III. Methodology
3.2 Cut-off Point
After implementing the Logit Model, we can classify every firm as default group or non-default group by using a cut-off point. Traditionally, we use 0.5 as our cut-off point. This means that if the predicted bankruptcy probability of a company is higher than 0.5, we will classify the firm as the default group; if the predicted bankruptcy probability of a company is
10
lower than 0.5, we will classify the firm as the non-default group. But whether the best value of cut-off point is 0.5 is a debatable problem. So we then employ the maximum KS value method (Mays,2001) to find the better cut-off point. KS value is the difference between cumulated percentages of default firm’s number and the non-default one. The range that max KS value falls in is the cut-off point we want. Table3.1 shows the general guide to the quality of the KS.
Table 3.1 The Quality of the KS Value
KS value quality
Less than 20% The scorecard’s probably not worth using 20%-40% Fair
41%-50% Good
51%-60% Very good
61%-75% Awesome
Greater than 75% Probably too good to be true ( be suspicious that something is wrong)
11
IV. Data
This section can be separated into three parts. The first part states the definition of financial distress according to TEJ database; the part about sample data expresses the period and the number of the samples; the final part is the independent factors choosing.
4.1 Definition of Financial Distress
A company encounters financial difficulties and defaults when it fails to service its debt obligation. Many researchers have studied corporate bankruptcy; different people have come up with different definitions that basically reflect their special interest in the field. In this study, we will use the definitions of financial distress and quasi financial distress in TEJ database as default event.
4.2 Sample Data
Our sample firms must be listed on Taiwan Stock Exchange Corporation (TSE) or GreTai Security Market (GTSM or OTC). Because the characteristics of banking, security and insurance industries are different from others, we exclude these industries from our sample firms. Besides, we also exclude the firms of which financial reports are incomplete.
We collect data of the sample firms from TEJ database. The study period is 1992-2009.
If the firms experienced the financial distress situations mentioned in section 4.1 during this period, we classify these firms as default group. The non-default firms are firms that remain trading on TSE or GTSM during 1992-2009. The healthy or non-default firms we select are chosen on 1:1 basis. The industry and size of the healthy firm match with the default one.
That is, the non-default firm’s industry and firm size is similar to the default one.
We have two kinds of data, financial ratios and macroeconomic factors. We choose financial ratios from financial year report one year before the firms suffering from financial
12
distress. We use sum of season macroeconomic factors. If financial distress breaks out in time t year, then we collect the first and second quarter of time t year, third and fourth quarter of the last year of time t year, and then sum these four quarts data together.
We use the observations between 1992 and 2007 as the estimation sample, and the observations from 2008 to 2009 as the prediction sample validation group to examine the model’s accuracy. Finally, there are 174 non-default firms and 174 default firms in the estimation sample, and 29 non-default firms and 29 default firms in the prediction sample.
The number of estimation sample and prediction sample firms is shown in Table 4.1.
Table 4.1 Number of Sample Companies
Sample period No. of non-default firms No. of default firms
Estimation sample 1992~2007 174 174
Prediction sample 2008~2009 29 29
The data comes from TEJ database which the period is from 1992 to 2009. The sample firms are listed either on Taiwan Stock Exchange Corporation (TSE) or on GreTai Security Market (GTSM or OTC).
4.3 Factors choosing
The chosen independent variables can be classified into two kinds of variables, that is, financial ratios and macroeconomic factors respectively. The detail of these factors would be discussed subsequently.
4.3.1 Financial ratios
In this study, we collect inputs according to six category measures as follows.
1. Long-term solvency measure
Long-term solvency ratios are intended to address the firm’s long-run ability to meet its obligations, or more generally, its financial leverage. We choose “Debt Ratio” and
13
“ Equity Long-term liabilities Fix assets
+ ” in this category.
2. Short-term solvency or Liquidity measure
Short-term solvency ratios as a group are intended to provide information about a firm’s liquidity. The primary concern is the firm’s ability to pay its bills over the short run without undue stress. Consequently, these ratios focus on current assets and current liability. We choose “Current Ratio” and “Quick Ratio” (Acid Test Ratio) in this category.
3. Asset management or Turnover measure
Turnover ratios are intended to describe how efficiently, or intensively, a company uses its assets to generate sales. We choose “Inventory Turnover Ratio”, “Receivables Turnover Ratio”, and “Total Asset Turnover Ratio” in this category.
4. Profitability measure
Profitability measures are intended to measure how efficiently the company uses its assets and how efficiently the company manages its operations. The focus in this group is on net income. We choose “Profit Margin” and “Return on Total Assets” in this category.
