As the core of the effective financial crisis prevention, enterprise finance crisis prediction has been the focal attention of both theorists and businessmen. Financial crisis predictions need to apply a variety of financial and operating indicators for its analysis. Therefore, a new evaluation model based on nonlinear programming is established, the nature of the model is proved, the detailed solution steps of the model are given, and the significance and algorithm of the model are thoroughly discussed in this study. The proposed model can deal with the case of missing data, and has the good isotonic property and profound theoretical background. In the empirical analysis to predict the financial crisis and through the comparison of the analysis of historical data and the real enterprises with financial crisis, we find that the results are in accordance with the real enterprise financial conditions and the proposed model has a good predictive ability.
Transportation, as a basic part of the integrated economic system, plays a pivotal role in the development of every country. China’s transportation industry is now also facing some problems. For example, the financial management level of the transport organization is not high, resulting in the hardships in the operation of the transportation companies [
Meanwhile, the stock market is the “barometer” of the economy. Therefore, the sound and orderly development of the listed transportation companies is important in China’s economy. Transportation, a basic industry in every nation, was badly affected in the world financial crisis of 2008. Therefore, it has become significant to predict the financial crisis of listed Chinese transportation companies. An empirical study in the related field can also contribute to the transportation research worldwide.
In order to effectively prevent the enterprise financial crises, experts, scholars, and practitioners have been very interested in the tools that can predict business failures. Based on the in-depth analysis of the theory and the practice of enterprise financial crisis prediction in the Chinese transportation industry, we establish a new enterprise financial crisis prediction model based on the method of nonlinear programming evaluation and conduct the empirical research.
The literature on the enterprise financial crisis prediction is very rich. Experts and scholars have done a large number of quantitative researches on enterprise financial crisis since the 1930s [
It can be found through the literature study and comprehensive review of the financial crisis prediction methods that we must overcome the shortcomings of the traditional models so as to build a scientific, fast, and effective model for the enterprise financial crisis prediction, the top priority of which is to learn from the strong points of each model and build an accurate and isotonic model.
Nonlinear programming (NLP) is the process of solving an optimization problem defined by a series of equalities and inequalities, collectively termed constraints, over a set of unknown real variables, along with an objective function to be maximized or minimized, where some of the constraints or the objective functions are nonlinear. In the nonlinear programming evaluation model, it is necessary to obtain the unknown variables
In order to clearly describe the two properties, that is, the ordering of the present indicators and the similarities between the evaluation results and value of the indicators, we, firstly, build the following nonlinear programming model:
The comprehensive evaluation model reflects the following significances. The constraints express the consistency of the evaluation results; that is, there is never the contradiction logical structure The first term of the objective function reflects the consistency degree of the comprehensive evaluation results of the model and the order of the initial information. If they are inconsistent, this part will play a role of punishment. The second term of the objective function reflects the gap between the evaluation scores and the indicator values, which ensures the consistency between them. In fact, it can be found that, for any transform of
The discussion of the related properties of the nonlinear programming evaluation model starts with formula (
The solution of the optimal formula (
Any set of the real numbers
If the equation is not limited to specific forms, the solution may not be unique for the general form of formula (
A counterexample shown in Table
Indicator values of a counterexample.
Indicator 1 | Indicator 2 | |
---|---|---|
Enterprise 1 | 2 | 3 |
Enterprise 2 | 3 | 4 |
Take the absolute value
The first summation term in formula (
The absolute value of the nonlinear programming evaluation model (
One case can prove this nature as seen in Table
Nonisotonic indicator value in formula (
Indicator 1 | Indicator 2 | Indicator 3 | |
---|---|---|---|
Enterprise 1 | 1 | 4 | 517 |
Enterprise 2 | 2 | 5 | 3 |
Let all the indicators have the same weight, namely,
Seen from this property, the initial programming model cannot keep the isotonic nature in the absolute values.
