Prediction of default probability for construction firms using the logit model.
Tserng, H. Ping ; Chen, Po-Cheng ; Huang, Wen-Haw 等
Introduction
The construction industry is always the vanguard of national
economic development. This industry is the foundation and connector
between other industries. However, contractors are facing numerous
difficulties and a highly competitive environment. Historical U.S. data
indicates that the failure rate among construction firms has reached a
critical level (Kangari et al. 1992). Numerous risks occur during the
life cycle of construction objects (Zavadskas et al. 2010). Meanwhile,
some highlighted characteristics of the construction industry and
construction projects, such as uniqueness, long term investment, large
investment capital, etc. result in the industry having unique financial
characteristics. One of the required conditions of a competent
construction contractor is the use of proper processes and construction
project completion (Plebankiewicz 2010). High default risk may prevent
contractors from completing a construction project. Tserng et al.
(2011a) also indicated the importance of identifying potentially failing
contractors; thus enabling clients to avoid awarding contracts to
contractors likely to default. In order to monitor the financial risk or
any adverse effects on joint venture projects or cooperative projects,
prime construction contractors are concerned about the financial health
of their sub-contractors and vice versa (Tserng et al. 2011b). Recently,
interest has grown in predicting the default likelihood of contractors.
Contractor financial ratios, which can be calculated from
information contained in financial statements, are useful data for
predicting company default probability. Financial statements summarize
the value of a company at the end of a specific period, as well as
assessing company operations, indicating and highlighting performance in
all related sectors (Ross et al. 2010). Financial ratios serve as the
fundamental basis for evaluating company financial capabilities, and
provide useful information for predicting firm likelihood of default.
The usages of financial ratios in construction companies can provide an
early warning mechanism that offers an effective monitoring tool to
avoid continuing poor corporate performance or insolvency. Beaver (1966)
and Altaian (1968) were the first to use financial ratios to analyse and
predict the default probability, and their work was subsequently
continued by Abidali and Harris (1995), and Edum-Fotwe et al. (1996).
These studies focused on applying statistical methods to financial
ratios analysis to determine the likelihood of corporate default.
Furthermore, most of the previous investigations examined industries in
general, rather than specifically focusing on construction industry
concerns.
Logit regression analysis performs well in identifying the
likelihood of an outcome belonging to one of the two discrete classes of
failure versus non-failure. Additionally, no assumption is made
regarding the distribution of the independent variables, and no normally
distributed requirement of multivariate variables. Owing to less
demanding conditions, the logit regression is more useful in practice.
The Logit model is widely used in numerous domains, especially in
relation to credit risk and health sciences. In credit risk analysis,
the Logit model is a common technique used in credit scoring to
determine default probability. Financial institutions build up the
credit scoring model based on consumer application and credit reference
agency data (Ohlson 1980; Bellotti, Crook 2009). In health sciences, the
Logit model is a multivariable analysis tool for modelling dichotomous
outcomes. The Logit model is widely used and appropriate for models of
disease state (diseased/healthy) and decision making (yes/no) (Bagley et
al. 2001). Moreover, the strong development of information technology
and the wide application of the Internet simplify the collection of
contractor financial data from the biggest market, the U.S., which has a
long history and modern, convenient systems of storing data. This study
uses the Logit model to analyse the relationship of financial ratios to
the default probability of construction firms. This investigation
estimates and quantifies the default risk of construction firms by
applying the Logit model to analyse historical data from the financial
statements of firms participating in the US market.
The remainder of this investigation is divided into six sections:
Section 1 reviews the literature on construction industry
characteristics and research on default probability prediction; Section
2 then introduces the research methods; next, Section 3 describes data
set and input selections; Section 4 presents single variable analysis
and empirical results; Section 5 then describes multivariate analysis
and the empirical results; finally, the final section presents
conclusions.
