Introduction

The accounting principle of going concern is one of the most important to consider in the preparation of corporate financial statements, as much of the financial information is based on the assumption that the company will maintain its regular development in the future. Current international accounting standards require the auditor to assess the ability of a company to continue. These assessments are useful for forecasting and providing possible explanations for bankruptcy. Therefore, the prediction of audit opinions rated by going concern has been the focus of accounting and financial research in recent years (^{Goo, Chi, and Shen, 2016}; ^{Martens, Bruynseels, Baesens, Willekens, and Vanthienen, 2008}; ^{Yeh, Chi, and Lin, 2014}). Existing research has developed predictive models for different industries. For example, Kuruppu, Laswad, and Oyelere (2012) for industrial companies; ^{Myers, Schmidt, and Wilkins (2014)} for the financial industry; and Chen, Chi, and Wang (2015) for the biotechnology industry. However, no specific model has been created to reflect the special characteristics of the football industry. Having a model adapted to the characteristics of football clubs would help the different interest groups to evaluate the expectations of continuity of the clubs, and in particular the auditors, who, for example, and at European level, must comply with the requirements of the new legal framework of Fair Play Financial (FFP) on the issuance of a going concern opinion of football clubs (^{UEFA, 2015}). This paper attempts to fill this gap in the research by developing a specific model for predicting going concern rated audit opinions for football clubs. This work can therefore be seen as a first attempt to formulate global hypotheses on the continuity of clubs in the international arena and subsequently confirm the predictive power of the model developed for clubs in a particular region or country.

In 1999, the Union of European Football Associations (UEFA) decided to initiate a system of club licensing for the participation of clubs in European competitions (UEFA, 2008). According to the UEFA, the initial purpose was to explore the possibility of creating a salary cap, but it was soon decided that this could not be done without first creating a legal framework. The rules of the licensing system are established by the UEFA, and the licensing is supervised by the different national federations with the aim of bringing the members of these federations closer to their clubs. Initially, the licensing system laid down rules relating to sports development, infrastructure, personnel and administration, and legal and financial issues. The financial requirements focused on the provision of audited financial statements and on the fact that clubs should not have debts with other clubs or players. These requirements were applied from the 2004/05 season onwards and were extended in the 2008/09 season to include late payments to the tax authorities and the booking of budget forecasts. This whole process culminated in 2009 with the introduction of the FFP. One of the main indicators set out in the FFP regulation is the opinion of the auditor regarding the continuity of the activity of the club. The going concern indicator requires that the report of the auditor, concerning the annual financial statements presented in accordance with articles 47 and 48 (relating to the annual accounts), must express or qualify an opinion with respect to going concern. In the event of receiving a going concern opinion under article 52 (future financial information), the licensee must prepare and submit interim financial information to demonstrate to the supervisor its ability to continue until the end of the license season. The going concern opinion therefore becomes an essential part of a football club, enabling it to participate in both European and national competitions (^{UEFA, 2015, Article 45.2, item “e”}).

This study aims to shed some light on the research of going concern opinion prediction in the football industry. To this end, it develops a new model that is exclusive to the industry. In the construction of this new model, financial and non-financial information for the 2005-2016 period has been used for a sample of 40 Spanish professional football clubs, which has provided a total of 140 observations/year, half of them going concern clubs and the other half without this rating. Different methodologies (logistic regression, multiple multi-discriminant analysis, artificial neural networks, and decision trees) have been applied to the data in this sample and have been successfully used in the previous literature on prediction of going concern (^{Inoue and Kilian, 2005}; ^{Martens et al., 2008}; ^{Yeh et al., 2014}). The results obtained have made it possible to know the factors that are the best predictors of continuity in the football industry, with accuracy rates higher than 90%. These results are important for the various stakeholders in the industry, such as auditors, investors, club managers, and governing bodies, whom it would help to improve the financial control of clubs.

The rest of the study is organized as follows: Section 2 presents a review of the literature on going concern audit opinion prediction. Section 3 provides a summary of the scope and objectives of the FFP regulation. Section 4 presents the methods used. Section 5 details the data and variables used in the research; and section 6 analyses the results obtained. Finally, the conclusions of the study and their implications are presented.

