Multicriteria decision support methodologies for auditing decisions: The case of qualified audit reports in the UK

European Journal of Operational Research 180 (2007) 1317–1330 www.elsevier.com/locate/ejor

O.R. Applications

Multicriteria decision support methodologies for auditing decisions: The case of qualified audit reports in the UK Fotios Pasiouras a

a,b

, Chrysovalantis Gaganis a, Constantin Zopounidis

a,*

Financial Engineering Laboratory, Department of Production Engineering and Management, Technical University of Crete, University Campus, Chania 73100, Greece b Coventry Business School, Coventry University, Priory Street, CV1 5FB Coventry, UK Received 28 January 2005; accepted 6 April 2006 Available online 30 June 2006

Abstract All UK companies are required by company law to prepare financial statements that must comply with law and accounting standards. With the exception of very small companies, financial accounts must then be audited by UK registered auditors who must express an opinion on whether these statements are free from material misstatements, and have been prepared in accordance with legislation and relevant accounting standards (unqualified opinion) or not (qualified opinion). The objective of the present study is to explore the potentials of developing multicriteria decision aid models for reproducing, as accurately as possible, the auditors’ opinion on the financial statements of the firms. A sample of 625 company audited years with qualified statements and 625 ones with unqualified financial statements over the period 1998–2003 from 823 manufacturing private and public companies is being used in contrast to most of the previous works in the UK that have mainly focused on very small or very large public companies. Furthermore, the models are being developed and tested using the walk-forward approach as opposed to previous studies that employ simple holdout tests or resampling techniques. Discriminant analysis and logit analysis are also used for comparison purposes. The out-of-time and out-of-sample testing results indicate that the two multicriteria decision aid techniques achieve almost equal classification accuracies and are both more efficient than discriminant and logit analysis. Ó 2006 Elsevier B.V. All rights reserved. Keywords: Multicriteria analysis; Auditing; Classification; Case study

1. Introduction and background information The development of auditing models, although quite important has received relatively little atten* Corresponding author. Tel.: +30 28210 37236; fax: +30 28210 37529. E-mail address: [email protected] (C. Zopounidis).

tion compared to other financial decision making problems such as bankruptcy prediction and credit risk assessment where hundreds of papers have been published. This is surprising since the quality, reliability, and transparency of published audited financial statements are essential to the efficient allocation of resources in the economy (Rezaee, 2005) and auditors can be benefited by

0377-2217/$ - see front matter Ó 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.ejor.2006.04.039

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the employment of such models during the auditing procedure. In the UK, all companies are required by company law to prepare financial statements that must comply with the existing legislation and accounting standards. With the exception of very small companies (i.e., turnover less than 1 million GBP, balance sheet total less than 1.4 million GBP, and less than 50 employees) financial accounts must be audited by UK registered auditors, who prepare a report that contains a clear expression of opinion. An unqualified opinion, is expressed when the financial statements, give a true and fair view and have been prepared in accordance with relevant accounting standards and other requirements. A qualified opinion is issued when there is either a limitation on the scope of the auditor’s examination that results in insufficient evidence to express an unqualified opinion or the auditor disagrees with the treatment of the disclosure of a matter in the financial statements and the statements may not or do not give a true and fair view of the matters on which the auditors are required to report or do not comply with relevant accounting or other requirements. The auditors are also required to add an explanatory paragraph in their report whenever there is ‘‘substantial doubt’’ about a client’s ability to continue its operations as a going-concern. Hence, the going-concern uncertainty opinion is issued by the auditor to a client company when that company is at risk of failure or exhibits other sings of distress that threaten its ability to continue as a goingconcern. While the issuance of a wrong opinion can have consequences for auditors, the identification of falsified financial statements is a difficult task using normal audit procedures (Porter and Cameron, 1987; Coderre, 1999). However, with the employment of classification models, auditors can simultaneously screen a large number of firms and direct their attention to the ones that the model will identify as having a high probability of receiving a qualified opinion, hence saving time and money. Laitinen and Laitinen (1998) classify prior studies on qualified audit report information relevant to the present one into the following three categories: (i) studies that use audit report information for the construction of bankruptcy prediction models (e.g., Keasey and Watson, 1987; Hopwood et al., 1989), (ii) studies that deal with the construction of bankruptcy models for making audit opinions relative to going-concern (e.g., Koh and Killough, 1990;