1. Literature review
1.1. General and financial characteristics of construction industry
The construction industry differs from other industries in its
organization and products, stakeholders, large projects, processes, and
operating environment. Construction industry activities include the
building of new structures, including site preparation, as well as
additions and modifications to existing ones. The construction industry
also includes maintenance, repair, and improvements of these structures.
Since the construction industry includes numerous sub-sectors, it is
difficult to clearly define the construction industry, despite general
agreement about its characteristics. Barrie and Paulson (1992)
identified the general characteristics of the construction industry as
being that most of construction projects are unique, have long life time
expectancy, and involve a long cycle from design to production.
Due to the distinctive operational behaviours of the construction
industry, its financial characteristics also differ from other
industries. Some of these characteristics are as follows: (a) The
construction industry requires large amounts of cash; (b) Contractors
must always implement several projects simultaneously, causing them to
tend to decrease the payback period, meaning short term finance is
invariably required; (c) Inventories of construction firms occupy a
large proportion of total assets since they include construction in
progress and materials. As a consequence, construction firms have high
current ratio and low quick ratio (Barrie, Paulson 1992); (d)
Contractors always have a lot of valuable machines and equipment, for
example, cranes, boats, shaped steel store, that cause the book value of
total asset to be very high, and usually under the affection of
depreciation.
1.2. Recent research on default probability prediction
Since the construction industry has its own general characteristics
and financial risks, recently numerous investigations have used
financial ratios to predict construction company failure. Several
approaches have been adopted, including multiple discriminant analysis
(MDA) (e.g. Mason, Harris 1979; Severson et al. 1994; Abidali, Harris
1995), ratio analysis (e.g. Chan et al. 2005; Huang 2009), and logit
regression (e.g. Severson et al. 1994; Russell, Zhai 1996; Tserng et al.
2011a). Among these methods, the logit regression analysis performs well
in identifying the likelihood of an outcome being in one of the two
discrete classes: failure versus non-failure. Besides, no assumptions
are made with respect to the distribution of the independent variables,
and the multivariate variables are not required to be normally
distributed. These less demanding condition increase the usefulness of
the logit regression.
2. Methodology
This study performs the univariate and multivariate ratio analysis
by using the Logit model to predict construction contractor default. The
financial ratios are classified into five groups, and the best ratio of
each financial group is selected for combination into four multivariate
ratio analyses. In the multivariate ratio analysis process, the market
to book ratio is especially considered to assess the impact of the
market factor on the probability of construction firm insolvency. Three
maturities of the forecasting time are considered in default prediction,
namely one, two, and three years before the default. To avoid
over-fitting in the result, an iterative method called leave-one-out
cross-validation (LOOCV) is adopted in the modelling. For model
evaluation, the receiver operation characteristic (ROC) curve is
utilized to determine the goodness of the Logit models via single
variables or the combinations of multivariables.
2.1. The Logit model
Ohlson (1980) pioneered the approach of using the logistic
regression model to predict business bankruptcy. Later, researchers
pursued using the logistic regression model to predict construction
contractor performance (Jaselskis, Ashley 1991; Russell, Jaselskis 1992;
Severson et al. 1994). A binary logistic regression model can
effectively show the correlation between independent variables of binary
response and a group of explanatory variables (Luo, Lei 2008). The
output of the logistic regression model is between 0 and 1, indicating
two separate events (default and non-default). The model is suitable for
demonstrating the likelihood of occurrence of an event by probabilities.
The probability p of y = 1 is the research object, while the independent
variables [X.sub.1], [X.sub.2] ... [X.sub.k] are the explanatory
variables of firm default probability (Luo, Lei 2008). Finally, Eqn (1)
shows the logistic function:
P = (y = 1| Explanatory variables) = 1/1 + [e.sup.-z], (1)
where: P denotes the default probability; and Z represents the
linear regression of explanatory variables. Z = [[beta].sub.0] +
[[beta].sub.1] [X.sub.1] + [[beta].sub.2] [X.sub.2] + [[beta].sub.3]
[X.sub.3] + [[beta].sub.4] [X.sub.4] + ... + [[beta].sub.k] [X.sub.k].
