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Towards Valuation Multidimensional Business Failure Risk for the Companies Listed on the Bucharest Stock Exchange

  • Ştefan Cristian Gherghina
  • Georgeta Vintilă
Conference paper
Part of the Eurasian Studies in Business and Economics book series (EBES, volume 3/2)

Abstract

Current research aims at developing a comprehensive financial instrument towards valuation business failure risk for a sample of 69 companies listed on the Bucharest Stock Exchange in 2013. There were considered several financial ratios such as liquidity ratios (e.g., current ratio, quick ratio, cash ratio), indebtedness ratios (e.g., general indebtedness ratio, financial stability ratio, global financial autonomy ratio, financial independence ratio, borrowing capacity ratio, long-term financial autonomy, leverage ratio, debt service coverage ratio), as well as solvency ratios (e.g., global solvency ratio and patrimonial solvency ratio). By taking into consideration the large number of selected ratios, we employed the principal component analysis as multidimensional analysis technique which ensures the non-redundant decomposition of the total variability out of the initial causal space through a lower number of components. Thereby, there were retained five principal components (being underlined liquidity, financial autonomy, financial independence, debt service coverage ratio, and solvency) which cumulate 90.5895 % of the initial information. Subsequently, based on the selected principal components we reported the aggregate business failure risk indicator.

Keywords

Business failure risk Principal component analysis Correlation matrix Eigenvectors Eigenvalues 

1 Introduction

The financial stability of a company within a highly competitive business environment is influenced by its financial solvency at the inception, its ability, relative flexibility, and efficiency towards cash creating from its continuous operations, its access to capital markets, as well as its financial ability and standing strength when faced with unplanned cash short-falls. In fact, business failure happens when the companies record serious losses, withal the corporations becoming insolvent with liabilities, therefore generating great loss to stockholders, managers, investors, and employees (Li and Sun 2011). Therefore, we notice the inability of the corporations to pay their obligations due to inadequate working capital (Zeytinoglu and Akarim 2013).

Beaver (1966) employed a univariate research to each of the 30 different ratios by selecting a sample of 79 failed companies, as well as 79 nonfailed companies operating in 38 different industries. There was found that net income to total debt had the highest predictive ability (92 % accuracy 1 year prior to failure), followed by net income to sales (91 %) and net income to net worth, cash flow to total debt, and cash flow to total assets (each with 90 % accuracy). The first researcher who used discriminant analysis to predict the failure of firms from different industries is Altman (1968), the accuracy of the employed model towards predicting bankruptcy being estimated at 95 % 1 year prior to bankruptcy and 72 % 2 years prior to bankruptcy. Deakin (1972) showed that the model employed by Altman (1968) is better than the model applied by Beaver (1966) on the short term (1 year), whereas the model of Beaver (1966) is better on the long term (5 years), as regards the error classification rates. By considering the fact that the usefulness of accounting information is a function of the predictive ability of the information and the ability of users to interpret the data, Libby (1975) found a narrow set of financial ratios which allowed a high degree of accuracy in prediction.

Therefore, a variety of statistical techniques (such as linear discriminant analysis, LDA; multivariate discriminant analysis, MDA; quadratic discriminant analysis, QDA; multiple regression; logistic regression, logit; probit; factor analysis, FA), neural networks topologies (such as network architectures including multi-layer perception, MLP; radial basis function network, RBFN; probabilistic neural network, PNN; auto-associative neural network, AANN; self-organizing map, SOM; learning vector quantization, LVQ; cascade-correlation neural network, Cascor), as well as other intelligent techniques (such as vector machines, fuzzy logic, isotonic separation) have been applied to solve bankruptcy prediction problem (Kumar and Ravi 2007). Moreover, Tsai (2009) compared five well-known feature selection methods used in bankruptcy prediction and showed that the t-test feature selection method outperforms the correlation matrix, the stepwise regression, the principal component analysis (hereinafter ‘PCA’), and factor analysis (FA).

Current research aims at developing a comprehensive financial instrument towards valuation business failure risk for a sample of companies listed on the Bucharest Stock Exchange (BSE) by employing the PCA for an extensive set of financial ratios. According to McGurr and DeVaney (1998), financial ratios and cash flow information are chief variables as regards business failure prediction. However, gathering as much financial ratios as possible as predictors in order to make a prediction is a fundamental step in the area. The novelty of current chapter is emphasized by the financial instrument which will be developed with the purpose of valuation business failure risk related to the companies listed in Romania, being considered an extensive set of financial ratios. The utility of this study is underlined by the information provided to managers in order to set the financial policies, respectively to the investors worldwide for investment decision making.

