industry.
2.1 Default prediction researches
There have existed numerous approaches to the corporate failure prediction in general business area so far. Beaver was the first scholar using financial ratio in predicting bankruptcy. After Beaver, a lot of other researchers employed different methods such as multivariate discriminant analysis (Altman, 1968), logit (Ohlson, 1980) or probit (Zmijewski, 1984). These models were then developed in accordance with the information form financial statements to evaluate strengths and shortcomings of a company’s financial status.
The application of financial ratio models to determine a business’ profitability, and hence chances of its survival, attracted many researchers’ concern in both general business (Altman, 1967; Beaver, 1968; Taffler, 1983; Robertson (1984); Keasey and Watson, 1986) and the construction domain alike (Mason and Harris, 1979; Kangari, 1988; Abidali, 1990; Russell and Jaselski, 1992; Langford et al., 1993; Ramsey Dawber, 1993)
1. Fitz Patrick (1932)
The first author to use financial ratio model was Fitz Patrick (Fitz Patrick, 1932).
He studied 19 bankrupt firms and 19 non-bankrupt ones. The research found 3 years before bankruptcy, the financial ratios were significantly changed.
8 2. Beaver (1967)
William H. Beaver is one of the first developers of business failure prediction using quantitative method. The methodology adopted by him is discriminate analysis (DA). He collected data from Moody’s Industrial Manual – 79 firms that collapsed during 1954 to 1964. None of these companies was construction firm; they mostly were in manufacturing sector. Non-defaulted firms in the same industry and asset size were also assembled to distinguish and discriminate against the distressed firm.
There were 30 ratios commonly used in the financial literature in Beaver’s study.
His research aims to discover the capability of these ratios to differentiate the bankrupted group from the non-bankrupted one. In his study, various methods such as mean values, mean asset size, dichotomous classification tests and analysis of likelihood ratios were integrated to analyze the ratios. After finalizing the calculated process of these ratios for the period of 5 years prior to bankrupt, the result of Beaver’s study indicated that the cash flow – total debt ratio was the overall best predictor. Another contributor of his research was the affirmation of using accounting data in the forecast of business bankrupt. What could be drawn from his study was that using financial ratio could give the early warning of 5 years before bankruptcy.
3. Altman (1968)
Beaver’s research has certain values when pointing out the importance of using financial ratio in predicting default; however the discriminatory power of the independent ratio makes this research not a perfect one. To address this drawback, E.Altman (1968) developed Beaver’s method and established an innovative model named mutlti-variate approach. In this research, Altman also reconfirmed the principal role of using financial ratios as a predictor of corporate. Altman used 33 failed
9 manufacturing firms matching up with the same number of non-failed firms in the period of 1946 to 1965. The criteria of matching were the same industry and roughly similarity in asset size. Using the Multiple Discriminant Analysis (MDA) technique in the study, the 22 financial ratios served as input variables to analyze. The stepwise method then applied to choose an optimal combination of five variables from the 22 ratios initially selected. Finally, Altman’s model proposed a following linear function using five variables
Z = 1.2X1+ 1.4X2 +3.3X3+ 0.6X4 +1.0X5 (1) Whereas:
X1: Working Capital/Total Assets
X2: Retained Earnings since Inception/Total Assets X3: Earnings before Taxes and Interest/Total Assets X4: Market Value of Equity/Book Value of Total Debt X5: Turnover/Total Assets.
Accordingly, businesses were classified as follows:
Z - score less than 1.8 implied certainty of imminent failure;
Z - score between 1.8 and 2.7 revealed the “zone of ignorance” or ‘grey area’ , where companies were deemed to be at risk; and
Z - score greater than 2.7 (initially 2.9), indicated a potential for long term solvency.