Generally, parameters p can be estimated using the maximum
likelihood method to maximize the log-likelihood function:
log L([beta]) = [n.summation over (i = 1)][y.sub.i] log[p.sub.i] +
(1 - [y.sub.i]) lob(1 - [p.sub.i]), (2)
where: [p.sub.i]: depends on the covariates [X.sub.i] and a vector
of parameters [beta] through the Logit transformation of equation
[z.sub.i] = [[beta].sub.0] + [[beta].sub.1] x [X.sub.1] + [[beta].sub.2]
x [X.sub.2] + [[beta].sub.3] x [X.sub.3] + [[beta].sub.k] x [X.sub.k],
[y.sub.i]: a qualitative variable comprising one of two values, with 0,1
representing the non-default and default event, respectively; [X.sub.i]:
the explanatory variables of firm default probability.
2.2. Model validation
The derived logit model has to be validated to strictly test its
prediction ability. A validation process called leave-one-out
cross-validation (LOOCV) is used to verify the fitness of the derived
model in out-of sample forecasts, and the model prediction ability is
evaluated using ROC curve.
2.2.1. ROC curve
Assessing the model misclassification rate by setting a specific
cut-off point is a traditional method of model validation in default
prediction. The cut-off point setting depends on the assumed
misclassification costs of Type I error (the actual is default and the
prediction is non-default) and Type II error (when the actual is
non-default and the prediction is default). However, it is difficult to
assume the misclassification costs when making an assessment, and the
cut point setting varies among different models creating potential
difficulties in comparison (Bellotti, Crook 2009). To fully perform
model prediction, this study adopts a receiver operation characteristic
(ROC) curve for the comparison. Table 1 lists the different fractions of
the ROC curve.
For every possible cut-off point, positive means the prediction
model is identified as the default, while negative indicates that the
prediction is non-default. Furthermore, True Positive (TP) shows that
the actual default is correctly classified as positive, while the actual
non-default correctly classified as negative is termed the True Negative
(TN). Meanwhile, False Negative (FN), which is generally known as type I
error, occurs when the actual default is classified as negative. In
contrast to False Negative, False Positive (FP) is termed as the type II
error that shows the actual non-default mistakenly classified as default
(Akobeng 2007).
In the ROC curve, the true positive rate (Sensitivity) is plotted
as a function of the false positive rate (1-Specificity) for the full
range of possible cut-off points. That is, each point on the ROC plots
the type II error versus one minus the type I error corresponding to
each possible cut-off point.
The ROC graph is applied in the area under the ROC curve, called
AUC, which is calculated as the proportion of the area below the ROC
relative to the total area of the unit square. A model with prefect
discrimination power has a ROC that passes through the upper left
corner, resulting in an AUC equalling 1; while a ROC that is a diagonal
line from the bottom left corner to the upper right corner indicates a
random model, resulting in an AUC of 0.5. Therefore, the closer the AUC
is to 1, the higher the differentiation ability of the model. The AUC
value can help to verify the fit of the model results to the actual
event, and therefore is utilized as the selection criteria for
determining the importance of the single variables, and for showing the
prediction performance of the multivariable models.
2.3. Cross-validation
One of the purposes of this study is to establish a model that
relies on the Logit model to predict the default probability of the
construction firms. Constructing a prediction model requires the
cross-validation step to avoid the over-fitting problem. The
over-fitting problem indicates that the established model only perform
well for in-sample data, but fails to make accurate predictions when
using out-of-sample data. This investigation uses a crucial process,
leave-one-out cross-validation (LOOCV) for the model construction.
Leave-one-out cross-validation (LOOCV) involves using a single
observation from the original sample as the validation data, and the
remaining observations as the training data. This process is repeated
until each observation in the sample has been used once as the
validation data. The model validation result is taken as the average of
the (Area Under Curve) AUC in each round.
