Bankruptcy Prediction Ahead of Global Recession: Discriminant Analysis
Applied on Romanian Companies in Timis County
Abstract
The purpose of this paper is to evaluate the potential of financial ratio analysis performed by employing public
data on predicting bankruptcy during the economic crisis period. The population subjected to our study was
composed of the 26,980 Romanian companies from Timis County that submitted financial reports for 2007 to the
fiscal authorities. Based on the financial data that was published from these reports by the Romanian Ministry of
Public Finance, 12 financial ratios for each of the 26,980 companies have been computed. The 12 ratios were
chosen by taking into consideration the recommendations of the literature, as well as the availability of financial
data. We were aware of the fact that other sources of information might improve the prediction of bankruptcy,
but, as the access of the external stakeholders to such information sources is limited, we decided to search for
bankruptcy predictors only within the financial data published online by the Ministry of Finance, which is easily
available to everybody. The statistical analysis of the correlation between the values of each financial ratio and
the frequency of the bankruptcy event led to the retention of 5 ratios as possible explanatory variables in a
bankruptcy prediction model. The initial analysis also led to the reduction of the target population to 4,327
companies. By means of discriminant analysis, we proposed a model capable of predicting bankruptcy for the
target population with an out-of-sample accuracy of 69.3%.Our findings show that the financial statements from
one year prior to the beginning of the economic crisis in Romania reflect the weakness that make the companies
susceptible to bankruptcy. We believe our model to be of practical use, as it is able to accurately discriminate
between bankrupt and non-bankrupt firms over a 5-year period, by only employing synthetic publicly available
financial data.
Keywords: bankruptcy, financial ratios, economic crisis, discriminant analysis, accuracy rate
1. Introduction
The financial ratio analysis was introduced by American banks around 1850 as a tool for evaluating
the credit-worthiness of a company(Horrigan, 1968).Starting with only one ratio (the current ratio), the
methodology employed in the financial ratio analysis has constantly developed (Beaver, 1966). At the
beginning of the 1950s, an increasing number of academics were criticizing the capacity of the
financial ratio analysis to evaluate business performance or to predict business failure(Altman, 1968).
Under these circumstances, Beaver (1966) proved the ability of financial ratios to predict business
failure by performing a univariate analysis over 2 samples of failed and non-failed firms. In his
conclusions, he suggested a multivariate analysis as a method for developing a more accurate model
for business failure prediction. Altman (1968) developed a multivariate model through the help of
discriminant analysis, with his work remaining as an essential reference for all later works in the field.
In the context of the current economic crisis, there is much debate in the academic field concerning the
possibilities of predicting such macro-economic events. Instead, the focus of our research was set at
micro-economic level.
It is clear from all statistics that the occurrence of the economic crisis has increased the failure risks at
company level. Reports of the National Bank of Romania (see, for instance, National Bank of
Romania, 2012) show a continuous increase of the rate of non-performing loans in the corporate sector
nationwide, with the value of 16,76% from the third quarter of 2012 placing Romania on the 4th
position within the EU, right after Ireland (18,74%), Lithuania (17,96%) and Greece (17,16%).
Reports of the International Monetary Fund (2013) from the third quarter of 2012 were placing
Romania after the same criterion on the 5th position in a list of 70 countries with available data
worldwide.
Reports of the National Trade Register Office (2013) show a growth in the number of corporate
bankruptcies in the first 2 years following the acknowledgement of the economic crisis in Romania,
with a moderate decrease in 2011 and 2012.
Chart 1 Number of corporate bankruptcies in Romania
21,692
25,000
20,000
18,421
19,651
15,148
14,483
15,000
10,000
5,000
0
2008
2009
2010
2011
2012 (no)
At the present time, Romania has just over 1 million active companies. Accepting the idea that the
economic crisis has increased the failure risks at company level, we assumed that these risks have
materialized during the crisis period for the most vulnerable companies. On this basis, a strong
challenge is to test whether indicators of this type of vulnerability could be found in the financial
statements of the companies 1 year prior to the beginning of the crisis (2007).
The population initially subjected to our study contained all companies from the Timis County that
submitted financial statements to the Public Finance Administration in 2007 (26.980 companies).
”Company failure” was defined as the declaration of bankruptcy according to the Romanian
Law85/2006. In this research, the authors focused on the occurrence of bankruptcy during the crisis
period (2008 – 2012).
The authors were aware of the fact that other sources of information could be more effective in the
prediction of bankruptcy: internal cash – flow reports, data supplied by the Center of Payment
Incidents or the Center of Credit Risks, etc. Still, the access of the external stakeholders to such
information sources is limited. Therefore, we decided to search for bankruptcy predictors within the
financial data published online by the Ministry of Finance, which is easily available to everybody.
Strong correlations between financial ratios and the probability of business failure would offer
important proof of the potential of financial ratio analysis performed by employing public data on
predicting bankruptcy.
In the event that strong predictors of bankruptcy would be found, our research would continue with the
elaboration of a scoring model capable of predicting corporate bankruptcy.
2. Explanatory variables
The selection of the financial ratios that would be tested for their prediction of bankruptcy capacity
was done considering the recommendations of the literature, as well as the limitations of the data
available. In this matter, the attention of the authors was not focused on obtaining all data
recommended by existing literature. The main purpose of the research was not to test if the variables
recommended by foreign literature can help predict the bankruptcy of the Romanian firms, but rather
to test if the public financial data existent in Romania can be used efficiently in the estimation of the
bankruptcy probability.
In the light of this approach, we used the financial data of the Timis County companies that was
publicly available to build as many of the recommended ratios as it was possible. In addition, we built
several ratios of our own, based on specific suppositions, within the limits of the data available.