Koh, 1991; Hopwood et al., 1994), and (iii) studies that explain or predict qualifications in audit reports (e.g., Dopuch et al., 1987; Laitinen and Laitinen, 1998; Spathis et al., 2002, 2003). The present study falls into the third category of the above mentioned studies. The purpose of the study is to extent the auditing literature by investigating the efficiency of two multicriteria decision aid (MCDA) approaches, namely UTADIS (UTilite´s Additives DIScriminantes) and MHDIS (Multigroup Hierarchical DIScrimination) in the development of classification models for replicating auditors’ opinion in the UK. The major advantage of UTADIS and MHDIS is that they are not making any assumptions, as the traditional statistical and econometric techniques,1 about the normality of the variables or the group dispersion matrices (e.g., discriminant analysis) and they are not sensitive to multicollinearity or outliers (e.g., logit analysis). In recent years, neural networks (NNs) have also been very popular in studies in finance and accounting such as auditing (e.g., Hansen et al., 1992; Fanning and Cogger, 1998), bankruptcy prediction (e.g., Charitou et al., 2004) and credit risk assessment (e.g., Atiya, 2001) to name a few. However, numerous researchers document various disadvantages of NNs. For example, Salchenberger et al. (1992) mention the inability to explain conclusions or how they are reached (i.e., the so called ‘‘blackbox’’ operation) and the lack of formal theory which imposes a need for expertise on the user. Calderon and Cheh (2002) also point out that NNs are subject to problems of local minima, and can be tedious and extremely time-consuming to build. Results can also be very sensitive to specification of learning rates, momentum and other processing elements, and there is no clear guidance on selecting these parameters.

1 Barniv and McDonald (1999) summarize some of the problems related to discriminant, logit and probit that were mentioned in previous studies. Logit and Probit are sensitive to: (a) data properties, such as departure from normality of financial variables (Frecka and Hopwood, 1983; Richardson and Davidson, 1984; Hopwood et al., 1988); (b) overall small sample size (Noreen, 1998; Stone and Rasp, 1991); (c) multicollinearity (Aldrich and Nelson, 1984; Stone and Rasp, 1991). The basic assumptions of discriminant analysis (DA) such as normality, symmetry and equal covariance matrices are also usually violated. Hopwood et al. (1994) point out that DA is generally sensitive to departure from normality and both logit and probit analyses are sensitive to extreme non-normality.

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The present study extents the literature in several ways. First, it is the first study that employs MCDA approaches for the development of auditing models in the UK as opposed to previous studies that used probit (Lennox, 1999) and logit (e.g., Keasey et al., 1988; Ireland, 2003). Second, this study considers various types of companies (based on ownership type) in contrast to the majority of previous UK studies, which are limited by the type of companies analyzed. Keasey et al. (1988) examined the audit qualifications on very small companies, while Citron and Taffler (1992, 2000) and Lennox (1999) analyze listed UK companies that are very large publicly owned companies. Ireland (2003) examined audit reports for public and private, listed and non-listed companies, but from a different perspective. In the study of Ireland (2003) the aim was the investigation of the relationship between published audit reports and observable company characteristics. Consequently, the focus of interest was on the significance of the overall explanatory power of the model and the significance of the coefficients of the variables, while no attention was given to the classification ability of the model. However, when the objective is the development of a classification model for distinguishing between qualified and unqualified financial statements, as in the present study, the focus of interest is on whether these statements can be correctly classified. Third, the present study develops and validates the models using an approach similar to the walk-forward methodology that is being used by Moody’s for its credit risk models, in contrast to previous studies in auditing that relied on the use of specific training and holdout samples or re-sampling techniques. The rest of the paper is organized as follows: Section 2 describes the sample data used in this study and the methodology followed for developing the testing the auditing models. Section 3 presents the empirical results of the analysis, while the last section discusses the concluding remarks along with some possible future research directions. 2. Sample and methodology 2.1. The dataset The data for this study were obtained from the financial analysis made easy (FAME) database of Bureau van Dijk’s company that is specialized on UK and Ireland. Apart from financial data, FAME also reports whether the firms received an auditor’s