3. Data collection
This study empirically investigates a large cross-section of
construction contractors. Data is collected from the Compustat
Industrial files and the Center for Research on Securities Prices
(CRSP). This investigation emphasizes on construction contractors with
December fiscal yearends by choosing firms with SIC codes ranging
between 1,500 and 1,799. Similar to the studies of Severson et al.
(1994) and Russell and Zhai (1996), the sample contractors are drawn
from three construction categories:
--Major Group 15: Building construction, general contractors, and
operative builders;
--Major Group 16: Heavy construction other than building
construction contractors;
--Major Group 17: Construction special trade contractors.
The study population comprises 119 construction contractors, of
which 29 defaulted. The observation period ranges from 1970 to 2006. The
following are principles of data screening:
1) To consider the long term impact of the financial ratios, the
selected construction contractors require at least five years of
continuous data in Compustats;
2) Using a broad definition of bankruptcy, default events are
defined by CRSP delisting codes of 400, 550 and 585, which are referred
to as the reasons of bankruptcy, liquidity or poor performance,
respectively;
3) The selected financial ratios can encompass all aspects of a
contractor finance situation, including the liquidity, profitability,
leverage, activity of a firm and even the market factor. Furthermore,
these ratios have been used in at least two studies dealing with
construction finance.
The final sample consists of 87 contractors, 29 of which defaulted
while 58 are non-defaulted, including 1560 firm-year observations.
Twenty-one financial ratios of each observation are collected and used
to implement the Logit models. Table 2 lists the definitions and summary
statistics of these ratios.
4. Single variable analysis and empirical result
Through applying the Logit model for each single variable with
validation process, the estimated default probabilities of each sample
can be assessed corresponding to each univariate Logit models. The ROC
curve is utilized to demonstrate the prediction performance of 21
univariate logit analyses constructed by different single variables.
Table 3 lists the AUC of each maturity of 21 single variables. AUCs
exceeds 0.5 (AUC = 0.5 indicates a random model) in the case of six
variables (Var 17, Var 11, Var 7, Var 3, Var 15, Var 1), where AUCs
exceeds 0.5 in years 1, 2 and 3. The AUCs of return on assets ratio
(ROA) exceeds 0.7; therefore, the ROA performs best in default
prediction in univariate logit analysis.
For the multivariate analysis, the variable selection criteria are
based on the AUC results of 21 variables. The results of the AUC of
single financial ratios that exceed 0.5 are considered for multivariate
analysis, and thus Var 1 (current ratio) and Var 3 (net working capital
to total asset) in the liquidity group are selected. The selected
financial ratio of the leverage group is Var 7 (debt ratio). The Var 11
(accounts payable turnover ratio) and Var 15 (the turnover of the total
assets) of the turnover group are also valid, and the last selected
financial ratio is Var 17 (return on asset-ROA) of the profitability
group. Besides, Var 21 (book to market ratio) is also considered to make
a general assessment, and also to investigate the influence of market
factor for default prediction. Table 4 lists the selected financial
ratios used in the multivariable analysis.
5. Multivariate analysis and the empirical result
To perform the multivariate analysis, this study first combines
only one single ratio of each financial group (Liquidity group, Leverage
group, turnover group, and Profitability group) to establish two
multivariate Logit models (models 1 and 3). Including one single ratio
of each financial group in a combination can help avoid repetition and
close correlation between ratios in the same group. Additionally, market
factor is considered and combined with other financial groups to create
two multivariate Logit models (models 2 and 4). Therefore, four
combinations are selected to perform the multivariate analysis with
logit function. Table 4 lists the combinations of four models.
For the multivariate analysis, the value of a combo, Z, is
calculated by multiplying the regression coefficient and ratio value
correlatively, then transferred into default probability using the Logit
model. Table 6 lists the coefficient estimates for the logit
regressions.
Table 6 shows that Var 7 is statistically significant (p < 0.01)
in model 2, model 3 and model 4; meanwhile, Var 17 and Var 21 are
significant (p < 0.01) in all of the 4 models. Thus, these three
ratios have better default prediction ability.