Table 1
No
1
2
3
4
5
6
7
8
9
10
11
12
Ratio tested as explanatory variables
Total assets turnover ratio
Fixed assets turnover ratio
Inventory conversion ratio
Costumer receivables collection period
Fixed assets ratio
Current assets ratio
Autonomy ratio
Debt ratio
Solvency ratio
Equity working capital (100,000 RON)
Profitability ratio
Return on equity
Symbol
Atr
Fatr
Icr
Crcp
Far
Car
Ar
Dr
Sr
Ewc
Pr
ROE
Formula
Sales / Total Assets
Sales / Fixed Assets
(Inventory / Sales) x 360
(Receivables / Sales) x 360
Fixed Assets / Total Assets
Current Assets / Total Assets
Equity / Total Assets
Debt / Total Assets
Total Assets / Debt
Equity - Fixed Assets
Net profit / Sales
Net profit / Equity
The average total assets turnover ratio for bankrupt firms (0.99) was superior to the average total
assets turnover ratio for the healthy firms (0.78). This was contrary to our previous expectations, as
total assets turnover ratio is recognized as an important factor for generating return on assets. A high
total assets turnover ratio was expected to be associated with high return on assets (Liesz, 2002) and,
as a consequence, with high profits, high autonomy ratio and low bankruptcy risks.
In addition, high total assets turnover ratios have the potential of generating economies of scale, thus
stimulating the profitability ratio, the second factor that determines the level of the return on assets in
the du Pont vue.
The bankruptcy state occurs as an effect of the firm’s incapacity to pay its debt, thus being a possible
secondary consequence of the financing process. The firm mobilizes financing sources to support its
assets. By operating the assets, it generates production and sales. The selling price should insure a
certain profit margin, but it must first cover the costs. Considering that the costs are a financial
reflection of the resources consumed in order to produce and sell the product, by cashing the price
(that covers the cost), a company recovers the financing sources invested in the resources consumed to
produce and sell the product. This process is essential for insuring the payment capacity of the
company and thus for avoiding bankruptcy.
Table 2
No.
Total assets turnover ratio
Healthy Bankrupt % Bankruptcy
1 Total assets turnover ratio < 0.1
27.9%
22.3%
5.8%
2 0.1 <= Total assets turnover ratio < 0.5
11.0%
12.8%
8.2%
3 0.5<= Total assets turnover ratio < 1
15.1%
18.8%
8.8%
4 1 <= Total assets turnover ratio < 2
21.5%
24.0%
7.9%
5 2 <= Total assets turnover ratio < 3
9.8%
11.2%
8.1%
6 3 <= Total assets turnover ratio < 5
7.6%
6.5%
6.1%
7 Total assets turnover ratio >= 5
7.1%
4.4%
4.6%
Aproximately a quarter of the companies had total assets turnover ratios of values very close to 0. The
cause for this was that in 2007, these companies had recorded almost no sales. The percentage of
bankrupt firms in the total population was of 7.16%. The group of bankrupt companies included all
companies that declared bankruptcy during the 5 years following the date of the financial reports from
which the financial data was extracted for analysis (2008 – 2012). The class of companies with total
assets turnover ratios close to 0 had a lower bankruptcypercentage than the average. The
bankruptcypercentage overlaps the average for the companies with total assets turnover ratios between
0.1 and 3 and drops below average for the class of companies with total assets turnover ratios higher
than 3. This suggests that the population being analyzed is very heterogeneous and therefore different
categories would demand for separate analysis.
Table 3
No.
Fixed assets turnover ratio
Healthy Bankrupt % Bankruptcy
1 Fixed assets turnover ratio < 0.1
22.8%
16.9%
5.9%
2 0.1 <= Fixed assets turnover ratio < 1
12.8%
12.7%
7.7%
3 1<= Fixed assets turnover ratio < 2
9.3%
10.7%
8.8%
4 2 <= Fixed assets turnover ratio < 4
11.8%
11.9%
7.8%
5 4 <= Fixed assets turnover ratio < 10
14.9%
17.2%
8.9%
6 10 <= Fixed assets turnover ratio < 20
8.8%
10.4%
9.1%
7 Fixed assets turnover ratio >= 20
19.6%
20.3%
8.0%
Within the entire population of firms in Timis County (26,980), the average fixed assets turnover ratio
for bankrupt firms was of 2.07, while the average fixed assets turnover ratio for healthy firms was of
only 1.27.
For fixed assets turnover ratios lower than 0.1, the percentage of bankrupt firms in the total number of
firms was lower than the average. This situation was in accordance with the fact that a higher
percentage of healthy firms had in 2007 sales of values very close to 0 and thus registered fixed assets
turnover ratios very close to 0 (which makes our choice for the term ”healthy” questionable).
For fixed assets turnover ratios greater than 0.1, we expected high percentages of bankruptcy at low
values of the ratios and a decrease of the incidence of bankruptcy as the rotations increased. This was
not the case.
Table 4
No.
Inventory conversion ratio
1 Inventory conversion ratio < 0
Healthy Bankrupt % Bankruptcy
0.1%
0.1%
4.2%
2
3
4
5
6
7
0 <= Inventory conversion ratio < 1
1<= Inventory conversion ratio < 6
6 <= Inventory conversion ratio < 30
30 <= Inventory conversion ratio < 90
90 <= Inventory conversion ratio < 180
Inventory conversion ratio >= 180
38.2%
6.4%
14.9%
17.4%
9.4%
13.6%
25.2%
5.6%
18.6%
22.8%
11.5%
16.2%
5.2%
6.9%
9.5%
9.9%
9.3%
9.1%
The inventory conversion ratio stands for an approximation of the period (in days) necessary for the
financing sources invested in inventory to pass into a different asset form (receivables or cash),
according to the specific of the operating cycle of the business.
The state of bankruptcy involves the incapacity of the company to repay its debt. The operating cycle
of a company is configured in ways that should allow the financing sources (including debt) invested
into inventory or receivables to be released under the form of cash in time for the capital
reimbursements to be made.
The longer the operating cycle, the longer the period in which the financing sources invested into
cyclic assets (inventory plus receivables) are retained (under the form of cyclic assets). As the
inventory conversion ratio estimates a segment of the duration of the operating cycle, we would expect
higher inventory conversion ratios to be associated with higher levels of the bankruptcy risk.