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qualified or unqualified opinion.2 The sample used in this study involves 823 manufacturing private and public, listed and non-listed companies with assets above 27 million euros, turnover above 40 million euros and over 250 employees, operating in the UK, over the period 1998–2003. We concentrate on UK firms only to avoid differences in accounting and auditing requirements and procedures among countries. For example, even within the EU where a number of Council Directives for harmonization of accounting and auditing standards (78/660/EEC, 83/349/EEC, 84/253/EEC, 86/635/EEC, 91/674/EEC) have been issued since the 1980s, there are still important differences among the EU member states3 (Federation des Experts Comptables Europeens, 2000a,b4; International Forum on Accountancy Development, 20015; Brackney and Witmer, 2005). For example, FEE (2000a) in its survey on the accounting standard setting in Europe states that there are differences in structure and in operation between standard setters in Europe, while the scope of standard setting also differs widely. IFAD’s GAAP 2001 survey also outlines broad differences among the EU member states. A comparison of country’s accounting requirements and IAS for 80 key financial statement items revealed that the number of differences ranged from 20 (Ireland) to 42 (Austria). Brackney and Witmer (2005) point out that, in general, financial reporting has tended to be more 2

The only audit information with respect to auditor’s opinion available in FAME is whether the auditor issued a qualified or unqualified opinion. Hence, we had no further information to distinguish whether qualifications are due to disagreements (e.g., accounting treatment or disclosures), limitations on scope (i.e., lack of evidence) or going-concern issues. 3 A recent regulation that was proposed in February 2001, and finally adopted by the Council of the EU in June 2002 requires that all Community companies listed on a regulated market, including banks and insurance companies should prepare their consolidated financial statements in accordance with International Accounting Standards, at the latest by 2005. Furthermore, in May 2003 the EC also published a 10-point plan (IP/03/715) for improving and harmonizing the quality of independent audits throughout the EU. 4 Fe´de´ration des Experts Comptables Europe´ens (FEE) is the representative organization for the accountancy profession in Europe. 5 The International Forum on Accountancy Development (IFAD) was created as a working group between the Basel Committee, the International Federation of Accountants, IOSCO, the large Accounting Firms, OECD, UNCTAD, and the World Bank and regional development banks, which flowed from the East Asian crisis.

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important and more transparent in countries with a stronger equity culture (e.g., Ireland, UK) and less important and transparent in countries where debt financing dominates (e.g., France, Germany). During 2001, 275 European listed companies were preparing their consolidated financial statements under IAS, 300 under US GAAP, and the remainders (about 6500 companies) were using their national GAAP (IASPlus, 20016). Furthermore, another FEE Survey (2000b) on the auditor’s report in Europe revealed a high degree of variation in the wordings of statutory auditor’s report between EU Member States. The variations were caused in part by differences in auditing standards and, more significantly by differences in national laws and regulations governing the subject matter and form of auditor’s reports. The absence of a harmonized approach to statutory auditing in the EU had already been mentioned a few years ago by the EC which organized in 1996 a wide-ranging reflection on the scope and need for further action on the statutory audit function. It is therefore clear that it is not possible to draw a sample among various countries due to differences in accounting and auditing requirements and procedures among countries. Hence, the nature of the problem itself limits the applicability of the model in the country for which it is developed and that is why all previous studies (including the present study) have focused on individual countries. However, it should be mentioned that the overall framework (i.e., variables selection process, selection of classification techniques, development and evaluation process) can be easily adopted while using data from other countries to re-estimate the weights of the variables in the models. Hopefully, once the International Accounting Standards will be implemented in the EU, a sample pooled across several countries could be used, allowing us to consider country-specific variables as well. From the total of 823 firms, 363 received a qualified opinion for at least one year during the above period (sub-sample A) while the remaining received unqualified opinions throughout the whole period (sub-sample B). Some of the firms in sub-sample A received qualified opinions for more than one year, resulting in an observation dataset of 625 firm-year observations with qualified reports.