Methodology

As stated above, in order to resolve the research question, different methods in the construction of the going concern audit opinion prediction model of the football industry were used. The use of different methods aims to achieve a robust model, which is contrasted not only through a classification technique, but by applying all those that have shown success in previous literature. Specifically, logistic regression, multiple discriminant analysis, artificial neural networks, and decision trees have been used. A synthesis of the methodological aspects of each of these classification techniques appears below.

Logistical Regression

The logistic regression model (Logit) is a non-linear classification model, although it contains a linear combination of parameters and observations of explanatory variables (^{Hair et al., 1999}). The logistic function is delimited between 0 and 1, thus providing the probability that an element is in one of the two established groups. Parting from a dichotomous event, the Logit model predicts the probability that the event will or will not occur. If the probability estimate is greater than 0.5, then the prediction is that it does belong to that group, otherwise it would assume that it belongs to the other group considered. To estimate the model, it is necessary to start from the quotient between the probability that an event occurs and the probability that it does not occur. The probability that an event occurs will be determined by expression (1).

where β₀ is the constant term of the model, and β₁,…,β_k are the coefficients of the variables.

Multiple discriminant analysis

Multiple discriminant analysis (MDA) is a statistical technique that allows both the analysis of whether there are differences between the groups with respect to the variables considered, and the sense in which these differences occur. It also allows the elaboration of a systematic classification model of unknown individuals in any of the groups analyzed (^{Fisher, 1936}). It involves identifying the linear combination of two or more independent variables that best discriminate between the groups defined a priori. The weighting of each variable will be carried out in such a way that it maximizes the variance between-groups as opposed to the variance within-groups. The equation of the discriminant function will be determined by expression (2).

where Z_jk is the discriminant score Z for the discriminant function j for object k; a is the constant; W _i represents the discriminant weighting for the independent variable i; and X _ik is the independent variable i for object k.

The procedure used to estimate the different weights (W _i ) is that of Ordinary Least Squares, with the objective of estimating the values of the parameters that allow making more accurate predictions, thus minimizing the error term. ^{Hair et al. (1999)} establish that MDA is the appropriate statistical technique to contrast the hypothesis that the means of the groups of a set of independent variables, for two or more groups, are equal. To do this, MDA multiplies each independent variable by its corresponding weighting and adds these products together. The result is a single composite discriminant Z score for each individual in the analysis. By averaging the discriminant scores for all individuals within a particular group, the group mean is obtained. This group mean is known as centroid. When the analysis encompasses two groups, there are two centroids; with three groups, there are three centroids, and so on. The centroids indicate the most common situation of any individual in a given group, and a comparison of the centroids of the groups shows the sections in which the groups are found along the dimension being contrasted.

Multilayer perceptron

The Multilayer Perceptron (MLP) is a forward-feeding, supervised artificial neural network model that consists of a layer of input units (sensors), another output layer, and a number of intermediate layers, called hidden layers as long as they have no connections to the outside. Each input sensor is connected to the units of the second layer, these in turn to those of the third layer, and so on (Figure 1). The objective of the network is to establish a correspondence between a set of input data and a set of desired outputs.

Source: own elaboration.

Figure 1 MLP architecture  

Nuñez de Castro and Von Zuben (2001) confirmed that learning in MLP was a special case of functional approach, where there is no assumption about the model underlying the analyzed data. This process involves finding a function that correctly represents the learning patterns, as well as carrying out a generalization process that allows for efficient treatment of individuals not analyzed during such learning (Flórez and Fernández, 2008). In order to do so, W weights are adjusted from the information coming from the sample set, considering that both the architecture and the network connections are known. The objective is to obtain those weights that minimize the learning error. Given a set of pairs of learning patterns {(x1, y1), (x2, y2)… (xp, yp)} and an error function ε (W, X, Y), the training process involves the search for the set of weights that minimizes the learning error E(W) (Shang and Benjamin, 1996), as is expressed in (3).