Indeed, preliminary calculations showed that low inventory conversion ratios are more specific to
healthy firms than to the firms that would later go bankrupt. As reflected in the table above, 44,7% of
the healthy firms convert their inventory in up to 6 days, while only 30,9% of the firms that would
later go bankrupt convert their inventory in the same interval.
Inventory conversion ratios of more than 6 days appear to be more specific to bankrupt firms than to
healthy ones.The average inventory conversion ratio for all healthy firms was of 47.79 days, while the
average ratio for the bankrupt firms was of 56.17 days. It is clear nevertheless that the causes that
determined the inventory conversion period are important also. For instance, retail sectors logically
have lower inventory conversion periods. It is possible that such sectors would present lower
bankruptcy rates for other reasons, thus artificially suggesting a connection between the inventory
conversion ratio and the risk of bankruptcy.
We also kept in mind that the inventory conversion ratio might present important deviations from the
real inventory conversion period, for reasons such as seasonality.
Furthermore, it was clear from the available statistics that the economic crisis stimulated significantly
the risk of bankruptcy. The data used in our analysis was taken from the financial statements of 2007
(one year prior to the beginning of the crisis in Romania). Since 2008, under crisis conditions, we have
expected higher negative variations of the ratios for the companies that would go bankrupt. An
analysis of the volatility of the ratios will thus make the subject of our future research.
Still, the purpose of the present research was not to understand the causes of company bankruptcy, nor
to analyze the connection between the volatility of the financial ratios and the risk of bankruptcy, but
to test the capacity of the static analysis (on financial ratios from 2007)to evaluate the risk of
bankruptcy during the crisis period.
Table 5
No.
1
2
3
4
5
6
7
Costumer receivables collection period
Costumer receivables collection period < 1
1 <= Costumer receivables collection period < 15
15<= Costumer receivables collection period < 30
30 <= Costumer receivables collection period < 60
60 <= Costumer receivables collection period < 90
90 <= Costumer receivables collection period < 180
Costumer receivables collection period >= 180
Healthy Bankrupt % Bankruptcy
17.2%
7.7%
3.6%
16.5%
8.9%
4.3%
9.7%
6.2%
5.1%
14.5%
14.8%
7.9%
9.5%
10.8%
8.7%
14.2%
22.0%
11.5%
18.5%
29.5%
11.8%
The costumer receivables collection period is a ratio that attempts to estimate the average duration in
which the receivables are being collected from costumers. It is calculated based on the hypothesis of
the uniformity of sales and collections throughout the duration of the year. This means that the ratio
would be more accurate for companies without important seasonal fluctuations. On the other hand, we
would expect companies with important seasonality fluctuations to be more vulnerable, as the seasonal
fluctuations usually generate working capital problems. The literature mentions working capital
problemsas an important cause of bankruptcy(Bradley, 2004), especially in the case of small and
medium size companies.
Bradley &Rubach (2002)performed a study on 131 American companies filing for bankruptcy
indicated that 66% of the studied population accused the difficulties in cashing the receivables as an
important cause of their financial problems. The conclusion of the study is that failure to collect trade
credit stands for an important factor of bankruptcy, alongside with general poor management of the
working capital.
The preliminary inspection of the data sustains the prediction capacity of the costumer receivables
collection period, as the average percentage of bankruptcies increases with the growth of the ratio.
We were able to calculate the costumer receivables collection period ratio only for the companies that
registered in 2007 turnovers greater than 0. This was the case for 18,936 healthy companies (75.6% of
the total number of healthy companies) and 1,588 companies that would go bankrupt in the following
5 years (82.2% of the total number of the bankrupt companies group).The ratio was thus calculated for
a total of 20,524 companies, for which the average bankruptcy rate was of 7.74%.
As shown in the table above, most bankrupt firms tend to group under high costumer receivables
collection period levels, with the percentage of bankrupt firms overlapping the average percentage
from levels of the collection period of over 30 days.
The average costumer receivables collection period for healthy firms was of 96.82 days, while the
average period for bankrupt firms was of 112.23 days.
Table 6
No.
Fixed assets ratio
1 Fixed assets ratio < 0.1%
2 0.1% <= Fixed assets ratio < 25%
3 25%<= Fixed assets ratio < 45%
Healthy Bankrupt % Bankruptcy
24.0%
17.2%
5.2%
30.8%
39.9%
9.1%
12.7%
15.0%
8.4%
4
5
6
7
45% <= Fixed assets ratio < 60%
60% <= Fixed assets ratio < 80%
80% <= Fixed assets ratio < 90%
Fixed assets ratio >= 90%
8.6%
11.0%
5.3%
7.5%
9.9%
10.2%
3.9%
3.9%
8.2%
6.7%
5.3%
3.8%
The fixed assets ratio reflects the percentage of the fixed assets in the total value of the assets. Seen in
the view of the financing process, this ratio shows the proportion in which the financing sources were
invested in long-term resources. The long-term resources would be exploited for a long period of time
and would release the financing sources gradually, over their economic lifespan.
We hypothesized that high fixed assets ratios would induce rigidity, making it for the company harder
to adapt to changes that affect the volume of activity. In order for the financing sources invested in
fixed assets to be fully recovered in the form of cash, the fixed assets need to be exploited at maximum
capacity over their economic lifespan. A decrease in the level of activity (generated for example by a
decrease of market demand) could keep a part of the financing sources invested in fixed assets from
ever being recovered.
At the same time, fixed assets usually generate fixed costs, which increase the breakeven point and
with it, the operating risks.
Table 7
No.