The model correctly classified 95 percent of the total 66 sample firms (correctly classifying 94 percent as bankrupt firms and 97 percent as non-bankrupt firms) one-year prior to bankruptcy. The percentage of the accuracy fell down with increasing number of years before bankruptcy. This technique has a strong reputation in the history of
10 corporate bankruptcy models until the 1980s and is weidely applied as the baseline for comparative studies.
4. Ohlson (1980)
Ohlson (198) is another researcher using financial ration as predictors of bankruptcy to develop his bankruptcy prediction model. His research analyzed nine financial ratios of firms’ size, leverage, liquidity and performance, using logistic regression. Data were gathered from 1970 to 19976 and included 105 defaulted and 2,058 non-defaulted industrial enterprises. His model’s kernel function was built as follows:
Probability of defa
ult 1 1
1
z
z z
e
e e
Z = -1.3-0.4X1 + 6.0X2 – 1.4X3 + 0.1X4 – 2.4X5 -1.8X6 + 0.3X7 – 1.7X8 -0.5X9
Where:
X1= Log (Total Assets / GNP Price-level Index) X2 = Total Liabilities / Total Assets
X3 = Working Capital / Total Assets X4 = Current Liabilities / Current Assets
X5 =1 if total liabilities exceed total assets, o if otherwise X6 = Net Income / Total Assets
X7 = Funds provided by Operation / Total Liabilities
X8 = 1 if net income was negative for the last two years, 0 if otherwise
11 X9 = Measure of Change in Net Income
5. Taffler (1983)
In the UK, another two authors Taffler and Tishaw (1977) adopted a similar methodology as other seniors’, basing on a sample of 92 manufacturing companies. The resulting Z score equation was based on a combination of four categories ratios;
however, undisclosed coefficients:
Z = c0 + c1X1 + c2X2 + c3X3 + c4X4 (2) Where:
X1: Profit before Tax/Current Assets (53%) X2: Current Assets / Current Liabilities (13%) X3: Current Liabilities/Total Assets (18%) X4: No Credit Interval (16%)
The percentages give guidance to the relative weightings of the ratios. Taffler and Tishaw declared a 99% successful classification based on the original 92 companies from which the model was conducted. However, this success assurance lost its value when the model was re-tested by Taffler (1983) with a sample includes 825 companies.
The two models were developed by Altman and Taffler both bolstered the significance of the ratio variable of turnover to total assets as a positive indicant that contributed to corporate bankruptcy.
6. Robertson (1984)
In an effort to address the question of a theory on corporate failure, Robertson (1984) developed a ratio model that worked with general applicability to all industries.
He declared that there were a priori determinants of corporate failure from their financial ratios. Robertson suggested ratios expressing trading stability, declining profits, declining working capital and increases in borrowing as predictive
12 characteristics. Instead of the simple turnover to total assets utilized by Altman (1983) and Taffler (1983); Robertson (1984) utilized the ratio of turnover less total assets to turnover, to display the importance of trading stability in his model. The outcome model combined five ratio variables were presented as Equation 3:
Z = 0.3X1+ 3.0X2 +0.6X3+ 0.3X4 +0.3X5 (3) Whereas:
X1: (Turnover – Total Assets)/Turnover;
X2: Profit before Tax/Total Assets;
X3: (Current Assets – Total Debt)/Current Liabilities;
X4= (Equity – Total Borrowings)/Total Debt; and X5= (Liquid Assets – Bank Overdraft)/Creditors.