The rest of the chapter is organized as follows. The next section provides a literature review on using PCA within financial research. Section 3 provides the research design and methodology in terms of data, variables, and statistical procedure used for the study. Empirical results of the investigation are given and discussed in Sect. 4. Some general conclusions are drawn in the last section.

2 Literature Review

PCA was developed by Pearson (1901), being an analogue of the principal axes theorem in mechanics and registering a noteworthy usefulness as regards exploratory data analysis and developing prediction models. Furthermore, the method was later independently developed by Hotelling (1933, 1936). Depending on the field of application, PCA it is also named the discrete Karhunen–Loève transform (KLT), the Hotelling transform, or proper orthogonal decomposition (POD). Canbas et al. (2005) proposed a methodological framework towards creating an integrated early warning system (hereinafter ‘IEWS’) which could be used for detection of banks which are facing serious problems, by selecting 40 privately owned Turkish commercial banks (21 banks failed during the period 1997–2003), being combined three parametric models (discriminant, logit, and probit) with another parametric approach, namely PCA. Therefore, PCA was employed in order to investigate the basic financial characteristics of the banks, whereas discriminant, logit, and probit models were estimated based on these characteristics to construct the IEWS. Bataille et al. (2007) applied PCA in order to extract the cyclical factors from companies’ data possibly used in the construction of the scores by the Bank de France and from these scores themselves. By employing PCA within the Turkish banking sector, Boyacioglu et al. (2009) selected 20 financial ratios with six feature groups covering capital adequacy, asset quality, management quality, earnings, liquidity, and sensitivity to market risk and retained only seven factors which explain 80.384 % of the total variance. Hu and Ansell (2009) applied sequential minimal optimization (SMO) to develop default prediction model in the US retail market. There were considered 67 potential performance variables, covering both internal and external company measures, at long last based on PCA five key principal components being retained for each of the final models. Li and Sun (2011) developed a hybrid method for business failure prediction by integrating PCA with multivariate discriminant analysis and logistic regression. There was emphasized a dominating predictive performance in short-term as regards business failure prediction of Chinese listed companies.

3 Research Design and Methodology

3.1 The Sample and Variable Selection

Initially, the dataset comprised all the companies from the exchange segment ‘BSE’, respectively 104 companies, over the year 2013. Afterwards, there were removed 20 companies from the tier ‘Unlisted’, one company from the tier ‘Int’l’, one company from the tier ‘Other Int’l’, 11 companies from financial intermediation sector (three banks, five financial investment companies, and three financial investment service companies), as well as two companies without financial data on the website related to the BSE. The industry membership of selected sample is varied as follows: wholesale/retail (4), construction (8), pharmaceuticals (4), manufacturing (20), plastics (3), machinery and equipment (8), metallurgy (3), food (2), chemicals (3), basic resources (5), transportation and storage (2), tourism (3), and utilities (4). The source of our data is depicted by the Annual financial information (key financials) which was reported on the BSE website for each company.

Table 1 reveals the description of all the variables employed within empirical research.
Table 1

The description of all the variables employed within empirical research

Variable

Definition

Liquidity ratios

CR (v1)

Current ratio = Current assets / (Bank loans [amounts payable in a period below 1 year] + Trade suppliers [amounts payable in a period below 1 year])

QR (v2)

Quick ratio = (Current assets − Inventories) / (Bank loans [amounts payable in a period below 1 year] + Trade suppliers [amounts payable in a period below 1 year])

CR (v3)

Cash ratio = (Current assets − Inventories − Receivables) / (Bank loans [amounts payable in a period below 1 year] + Trade suppliers [amounts payable in a period below 1 year])

Indebtedness ratios

GIR (v4)

General indebtedness ratio = Total liabilities / Total assets = (Bank loans [amounts payable in a period below 1 year] + Trade suppliers [amounts payable in a period below 1 year] + Bank loans [amounts payable in a period above 1 year] + Deferred income) / (Non-current assets + Current assets + Prepayments)

FSR (v5)