Current assets ratio
Healthy Bankrupt % Bankruptcy
1 Current assets ratio < 10%
7.5%
3.9%
3.8%
2 10% <= Current assets ratio < 20%
5.3%
3.9%
5.3%
3 20%<= Current assets ratio < 40%
11.0%
10.2%
6.7%
4 40% <= Current assets ratio < 55%
8.6%
9.9%
8.2%
5 55% <= Current assets ratio < 75%
12.7%
15.0%
8.4%
6 75% <= Current assets ratio < 99.9%
30.8%
39.9%
9.1%
7 Current assets ratio >= 99.9%
24.0%
17.2%
5.2%
The current assets ratio reflects the percentage of the current assets in the total value of the assets.
Ignoring the existence of prepaid expenses, the sum of the fixed assets ratio and the current assets ratio
is equal to 1.
We believed that higher current assets ratios / lower fixed assets ratios would be associated with lower
probabilities of bankruptcy, based upon the assumption of a higher flexibility of the investments made
by the company.
The preliminary analysis of the data suggested a different scenario, as the average fixed assets ratio for
healthy firms was of 61%, while the average fixed assets ratio for (future) bankrupt firms was of
47.8%.
For the groups of firms with lower fixed assets ratios / higher current assets ratios, the probability of
bankruptcy was higher.
Table 8
No.
Autonomy ratio
1 Autonomy ratio < 0%
2 0% <= Autonomy ratio < 15%
Healthy Bankrupt % Bankruptcy
44.4%
42.8%
6.9%
13.2%
23.8%
12.2%
3
4
5
6
7
15%<= Autonomy ratio < 30%
30% <= Autonomy ratio < 45%
45% <= Autonomy ratio < 60%
60% <= Autonomy ratio < 80%
Autonomy ratio >= 80%
8.8%
7.0%
6.3%
8.0%
12.2%
11.7%
7.9%
4.9%
4.7%
4.2%
9.3%
8.0%
5.6%
4.4%
2.6%
The autonomy ratio shows the percentage of equity in total financing sources. We expected a lower
autonomy ratio / higher debt ratio to be associated with higher bankruptcy frequency. Indeed, the
average autonomy ratio for healthy firms was of 37.7%, while the average autonomy ratio for bankrupt
firms was of only 18.3%. The autonomy ratio and the debt ratio are correlated, as the autonomy ratio =
100% - the debt ratio. Under these circumstances, we decided to only use the autonomy ratio for
further testing.
Table 9
No.
1
2
3
4
5
6
7
Debt ratio
Debt ratio < 20%
20% <= Debt ratio < 40%
40%<= Debt ratio < 60%
60% <= Debt ratio < 80%
80% <= Debt ratio < 90%
90% <= Debt ratio < 99.9%
Debt ratio >= 99.9%
Healthy Bankrupt % Bankruptcy
12.2%
4.2%
2.6%
8.0%
4.7%
4.4%
8.5%
7.0%
5.9%
10.5%
12.2%
8.3%
6.6%
11.3%
11.6%
9.5%
17.5%
12.5%
44.6%
43.1%
6.9%
Within the bankrupt group, 42.8% of the companies had autonomy ratios lower the 0, which meant
debt ratios higher than 100%. The percentage of companies with negative autonomy ratios was even
higher for healthy firms. The negative autonomy ratios were a consequence of negative equity, a
situation created by the repeated registration of losses.
Starting with positive autonomy ratios (debt ratios of less than 100%), the bankruptcy frequency
generally gets lower as the autonomy ratio gets higher.
Table 10
No.
1
2
3
4
5
6
7
Solvency ratio
Solvency ratio < 100%
100% <= Solvency ratio < 105%
105%<= Solvency ratio < 125%
125% <= Solvency ratio < 166%
166% <= Solvency ratio < 250%
250% <= Solvency ratio < 500%
Solvency ratio >= 500%
Healthy Bankrupt % Bankruptcy
45.6%
43.3%
6.9%
5.4%
10.5%
13.2%
11.1%
18.7%
11.6%
10.4%
12.1%
8.3%
8.7%
7.1%
5.9%
8.1%
4.7%
4.4%
10.6%
3.6%
2.6%
The solvency ratio shows the capacity of the total assets to cover the total debt. Being perfectly
correlated with the autonomy ratio and the debt ratio, it was not included in the prediction model.The
average profitability ratio was of 2% for bankrupt firms and of 4.7% for the healthy ones. It could only
be calculated for 18,939 non-bankrupt firms and 1,588 bankrupt firms, as the rest of the population
registered no sales for the year 2007.
At positive profitability ratios, the bankruptcy frequency generally decreases as the profitability ratios
gets higher.
Table 11
No.
1
2
3
4
5
6
7
Profitability ratio
Profitability ratio < 0%
0% <= Profitability ratio < 1%
1%<= Profitability ratio < 5%
5% <= Profitability ratio < 10%
10% <= Profitability ratio < 25%
25% <= Profitability ratio < 50%
Profitability ratio >= 50%
Healthy Bankrupt % Bankruptcy
39.0%
40.4%
8.0%
6.2%
10.8%
12.6%
12.6%
17.4%
10.4%
9.0%
8.8%
7.5%
13.4%
10.6%
6.2%
10.5%
7.0%
5.3%
9.3%
5.0%
4.3%
The average return on equity for bankrupt firms (11%) was higher than the average return on equity
for the non-bankrupt group (9.7%). Correlating the bankruptcy incidence with the level of ROE is
made more difficult by the fact thata company can show mathematically positive ROE by registering
both losses and negative equity.
Table 12
No.
1
2
3
4
5
6
7
Return on equity
Return on equity < 0%
0% <= Return on equity < 1%
1%<= Return on equity < 15%
15% <= Return on equity < 40%
40% <= Return on equity < 75%
75% <= Return on equity < 100%
Return on equity >= 100%
Healthy Bankrupt % Bankruptcy
15.5%
13.7%
6.4%
10.0%
8.6%
6.2%
10.3%
11.9%
8.2%
14.0%
13.4%
6.9%
14.4%
15.9%
7.9%
17.3%
17.1%
7.1%
18.5%
19.3%
7.5%
3. Population of companies under analysis
The population initially subjected to analysis included all companies in the Timis County (Romania)
that submitted financial reports for 2007. Thus, data from 26,980 companies was evaluated, 1,933 of
which would go bankrupt within the 2008 – 2012 period.