2.2 Default prediction researches in construction industry
According to S. Thomas NG, “Pertinent forecasting techniques for construction company failures include the (1) ratio analysis; (2) multiple discriminant analysis; (3) conditional probability models; and (4) subjective assessment”. In completing the present study, the author read several relevant studies in the construction industry as follow:
1. Mason and Harris (1979)
Mason and Harris (1979) developed a six-variable model to assess construction organizations in UK. In this study, a sample of 20 bankruptcy and 20 non- bankruptcy firms was selected. Basing on the MDA), the discriminant function was developed as below equation. A positive Z-score indicated a long-term solvency, while a negative value was classified as a potential failure. Their model was conducted with a multiple regression approach and presented as:
13 Z =25.4 – 51.2X1+ 87.8X2 – 4.8X3 – 14.5X4– 9.1X5 – 4.5X6 (4) Where:
X1: Profit Before Tax and Interest/Opening Balance Sheet Net Assets;
X2: Profit before Tax/Opening Balance Sheet Net Capital Employed;
X3: Debtors/Creditors;
X4: Current liabilities/Current assets;
X5:Log10 (days debtors); and X6: Creditors Trend Measurement.
While a positive Z-score indicated a long-term solvency, a negative value revealed a potential bankruptcy. The variable profit before tax and interest to opening balance sheet net assets (X1) was indicated as a negative sign in the research. This implies that a higher value of a return on net assets produces a greater tendency for bankruptcy, which is rather unconvincing.
2. Abidali, 1990
Abidali also developed a Z-score model used in vetting construction companies on the tender lists. Using multivariate discriminant analysis to produce a predictive model including seven variables, 31 different variables were initially adopted. The best discriminating variable is selected according to Wilks Lambda criteria. The Z-score model is shown below in following equation:
Z =14.6 + 82.0X1 – 14.5X2 +2.5X3 – 1.2X4 + 3.55X5 – 3.55X6 – 3.0X7 (5)
Where:
X1 =Profit after Tax and Interest/Net Capital Employed;
X2 = Current Assets /Net Assets;
14 X3 =Turnover/Net Assets;
X4 =Short Term Loans/Profit before Tax and Interest;
X5 =Tax Trend over three years;
X6 =Profit after Tax Trend over three years; and X7 =Short Term Loan Trend over three years.
3. Russel (1988) and Jaselskis (1992)
While some previous researchers only focused on analyzing financial variables, Russell and Skibniewski (1988) deepened their research by presenting all the factors involved in the construction contractor prequalification decision-making process, which are closely related to contractor default risk. Beside financial soundness, management capability, and economic condition as well as technical expertise are also essential factors to construction contractors’ success. Their research model was introduced with 5 variables, cooperating 4 financial ratios and one management related variable:
Y = 2.27 – 7.72 X1 + 45.05 X2 + 13.94 X3 - 13,24 X4 – 34.42 X5 (6) Where:
X1: Cost Monitoring (not performed = 0; performed = 1);
X2: Under-Billings to Sales;
X3: Total Current Liabilities to Sales;
X4: Retained Earnings to Sales; and X5: Net Income before Tax to Sale.
The predictability of the model is rather well: among forty sample companies, there were only 12.5 % misclassified. However, many of introduced
15 factors are qualitative and largely depend on human judgment; incorporating them into the default prediction model with bias is potential.
4. Kangari et al. (1992)
By using multiple regression method, Kangari developed a performance index to grade a company by regressing 6 financial ratios. The researcher used the financial report of 126 construction companies and divided them into 6 groups. Financial ratios were used in the research as following:
- Current ratio.
- Total liabilities to net worth.
- Total asset to revenue.
- Revenues to net working capital.
- Return on total assets.
- Return on net worth.
2.3 Grey system model in prediction bankruptcy probability
In 1982, Professor Deng Ju-Long published “Control Problems of Grey Systems”, which signaled the coming of a new theory: the grey systems theory which managed to rapidly develop and even to impose. Grey systems theory is highly valued because of its practical applicability and been widely applied in analysis, modeling, prediction, control, decision making, in almost all areas: social, economic, mechanical and technical science, agriculture, industry, transport, petrology, meteorological,
16 ecological, hydrological, geological, financial, medical, military, and others (Liu and Lin, 2005). The main characteristic of grey system theory is that it manages to achieve good performance in analysis based on a small range of data and on a large number of variables.