5. Cash flow measure
A firm’s cash flow measures reveal whether the firm makes money or not, and whether the money generated in this period can meet its obligations. We choose “Cash Ratio” and
“Change in Cash flow” in this category.
6. Firm’s Size
The company with different size will have different ability of overcome financial distress.
We use the natural log of firm’s size as an input.
Table 4.2 shows the code and calculation of the financial ratios used in this paper. Table 4.3 shows the descriptive statistics of the financial ratios.
14
Table4.2 The Summary of Chosen Financial Ratios
Category Code Variable Equation
Solvency
measure FR1 Debt Ratio Total Liabilities Total Assets FR2 Equity Long-term liabilities
Fix assets +
Liquidity
measure FR3 Current Ratio Current Assets Current Liabilities
FR4 Quick Ratio Current Assets Inventory Current Liabilities
− Turnover
measure FR5 Inventory Turnover Ratio FR7 Total Asset Turnover
Ratio
Sales Total assets Profitability
measure FR8 Profit Margin Net income Sales FR9 Return on Total Assets Net income
Total assets Cash flow
FR10 Cash Ratio Cash
Current liabilities FR11 Change in Cash flow
Size FR12 Size Ln(Size)
The total number of variables is twelve. The solvency ability is measured by debt ration and (equity + long-term liabilities) / fix assets; the liquidity ability is measured by current ratio and quick ratio; the turnover ability is measured by inventory turnover ratio, receivable turnover ratio and total asset turnover ratio; the profitability is measured by profit margin and return of total assets (ROA); the cash flow aspect is measured by cash ratio and change in cash flow; the size measure equation is the log of size value.
Table4.3 Descriptive Statistics of Financial Ratios
Variable Mean Std Maximum Minimum
FR1 53.08892 21.49304 175.25 1.82
FR2 921.7876 4430.586 75199.76 -211.05
FR3 169.0488 171.9555 1732.41 10.56
FR4 104.9144 157.3101 1730.63 1.59
FR5 17.30365 81.09258 1381.73 -0.03
15
FR6 9.051305 31.01726 587 -1.48
FR7 0.882635 0.707633 4.73 -0.03
FR8 -34.4377 241.0873 73.67 -3668
FR9 -1.27308 18.08898 66.5 -93.38
FR10 0.151685 0.602335 4.869454 -1.61291
FR11 -155772 2812215 10869450 -4.6E+07
FR12 14.93189 1.405555 19.48802 10.79561
The variable codes are explained in Table 4.2.
4.3.2 Macroeconomic factors
In this study, we choose eight macroeconomic indicators which are listed in table 4.4.
The correlation of these indicators must not too large. So we check the correlations of these factors. Table 4.5 shows the coefficient correlation of them. Table 4.6 shows the descriptive statistics of macroeconomic indicators.
Table4.4 The Summary of Chosen Macroeconomic Factors Code Variable
MF1 Real Estate Determine Score MF2 Monitoring Indictors Score MF3 Leading Index
MF4 Floor area of Building Permit - Taiwan (Epd) MF5 Saving Rate--R.O.C(YEAR)
MF6 Unemployment Rate – U.S.A.
MF7 New privately owned housing started-U.S.A.
MF8 Import Goods – U.S.A.
MF1 data comes from Architecture and Building Research Institution, Ministry of the Interior; MF2 to MF5 measures are from Council for Economic Planning and Development; MF6 data is from US Department of Labor; MF7 data is from US Census Bureau; and MF8 data is from United States International Trade Commission (USITC). All factors are annual datum.
Table4.5 Correlation Coefficient of Macroeconomic Factors
MF1 MF2 MF3 MF4 MF5 MF6 MF7 MF8 MF1 1.0000 0.6458 0.1035 0.6187 0.0218 -0.0076 0.4032 -0.0111 MF2 0.6458 1.0000 0.0380 0.6134 0.1856 -0.1030 0.3590 -0.0687
16
MF3 0.1035 0.0380 1.0000 0.0451 -0.1043 -0.3651 0.3019 0.9850 MF4 0.6187 0.6134 0.0451 1.0000 0.3073 0.0924 0.2350 -0.0457 MF5 0.0218 0.1856 -0.1043 0.3073 1.0000 0.3831 -0.4929 -0.0833 MF6 -0.0076 -0.1030 -0.3651 0.0924 0.3831 1.0000 -0.6188 -0.3407 MF7 0.4032 0.3590 0.3019 0.2350 -0.4929 -0.6188 1.0000 0.1965 MF8 -0.0111 -0.0687 0.9850 -0.0457 -0.0833 -0.3407 0.1965 1.0000 The codes MF1 to MF8 can be referred to Table 4.4 which shows the detail of macroeconomic factors.