Hence, firms with multiple qualified audit opinions were included in the final sample, as many times as where the years over which they had received qualified opinions. An equal number of firm-year observations with unqualified reports from subsample B were then assigned randomly to the qualified ones by year, resulting in a total of 1350 observations.7 An important issue of concern in evaluating the classification ability of a model is to ensure that it has not over-fit to the training (estimation) dataset. As Stein (2002) mentions ‘‘a model without sufficient validation may only be a hypothesis’’. Prior research shows that when classification models are used to reclassify the observations of the training sample, the classification accuracies are biased upward. Thus, it is necessary to classify a set of observations that were not used during the development of the model, using some kind of testing sample. Previous studies on the development of models to replicate (or predict) auditors’ opinion used a sample of training firms for the development of the model and a secondary holdout sample for model testing, or resampling techniques such as jack-knife and bootstrap (e.g., Laitinen and Laitinen, 1998; Spathis et al., 2002, 2003). However, data availability on qualified financial statements can lead in problems while constructing an appropriate holdout sample. Furthermore, in implementing such an approach the number of firms with qualified statements to be included in the training and holdout samples is a crucial point: if too many qualified firms left out of the training sample (in-sample data) then overfitting becomes likely, whereas if too many qualified firms left out of the testing sample (outof-sample data) then it would be difficult to estimate the true performance of the model (Sobehart et al., 2000). On the other hand, resampling techniques, cannot take into account the population drifting. As Barnes (1990) points out, given inflationary effects, technological factors and numerous other reasons, including changing accounting policies, it is unreasonable to expect the distributional crosssectional parameters of financial ratios to be stable over time. To cope with these issues, this study employs a more thorough analysis combining out7

6

Available at http://www.iasplus.com/restruct/euro2001.htm# feb2001.

As all firms in sample are considered large ones (i.e., assets above 27 million euros, turnover above 40 millions euros and over 250 employees) we have not matched qualified and unqualified observations by size.

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Table 1 Sample used in the walk-forward approach for model development and testing Training

Model Model Model Model

1 2 3 4

Validation

Years

Unqualified

Qualified

Year

Unqualified

Qualified

1998–1999 1998–2000 1998–2001 1998–2002

112 234 409 572

112 234 409 572

2000 2001 2002 2003

122 175 163 53

122 175 163 53

of-time and out-of-sample tests based on a walk forward-testing approach. In general, the procedure is as follows (Sobehart et al., 2000; Stein, 2002):

whose data become available after 1999 (i.e., 2000). The process is then repeated using data for every year.

1. Select a year t0 (usually this will be the first year of the analyzed period). 2. Fit the model using all the data available on or before the selected year. 3. Once the model’s form and parameters are established for the selected time period, generate the model outputs for all the firms available during the following year t1. 4. Save the prediction as part of a result set. 5. Move the window up one year so that all the data through that year can be used for fitting (t1) and the data for the next year (t2) can be used for testing. 6. Repeat the above steps until all the process is repeated using data for every year. 7. Collect, the predictions obtained from each individual model that can be used to analyze the performance of the model in more detail.

2.2. Variables selection

Stein (2002) points out that the walk-forward approach has two significant benefits. First, it gives a realistic view of how a particular model would perform over time. Note that the model’s output for t1 is out of time for firms existing in previous year, and out-of-sample for all the firms whose data become available after t0. Second, it provides the ability to leverage to a higher degree the availability of data for validating models. Table 1 and Fig. 1 show the application of the walk-forward approach in our data-set. The first model was developed with data from years 1998 and 1999 and was then tested on data from the year 2000. We used a two-year window for the estimation of the first model, due to the small number of observations that were available from each year. Obviously, the outputs of model 1 for 2000 are out-of-time for firms existing in previous years (i.e., 1998–1999), and out-of sample for all the firms

The FAME database provides information for 40 financial ratios and annual changes in basic financial accounts. From these, only 8 met a data availability requirement of no more than 5% of missing values (Tabachnick and Fidell, 2001) in anyone of the two groups (i.e., qualified or unqualified), mainly due to many missing values in the qualified financial statements.8 These variables and their relation with audit decisions are briefly outlined below. We also consider a non-financial variable that is the credit risk assessment of a rating agency. Obviously, additional financial and non-financial variables such as cash flows, internal control procedures, board member’s qualifications and auditors’ independence, could be included in the model. However, such data were not available in our case. We hope that future research could improve upon this. CR and QR are the current ratio and quick ratio accordingly, that are among the most well known measures of liquidity. High liquidity, might increase the likelihood of a qualified audit opinion as assets might have been overstated (Ireland, 2003). On the other hand, lower liquidity might also increase the possibility of a qualified report increases the financial health of the firm deteriorates (Spathis, 2003). Prior empirical research in the UK indicates that companies with poor liquidity are more likely to receive going-concern modifications than other 8

The decrease from the 40 potential variables, to the eight ones that were finally considered for inclusion in the models has not raised serious concerns for two reasons. First, the retained variables cover all main aspects of a firm’s performance such as profitability, liquidity, gearing and annual trends. Second, a large number of variables could pose problems such as the applicability of the model on a daily basis as well as multicollinearity among the variables.