1. Ping, J. & Kejia, C. (2005)
Ping, J. and his colleague, Kejia, C. (2005) claimed that the theory of grey systems focuses more on the output of the systems rather than their structure and input.
Moreover the theory allows grey quantity and grey relationship within them. Two scholars applied grey system analysis to design an economic cycle monitor and early warning index system. Among many kinds of degrees of grey incidences, just the absolute degree of grey incidences was shown in their research.
2. Cheng, J. et al (2009)
In 2009, Cheng, J. et al. conducted a hybrid model which enabled the prediction of failure firms based on their past financial performance data, combining grey prediction and rough set approach. They used 14 financial ratios considered cover all the categories suggested by previous studies, including:(a) Solvency: current ratio;
quick ratio; liabilities/assets ratio; times interest earned ratio;(b) Managerial performance: average collection turnover,(c) Profitability : return on total assets; return on shareholders’ equity; operating income to paid-in capital; profit before tax to paid-in capital; earnings per share, (d) Financial structure: shareholder’s equity/total assets ratio, and (e) Cash flow: cash flow ratio; cash flow adequacy ratio; cash flow reinvestment ratio.
Cheng, J. et al.(2009) computed prediction value of the fourth year, the fifth year, the sixth year and the seventh year history data respectively for announcement and
17 comparing to history data. The final result was that grey prediction business failure prediction models in the 4th and the 5th dimensions had better performance than history business failure prediction models. Specially, accuracy of grey prediction business failure forecasting model in the 5th dimension has the best performance. The general results are very encouraging, compared with original rough set, and prove the usefulness and strengthen the effectiveness of the proposed method for company failure prediction.
3. Delcea, C. &Scarlat, E
Basing on grey system theory, Delcea, C. and Scarlat, E determined a “matrix of symptoms” which represented by economic- financial ratios, usually used by analysts to make predictions and suggestions. The ability to create such a matrix of symptoms implies that given level of symptom’s intensity, they could determinate if the analyzed firm presents some “diseases”. In their analysis, the researchers introduced the existence of 9 symptoms as it follows:
S1: Solvability (positive symptom - it shows the capacity of a firm to pay its debt within the time prescribed – as the firm is solvent, its financial situation is better)
S2: Quick Ratio (positive symptom)
S3: Working Capital (positive symptom)
S4: EBIT-Yield (positive symptom)
S5: Interest Cover Ratio (positive symptom)
S6: Profit Margin (positive symptom)
S7: Return On Equity (positive symptom)
S8: Return On Total Assets (positive symptom)
S9: Gearing (negative symptom)
18 This analysis found a way by which a possible “disease” or bankruptcy can be anticipated, and found a way to highlight the occurrence of such a phenomena. However, due to the fact that the accuracy of the methodology was not proved, the doubtfulness of the method’s reliability is inevitable.
2.4 Summary
Financial ratio is regarded as one of the most popular methods to determine the profitability and the potential turndown of a business. The mentioned researches proposed many financial ratios, which are generally classified in five groups: (1) Liquidity; (2) Profitability; (3) Leverage; (4) Solvency; and (5) Activity. The way these ratios reflect the firm financial situation was also be displayed. Truthfully, Grey system theory was rapidly improved because of its high value in application and the application of grey system theory to deal with the prediction firm default probability problem was very effective. This sparks my interest in improving the effectiveness of Grey System Theory in the default probability of the construction firms.
19
CHAPTER 3: METHODOLOGY
3.1 Grey system theory
Widespread divisions in the activities of scientific research and the technological advancement have led to a tendency in the modern spectrum of science and technology.
This tendency is indicated by the rapid rise of many cross-disciplinary research activities as well as appearance of many important theories. Grey systems theory is one of such significant cross disciplinary theories. The release of “The Control Problems of Grey Systems” by Professor Deng Ju Long (1982) of China marked an important and fruitful area of research with strong and successful practical applications. As mention above, grey systems theory, because of its efficacy, has been popularly applied in analysis, modeling, prediction, control, decision making in almost all areas: social, economic, mechanical and technical science, agriculture, industry, transport, petrology, meteorological, ecological, hydrological, geological, financial, medical, military, and others.