Table4.6 Descriptive Statistics of Macroeconomic Factors
Variable Mean Std Maximum Minimum
MF1 40.84211 8.98309 60 27
MF2 92.15789 21.92478 135 48
MF3 300.5842 72.86198 423.7 193.9
MF4 9049.105 2984.417 13611 4134
MF5 27.13158 1.636847 31.25 24.15
MF6 22.28947 4.401375 31.4 16.2
MF7 5908.421 1417.039 7916 2489
MF8 380578.9 165694 704411 164530
The codes MF1 to MF8 can be referred to Table 4.4 which shows the detail of macroeconomic factors.
17
V. Empirical Result
In this study, we compare the financial distress models with and without macroeconomic factors. We use “Model 1” represent the model without macroeconomic factors, and “Model 2”
represent the model with macroeconomic factors. In section 5.1, we show the estimation result of Model 1. In section 5.2, we show the estimation result of Model 2. In section 5.3, we show the performance of prediction sample and compare the difference of the two models.
5.1 Without Macroeconomic factors
In section 3.1, we have introduced the Logit Model method. Equation (3-3) shows the probability concept of Logit Model. We use MLE to estimate the coefficients in Logit model, these coefficient estimates of model 1 is shown in Table 5.1. The regression for company k is as following
where FR1 is debt ratio, FR2 is equity plus long-term liabilities over fix assets, FR3 is current ratio, FR4 is quick ratio, FR5 is inventory turnover ratio, FR6 is receivables turnover ratio, FR7 is total asset turnover ratio, FR8 is profit margin, FR9 is return on total assets, FR10 is cash ratio, FR11 is change in cash flow, FR12 is ln(size).
So the probability equation of company k is
According to the parameters estimated in Table 5.1, the regression of the equation (5-1) is as following:
18
Table5.1 Coefficient Estimate of Model 1
B S.E. Wald Test P-value Exp(B)
FR1 0.0629 0.0116 29.4197 0.0000* 1.0649
FR2 0.0001 0.0001 0.5519 0.4575 1.0001 FR3 -0.0111 0.0037 8.9826 0.0027* 0.9890
FR4 0.0146 0.0043 11.6940 0.0006* 1.0147
FR5 -0.0007 0.0045 0.0267 0.8703 0.9993 FR6 0.0037 0.0042 0.7729 0.3793 1.0037 FR7 -1.3707 0.3317 17.0795 0.0000* 0.2539 FR8 -0.0062 0.0064 0.9276 0.3355 0.9939 FR9 -0.0742 0.0213 12.1457 0.0005* 0.9285 FR10 -0.5977 0.4357 1.8819 0.1701 0.5501 FR11 0.0000 0.0000 0.0344 0.8529 1.0000 FR12 0.0899 0.1307 0.4727 0.4917 1.0940 Constant -3.2677 2.1709 2.2658 0.1323 0.0381 FR1 is debt ratio, FR2 is equity plus long-tern liabilities over fix assets, FR3 is current ratio, FR4 is quick ratio, FR5 is inventory turnover ratio, FR6 is receivables turnover ratio, FR7 is total asset turnover ratio, FR8 is profit margin, FR9 is return on total assets, FR10 is cash ratio, FR11 is change in cash flow, FR12 is ln(size). In P-value column, signal * means 1% significant. The Exp(B) is the exponential value of coefficient B for the calculation of failure probability in equation (5-1).
The estimated parameters illustrate that debt ratio, current ratio, quick ratio, total asset turnover ratio, and ROA are very significant at 1%. However, other financial ratios are of insignificance.
After estimating the coefficients, we have prediction probability of every company. The following step is to find a better cut-off point in order to sort companies into failed or non-failed catalogs. We use the Maximum KS value method to select cut-off value. Table 5.2 shows the summary of selection process. Figure 5.1 shows the figure of cumulative percentage of failed and non-failed companies. The max KS value is 66.09% and in the score range of 0.35 to 0.45. Thus we choose the upper bound 0.45 as Model 1’s cut-off point.
Table 5.3 shows the performance of estimation sample using Model 1, the correct prediction percentage of failed firms is 86.21%, the correct prediction percentage of
19
non-failed firms is 79.89%, and the correct percentage of total prediction is 83.05%. Thus the prediction ability performance of the model which uses financial ratios as its inputs is well.
Note that table 5.3 also implies the type I error rate is 13.79% and type II error rate is 20.11%.
Table5.2 The Process of Finding Maximum KS Value
Score
The max KS value is 66.09% noted by bold number in the table and we choose the upper bound 0.45 as the cut-off point of Model 1.