Financial stability ratio = Liabilities (amounts payable in a period above 1 year) / Invested capital = Bank loans (amounts payable in a period above 1 year) / (Bank loans [amounts payable in a period above 1 year] + Shareholders’ equity)

GFAR (v6)

Global financial autonomy ratio = Total liabilities / Shareholders’ equity = (Bank loans [amounts payable in a period below 1 year] + Trade suppliers [amounts payable in a period below 1 year] + Bank loans [amounts payable in a period above 1 year] + Deferred income) / Shareholders’ equity

FIR (v7)

Financial independence ratio = Shareholders’ equity / (Bank loans [amounts payable in a period above 1 year] + Shareholders’ equity)

BCR (v8)

Borrowing capacity ratio = Shareholders’ equity / Bank loans (amounts payable in a period above 1 year)

LTFAR (v9)

Long-term financial autonomy = Liabilities (amounts payable in a period above 1 year) / Shareholders’ equity = Bank loans (amounts payable in a period above 1 year) / Shareholders’ equity

LR (v10)

Leverage ratio = Total assets / Shareholders’ equity = (Non-current assets + Current assets + Prepayments) / Shareholders’ equity

DSCR1 (v11)

Debt service coverage ratio1 = Gross profit or loss / Interest expense

DSCR2 (v12)

Debt service coverage ratio2 = Financial year net profit or loss / Interest expense

Solvency ratios

GSR (v13)

Global solvency ratio = Total assets / Total liabilities = (Non-current assets + Current assets + Prepayments) / (Bank loans [amounts payable in a period below 1 year] + Trade suppliers [amounts payable in a period below 1 year] + Bank loans [amounts payable in a period above 1 year] + Deferred income)

PSR (v14)

Patrimonial solvency ratio = Shareholders’ equity / Total assets = Shareholders’ equity / (Non-current assets + Current assets + Prepayments)

3.2 Statistical Procedure

PCA depicts a multidimensional data analysis technique which ensures the decomposition expressed through a lower number of components (Han and Kamber 2006), as well as non-redundant of the total variability out of the initial causal space (Jolliffe 2002). The principal components are orthogonal vectors which capture as far as from the variance corresponding to the original vector variables as follows: the first principal component contains the maximum variance from the original variables’ variance, whereas the second principal component is calculated to have the second most variance, being uncorrelated (in a linear sense) with the first principal component, and so on (Hand et al. 2001; Han and Kamber 2006; Hastie et al. 2009). The initial causal space is determined by the 14 variables as regards liquidity (e.g., current ratio, quick ratio, cash ratio), indebtedness (e.g., general indebtedness ratio, financial stability ratio, global financial autonomy ratio, financial independence ratio, borrowing capacity ratio, long-term financial autonomy, leverage ratio, debt service coverage ratio), and solvency (e.g., global solvency ratio and patrimonial solvency ratio), respectively v1, v2, …, v13, v14. Therefore, each of the 69 companies listed on the BSE in 2013, selected in order to develop current empirical investigation, is distinguished through 14 variables (Witten and Frank 2005).