Property
For nonlinear programming, formula (
The optimal solution
In formula (
In formula (
In this objective constraint, we can get a weighted average result, which also shows the generality of this model; that is, it includes the evaluation with a weighted average.
Based on the theoretical and comparative analysis above, the nonlinear programming evaluation model has the following three obvious characteristics.
The essence of the grading prediction of enterprise financial crisis is to characterize the nature of the financial crisis with a number of complex and various indicators to grade a group so as to get different scores and thereby delineate different grades. In this study, we learn from the existing literature of the weight determination of financial indicators and introduce the concept of Trailing Twelve Months (TTM) in addition to the traditional typical financial indicators. We use the improved fuzzy analytic hierarchy process (FAHP) to filter out small fluctuations automatically, to reflect the true enterprise financial positions, and to get the objective and normalized results.
As listed companies are the interest focus of the Chinese society, the financial data of the listed companies are comparable, open, and normal. Therefore, it is feasible to select the listed companies as a research object. In this study, the listed companies of A Share in Shanghai and Shenzhen Stock Exchange are selected as the main sources of data. Based on the industry representation and the asset size, 40 valid samples are selected from the latest annual report of 2009 and 2010 from the authoritative security websites like Sohu Security (available at
Based on the definition of financial crisis and the previous researches, this study establishes an objective and rational index system for the financial crisis prediction model. The selected financial indicators are Assets Operation Ability
Index weights based on the improved fuzzy analytic hierarchy process.
Indicator | Weight | Indicator | Weight | Indicator | Weight | Indicator | Weight |
---|---|---|---|---|---|---|---|
|
0.1845 |
|
0.0508 |
|
0.0399 |
|
0.0352 |
|
0.0369 |
|
0.0508 |
|
0.0399 |
|
0.0352 |
|
0.0369 |
|
0.0508 |
|
0.0399 |
|
0.0352 |
|
0.0369 |
|
0.0508 |
|
0.2173 |
|
0.1723 |
|
0.0369 |
|
0.195 |
|
0.0352 |
|
0.0574 |
|
0.0369 |
|
0.0399 |
|
0.0352 |
|
0.0574 |
|
0.2033 |
|
0.0399 |
|
0.0352 |
|
0.0574 |
Process the indicators and get the data normalized.
Determine the indicator weights based on FAHP and calculate them into Model (
Solve Model (
Rank the enterprises, set the criteria scores for the enterprises with financial crisis, and identify the enterprises with potential financial crises.
Based on the implementation steps of the model and the weight values obtained with FAHP, we know that the weight of the
Descriptive statistics of indicators.
Sample | Min. value | Max. value | Average value | Standard deviation | Variance | |
---|---|---|---|---|---|---|
|
37 | 0.008 | 32.414 | 4.73782 | 5.926520 | 35.124 |
|
38 | 0.6586 | 822.6889 | 63.117285 | 155.5260584 | 24188.355 |
|
38 | 0.0016 | 4.8035 | 1.207797 | 1.1022243 | 1.215 |
|
37 | 0.2252 | 50.9921 | 7.179803 | 9.7856580 | 95.759 |
|
38 | 0.0016 | 2.1875 | 0.645392 | 0.5910114 | 0.349 |
|
35 | 0.3402 | 25.6567 | 2.454467 | 4.3723699 | 19.118 |
|
38 | 0.2148 | 25.6567 | 1.779808 | 4.1654628 | 17.351 |
|
36 | 3.8248 | 121.0434 | 57.857497 | 25.2679304 | 638.468 |
|
37 | −84.3018 | 1.0359 | −2.169953 | 13.6857142 | 187.299 |
|
35 | −87.1165 | 45.6127 | 5.827611 | 25.6430196 | 657.564 |
|
37 | −299.1074 | 45.6127 | −0.534708 | 55.3739147 | 3066.270 |