Of the non-bankrupt firms, 6,108 (24.4%) registered no sales in 2007 while 13,129 (52.4%) registered
losses, thus consuming equity. Of the entire non-bankrupt population, 30.1% had no employees (7,549
companies) and 33.0% had public arrears (8,275 companies).
Of the bankrupt firms, 345 (17.8%) registered no sales in 2007 while 973 (50.3%) registered losses. Of
the entire bankrupt population, 22.4% had no employees (433 companies) and 5.1% had public arrears
(98 companies).
Preliminary evaluation of the data suggestedimportant lack of homogeneity, which demanded for a
more focused analysis.
After making adjustment for missing observations and unreasonable values several filters have been
applied in order to increase the level of homogeneity in the target population. Companies reporting
values of Atr, Fatr, Icr, Crcp, Far, Ewcand Roeoutside +/- 1.5* Interquartile Range from Tukey’s
Hinges have been removed in order to reduce extreme and mild outliers. Companies with a negative
Arhave also been removed. Regarding profitability, companies with Pr between 0 and 50% have been
retained.
Table 13 Data selection process
Data sets
Initial Population
Adjusted Population
Target Population
Description
All companies from Timis
county which submitted
financial reports for 2007
Companies with missing
observations and
unreasonable values have
been removed
Fatr, Far, Icr, Crcp, ,
Ewcand Roe within +/1.5* Interquartile Range;
Ar>0; 0<Pr<50%
Number of
companies active
at the end of 2007
Drop in the
number of
companies from
initial population
*Number of
companies
insolvent in
2008 -2012
26,860
-
1,907
16,158
40%
1,315
4,327
84%
266
*No new companies have been included so specified numbers refer only to companies active at the end of 2007 which
became insolvent in the following five years.
The statistical description of the target population variables has been performed in Appendix Table
A1From the reported values of skewness, kurtosis and associated standard errors serious departure
from normality can be noticed for these candidate variables.
4.Existing literature on statistical methods for bankruptcy prediction
The literature in the field of bankruptcy prediction offers a large variety of models in correlation with
the elaboration method: artificially intelligent expert system models, univariate models, multiple
discriminant analysis, linear probability models, logit models, probit models, cumulative sums models,
partial adjustment processes, recursively partitioned decision trees, case-based reasoning models,
neural networks, genetic algorithms, rough sets models(Aziz& Dar, 2006).The most popular statistical
methods in the prediction of corporate bankruptcy are discriminant analysis and logistic
regression(Ben-Ameur et al., 2005).
Altman(1968) employed discriminant analysis to generate a scoring model capable of predicting
bankruptcy for American manufacturing firms. In the construction of the model, Altman used a paired
sample of 66 firms, 33 of which were to declare bankruptcy and 33 were to remain healthy. Using data
from the annual financial reports, the model was able to predict the state of the company within 1 year
with an accuracy of 94% (on the initial sample). Two years prior to the event, the prediction accuracy
of the model was of 72%. On a secondary sample, the model proved an accuracy of 96%, 1 year prior
to the event.
Schumway (2001) proposed a hazard model for estimating the probability of bankruptcy, contesting
the prediction capacity of what he called static models (models based on data from a single period).
Testing the hazard technique, he argues that half of the variables employed by Altman (1968)are not
related to the bankruptcy probability. The data set subjected to the analysis included only nonfinancial publicly-traded companies. By having to meet specific requirements, it was considered that
publicly-traded companies were more homogeneous. Extreme values were eliminated by taking out of
the sample all companies for which a variable registered values over the 99th percentile or below the
first percentile. The function proposed by employing the hazard technique classified 96.6% of the
bankrupt firms above the median probability of bankruptcy, proving from this point of view superior
to functions created through discriminant analysis.
Kahya&Theodossiou(1999) develop a stationary financial distress model for American publicly-traded
companies by employing the statistical methodology of time series cumulative sums. The sample used
to develop the model included 117 healthy firms and 72 bankrupt firms. Their conclusions suggest a
higher stability of the model over time, compared to models developed through linear discriminant
analysis or logit.
Starting from the suggestions of the literature that generic bankruptcy prediction models loose
accuracy when applied to a single industry field, He & Kamath (2006) test the prediction power of the
Ohlson model (1980) and the Schumway model (2001) on a sample of 40 over the counter traded
smallretail firms. First, the 2 models were re-estimated based on a sample of 354 firms that included
the 40 retail firms (177 bankrupt firms and 177 non-bankrupt firms). The results showed significant
accuracy of the 2 models when using financial data 1 year prior to the bankruptcy event (92%
accuracy for Schumway model and 88% accuracy for Olhson model on the 354 firms sample), with an
important decrease in precision as the lead-time from bankruptcy increased.
Ugurlu & Aksoy (2006) compared the the effectiveness of discriminant analysis and logit –based
methodologies in the constructions of functions capable of predicting bankruptcy. The study used a
sample of 54 companies listed at the Istanbul Stock Exchange. Financial data was collected for the
period 1996 – 2003, which included an economic growth period followed by a period of economic
crisis. The model constructed through logistic regression (94.5% accuracy one year prior to
bankruptcy) was found to have more predictive power than the model developed through discriminant
analysis.
Rashid & Abbas (2011) employed discriminant analysis to develop a function capable of predicting
bankruptcy for Pakistan companies. The sample subjected to the study was composed of 26 bankrupt
companies and 26 non-bankrupt companies. The researchers tested 24 financial ratios for their
predictive capacities and retained 3 of them in a Z-score model. The accuracy of the model on the
initial data sample was of 76.9%, 1 year prior to bankruptcy.
Amor et al. (2009) test the Alman (1968) model and the Legault &Veronneau (1986) model on a
sample of 633 Canadian unlisted companies, before developing a specific model through the use of
logistic regression. The sample included companies that demanded for finance in 2005, 2006 or 2007.