20
Figure5.1 KS Value in Model 1
KS
This picture is to find the maximum KS value which is denoted by the line with triangle spots. The line with diamond spot is the cumulative percentage of failed companies and the line with square spot is the cumulative percentage of non-failed companies. The KS value is calculated by the cumulative percentage of non-failed companies minus the cumulative percentage of failed companies.
Table5.3 Model 1 Performance of Estimation Sample
Sample
The estimation sample is to evaluate the coefficients of parameters in model 1. Based on the coefficients calculated via MLE method, the correct percentage of observed failed firms is 86.21% and the correct percentage of observed non-failed firms is 79.89%. The overall correct percentage is 83.05% where the cut-off point is 0.45.
21
5.2 With Macroeconomic factors
Similarly, the coefficient estimate of model 2 is shown in Table 5.4. The regression for company k is as following:
*
1 2 3 4 5 6 7
8 9 10 11 12 1 2
3 4 5 6 7 8
ˆ FR1 FR2 FR3 FR4 FR5 FR6+ FR7
FR8 FR9 FR10 FR11 FR12 MF1 MF2
MF3 MF4 MF5 MF6+ MF7 MF8
k k k k k k k k
where FR1 is debt ratio, FR2 is equity plus long-tern liabilities over fix assets, FR3 is current ratio, FR4 is quick ratio, FR5 is inventory turnover ratio, FR6 is receivables turnover ratio, FR7 is total asset turnover ratio, FR8 is profit margin, FR9 is return on total assets, FR10 is cash ratio, FR11 is change in cash flow, FR12 is ln(size). MF1 is real estate determine score, MF2 is monitoring indictors score, MF3 is leading index, MF4 is floor area of building permit –Taiwan (Epd), MF5 is saving rate-R.O.C(year), MF6 is unemployment rate-U.S.A., MF7 is new privately owned housing started (SA), MF8 is import goods-U.S.A.
And the probability equation of company k is
12 8
where βik and λjk are the coefficients of financial ratios parameters and macroeconomic factors, and c is the constant term.
According to the coefficients of parameters estimated in Table 5.4, the regression in equation (5-2) is as following:
ˆ* 4.5398 0.0645FR1 0.0001FR2-0.0106FR3 0.0141FR4-0.0006FR5 0.0036FR6 -1.3940FR7-0.0067FR8-0.0716FR9 0.6137FR10 0.0000FR11 0.1112FR12 0.0304MF1
0.0028MF2-0.0061MF3-0.0001MF4 0.0131MF5-0.0151MF6+0.00
y = −k + + + +
− + + +
+ + 00MF7 0.0000MF8+
22
Table5.4 Coefficient Estimate of Model 2
B S.E. Wald P-value Exp(B)
FR1 0.0645 0.0118 29.7136 0.0000* 1.0667
FR2 0.0001 0.0001 0.3307 0.5653 1.0001
FR3 -0.0106 0.0038 7.7754 0.0053* 0.9894
FR4 0.0141 0.0044 10.2917 0.0013* 1.0142
FR5 -0.0006 0.0045 0.0183 0.8924 0.9994
FR6 0.0036 0.0044 0.6929 0.4052 1.0036
FR7 -1.3940 0.3412 16.6904 0.0000* 0.2481
FR8 -0.0067 0.0070 0.9086 0.3405 0.9933
FR9 -0.0716 0.0221 10.4931 0.0012* 0.9309
FR10 -0.6137 0.4492 1.8670 0.1718 0.5413
FR11 0.0000 0.0000 0.0178 0.8938 1.0000
FR12 0.1112 0.1374 0.6555 0.4182 1.1177
MF1 0.0304 0.0400 0.5773 0.4474 1.0308
MF2 0.0028 0.0127 0.0470 0.8283 1.0028
MF3 -0.0061 0.0233 0.0688 0.7931 0.9939
MF4 -0.0001 0.0001 0.3173 0.5732 0.9999
MF5 0.0131 0.3190 0.0017 0.9673 1.0132
MF6 -0.0151 0.0682 0.0493 0.8243 0.9850
MF7 0.0000 0.0004 0.0110 0.9165 1.0000
MF8 0.0000 0.0000 0.1324 0.7160 1.0000
Constant -4.5398 8.3923 0.2926 0.5885 0.0107
FR1 is debt ratio, FR2 is equity plus long-tern liabilities over fix assets, FR3 is current ratio, FR4 is quick ratio, FR5 is inventory turnover ratio, FR6 is receivables turnover ratio, FR7 is total asset turnover ratio, FR8 is profit margin, FR9 is return on total assets, FR10 is cash ratio, FR11 is change in cash flow, FR12 is ln(size). MF1 is real estate determine score, MF2 is monitoring indictors score, MF3 is leading index, MF4 is floor area of building permit –Taiwan (Epd), MF5 is saving rate-R.O.C(year), MF6 is unemployment rate-U.S.A., MF7 is new privately owned housing started (SA), MF8 is import goods-U.S.A. In P-value column, signal * means 1%
significant. The Exp(B) is the exponential value of coefficient B for the calculation of failure probability in equation (5-2).