The principal components related to the researched causal space are described by a vector with 14 dimensions, noted with w:
$$ \mathrm{w}=\left(\begin{array}{c}\hfill {\mathrm{w}}_1\hfill \\ {}\hfill {\mathrm{w}}_2\hfill \\ {}\hfill \dots \hfill \\ {}\hfill {\mathrm{w}}_{13}\hfill \\ {}\hfill {\mathrm{w}}_{14}\hfill \end{array}\right) $$
(1)
Hence, each coordinate \( {\mathrm{w}}_{\mathrm{i}} \) of the aforementioned vector is a principal component defined in relation with the original variables through the following linear combination:
$$ {\mathrm{w}}_{\mathrm{i}}={\upalpha}_1^{\left(\mathrm{i}\right)}*{\mathrm{v}}_1+{\upalpha}_2^{\left(\mathrm{i}\right)}*{\mathrm{v}}_2+\dots +{\upalpha}_{13}^{\left(\mathrm{i}\right)}*{\mathrm{v}}_{13}+{\upalpha}_{14}^{\left(\mathrm{i}\right)}*{\mathrm{v}}_{14} \mathrm{i} = 1,\ 2, \dots,\ 13,\ 14 $$
(2)
The coefficients \( {\upalpha}_{\mathrm{j}}^{\left(\mathrm{i}\right)} \) are the coordinates of the eigenvectors corresponding to the covariance matrix related to the original variables v1, v2, …, v13, v14, whereas the variances of the principal components are the eigenvalues of the covariance matrix. Furthermore, the aim is to solve the following extreme problem and the optimal criteria could be maximum or minimum depending on the nature of the function ϕ:
$$ \left\{\begin{array}{c}\hfill \mathrm{opt} \upphi \left(\mathrm{v},\ \mathrm{w}\right)\hfill \\ {}\hfill \mathrm{w}={\mathrm{A}}^{\mathrm{t}}*\mathrm{v}\hfill \end{array}\right. $$
(3)
We will consider the fact that the vectors \( {\upalpha}^{\left(\mathrm{i}\right)} \) are the columns of the matrix A of dimension 14 × 14 having the following form:
$$ \mathrm{A}=\left(\begin{array}{ccccc}\hfill {\upalpha}_1^{(1)}\hfill & \hfill {\upalpha}_1^{(2)}\hfill & \hfill \dots \hfill & \hfill {\upalpha}_1^{(13)}\hfill & \hfill {\upalpha}_1^{(14)}\hfill \\ {}\hfill {\upalpha}_2^{(1)}\hfill & \hfill {\upalpha}_2^{(2)}\hfill & \hfill \dots \hfill & \hfill {\upalpha}_2^{(13)}\hfill & \hfill {\upalpha}_2^{(14)}\hfill \\ {}\hfill \dots \hfill & \hfill \dots \hfill & \hfill \dots \hfill & \hfill \dots \hfill & \hfill \dots \hfill \\ {}\hfill {\upalpha}_{13}^{(1)}\hfill & \hfill {\upalpha}_{13}^{(2)}\hfill & \hfill \dots \hfill & \hfill {\upalpha}_{13}^{(13)}\hfill & \hfill {\upalpha}_{13}^{(14)}\hfill \\ {}\hfill {\upalpha}_{14}^{(1)}\hfill & \hfill {\upalpha}_{14}^{(2)}\hfill & \hfill \dots \hfill & \hfill {\upalpha}_{14}^{(13)}\hfill & \hfill {\upalpha}_{14}^{(14)}\hfill \end{array}\right) $$
(4)
Likewise, we will suppose the fact that v is the vector whose coordinates are the original variables \( {\mathrm{v}}_1 \), \( {\mathrm{v}}_2 \), …, \( {\mathrm{v}}_{13} \), \( {\mathrm{v}}_{14} \), whilst w is the vector whose coordinates are the principal components \( {\mathrm{w}}_1 \), \( {\mathrm{w}}_2 \), …, \( {\mathrm{w}}_{13} \), \( {\mathrm{w}}_{14} \). Therefore, the linear combinations which define the principal components could be written as below:
$$ \left\{\begin{array}{c}{\mathrm{w}}_1={\propto}_1^{(1)}*{\mathrm{v}}_1+{\propto}_2^{(1)}*{\mathrm{v}}_2+\dots +{\propto}_{13}^{(1)}*{\mathrm{v}}_{13}+{\propto}_{14}^{(1)}*{\mathrm{v}}_{14}\\ {}{\mathrm{w}}_2={\propto}_1^{(2)}*{\mathrm{v}}_1+{\propto}_2^{(2)}*{\mathrm{v}}_2+\dots {+\propto}_{13}^{(2)}*{\mathrm{v}}_{13}+{\propto}_{14}^{(2)}*{\mathrm{v}}_{14}\\ {}\dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \\ {}{\mathrm{w}}_{13}={\propto}_1^{(13)}*{\mathrm{v}}_1+{\propto}_2^{(13)}*{\mathrm{v}}_2+\dots {+\propto}_{13}^{(13)}*{\mathrm{v}}_{13}+{\propto}_{14}^{(13)}*{\mathrm{v}}_{14}\\ {}{\mathrm{w}}_{14}={\propto}_1^{(14)}*{\mathrm{v}}_1+{\propto}_2^{(14)}*{\mathrm{v}}_2+\dots {+\propto}_{13}^{(14)}*{\mathrm{v}}_{13}+{\propto}_{14}^{(14)}*{\mathrm{v}}_{14}\end{array}\right. $$
(5)

4 Empirical Results and Discussion

4.1 Descriptive Statistics

Table 2 shows descriptive statistics as regards all the variables employed within empirical research. By taking into consideration the fact that there are differences as regards the measurement order, as well as measurement units of the selected variables in order to develop the comprehensive financial instrument towards valuation business failure risk on the BSE, we will employ the procedure of data standardization. Thus, data standardization supposes the completion of the following steps: mean-centering (it involves the subtraction of the variable averages from the data), alongside reduction (it involves dividing the variables’ values to their standard deviation, employed to the centered variable).
Table 2

Descriptive statistics

 

N

Mean

Median

Min

Max

Std. dev.