The studied phenomenon was the business failure, that was defined as the failure to pay the credit debt
for 3 months in a row. The initial sample was composed by paired failed and non-failed firms. After
the elimination of extreme values, 306 failed firms and 327 non-failed firms were retained. By reestimating the Altman model, the researchers obtained a 78.8% accuracy, 1 year prior to the event,
while the re-estimated Legaultand & Veronneau model insured a 73.4% accuracy. The model
conceived by the authors through logistic regression offered an accuracy of 77.46%, 1 year prior to the
event. The accuracy of the model overlapped the accuracy of the Altman model 2 years prior to the
event (67.27% to 61.1%).
Stroe & Bărbuță–Mișu (2010) adjusted the Conan – Holder model to the specificity of the Romanian
constructions sector. The adjusted function shows a prediction accuracy of 77.78%, using financial
data from 2006 for 10 out of sample companies.
5. Applied methodology and findings
In order to find a relation between available financial indicator in 2007 and the event of
bankruptcy between 2008 and 2012 the method of discriminant analysis (DA) has been chosen. As
the first step all the candidate variables have passed through an evaluation process in order test their
discrimination capacity and to find the most adequate functional form to the bankruptcy probability.
Wilk’s Lambda with F distribution have been used to test how well each variable make a separation
between the two groups. Details of the test can be seen in Appendix Table A2. The variable Roe has
been the only one dropped after testing (not significant at 0.10 level). Variable Fatr (not significant at
0.05 level but significant at 0.10 level) have been kept as a possible candidate. After scatter plot
inspection of the relation between the 20-quantiles (vingitiles) of the discriminat variables and the
bankruptcy rate the variable Ewc have been detected to present a u-shape relation. All the other
variables have been hypothesized to affect bankruptcy rate linearly. R-squared of linear/quadratic have
also been computed (see Appendix Charts A1-A4 ). Quadratic transformation1 of variable Ewc has
been tested to assess the opportunity of expanding DA to nonlinearity. The results show that if
quadratic transformation is applied to Ewc, Wilk’s Lambda is improved.
The method of DA is applied in two distinct stages. In the first stage canonical Linear Discriminant
Analysis (LDA) is used in order to estimate the score function also known as canonical discriminant
function. In the second stage the score from the previous stage is used to make classifications using
predictive LDA and Quadratic Discriminant Analysis (QDA) by mean of the posterior probability in
the Bayesian framework.
The results obtained by using canonical Linear Discriminant Analysis (LDA) also known as Fisher
approach to discriminant analysis are shown in Table 14 below. Traditionally this method finds the
linear combination between variables that maximize the separation between groups. However the
method has been expanded by introducing the square of Ewc to account for u-shape effect of this
variable. The advantage of this method is that it makes no explicit hypothesis on the variables
distribution.
Table 14Expanded Canonical Linear Discriminant Functions
Score Function A
Predictor Variables
Raw
coef.
Fixed assets turnover ratio (Fatr)
Fixed assets ratio (Far)
0.014
2.119
Standard
coef.
Score Function B
Pooled
Within
Groups
Correl.
Raw
Coef.
Pooled
WithinGroups
Correl.
Standard
coef.
0.138
-0.116
-
-
0.546
0.429
1.724
0.444
0.432
Quadratictransformation𝑭(𝑬𝒘𝒄) = 𝟎. 𝟏𝟔𝟏𝑬𝒘𝒄 − 𝟎. 𝟒𝟎𝟔𝑬𝒘𝒄𝟐 has been computed using the unstandardised
coefficients from eq. 1, Table Score B.
1
-0.561
Costumer receivables collection
period (Crcp)
-0.006
-0.385
Inventory conversion ratio (Icr)
-0.002
-0.104
Autonomy ratio (Ar)
1.804
0.492
Equity working capital (Ewc)
0.157
Ewc Squared
-0.406
Profitability ratio(Pr)
-0.128
(Constant)
-1.009
-0.564
-0.006
-0.421
-0.355
-0.003
-0.121
-0.357
0.640
1.750
0.478
0.643
0.115
0.297
0.161
0.118
0.298
-0.402
-0.459
-0.403
-0.461
-0.018
0.295
-
-
-
-
-0.406
-0.677
Wilk’s Lambda
0.950 (p=0.000)
0.950 (p=0.000)
Cannonical Correlation
0.224
0.223
Area Under ROC Curve
0.752 (p=0.000)
0.749 (p=0.000)
From the above table a difficulty can be remarked in explaining the role of Pr and Fatr in
Function Score A. Their coefficients have opposite signs with the correlation coefficients between
them and the score function. With a minor loss in the canonical correlation and the area under the Roc
curve (see also Appendix Chart A5 and Table A3) the Function Score B is retained for further analysis.
Hence, keeping a balance between in-sample accuracy , economic reasoning and parsimony the
following model is considered for further analysis:
𝑆𝑐𝑜𝑟𝑒𝐵 = 𝛼 + 𝛽1 𝐹𝑎𝑟 + 𝛽2 𝐶𝑟𝑐𝑝 + 𝛽3 𝐼𝑐𝑟 + 𝛽4 𝐴𝑟 + 𝛽5 𝐸𝑤𝑐 + 𝛽6 𝐸𝑐𝑤 2
As the correlation coefficients between the discriminating variables and the score function B in Table
14 suggest, the variable contributing the most and in the same direction to the Score B is Ar and the
least influential variable is Icr
The bankruptcy rate corresponding to five intervals of the above score function, each containing equal
number of companies, is shown below.
