Interconnection between Achieved Level of Return on Equity and Evaluation Scale of the Kralicek ́ S Model

A large number of diagnostic and predictive models exists using different or no statistical methodology. Often, diagnostic and predictive models differ in focus on branch of company, size of company, tradability of shares, country of usage, and focus on maturity of the market environment. Many of the models are widely used, however, their explanatory power is not known. Good examples of these models are those used in banks in the process of credit worthiness assessment. Some of them are created based on the Q-Test model. However, not only banks need to check the financial situation of companies but also basic users like suppliers, customers and other business partners. This article deals with Kralicek ́s Q-Test which is one of the well-known financial diagnostic models in Europe including the Czech Republic. Its five grade rating scale reveals little about the level of prosperity of analysed companies. An assumption exists that grade 1 means excellent financial health. However what exactly does it mean? Can it be assumed that this means a negligible to zero probability of bankruptcy and simultaneously a sufficient or a high profitability? The question is what is the level of prosperity connected with the grades achieved on the Q-Test evaluation scale from1to 5. The prosperity of the company is uniquely linked to the return on equity. Another question is whether the QTest is able to express a level of prosperity and not only a level of creditworthiness of companies. That is why the research based on analysis of dataset of 1504 Czech companies was carried out. Following the research a scale was made of achieved return on equity (ROE). ROE levels are expressed by the following: implicit cost of equity (re), riskfree rate (rf), positive ROE, negative ROE and negative equity (or insolvency). The researched found that the Q-Test’s informative value is comparable to the predictive models based on statistic techniques.


Introduction
Financial models can be divided in the category of diagnostic and predictive models. Alternatively they can be classified into category bankruptcy models and prosperity models. The bankruptcy models accuracy is known just during their creation using statistical methods and sample of companies for testing. A review of the literature indicates that probably the first researcher using ratio analysis to compare companies that had failed and companies that had not was P. J. Fitzpatrick (Fitzpatrick, 1931). His model consists of 13 financial ratios to indicate failure using uni-variate analysis for creation. However, prediction power was not significant.
Further progress was when W. Beaver (Beaver, 1966) used Univariate Logistic Regression to creation of model to predict financial distress. His innovation was also in using of ratios associated with cash flows. He worked with 30 financial ratios that he chose as the best indicators of a company's financial distress. These indicators can be divided into six groups: x Ratios related to cash flow, x ratio of liabilities to total assets, x ratio of liquid assets to total assets, x ratio of liquid assets to current liabilities, Institute of Business Economics and Administration University of Pardubice, Pardubice City, Czech Republic 14 ISSN 1849-5664 (online)http://researchleap.com/category/international-journal-of-management-science-and-business-administration ISSN 1849-5419 (print) International Journal of Management Science And Business Administration Vol. 2, No. 5, April 2016, pp. 13-20 x the ratios of turnover, x ratios of net profit. Later, Beaver's model used on to measure the credit risk of bonds issued by companies. Probably the best known bankruptcy models creator is E. I. Altman's with his Z-score (Altman, 1968). This statistical model combines five financial ratios using multivariate discriminant analysis for purpose of forecasting failure in a diverse mix of entities. His pioneer study was based on a sample of 66 publicly traded, manufacturing companies. Altman's model had high predictive power for the initial sample one year before failure with accuracy amounting to 95%.
Type I errors, those that predict a bankruptcy that does not occur, were shown for 6% of the companies analysed. Type II errors also were shown for 6% of the firms analysed. Type II errors predict a solvent firm that files bankruptcy (Altman, 1993). In 1980 Ohlson used log it analysis to develop a model to predict the health of companies (general application) with accuracy of 96% according to author. He worked with data sets obtained from 105 bankrupt companies and 202 non-bankrupt companies (Ohlson, 1980). Historical overview of model's creation is stated in table 1. On the contrary, the prosperity models were created on thebasisof logicalassumptions without empiric research and these models do not have determined accuracy. For example the Grünwald´s index (Grünwald & Holečková, 2007), Doucha´s Balance analysis I., II., III. (Doucha, 1996), Tamari risk index (Tamari, 1966) and Index of creditworthiness (see more Zalai, 2010) are concerned. The Czech index IN99 (Neumaierová 2002), based on which the financially healthy company is the company with positive economic value added, represents the exception.

Kralicek´s Q-test
This test can be classified as a diagnostic model. This one-dimensional grading test was created in the year 1991 by the Austrian economist Peter Kralicek. It is mainly used in the German speaking countries under the name Quick test, Qtest or Kralicek´s Fast Test. This model is different as with the increasing achieved value also the insolvency probability increases too. It uses the point evaluation (from 1 up to 5, like in the school) and is totally unique as in particular evaluated areas of the company economy (level of self-financing, duration of the debt payment, CF in % of revenues, return on assets) it does not distinguish their importance, and thus it does not assign different weights. The resulting grade is the arithmetic average of ratings achieved in particular evaluated areas (( + + + )/4). The company classified with the grade 1 and 2 is considered to be financially healthy, and the one with the grade 4 and 5 is pointed to the bankruptcy. See more in table 2.

Methodology and Results
In order to apply the Q-test on the analysed sample of companies it is necessary to calculate the values , , , stated in the Tab   Comparison of Q-test and ROE classification frequency is stated in Fig. 1. There is possible to observe quite different frequencies.

Figure 1: Classification frequency
Source: Author Figure 2 illustrates in graphic form the differences between Q-test grades a ROE & distress test grades. These differences take interval <-4; 4>. Zero difference means completely correct diagnosis. Higher difference means lower informative value. It is seen that frequencies are normally distributed. In figure 2 and also in table 4 is stated that Q-test grade meets the grade of ROE & distress test absolutely in 39.89%. If we are more benevolent and accept also the variation +/-1 grade (in 5 degrees scale) informative value of Q-test is 77.59%. In this case was stated informative value of Q-test on base of deviation quantification. See more in table 4.  However, this method is not suitable for comparison with other above mentioned models. This is because most of these models have three degrees (intervals) scale (e. g. (Karas&Režnáková, 2014) and (Homolka, Doležal&Novák, 2014)).

Conclusion
Prosperity models should measure financial condition of the companies above all in the area of creditworthiness and profitability. In contrast, bankruptcy models are not entirely different. All of bankruptcy models are predictive with one primary goal. The goal is to estimate, if analysed companies might go bankrupt or not in which case the situation is obvious. However, in case of prosperity models the answer is unclear. For example we might obtain information about a good financial health, however we do not know what exactly it means. It can be assumed that the analysed company will not be profitable while heading for bankruptcy. Often, detailed information on the level of profitability is needed. Unfortunately, there is no information available with most of the existing prosperity models relating to the interpretation of their results and to the accuracy of prosperity prediction.
Precisely this is the case of the Q-Test. It is difficult to establish whether we can ultimately rely on results of the Q-test´s classification (e.g. with the probability of 75%) or, on the contrary, whether the success rate of the model is too low (e.g. 10%). That is why the author aimed to quantify the reliability of the Q-Test. For this purpose author´s own