Most analytical models used to minimize the error function employ methods that require the evaluation of the local gradient of the E(W) function; but techniques based on second order derivatives may also be considered (Flórez and Fernández, 2008). Furthermore, and in order for the MLP to be able to report on the importance of each variable in the results of the model built, it is possible to perform a sensitivity analysis (^{Yang, Shen, Ong, and Xiao-Ping Li, 2008}). This analysis consists of taking 100% of the data and dividing them into groups, each group of data is then processed in the network built as many times as there are model variables. Each time, the value of one of the variables is modified by giving it a zero value. The answers of the network are evaluated in relation to the objective values or already known values of classification through the expression (4).

where Φx_ij (0) is the value of the network output when the variable X_ij has a value of zero; Φx_ij is the classification value already known; X_i is the variable with an importance to be established; and S_xi is the sensitivity value of the variable.

Decision Trees

A Decision Tree (DT) is a graphical and analytical way to carry out the classification of data through different possible paths (^{Kingsford and Salzberg, 2008}). Each of the tree nodes represents the different attributes of the data, the tree branches represent the possible paths to follow to predict the class of a new example, and the terminal nodes or leaves establish the class to which the test example belongs if followed by the branch in question. The DT description language corresponds to the formulas in the DNF (Disjunctive Normal Form). Thus, and in the case of having 3 attributes (A, B, and C), each of them with two values, xi and ¬xi, where i = 1, 2, 3; 2n, combinations can be built in CNF (Conjunctive Normal Form). Each of the combinations in CNF describes a part of the tree, so there would be disjunctives for the tree of the form expressed in (5).

These difficulties are descriptors of the built tree, so 22n possible descriptions could be formed in DNF. Since the order of DT is very large, it is not possible to explore all the descriptors to see which is the most suitable, therefore, heuristic search techniques are used to find an easy and quick way to do it. Most DT construction algorithms are based on the Hill Climbing strategy. This is a technique used in Artificial Intelligence to find the maxima or minima of a function through a local search. It is an algorithm that starts with an empty tree, then it is segmented into sets of examples, choosing in each case the attribute that best discriminates between classes, until the tree is completed. A heuristic function is used in order to know which attribute is the best; this choice is irrevocable, as such it must be ensured that it is the closest to the optimal one.

Results

For the analysis of the results obtained in this work, a descriptive study of the variables used is presented first. Subsequently, the development of the prediction model applying the proposed methods is shown.

Descriptive Analysis

The main descriptive statistics of the variables that comprise the sample appear in Table 3. Football clubs with a going concern opinion (GCO = 1), when compared to those without (GCO = 0), are characterized by a higher average liquidity value (LQR), a higher ratio of sales to total assets (ATR), and a higher level of indebtedness (LVR). On the other hand, all other variables have lower average values. In addition, there is also a moderate dispersion in the distribution of the variables analyzed, which can be extended to the entire sample. Table 4 shows the correlation between the variables. According to the results obtained, it can be deduced that the independent variables present a high correlation with respect to the dependent variable (GCO), with some exceptions. This allows inferring that, in principle, the set of variables selected may be appropriate for the development of the desired model.

Classification Results

Table 5 presents the classification results obtained with the different methods proposed. It is observed that the explanatory variables that have been significant coincide in the selection made by the majority of methods. Also, the highest degrees of precision are obtained with MLP and DT (around 90%), while with Logit and MDA the precision is lower (around 80%). These results are consistent with the conclusions of Jones, Johnstone, and Wilson (2017), who in their study on a comparative analysis between classification methods applied to the prediction of financial difficulties conclude that computational methods are more precise, although statistical techniques still offer reliable results.

Figure 2 shows the classification results of each method in the computational algorithm used. This algorithm starts with the set of selected independent variables and performs 100 iterations; taking at random, for each iteration, 80% of the data for training and 20% for testing. Once the 100 iterations have been carried out, the definitive classification percentages are obtained using the mean of the successes on the test data set.

Source: own elaboration.