Table 15Bankruptcy rate on five intervals of Score B
Intervals for Score B
Bankruptcy
Healthy
Bankrupt
Total
I. Score B  -0.83475
83.6%
16.4%
100.0%
II. -0.83474  Score B  -0.21214
94.1%
5.9%
100.0%
III. -0.21213  Score B  0.30866
94.9%
5.1%
100.0%
IV. 0.30867 Score B  0.86723
97.8%
2.2%
100.0%
V. 0.86724  Score B
98.8%
1.2%
100.0%
An optimal cut-off point for the score value can be identified by mean of Youden criterion, which
involves maximizing the difference between sensitivity and the false positive rate (1-specificity). The
value obtained for Score B by applying this criterion is -0.393 with Specificity (SPC) of 69.07% ,
Sensitivity (SNS) of 68.79% and Accuracy Rate (AR) of 69.05%. This optimal value is situated in
interval II , below the central interval. A visual assessment of the separation realized by this cut-off
value can be seen in Appendix Chart A6 .If the central value of 0 is used as cut-off the AR would drop
to 55.81% (SPC=54.27% and SNS=79.32%).
An important statistical property of score function B is that the normality hypothesis hold for the
bankrupt group as it can be seen from the values of skewness and kurtosis in Appendix Table A4.
Hence the normality hypothesis is only partly justified in the following stage
For the purpose of classification and in-sample accuracy testing two approaches to discriminant
analysis have been followed in the Bayesian framework: predictive LDA, also known as Mahalanobis
approach to DA, and predictive QDA which is the extension of the former in the case of unequal
covariance matrices. Both methods make explicit use of the multivariate normal hypothesis regarding
the discriminant variables. One stream of literature, followed by statistical packages like STATA,
computes the posterior probability in both LDA and QDA starting from the original discriminant
variables. Other packages, like SPSS, start from the canonical score function computed in the previous
step and do not use directly the discriminant variables to obtain the posterior probability. The SPSS
approach was followed in this study. The two approaches rely on the same basic assumptions but are
equivalent only in certain conditions. If the covariance matrix is assumed to be the same across groups
LDA is to be applied. QDA relax this assumption and allow the covariance matrices to differ. Because
we use only one canonical discriminant function (Score B) to compute the posterior probability the
usual Box’M of equality between the covariance matrices reduces to the differences between the
variances of score B for the two groups. Even if according to Box’M test (F=0.550, p=0458) and
Levene test (F=710, p=0.399) the null hypothesis of equal variances cannot be rejected an
improvement of the Accuracy rate can be seen if we allow for different variances in QDA. The prior
probabilities are assumed to be 0.5 for each group. The results are presented in the following table.
Table 16In-sample classification results with predictive (Bayesian) DA
Score Function B
Model
Classification
Specificity
Sensitivity(*)
Accuracy Rate
Estimation sample
69.64
67.67
69.5
Expanded LDA
Leave-one-out
classification(**)
69.59
66.54
69.4
Expanded QDA
Estimation sample
70.48
65.79
70.20
(*) Sensitivity is computed considering bankruptcy as the state to be predicted
(**) In leave-one-out classification each observation is classified by the functions derived from all observations
other than that observation and the posterior probability is computed starting from the original discriminant
variables
The Accuracy rate is the same for the two score functions under QDA assumptions and slightly lower
under LDA.
In order to validate the model B on a spatial out-of-sample base, the companies from the target
population have been randomly split in two approximately equal groups: an estimation group (2165
companies) and a validation group (2162 companies). In the table below it can be seen that the score
function 𝐵′ , computed on the estimation sample, has slightly different coefficients from score function
B.
Table 17Expanded Canonical Linear Discriminant Function on 50% of target population
Predictor Variables
Score Function𝐵′
Raw coef.
Fixed assets ratio
Standard
coef.
Pooled WithinGroups Correl.
1.712
0.446
0.431
Costumer receivables collection
period
-0.006
-0.419
-0.549
Inventory conversion ratio
-0.004
-0.173
-0.393
Autonomy ratio
1.729
0.470
0.623
Equity working capital (Ewc)
0.132
0.098
-0.459
Ewc Squared
-0.417
-0.415
-0.459
Constant
-0.643
Wilk’s Lambda
0.944(p=0.000)
Cannonical Correlation
0.236
The Score Function 𝐵′ coefficients have been used to produce posterior probabilities and
classifications for the validation sample. The accuracy indicators are presented in the table below.
Table 18Out-of -sample classification results with predictive (Bayesian) DA
Score Function𝐵′
Model
Expanded LDA
Classification
Specificity Sensitivity
Accuracy
Rate
Estimation sample
69.9
68.8
69.8
Leave one out
classification
69.8
68.1
69.7
Validation sample
69.2
68.0
69.1
Estimation sample
70.3
68.8
70.20
Validation sample
69.5
66.4
69.3
Expanded QDA
6. Conclusions and further research
Statistical analysis showed that the fixed assets ratio, the costumer receivables collection period, the
inventory conversion ratio, the autonomy ratio and the equity working capital can be used in the
prediction of bankruptcy. These ratios can be calculated using the synthetic financial statements that
are publicly available by the Romanian Ministry of Public Finances.
Our findings show that the financial statements from one year prior to the beginning of the economic
crisis in Romania reflect the weaknesses that make the companies susceptible to bankruptcy. We
believe our model to be of practical use, as it is able to accurately discriminate between bankrupt and
non-bankrupt firms over a 5-year period, by employing synthetic publicly available financial data.
However further research is needed. In our opinion several directions should be followed. First of all
the fact that out-of-sample testing have been realized on a spatial basis, not on a temporal one, has
serious practical implications. A more desirable temporal out-of sample testing is difficult to
accomplish due to long forecasting horizon (5 years) and unstable economic conditions, ante and postrecession. In our view the realism of expecting that the same Score function will describe companies
in Timis County after five years of recession and produce similar result is debatable. A more realistic
approach would be to reduce the 5-year forecast horizon thus creating the possibility of testing the
model sooner and at a higher frequency. Improving the model by using information from full financial
statements is another direction that deserves much attention and effort. Not in the last, testing the
accuracy of other statistical methods, including logistic regression (logit) and nonparametric
discriminant methods could bring considerable improvement. A special attention should be given to
kernel based discriminant methods and other nonparametric methods which allow the avoidance of the
normality assumption.