The estimated parameters of model 2 illustrate the same results as model 1 which debt ratio, current ratio, quick ratio, total asset turnover ratio, and ROA are very significant at 1%.
However, all macroeconomic factors are not significant.
Table 5.5 shows the summary of selection process. Figure 5.2 shows the figure of
23
cumulative percentage of failed and non-failed companies. The max KS value is 66.67% and in the score range of 0.45 to 0.50. Thus we choose the upper bound 0.5 as Model 2’s cut-off point.
Table 5.6 shows the performance of estimation sample using Model 2, the correct prediction percentage of failed firms is 83.33%, the correct prediction percentage of non-failed firms is 83.33%, and the correct percentage of total prediction is 83.33%. Thus the prediction ability performance of the model which adds macroeconomic factors as its inputs is better than the model only use financial ratios as its inputs. From table 5.6, we know the type I error rate is 16.67% and type II error rate is 16.67%.
Table5.5 The Process of Finding Maximum KS Value
Score
24
total 174 174 100.00% 100.00%
The max KS value is 66.67% noted by bold number in the table and the score range is 0.45 to 0.5. Here we choose the upper bound 0.5 as the cut-off point of Model 2.
Figure5.2 KS Value in Model 2
KS
This picture is to find the maximum KS value which is denoted by the line with triangle spots. The line with diamond spot is the cumulative percentage of failed companies and the line with square spot is the cumulative percentage of non-failed companies. The KS value is calculated by the cumulative percentage of non-failed companies minus the cumulative percentage of failed companies.
Table5.6 Model 2 Performance of Estimation Sample
Sample
The estimation sample is to evaluate the coefficients of parameters in model 2. Based on the coefficients calculated via MLE method, the correct percentage of observed failed firms is 83.33% and the correct percentage of observed non-failed firms is 83.33%. The overall correct percentage is 83.33% based on the cut-off point 0.5.
5.3 Prediction Sample Performance
25
In previous sections, we have figure out the coefficients and cut-off point. The coefficients of Model 1 are shown in Table 5.1; the coefficients of Model 2 are shown in Table 5.4; the cut-off point of Model 1 is 0.45; the cut-off point of Model 2 is 0.50. So we use these information to see how the prediction performance of the two models.
Table 5.7 shows the prediction performance of Model 1. The correct prediction percentage of failed firms is 86.21%, the correct prediction percentage of non-failed firms is 82.76%, and the correct percentage of total prediction is 84.48%. The type I error rate is 13.79% and type II error rate is 17.24%.
Table 5.8 shows the prediction performance of Model 2. The correct prediction percentage of failed firms is 86.21%, the correct prediction percentage of non-failed firms is 86.21%, so the correct percentage of total prediction is also 86.21%. The type I error rate is 13.79% and type II error rate is 13.79%, too.
Therefore, the model with macroeconomic factors is better than the model without ones.
This result proves that the factor of macroeconomic affects firms’ financial situation in Logit default model.
Table5.7 Model 1 Performance of Prediction Sample
Sample
The prediction sample is to verify the currency of model 1. The correct percentage of observed failed firms is 86.21% and the correct percentage of observed non-failed firms is 82.76%. The overall correct percentage is 84.48% based on the cut-off point 0.45.
26
Table5.8 Model 2 Performance of Prediction Sample
Sample
The prediction sample is to verify the currency of model 2. The correct percentage of observed failed firms is 86.21% and the correct percentage of observed non-failed firms is 86.21%. The overall correct percentage is 86.21% based on the cut-off point 0.5.
We also compare the probabilities of the 29 prediction sample in 3-year before financial distress occur. Let year t be the time of financial distress occurs. Figure5.3 to figure5.6 show the firms’ probabilities of year t – 1, t – 2, and t – 3.
In figure 5.3, we can see the failed firms’ changes of probability in each year by using Model 1. There are 12 positive changes from year t – 3 to t – 2, and 23 positive changes from
In figure 5.3, we can see the failed firms’ changes of probability in each year by using Model 1. There are 12 positive changes from year t – 3 to t – 2, and 23 positive changes from