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Model 1

1998

2000

1999

2001

2002

2003

2001

2002

2003

2002

2003

2000

Model 2

1998

1999

2000

2001

Model 3

1998

1999

2000

2001

2002

Model 4

1998

1999

2000

2001

2002

2003 2003

Observations used for the development of the model

Available observations not used in the particular model

Observations used for out-of-time validation of the model

Observations used for out-of-sample validation of the model

Fig. 1. The application of the walk-forward approach.

companies, however, liquidity does not have a significant impact on non-going-concern modifications (Ireland, 2003). Laitinen and Laitinen (1998) also report that there were not significant differences in terms of liquidity between Finnish firms that received qualified and unqualified opinions. SFTA corresponds to the capital strength of the firm, as measured by the shareholders funds9 to total assets ratio. Numerous studies report that firms with higher probability of default are more likely to receive qualified opinions (e.g., Bell and Tabor, 1991; Reynolds and Francis, 2001). Ireland (2003) also reports that UK firms with higher gearing are more likely to receive both going-concern and non-going-concern modifications than other firms, while Laitinen and Laitinen (1998) indicate that the higher the share of equity in the balance 9 Shareholders’ funds is calculated as: Issued capital + Share premium account + Revaluation reserves + Profit (loss) account + Other reserves.

sheet of Finish firms, the higher the probability that the audit report is unqualified. Trends in ratios and financial accounts have also been found to be important in the past. Dopuch et al. (1987) indicate that the change in the ratio of total liabilities to total assets was one of the most significant variables, while Laitinen and Laitinen (1998) show that the likelihood a qualified audit report was negatively related to the growth of the firm. In the present study, on the basis of data availability, we examine the annual changes in current assets (CACH), total assets (TACH) and current liabilities (CLCH). ROA and EBIT, correspond to return on total assets and earnings before interest and taxes margin, respectively. Numerous studies indicate that firms which receive qualified opinions or have falsified financial statements are less profitable ones (Loebbecke et al., 1989; Summers and Sweeney, 1998; Laitinen and Laitinen, 1998; Beasley et al., 1999; Spathis, 2002; Spathis et al., 2002). This is also

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Table 2 Descriptive statistics (whole sample, N = 1350) Unqualified

CR QR SFTA CACH TACH CLCH ROA EBIT CREDIT

Qualified

Mean

St. Dev.

Mean

St. Dev.

1.78 1.41 32.99 12.62 10.25 14.82 5.40 6.38 3.08

3.06 3.06 26.39 49.21 45.30 67.63 14.28 13.45 1.17

2.00 1.67 30.27 11.65 7.11 16.47 5.99 0.13 1.93

4.53 4.54 34.12 80.85 69.78 99.32 39.10 18.88 1.26

Kolmogorov–Smirnov z

Kruskal–Wallis v2

11.65** 12.43** 1.66** 8.36** 8.70** 8.22** 7.91** 5.69** 6.88**

4.44* 3.95* 3.13 17.74** 25.48** 2.52 62.11** 84.70** 259.93**

Notes: CR: current ratio, QR: quick ratio, SFTA: shareholders funds to total assets ratio, CACH: current assets annual change, TACH: total assets annual change, CLCH: current liabilities annual change, ROA: return on total assets, EBIT: earnings before interest and taxes margin, CREDIT: the credit risk assessment assigned by CRIF Decision Solutions Limited. The Kolmogorov–Smirnov compares the cumulative probabilities of values in the dataset with the cumulative probabilities of the same values in the normal distribution. High p-values (i.e., no statistically significant) indicate that there is no evidence against the null hypothesis that the sample has been drawn from a normal distribution. The Kruskal–Wallis test indicates whether there are statistically significant differences between the two groups. ** Significant at the 1% level. * Significant at the 5% level.