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APPENDIX
Table A1 Statistical description of discriminant variables
(a) Healthy companies group
Healthy
Mean
95%
Confidence
Interval for
Mean
Median
Std.
Deviation
Minimum
Maximum
Fatr
Ewc
(100,000)
Icr
Crcp
Far
Ar
Pr
Roe
9.199
8.885
28.089
26.758
60.235
58.226
0.408
0.400
0.412
0.403
-.0854
-.1074
0.147
0.143
.5883
.5758
9.514
29.420
62.244
0.416
0.420
-.0633
0.151
.6007
4.905
10.222
5.529
43.265
39.549
65.299
0.370
0.260
0.368
0.277
-.0049
.71669
0.098
0.138
.5693
.40447
Skewness
0.015
0.000
0.000
0.012
0.001
45.952 200.335 324.131
1.000
0.999
1.671
1.893
1.583
0.452
0.385
(0.038) (0.038) (0.038) (0.038) (0.038)
-2.50
0.000
0.00
1.72
0.500
2.24
-0.538
0.864
0.48
(0.038) (0.038) (0.038)
Kurtosis
2.169
(0.077)
1.182 -0.415
0.089
(0.077) (0.077) (0.077)
3.057
(0.077)
2.377 -0.843 -0.988
(0.077) (0.077) (0.077)
Note: standard error in ()
(b) Bankrupt companies group
Bankrupt
Fatr
Mean
95%
Confidence
Interval for
Mean
Median
Std.
Deviation
Minimum
Maximum
10.330
9.116
11.543
42.868 95.562
37.186 86.583
48.550 104.542
6.659
10.053
26.822
47.067
Skewness
Kurtosis
Icr
Crcp
78.944
74.381
0.302
0.275
0.328
Ewc
(100,000)
0.245
-.2930
0.220
-.4058
0.270
-.1802
0.108
0.094
0.123
.6293
.5754
.6831
0.239
0.220
0.180
0.206
0.051
0.120
.5816
.44596
Far
Ar
0.137
0.000
0.000
0.034
0.001
45.539 198.646 313.062
0.983
0.967
1.57
1.178
0.837
1.129
1.164
(0.149) (0.149) (0.149) (0.149) (0.149)
1.962
0.694
-0.083
0.654
0.875
(0.297) (0.297) (0.297) (0.297) (0.297)
Note: standard error in ()
-.1635
.93427
Pr
Roe
-2.49
0.000
.00
1.70
0.493
2.15
-0.31
1.161
0.833
(0.149) (0.149) (0.149)
-0.236
0.346
1.174
(0.297) (0.297) (0.297)
Chart A1 Hypotethises linear relation between discriminant variables and bankruptcy rate
a.Autonomy ratio
b.Costumer receivables collection period
c.Fixed assets ratio
d.Inventory conversion ratio
e.Profitability ratio
f.Fixed assets turnover ratio
Table A2 Test of null hypothesis of equal means between Healthy Group and Bankrupt Group
Wilks'
Lambda
Discriminant Variables
F
df1
df2
Sig.
Autonomy ratio
0.9789
93.372
1
4325
.000
Costumer receivables collection period
0.9837
71.761
1
4325
.000
F(Ewc)
0.9884
50.686
1
4325
.000
Fixed assets ratio
Inventory conversion ratio
Equity working capital (Ewc)
Profitability ratio
Fixed assets turnover ratio
Return on equity
0.9904
0.9934
0.9954
0.9954
0.9993
0.9994
42.090
28.805
20.091
19.817
3.059
2.531
1
1
1
1
1
1
4325
4325
4325
4325
4325
4325
.000
.000
.000
.000
.080
.112
Chart A2 U-shape relation between Equity working capital (Ewc) and Bankruptcy Rate
18.0%
16.0%
Bankruptcy Rate
14.0%
12.0%
R² = 0.611
10.0%
8.0%
6.0%
4.0%
2.0%
0.0%
-2.0
-1.0
0.0
1.0
2.0
20-Quantiles of Equity working capital (Ewc)
ChartA3Nonlinear transformation of Equity working capital,𝑭(𝑬𝒘𝒄) = 𝟎. 𝟏𝟔𝟏𝑬𝒘𝒄 − 𝟎. 𝟒𝟎𝟔𝑬𝒘𝒄𝟐
0.5
0
-3
-2
-1
-0.5
F(Ewc)
-1
-1.5
-2
-2.5
-3
-3.5
Ewc
0
1
2
Chart A4Relation (assumed linear) between F(Ewc) and Bankruptcy Rate
18.0%
Bankruptcy Rate
16.0%
14.0%
12.0%
10.0%
R² = 0.7109
8.0%
6.0%
4.0%
2.0%
0.0%
-1.3500 -1.1500 -0.9500 -0.7500 -0.5500 -0.3500 -0.1500 0.0500
20-Quantiles of F(Ewc)
Chart A5 ROC curve of expanded canonical LDA Score functions A and B
TableA3 Test of the Null hypothesis that the truearea under ROC Curve is 0.5
Discriminant Variables
Score A
Score B
Area
under
ROC
curve
.753
.749
Std.
Error
.015
.015
Asymptotic
Sig.
.000
.000
Asymptotic 95%
Confidence
Interval
Lower
Upper
Bound
Bound
.723
.782
.720
.779
Chart A6Histogram of Score B values for the two groups of companies. The optimal cut-off value
(-0.393) is marked by vertical line.
Table A4 Statistical description of Score B
Score B
Mean
95%
Confidence
Interval for
Mean
Median
Std. Deviation
Minimum
Maximum
Skewness
Healthy
0.0585
0.0278
0.0892
Bankrupt
-0.8929
-1.0174
-0.7684
0.1036
0.9979
-3.9377
2.6988
-0.3349
(0.0384)
0.2446
(0.0768)
-0.8991
1.0313
-3.6976
1.7762
-0.0654
(0.1493)
-0.1452
(0.2976)
Kurtosis
Note: standard error in ()