Among probability and statistics, fuzzy mathematics, and grey systems theory - three most-often applied theories and methods employed in studies of non-deterministic systems, the last one have proved to be the most effective method. Grey theory addresses the obstacles encountered in the utilizing of probability theory and statistical methods (the need of reasonable size samples and determination of certain distributions to draw a valid inferences) and those of fuzzy mathematics (which deals well with the study of problems with cognitive uncertainty phenomena, using so-called “membership functions”, based on experience). The main valued characteristic of grey system theory
20 is that it manages to achieve good performance in analysis conducted on a small range of data and on a large number of variables.
3.1.1. Methods of Grey Numbers’ Generation Based on Average
The shortage of data poses researchers a lot of problems. This is exclusively true in any economic analysis. There have many cases that the incomplete collected data set of an observed economic system causes the researchers many difficulties in the undertaken analysis. Also, on the collected data, it may happened that in the initial data set, some values to be abnormal, much higher or much lower than the other values of the series, and thus, make an analysis based on such a data set lead to erroneous results.
For the abnormal values’ existence, a probability can be to identify and to filter them out from the data set, and then it returns to the case where we have blanks in the data set.
Nevertheless, grey system theory gives us a method to solve this problem, namely, generate grey sequence method to give birth to new values for filling gaps in data sequence.
Consider the data sequence analyzed contains “empty” information which denoted with φ (k), in which k represents the position in the data sequence. In this case, the data sequence X indicates as follows (Liu, S.F., Lin, Y. (2006). Grey Information: Theory and Practical Applications. Springer, London):
X = (x(1), x(2),... , x(k −1),φ (k), x(k +1),..., x(n))
The number value φ (k) is in the range delimited by x(k −1) and x(k +1), and the two values stand for the lower and the upper limit of the unknown value.
21 x*(k) = 0.5x(k −1) + 0.5x(k +1) (3.1)
X*(k) is called a generated mean value of consecutive neighbors as being a generated average value based on two non-consecutive neighborhood values.
In grey systems modeling (GM), the mean generation of consecutive neighbors is often used. This method based on the raw sequence of data to build new sequences in order to reveal the particular trend, if any. In the firm analysis, the method of generating numbers based on average may be utilized if the objective of the research is to observe the evolution in time of a particular variable, and for certain periods of time, for various reasons, those are unknown to the researcher.
Take an example; we take into account the sequence, which represents the quantity of products by the firm Y (expressed in pieces) during a year, with monthly record:
C = C( c(1), c(2), c(4), c(6), c(9), c(10),c(11), c(12))
= (350,590,510,420,580,720,810,790)
As it can be seen, from a total of 12 months, we only know the quantities sold in 8 months, and for the remaining months, we can estimate the quantities by using the method of generating numbers based on average:
C(3) = 0.5*c(2) + 0.5*c(4) = 0.5*590 + 0.5*510 = 550
C(5) = 0.5*c(4) + 0.5*c(6) = 0.5*510 + 0.5*420 = 465 C(8) = 0.5*c(6) + 0.5*c(10) = 0.5*420 + 0.5*720 = 570 C(7) = 0.5*c(6) + 0.5*c(8) = 0.5*420 + 0.5*570 = 495
22 Follow these above steps; we gained the consequence of the quantities sold in 12 months:
C = C( c(1), c(2), c(3), c(4), c(5), c(6), c(7), c(8),c(9), c(10),c(11) c(12))
= (350,590,550,510,465,420,495,570,580,720,810,790).
3.1.2. Method of Grey Incidence Analysis
Grey incidence analysis method is one of the essential and principal sectors of
Grey incidence analysis method is one of the essential and principal sectors of