consistent with the previously mentioned argument that the possibility of a qualified report increases as the financial health of the firm deteriorates. Another potential explanation offered by Spathis (2002) is that the profitability orientation is tempered by managers’ own utility maximization, as defined by job security. As previously mentioned, several studies indicate that clients with a high probability of default are more likely to receive qualified opinions because their ability to continue is in greater doubt (e.g., Bell and Tabor, 1991; Krishnan and Krishnan, 1996; McKeown et al., 1991; Reynolds and Francis, 2001). While some of the previous studies used Altman’s z-score as a proxy of default (e.g., Reynolds and Francis, 2001; Spathis, 2003), such an approach may not be appropriate. The z-score model was developed for a particular industry (i.e., manufacturing), under different economic conditions and for the US. Therefore, without the necessary modifications the model may not be appropriate in the present. To avoid such problems, in the present study, we use the risk group assessments of CRIF Decision Solutions Limited, which are also available in FAME. The Quiscore provided by CRIF measures the likelihood of default (in a 0–100 scale) for the 12 months following the date of its calculation. On the basis of their QuiScore, CRIF classifies firms into the following five risk groups: secure, stable, normal unstable (or caution), high risk, which are used in the present study to access the overall risk of a firm (CREDIT).

The final set of variables is selected on the basis of a combination of a univariate test of significance, correlation analysis and human judgment as in Doumpos and Zopounidis (2002), Spathis et al. (2003), Doumpos et al. (2004), Gaganis et al. (2005) and Pasiouras et al. (2005), among others. Obviously, to classify the qualified and unqualified financial statements effectively, the variables should be able to discriminate between the two groups. In this case, the rule of thumb is to keep the number of variables small and exclude a variable unless its discriminating power is statistically significant (Kocagil et al., 2002). Therefore, in selecting the appropriate variables to be included in the auditing models, we focus on the significance of the financial variables at the univariate level using a Kruskal Wallis test of means differences.10 The results in Table 2 show that there are 7 variables, which are significant, at the 5% level, in discriminating (on a univariate basis) firms with qualified and unqualified statements. The Kolmogorov–Smirnov test also indicates that as in most studies in finance and accounting the variables are not normally distributed. The next step in the analysis was to examine the correlations among the aforementioned significant variables (Table 3). While as previously mentioned UTADIS and MHDIS are 10

At this point it should be mentioned, that as an anonymous reviewer suggested, univariate statistical significance, does not necessary predict how a variable will contribute in a multivariate model.

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Table 3 Correlation analysis results

CR QR CACH TACH ROA EBIT CREDIT

CR

QR

CACH

TACH

ROA

EBIT

CREDIT

1.000 0.996** 0.066* 0.035 0.080** 0.170** 0.209**

1.000 0.071* 0.037 0.073** 0.169** 0.193**

1.000 0.750** 0.054 0.073* 0.024

1.000 0.119** 0.073** 0.016

1.000 0.592** 0.275**

1.000 0.364*

1.000

Notes: CR: current ratio, QR: quick ratio, CACH: current assets annual change, TACH: total assets annual change, ROA: return on total assets, EBIT: earnings before interest and taxes margin, CREDIT: the credit risk assessment assigned by CRIF Decision Solutions Limited. ** Significant at the 1% level. * Significant at the 5% level. With bold are highly correlated variables (above 0.75 in absolute values).

not influenced by correlation, other techniques such as logit, might be especially problematic. Furthermore, there is no reason to include two variables that are highly correlated in the model, as they will essentially provide the same information, while increasing time and cost for the data selection as well as estimation time for the development of the models. The correlation between the two profitability ratios, ROA and EBIT, is moderate (0.56) however the proxies for annual changes and liquidity are highly correlated (correlations above 0.75 in absolute terms). One variable from each one of the highly correlated pairs was finally selected based on an auditor’s opinion.11 QR was preferred over CR because it is more stringent and TACH was preferred over CACH, because it covers both current as well as fixed assets. Ultimately, this combination of correlation analysis, Kruskal–Wallis test and auditor’s opinion led to the selection of the set of the follow-

ing 4 financial variables: QR, TACH ROA and EBIT. 2.3. Multicriteria classification approaches The problem considered in this case study is a classification one that involves the assignment of a finite set of alternatives A = {a1, a2, . . . , an} (e.g., financial statements) evaluated along a set of m criteria g1, g2, . . . , gm (e.g., our set of five variables) to a set of q classes12 C1, C2, . . . , Cq (e.g., unqualified/ qualified). The objective of the model development process in UTADIS and MHDIS, which are implemented in the present study, is to develop a criteria aggregation model that will be able to discriminate among financial statements that should receive qualified and unqualified opinions. In both methods, the developed criteria aggregation model has the form of an additive utility function: m X UTADIS: U ðaÞ ¼ pi u0i ðgi Þ;

11

As an anonymous reviewer suggested it would probably be better to rely on the opinion of a group of auditors, as in human information processing (HIP) studies, rather than only on one auditor’s opinion. While using more auditors might contribute to the objectivity of variable selection, it also adds complexity and it is more time consuming. At the same time, auditors working in a same firm, will more or less be looking at the same factors, hence auditors from different firms will have to be consulted if one really wants to obtain different opinions. In our case, considering the advantages and disadvantages of these approaches we relied only on one auditor. However, as the auditor was consulted only at a latter stage of the analysis, to contribute only towards the selection among very highly correlated variables, that would essentially provided quite similar information, we do not believe that a different approach (i.e., group of auditors) would had a significant impact on our results. In any case, one could keep in mind this discussion while interpreting our results.