One of the major characteristic of logit function is that default
probability increases with Z value. Therefore, the ratio with a positive
coefficient with Z value also exhibits with a positive correlation with
default probability. In Table 6, the estimated coefficients are
consistent with the common understanding that high debt ratio (Var 7)
and high book to market value (Var 21) increase default probability
(with a positive sign), whereas the other five ratios (Var 1, Var 3,
Var11, Var 15, Var 17) exhibits an opposite effect.
ROC curve area and accuracy
The assessed default probabilities with each combo in years 1, 2
and 3 are used in the model validation step. This study employs ROC
curve to evaluate the discriminatory ability of established multivariate
Logit models. Discriminatory ability means how effectively the models
can rank companies correctly from the riskiest one to the safest
according to the model's default probabilities.
Table 7 lists the AUC of four multivariate Logit models with
different years. All AUCs of the four multivariable Logit models exceed
0.7 in construction contractor default prediction. Besides, the ROC
curves of the four multivariable Logit models are shown in Figures 1, 2,
and 3.
Several findings can be obtained by comparing the results among the
models: First, as Table 7 shows, the AUCs of model 2 (0.7843; 0.7846;
0.7654) outperform those of model 1 (0.7107; 0.7475; 0.7630) in default
prediction over a one to three year timeframe. Similarly, the AUCs of
model 4 (0.7918; 0.7951; 0.7514) also exceed the those of model 3
(0.7433, 0.7698, 0.7503), indicating that combining the book to market
ratio (Var 21) with the financial factors (Var 3, Var 7, Var 17, Var 11
or Var 1, Var 7, Var 17, Var 15) for construction contractor default
prediction increases the model performance.
Second, the improvements obtained from adding the book to market
ratio (Var 21) in multivariate logit analysis are obvious in one year
prediction (from AUC = 0.7107 for Model 1 to AUC = 0.7843 for Model 2,
and from AUC = 0.7433 for Model 3 to AUC = 0.7918 for Model 4). These
differences can also be observed in Figures 1, 2, and 3. Because of
Models 2 and 4 considering the book to market ratio (Var 21), which is
an indicator of present firm situation, Model 2 and Model 4 offer a
means of making fast and precise short-term predictions.
Third, model 3 slightly outperforms Model 1. The AUC of Var 3 and
Var 11 being slightly higher than those of Var 1 and Var 15 in the
univariate analyses, demonstrating that the Var 1 and Var 15 adopt and
provide a better general view of the activity and directly relate to the
short term debt of a firm in multivariate analysis. The empirical result
of model 3 also indicates that 2-year prediction is the most suitable of
predicting default probability of construction firms.
Fourth, Model 4 is the best model in this study that could be used
to predict default probability. Like Models 1 and 2, Model 4 is based on
the ratios of the Model 3 but with the addition of the market factor
(Var 21). The AUC of Model 4 performs stably in one-year and two-year
prediction (AUC = 0.7918 and 0.7951), suggesting that Model 4 obtains a
better default prediction in the short term.
[FIGURE 1 OMITTED]
[FIGURE 2 OMITTED]
Conclusions and suggestions
Employing the Logit model to analyse construction firm financial
ratios in the U.S. market, and to quantitatively measure firm default
probability based on actual firm financial situation can provide
extremely useful information for relevant stakeholders, such as clients,
lending institutions, and surety underwriters. The models presented in
this study are validated to verify their effectiveness by comparison
with actual default events.