Liquidity ratios

v1

69

5.862

2.717704

0.058

75.49

10.35

v2

69

4.474

1.639651

0.04

74.72

9.77

v3

69

2.428

0.212318

0.003

72.51

9.06

Indebtedness ratios

v4

69

0.297

0.223472

0.005

1.5

0.29

v5

69

0.113

0.012258

−2.512

3.59

0.56

v6

69

0.307

0.208123

−10.927

9.76

2.07

v7

69

0.887

0.987742

−2.594

3.51

0.56

v8

69

8.255

0.308626

−222.434

233.57

43.83

v9

69

0.041

0.004281

−5.037

3.24

0.79

v10

69

1.147

1.376204

−16.282

17.32

3.75

v11

69

2036.403

0.603585

−269.187

93,450.54

12,162.36

v12

69

1633.504

0.364559

−269.187

76,225.61

9831.07

Solvency ratios

v13

69

12.867

4.474824

0.667

207.78

27.79

v14

69

0.475

0.624888

−1.665

0.96

0.51

Notes: The description of the variables is provided in Table 1

Table 3 provides the correlation matrix related to the original variables. We notice that there are high positive and statistically significant correlations between v1 and v2 (0.975), v1 and v3 (0.934), v1 and v13 (0.946), v2 and v3 (0.969), v2 and v13 (0.964), v3 and v13 (0.937), v6 and v9 (0.917), v6 and v10 (0.850). Moreover, the strong correlations between the selected variables mitigates the individual meaning of the variables and emphasizes the presence of informational redundancy. Thereby, PCA is employed with the purpose of reducing the dimensionality of the initial causal space, also considering a minimum loss of information.
Table 3

Correlation matrix

 

v1

v2

v3

v4

v5

v6

v7

v8

v9

v10

v11

v12

v13

v14

v1

1

             

v2

0.975**

(0.000)

1

            

v3

0.934**

(0.000)

0.969**

(0.000)

1

           

v4

−0.370**

(0.002)

−0.322**

(0.007)

0.231

(0.056)

1

          

v5

0.036

(0.770)

0.047

(0.699)

0.040

(0.742)

0.191

(0.115)

1

         

v6

0.049

(0.689)

0.041

(0.736)

0.034

(0.780)

0.080

(0.516)

0.039

(0.752)

1

        

v7

0.036

(0.770)

0.047

(0.699)

0.040

(0.742)

0.191

(0.115)

−1.000**

(0.000)

0.039

(0.752)

1

       

v8

0.036

(0.768)

0.025

(0.836)

0.031

(0.802)

−0.339**

(0.004)

0.020

(0.871)

0.093

(0.449)

0.020

(0.871)

1

      

v9

0.016

(0.899)

0.011

(0.929)

0.012

(0.923)

0.127

(0.298)

0.177

(0.145)

0.917**

(0.000)

0.177

(0.145)

0.007

(0.956)

1

     

v10

0.024

(0.846)

0.013

(0.913)

0.014

(0.906)

0.031

(0.799)

0.074

(0.544)

0.850**

(0.000)

0.074

(0.544)

0.087

(0.480)

0.718**

(0.000)

1

    

v11

0.137

(0.261)

0.125

(0.305)

0.080

(0.514)

0.134

(0.274)

0.036

(0.768)

0.014

(0.906)

0.036

(0.768)

0.031

(0.799)

0.008

(0.947)

0.023

(0.851)

1

   

v12

0.132

(0.280)

0.120

(0.326)

0.076

(0.536)

0.132

(0.279)

0.036 (0.767)

0.014

(0.908)

0.036

(0.767)

0.031

(0.800)

0.008

(0.948)

0.023

(0.849)

1.000**

(0.000)

1

  

v13

0.946**

(0.000)

0.964**

(0.000)

0.937**

(0.000)

−0.353**

(0.003)

0.077

(0.532)