MHDIS: U k ðaÞ ¼

i¼1 m X

pki uki ðgi Þ

i¼1 m X

U k ðaÞ ¼

and

pki uki ðgi Þ;

i¼1

k ¼ 1; 2; . . . ; q  1: 12 Both UTADIS and MHDIS make the assumption that the groups are ordered. Therefore Ck is preferred to Ck+1 , k = 1, 2, . . ., q. In our study we assume that C1 corresponds to the unqualified financial statements and C2 to the qualified ones, on the basis of previous studies which indicate that the financial health of the firms that receive qualified opinions in inferior to the ones receiving unqualified opinions.

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UTADIS leads to the development of a single additive utility function that is used to characterize all the financial statements and assign a score to each one of them. This score (global utility) measures the overall performance of each alternative along all criteria, in a scale between 0 and 1. The global utilities are calculated considering both the criteria weights pi (the criteria weights sum up to 1) and the performance of the alternatives on the evaluation criteria.13 Hence, the marginal utility functions u0i ðgi Þ (which also range between 0 and 1) provide a mechanism for decomposing the aggregate result (global utility) in terms of individual assessment to the criterion level. Both the criteria weights and marginal utility functions are specified as outputs during the model development process. In contrast to UTADIS, MHDIS distinguishes the groups progressively, starting by discriminating the first group from all the others, and then proceeds to the discrimination between the alternatives belonging into the other groups. To accomplish this task, instead of developing a single additive utility function that describes all alternatives (as in UTADIS), two additive utility functions are developed in each one of the q  1 steps, where q is the number of groups. In the first step, the method develops a pair of additive utility functions U1(a) and U1(a) to discriminate between the alternatives of group C1 and the alternatives of the other groups C2, . . . , Cq. The alternatives that are found to belong into class C1 (correctly or incorrectly) are excluded from further analysis. In the next step, another pair of utility functions U2(a) and U2(a) is developed to discriminate between the alternatives of group C2 and the alternatives of the groups C3, . . . , Cq. Similarly to step 1, the alternatives that are found to belong in group C2 are excluded from further analysis. This procedure is repeated up to the last stage (q  1), where all groups have been considered. In contrast to the UTADIS method, the utility functions in MHDIS dot no indicate the overall performance but rather serve as a measure of the conditional similarity of an alternative to the characteristics of group Ck when the choice among Ck and all the lower

13 One assumption of both UTADIS and MHDIS involves the monotonicity of the criteria. We refer to Zopounidis and Doumpos (1999, 2000) and Despotis and Zopounidis (1995) for further discussion on this issue and how to deal with, when it is not the case.

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groups Ck+1, . . . , Cq is considered (Doumpos and Zopounidis, 2002). As in UTADIS, the weights of the criteria in the utility functions as well as the marginal utility functions are outputs of the model development process. On the basis of the above function forms, the classification of any alternative is performed through the following classification rules (in UTADIS u1, u2, . . . , uq1 are thresholds that range between 0 and 1 and distinguish the set of q groups): UTADIS: If U(a) P u1 then a 2 C1 If U(a) 2 [u2, u1) then a 2 C1 ... If U(a) < uq1 then a 2 Cq MHDIS: If U1(a) P U1(a) then a 2 C1 Else if U2(a) P U2(a) then a 2 C2 ... Else If Uq1(a) P Uq1(a) a 2 Cq1 Else a 2 Cq

then

The objective of the model development process in both methods it to specify all the parameters of the model (i.e., marginal utilities, criteria weights, utility thresholds), that minimize the classification error in the training sample. UTADIS considers the magnitude of the violations while MHDIS considers both the magnitude as well as the number of violations. In both cases, the estimation of the parameters of the models is performed through mathematical programming. More precisely, UTADIS employs a linear programming formulation while in MHDIS each step of the hierarchal discrimination procedure, two linear programs and a mixed-integer one are solved. Further details for UTADIS and MHDIS can be found in Zopounidis and Doumpos (1999, 2000). 3. Empirical results The results obtained from the two multicriteria methods UTADIS and MHDIS are analyzed both in terms of the criteria (i.e., independent variables) weights and the classification accuracy of the models. Table 4 illustrates the contribution of each of the 5 criteria. The presented results correspond to the average weights (in %) over the 4 replications of the model development and testing process