[FIGURE 3 OMITTED]
The empirical result of the single variable model was used to
demonstrate the impact of twenty-one financial ratios on the
construction company insolvency. The result indicates that liquidity
plays an important role in the predicting of the default probability for
construction firms. Besides, for those ratios directly related to short
term and long term company debt, such as debt ratio (Var 7) and accounts
payable ratio (Var 11), which also strongly affect the default
probability. The validation process also indicates that the return on
assets ratio (Var 17) is the most suitable variable for univariate
analysis. However, numerous reasons may exist for a default, reflected
in various financial ratios. Therefore, basing such a prediction on just
one financial ratio may be insufficient to fully capture the default
phenomena. Most of the 21 variables have AUCs below 0.5. This indicates
that using the univariate logit model for default prediction cannot
fully satisfy the need for predicting default by construction
contractors. Notably, an unexpected finding of univariate logit analysis
was that using ROA (return on assets ratio) alone can achieve decent
performance in default prediction for the US contractors. ROA is a key
profit indicator for investors. In the United States, accounting
principles and asset recognition criteria are well developed, and ROA is
considered to more accurately reflect the real situation of a firm
rather than other countries. Since this investigation aims to develop a
general estimation method for predicting construction contractor
default, observing only the profitability of the construction
contractors for default prediction may lack consideration of other
aspects of financial abilities. Therefore, multivariate logit analyses
with different financial ratios are required to enable a whole financial
indicator to predict construction contractor default.
This study is the first to use multivariate analysis to assess the
simultaneous impacts of the four financial aspects, namely liquidity,
leverage, activity and profitability, on construction firm default
probability. Subsequently, the market factor (book to market ratio) is
taken into account. The empirical results indicate that the proposed
method is most accurate when combining multiple ratios in the analysis.
Using a combination of valid ratios can help capture all aspects of the
risk of bankruptcy. Notably, including market factor enhanced the
prediction performance when it was considered along with other financial
factors.
It is noteworthy that this paper places much emphasis on the data
collection and screening parts to obtain available construction
contractors samples in the United States for providing an overall
investigation in default prediction. All adopted financial data follow a
unified set of standards and principles--the Generally Accepted
Accounting Practice (GAAP), and the default events are defined by CRSP
publicly. Besides, using multivariate logit analyses with five financial
aspects (liquidity, leverage, turnover, profitability and market) enable
a whole financial indicator to predict construction contractor default.
For construction contractor default prediction in other world markets,
this paper could serve as a basis for investigation. Further research
could also collected financial data that follow the same accounting
principles and asset recognition criteria, i.e. international financial
reporting standards (IFRS). With the same accounting standards, the
collected data are consistent thus providing representative results of
the regions. Furthermore, the performance of financial ratios in
predicting construction default among different countries or regions
would also be an interesting global topic for further research. Finally,
this study only surveyed public listed construction contractors with SIC
codes between 1,500 and 1,799. For further study, this study recommends
expanding the sample to include non-publicly listed contractors and
broadening the research domain to include other financial ratios,
particularly market-related ones.
Acknowledgement
The authors would like to acknowledge the National Science Council,
Taiwan, for financially supporting this work under contract number
NSC-100-2221-E-002-220MY2 and NSC-100-2218-E-002-013.
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H. Ping TSERNG (a), Po-Cheng CHEN (a), Wen-Haw HUANG (b), Man Cheng
LEI (a), Quang Hung TRAN (a)
(a) Department of Civil Engineering, National Taiwan University,
No. 1 Roosevelt Rd., Sec. 4, Taipei, Taiwan
(b) Long Reign Development Co., 16F-2, No. 76, Sec. 2 Dunhua S.
Road, Taipei, Taiwan
Received 11 Aug 2011; accepted 11 May 2012
Corresponding author: H. Ping Tserng
E-mail: hptserng@ntu.edu.tw
H. Ping TSERNG is a Full Professor at the Department of Civil
Engineering of NationalTaiwan University. He is also a Corresponding
Member of Russian Academy of Engineering. He has a PhD degree in
Construction Engineering and Management from University of
Wisconsin-Madison and he is an Official Reviewer or Editorial Board
Member of several international journals. His research interests include
advanced techniques for project management, construction finance,
knowledge management, management information system, GPS/wireless sensor
network, and automation in construction.
Po-Cheng CHEN is a PhD candidate in the Department of Civil
Engineering at National Taiwan University. His research interests
include contractor default prediction, and construction finance.