0.049

(0.687)

0.077

(0.532)

0.029

(0.815)

0.013

(0.915)

0.024

(0.848)

0.097

(0.427)

0.092

(0.451)

1

 

v14

0.291*

(0.015)

0.258*

(0.032)

0.202

(0.096)

−0.730**

(0.000)

0.153

(0.210)

0.146

(0.232)

0.153

(0.210)

0.398**

(0.001)

0.109

(0.373)

0.242*

(0.045)

0.058

(0.638)

0.056

(0.646)

0.295*

(0.014)

1

Notes: **significant at 1 % level; *significant at 5 % level. The description of the variables is provided in Table 1

The bold values are statistically significant

4.2 The Results of Principal Component Analysis

Table 4 shows the eigenvalues of the correlation matrix (Table 3) and related statistics, the principal components being descending ordered according to the retained information, as percentage of the total variance. Likewise, Table 4 provides the percentage out of the initial information related to each of the 14 selected variables which is synthesized within the extracted principal components. Thereby, the first principal component explains 30.25 % of the total variance, the second principal component explains 19.94 % of the total variance, the third principal component explains 15.12 % of the total variance, the fourth principal component explains 13.86 % of the total variance, whereas the fifth principal component explains 11.39 % of the total variance. Besides, the first five principal components cumulate 90.5895 % of the total information.
Table 4

Eigenvalues of the correlation matrix and related statistics

Value number

Eigenvalue

% Total variance

Cumulative Eigenvalue

Cumulative %

1

4.235827

30.25590

4.23583

30.2559

2

2.792183

19.94417

7.02801

50.2001

3

2.116876

15.12054

9.14489

65.3206

4

1.941745

13.86961

11.08663

79.1902

5

1.595901

11.39930

12.68253

90.5895

6

0.649445

4.63890

13.33198

95.2284

7

0.366657

2.61898

13.69864

97.8474

8

0.146135

1.04382

13.84477

98.8912

9

0.053664

0.38331

13.89843

99.2745

10

0.051539

0.36814

13.94997

99.6427

11

0.036598

0.26142

13.98657

99.9041

12

0.013189

0.09421

13.99976

99.9983

13

0.000239

0.00170

14.00000

100.0000

Source: Author’s computations

The bold values are statistically significant

Figure 1 reveals the graph of the eigenvalues of the correlation matrix (Table 3) proposed by Cattell (1966).
Fig. 1

Eigenvalues of correlation matrix

Thus, we notice that after the fifth point out of the above graph, which depicts the fifth principal component, the slope is decreasing. Furthermore, according to Kaiser (1960) criterion, there are retained only the principal components which correspond to the eigenvalues greater than one. Hence, based on the graph revealed in Fig. 1, as well as Kaiser (1960) criterion, we will retain five principal components.

Table 5 provides the factor matrix, its elements being the correlation coefficients between the original variables and principal components.
Table 5

Factor coordinates of the variables, based on correlations

 

F1

F2

F3

F4

F5

v1

−0.954663

−0.119463

−0.175794

−0.040418

0.090462

v2

−0.956570

−0.121383

−0.187470

−0.054548

0.127763

v3

−0.917998

−0.135080

−0.220863

−0.088476

0.175321

v4

0.526955

−0.272281

−0.315411

0.047821

0.552125

v5

0.172186

−0.189849

−0.851779

0.266501

−0.361835

v6

0.002415

0.923415

−0.296022

0.051232

0.147434

v7

−0.172186

0.189849

0.851779

−0.266501

0.361835

v8

−0.075129

0.238316

0.167204

−0.110827

−0.688664

v9

−0.043759

0.898882

−0.108191

−0.009713

0.290320

v10

−0.024082

0.854492

−0.311309

0.094372

0.080239

v11

−0.232195

0.013118

0.269572

0.933027

0.028042

v12

−0.227470

0.013990

0.271030

0.933767

0.027571

v13

−0.950079

−0.113614

−0.153447

−0.091189

0.109282

v14

−0.461809

0.371213

0.240066

−0.101447

−0.611359

The bold values are statistically significant

The strong relationship expressed by the first (−0.954663) and by the second correlation coefficient (−0.956570) out of the first column from Table 5 emphasizes that the first principal component conveys the informational content of the original variables v1 and v2. Likewise, the second principal component expresses the informational content of the original variables v6 and v9, the third principal component expresses the informational content of the original variables v5 and v7, the fourth principal component conveys the informational content of the original variables v11 and v12, whereas the fifth principal component conveys the informational content of the original variables v8 and v14. Therefore, the first principal component (F1) underlines a synthetic indicator of liquidity, the second principal component (F2) is interpreted as an indicator of financial autonomy, the third principal component (F3) is an indicator of financial independence, the fourth principal component (F4) is an indicator of debt service coverage ratio, whereas the fifth principal component (F5) is construed as an indicator of solvency.