|
37 | −24.047 | 2200.512 | 59.97748 | 356.733666 | 127258.908 |
|
36 | −922.4338 | 1335755.3 | 36074.373 | 219601.4718631 | 48224806444.416 |
|
34 | −165.4261 | 1335755.3 | 38163.717486 | 225783.9996788 | 50978414510.938 |
|
39 | −10962.50 | 3716.6667 | −194.913345 | 1848.5586555 | 3417169.103 |
|
37 | −10962.50 | 3716.6667 | −201.117866 | 1897.6031169 | 3600897.589 |
|
36 | −92.6365 | 778.0531 | 32.868792 | 131.0271981 | 17168.127 |
|
37 | −507.069 | 704.248 | −3.89169 | 192.499040 | 37055.881 |
|
35 | −3172.059 | 710.442 | −61.40170 | 574.683821 | 330261.494 |
|
38 | −48692.973 | 4338.184 | −1161.34318 | 7843.469376 | 61520011.849 |
|
38 | −0.7772 | 5.0484 | 0.643659 | 1.0356570 | 1.073 |
|
39 | −0.29 | 13.75 | 3.4463 | 3.49247 | 12.197 |
|
35 | 0.0000 | 52.5087 | 8.664581 | 12.8255405 | 164.494 |
After normalization of the results, solve the above nonlinear programming problem with formulas (
Score and ranking of 40 enterprises.
Stock code | Evaluation score | Rank | Stock code | Evaluation score | Rank |
---|---|---|---|---|---|
600125 | 0.923 | 1 | 000520 | 0.241 | 21 |
600897 | 0.921 | 2 | 600018 | 0.201 | 22 |
600115 | 0.917 | 3 | 601880 | 0.177 | 23 |
000099 | 0.905 | 4 | 600548 | 0.150 | 24 |
002320 | 0.900 | 5 | 000900 | 0.108 | 25 |
600270 | 0.873 | 6 | 600026 | 0.102 | 26 |
300240 | 0.872 | 7 | 600428 | 0.087 | 27 |
600221 | 0.841 | 8 | 600896 | 0.086 | 28 |
600692 | 0.830 | 9 | 000582 | 0.081 | 29 |
601107 | 0.828 | 10 | 600033 | 0.066 | 30 |
600350 | 0.801 | 11 | 600387 | 0.059 | 31 |
600561 | 0.789 | 12 | 600798 | 0.050 | 32 |
601866 | 0.780 | 13 | 600087 | 0.033 | 33 |
601111 | 0.776 | 14 | 601919 | 0.031 | 34 |
601872 | 0.698 | 15 | 600575 | 0.019 | 35 |
000089 | 0.664 | 16 | 600717 | 0.011 | 36 |
600269 | 0.650 | 17 | 002040 | 0.008 | 37 |
600029 | 0.601 | 18 | 600317 | 0.007 | 38 |
601000 | 0.537 | 19 | 600190 | 0.004 | 39 |
000996 | 0.515 | 20 | 600279 | 0.002 | 40 |
As seen in Table
In this study, a new evaluation model based on the nonlinear programming is established, the properties of the model are proved in details, the specific steps of the solution process are demonstrated, and the significance of the model is discussed. With the good properties of isotonic and the profound theoretical background, the proposed model can deal with the missing data. As shown in the empirical analysis to predict the financial crisis and the comparison of the historical data and the reality of the enterprise financial crisis, the established prediction model of enterprise financial crisis can adapt well to the features of the financial crisis data with a higher predictive accuracy. The method in this study not only provides a new effective model for the prediction of enterprise financial crisis, but also expands the application of nonlinear programming evaluation method. The predication results can inspire the Chinese transportation enterprises and encourage them to find the financial crisis and explore the potential to improve their business. Furthermore, the international transportation enterprises can also make a thorough comparison so as to develop the correspondent competitive strategies.
This research is based on the grading classifications of enterprise financial crisis. The future study can focus on the combinations of the enterprise financial crisis prediction and the information technology and the decision support theory to develop the design and the prototype of the financial crisis prediction support system.
The author declares that there is no conflict of interests regarding the publication of this paper.