Wen-Haw HUANG is the CEO for Long Reign Development Company. He has
a MBA degree from Loyola Marymount University. Currently, he is a
part-time PhD student in the Department of Civil Engineering at National
Taiwan University. His research interests include contractor
prequalification, contractor default prediction, financial management,
and construction management.
Man Cheng LEI is a Master of Science in Civil Engineering from
National Taiwan University. Her research interests include construction
finance, construction management, and project performance evaluation.
Quang Hung TRAN is a Master of Science in Civil Engineering from
National Taiwan University, Taiwan. His research interests include
construction finance, risk management, and construction
prequalification.
Table 1. The fractions of ROC curve
Prediction Actual outcome
Default Non- Default
Positive True Positive False Positive **
(default) (TP)
Negative False Negative * True Negative
(non-default) (FN) (TN)
Note: * False Negative is known as type I error.
** False Positive is known as type II error.
Table 2. Statistical characteristics of the selected financial ratios
Group Ratios Sign
Liquidity Current ratio Var 1
measurement Quick ratio Var 2
ratios Net working capital to total asset Var 3
Current asset to net assets Var 4
Financial Total liabilities to net worth Var 5
leverage Retained earnings to sales Var 6
ratios Debt ratio Var 7
Times interest earned ratio Var 8
Revenue to networking capital Var 9
Asset Accounts receivable turnover Var 10
utilization Accounts payable turnover Var 11
or turnover Sales to net worth Var 12
ratios Quality of inventory Var 13
Fixed assets to net worth Var 14
Turnover of total assets Var 15
Revenue to fixed assets Var 16
Profitability Return on assets (ROA) Var 17
indicator Return on equity (ROE) Var 18
ratios Return on sales (ROS) Var 19
Profits to networking capital Var 20
Market value ratios Book to market ratio Var 21
Group Mean Standard
deviation
Liquidity 3.414 5.047
measurement 1.396 1.648
ratios 0.357 0.26
1.183 1.099
Financial 2.958 26.215
leverage 0.863 36.550
ratios 0.609 0.193
50.808 315.941
5.215 75.651
Asset 68.785 249.275
utilization 25.774 83.978
or turnover 8.446 130.550
ratios 19.629 54.336
1.249 10.384
1.571 0.995
10.712 22.687
Profitability 0.040 0.120
indicator -0.053 3.758
ratios 1.178 35.831
0.122 7.919
Market value ratios 0.946 0.321
Table 3. The result of AUC of 21 univariate Logit models in 1, 2, 3
year ahead bankruptcy prediction
Rank Var Ratios AUC
1 year 2 year
1 Var 17 Return on assets (ROA) 0.7830 0.7667
2 Var 11 Accounts payable turnover 0.6922 0.7005
3 Var 7 Debt ratio 0.6529 0.6546
4 Var 3 Net working capital to total asset 0.6123 0.6065
5 Var 15 Turnover of total assets 0.5989 0.5865
6 Var 1 Current ratio 0.5832 0.6107
7 Var 2 Quick ratio 0.5600 0.5687
8 Var 21 Book to market ratio 0.4806 0.4845
9 Var 18 Return on equity (ROE) 0.3845 0.4231
10 Var 4 Current asset to net assets 0.3730 0.4529
11 Var 13 Quality of inventory 0.2741 0.2631
12 Var 8 Times interest earned ratio 0.2739 0.3423
13 Var 12 Sales to net worth 0.2607 0.4043
14 Var 6 Retained earnings to sales 0.2515 0.2484