Table 6 discloses the coefficients related to the linear combinations which define the principal components representing the eigenvectors of the correlation matrix (Table 3).
Table 6

Eigenvectors of the correlation matrix

V

F1

F2

F3

F4

F5

v1

−0.463853

−0.071493

−0.120825

−0.029005

0.071608

v2

−0.464780

−0.072642

−0.128850

−0.039145

0.101135

v3

−0.446039

−0.080839

−0.151801

−0.063494

0.138781

v4

0.256038

−0.162946

−0.216785

0.034318

0.437053

v5

0.083662

−0.113615

−0.585436

0.191251

−0.286422

v6

0.001174

0.552618

−0.203458

0.036766

0.116706

v7

−0.083662

0.113615

0.585436

−0.191251

0.286422

v8

−0.036504

0.142620

0.114921

−0.079534

−0.545135

v9

−0.021262

0.537936

−0.074361

−0.006970

0.229812

v10

−0.011701

0.511371

−0.213966

0.067724

0.063516

v11

−0.112820

0.007851

0.185279

0.669573

0.022197

v12

−0.110524

0.008372

0.186282

0.670104

0.021825

v13

−0.461626

−0.067992

−0.105466

−0.065440

0.086506

v14

−0.224385

0.222153

0.164999

−0.072802

−0.483942

The score matrix is disclosed in the Appendix 1. Thus, based on the principal components’ coefficients, there were computed the scores related to the observations in the space of the principal components. The coordinates of the objects in the new space, respectively the projections of the objects on the space’ axes, are the valuations of the objects in relation with the new variables, being entitled the scores of the principal components. By taking into consideration the informational content, we will compute the coefficients of importance for each of the five principal components. Thereby, we mark as CI1 the coefficient of importance related to the first factor, as well as var(\( {\mathrm{w}}_1\Big) \) denotes the variance corresponding to the first principal component, CI1 = var(\( {\mathrm{w}}_1\Big) \)/\( \sum_{\mathrm{j}=1}^5\mathrm{v}\mathrm{a}\mathrm{r}\left({\mathrm{w}}_{\mathrm{j}}\right) \), thus ensuing the following values for the coefficients of importance: CI1 = 0.3340; CI2 = 0.2202; CI3 = 0.1669; CI4 = 0.1531; CI5 = 0.1258.

Therefore, the Appendix 2 provides the values of the aggregate business failure risk indicator (hereinafter ‘ABFRI’) for the companies listed on the BSE in 2013. The ABFRI was computed as following: ABFRI = \( \sum_{\mathrm{j}=1}^5{\mathrm{C}}_{\mathrm{i}}\left(\mathrm{j}\right) \)*Fj.

5 Concluding Remarks

By selecting a set of variables which comprised 14 financial ratios as regards liquidity, indebtedness, as well as solvency, related to 69 companies listed on the BSE in 2013, we employed PCA in order to develop a comprehensive financial instrument towards valuation business failure risk. Therefore, five principal components were retained, being underlined liquidity, financial autonomy, financial independence, debt service coverage ratio, alongside solvency, which cumulate 90.5895 % of the initial information. Subsequently, based on the selected principal components we computed the aggregate business failure risk indicator. The limitations of current empirical investigation are depicted by the short period of research. As future research avenues, we propose the development of a neural network model for business failure prediction, alongside employing the traditional statistical techniques, aiming at comparing the registered results.

Notes

Acknowledgement

This work was cofinanced from the European Social Fund through Sectoral Operational Programme Human Resources Development 2007–2013, project number POSDRU/159/1.5/S/134197 “Performance and excellence in doctoral and postdoctoral research in Romanian economics science domain”.

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Ştefan Cristian Gherghina
    • 1
  • Georgeta Vintilă
    • 1
  1. 1.Department of FinanceBucharest University of Economic StudiesBucharestRomania

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