Figure 2 Classification results in 100 iterations 

As indicated above, the results obtained show a set of significant variables that are repeated in almost all methodologies used (Figure 3). One of these variables is the size of the provincial market where the club is located (MSP), which has been significant in all four methods. The larger size of the market is related to a higher level of sales and attendance to the stadium, and is closely linked to the economic profitability of the club (^{Barajas and Rodríguez, 2010}; ^{Scelles, Szymansk, and Dermit-Richard, 2016}). For its part, the sports performance (PER) variable has been a recurrent ratio in three methods, reflecting the importance of the evolution of the sports scores of the club, closely related to a greater ability to generate income from sporting successes from the managing bodies of competitions, and income from other concepts such as television rights (^{Barajas and Rodriguez, 2010}; ^{Buraimo, Paraimo, and Campos, 2010}). Finally, the return on assets (ROA) variable has also been significant in three of the four methods used. ROA is a variable of great importance for business financial viability, as contrasted in numerous previous studies on insolvency prediction (e.g. ^{Atiya, 2001}; ^{Callejón, Casado, Fernández, and Peláez, 2013}; ^{Hu and Tseng, 2005}; ^{Lin and Piesse, 2004}). Therefore, clubs that show a small market size (MSP), a low sports performance ratio (PER), and a low return on assets (ROA) are more likely to receive a going concern opinion.

Source: own elaboration.

Figure 3 Selected variables 

These results for the football industry are different from those obtained for other sectors such as industry or finance. First, due to the variables of the football industry that have been significant in the model developed and that, logically, do not appear in the previous works on other sectors. Such is the case of the sport performance ratio and the size of the market. Second, only one variable has proved to be common with general models, this being return on assets (ROA). This profitability variable is practically significant in all previous models (^{Anandarajan and Anandarajan, 1999}; ^{Hung and Shih, 2009}; ^{Yeh et al., 2014}). Third, it has also been observed that certain variables that have been significant in previous generic works are not significant for the football industry. For example, indebtedness, corporate governance, auditor type, and intellectual capital, which have been prominent predictors of going concern for the manufacturing, commercial, and service sectors (^{Abbott, 2000}; ^{Anandarajan and Anandarajan, 1999}; ^{Beasley, 1996}; ^{Martens et al., 2008}; ^{Wang and Deng, 2006}; ^{Yeh et al., 2014}). Therefore, the significant variables in the going concern prediction model for the football industry form a unique and distinct set from that which has been appropriate for other sectors.

Finally, the results obtained in this study also demonstrate that MLP has been the method with the highest level of precision, significantly improving the results obtained in the previous literature on going concern opinion prediction in other industries (Belovary, Giacomino, and Akers, 2007; ^{Sánchez-Medina et al., 2017}; ^{Yeh et al., 2014}).

Conclusions

The principle of going concern is one of the most important in the preparation of financial statements. Due to this, it has been the focus of financial research for decades, which has developed models to assess the continuity of industrial and financial companies. However, no model has been developed exclusively for the football industry. The activity of football clubs is unique in many ways and, therefore, it seems important that auditors, as well as other stakeholders such as investors and managers, have specially designed tools for the management of these. In order to fill this gap in the literature, this study attempts to shed light on going concern prediction by developing an exclusive model for the football industry. This new model can constitute an empirical control instrument on the indicator referred to in the regulation of the FFP, and it can also improve the recommendations to clubs that present audit reports with going concern.

The model developed in this work has shown that profitability, sport performance, and the size market of the club are the best predictors of the continuity of football clubs. Moreover, with MLP methodology, it is possible to obtain high rates of accuracy in the prediction of audit opinions qualified by going concern (above 95%).

The importance of the football industry in countries such as Spain, where the industry represents a relevant pillar in the social-economic dynamism, suggests a greater involvement of research tasks. Addressing this gap from a scientific point of view, trying to improve the body of evidence that allows better prediction and analysis of clubs, leads to a milestone in research from which future lines of research can derive. Thus, it would be interesting to contrast the results of the present work against models developed with samples of clubs belonging to other regions of the world, for example, the South American Football Confederation (CONMEBOL for its acronym in Spanish) and the Confederation of North, Central America, and the Caribbean Football (CONCACAF), which would allow to know the moderating effect of other cultural and legislative environments on the viability of clubs. It would also be interesting to test the predictive capacity of this model to predict the audit opinion on going concern in other sports industries, since it considers performance characteristics of the football industry and these could be extrapolated to clubs of different disciplines.