15 Var 19 Return on sales (ROS) 0.1901 0.3229
16 Var 10 Accounts receivable turnover 0.1620 0.1780
17 Var 14 Fixed assets to net worth 0.1618 0.1864
18 Var 5 Total liabilities to net worth 0.1573 0.2040
19 Var 9 Revenue to networking capital 0.1350 0.2127
20 Var 20 Profits to networking capital 0.1235 0.1393
21 Var 16 Revenue to fixed assets 0.0302 0.2739
Rank AUC
3 year
1 0.7388
2 0.7119
3 0.6194
4 0.5942
5 0.5843
6 0.5951
7 0.4990
8 0.4809
9 0.4299
10 0.5076
11 0.2431
12 0.2365
13 0.4171
14 0.2415
15 0.3781
16 0.1791
17 0.1963
18 0.2185
19 0.0821
20 0.1022
21 0.3838
Table 4. The selected financial ratios for multivariable logit
analysis
Groups Var AUC
1 year 2 year 3 year
Liquidity group Var 1 0.5832 0.6107 0.5951
Liquidity group Var 3 0.6123 0.6065 0.5942
Leverage group Var 7 0.6529 0.6546 0.6194
Turnover group Var 11 0.6922 0.7005 0.7119
Turnover group Var 15 0.5989 0.5865 0.5843
Profitability group Var 17 0.7830 0.7667 0.7388
Market group Var 21 0.4806 0.4845 0.4809
Table 5. The combinations of models in the multivariate logit
analysis
Combo 1
Var3-Net working capital to total asset
Var7-Debt ratio
Var17-Return on asset
Var11-Accounts payable turnover
Variables
Combo 2
Var3-Net working capital to total asset
Var7-Debt ratio
Var17-Return on asset
Var11-Accounts payable turnover
Var21-Book to market ratio
Combo 3
Var1-Current ratio
Var7-Debt ratio
Var17-Return on asset
Var15-Turnover of total assets
Variables
Combo 4
Var1-Current ratios
Var7-Debt ratio
Var17-Return on asset
Var15-Turnover of total asset
Var21-Book to market ratio
Table 6. The coefficient estimates for the logit regressions
Panel A: Prior one-year:
Var1 Var3 Var7 Var11
Model 1 -0.636 ** 2.575 -0.042 ***
Model 2 -0.522 4.169 *** -0.029
Model 3 -0.108 3.210 ***
Model 4 -0.109 4.512 ***
Panel B: Prior two-year:
Var1 Var3 Var7 Var11
Model 1 -0.366 2.666 *** -0.037 *
Model 2 -0.433 3.591 *** -0.030 *
Model 3 -0.109 2.994 ***
Model 4 -0.118 * 3.767 ***
Panel B: Prior three-year:
Var1 Var7 Var11
Model 1 -0.209 1.574 * -0.055 ***
Model 2 -0.292 2.047 *** -0.051 ***
Model 3 -0.084 ** 1.978 ***
Model 4 -0.088 ** 2.393 ***
Panel A: Prior one-year:
Var15 Var17 Var21 Constant
Model 1 -2.433 *** -4.958
Model 2 -3.504 *** 2.297 *** -8.629 ***
Model 3 -0.438 ** -3.106 *** -5.241 ***
Model 4 -0.333 -3.915 *** 2.216 *** -8.570 ***
Panel B: Prior two-year:
Var15 Var17 Var21 Constant
Model 1 -3.339 *** -410 ***
Model 2 -4.173 *** 1.782 *** -6.909 ***
Model 3 -0.328 ** -4.113 *** -4.486 ***
Model 4 -0.267 * -4.797 *** 1.709 *** -6.801 ***
Panel B: Prior three-year:
Var15 Var17 Var21 Constant
Model 1 -3.755 *** -3.012 ***
Model 2 -4.184 *** 1.140 *** -4.488 ***
Model 3 -0.268 ** -4.793 *** -3.456 ***
Model 4 -0.228 * -5.167 *** 1.143 *** -4.913 ***
*** significant at the 1% level (two side test).
** significant at the 5% level (two side test).
* significant at the 10% level (two side test).
Table 7. Result of AUC of four multivariate Logit models
Multivariate AUC
Logit models 1 year 2 year 3 year
Model 1 0.7107 0.7475 0.7630
Model 2 0.7843 0.7846 0.7654
Model 3 0.7433 0.7698 0.7503
Model 4 0.7918 0.7951 0.7514