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Table 4 Average weights for the criteria in the 4 models Variable

QR TACH ROA EBIT CREDIT

UTADIS (%)

0.55 21.53 70.44 5.23 2.26

MHDIS (%) U1

U1

17.86 24.92 17.23 29.97 10.03

44.83 7.17 24.94 15.81 7.25

Notes: QR: quick ratio, TACH: total assets annual change, ROA: return on total assets, EBIT: earnings before interest and taxes margin, CREDIT: the credit risk assessment assigned by CRIF Decision Solutions Limited.

described in Section 2.1. In the case of UTADIS, there is always one function developed that describes all the firms in the sample. In the case of MHDIS, since the sample involves two groups, the hierarchical discrimination process consists of only one stage, during which two additive utility functions are developed. The utility function U1 characterizes the unqualified firms; whereas the utility function U1 characterizes the qualified ones. The results indicate that ROA is the most important criterion in the UTADIS model, with a weight of approximately 70%. From the other criteria, the most important is TACH, followed by EBIT with average weights equal to 21.53% and 5.23%, respectively. In the case of MHDIS, QR and ROA are the most important criteria that characterize the qualified firms, while TACH and EBIT are the most important criteria that characterise the unqualified ones (all with a weight above 20%). However, in the case of MHDIS the weights of the 5 criteria are quite more balanced, and all of them contribute to some extent in the two functions. Our results support in general the findings of previous studies. The importance of credit risk assessment seems to be low (in the UTADIS model) to moderate (in the MHDIS model) as was the z-score in the model developed by Spathis et al. (2003). Reynolds and Francis (2001) argue that companies are more likely to receive a qualified report if they are financial distressed and the financial statements were qualified in prior periods, while Spathis (2003) also reports that financial distress is among the most important variables. Ireland (2003) found that UK firms with high quick ratio are less likely to receive going-concern modifications while Spathis et al. (2003) found current assets to current liabilities ratio, that is similar to quick ratio employed in the

present study, to be among the most important factors. The two profitability ratios, ROA that is important in both models as well as EBIT that is important in the case of MHDIS model, indicate that firms which receive qualified opinions are less profitable ones. Similar findings were observed in previous studies (Loebbecke et al., 1989; Summers and Sweeney, 1998; Beasley et al., 1999; Spathis, 2002; Spathis et al., 2002). Finally, the importance of TACH may be due to assets’ overstating or misappropriation that is among the typical financial statement fraud techniques (Ziegenfuss, 1996; Beasley et al., 1999). Concerning the evaluation of the models in terms of their classification ability, the overall correct classifications at the training stage range between 71.7% and 77.2% for UTADIS (with an average equal to 74.3%), and between 70.9% and 75.5% for MHDIS (with an average equal to 73.2%; Table 5, Panel A). These results indicate that both the UTADIS and MHDIS models developed with the considered financial ratios are able to provide a satisfactory distinction between qualified and unqualified firms. UTADIS achieves slightly better classification results, however, these results refer to the same firms that were used to develop the models, and the potential upwards bias should be kept in mind. The classification ability of the models is tested further using the out-of-time and out-of-sample firms. Furthermore, at this stage in order to investigate the relatively efficiency of the proposed MCDA techniques we perform a comparative analysis with the results obtained through discriminant analysis (DA) and logit analysis (LA). Although the underlying philosophies of UTADIS and MHDIS and that of discriminant and logit analysis are different, their comparison in a common set of data is well documented, since they can all be applied to discriminate between qualified and unqualified firms. The models generated through DA and LA, are developed and tested following the same methodology used for the development of the classification model through UTADIS and MHDIS. More specifically, using the same 5 criteria, the models were developed using the previously described walk-forward approach. The results in Panel B of Table 5 indicate that the two multicriteria methodologies achiever higher classification accuracies on average than discriminant and logit analysis, with an overall accuracy equal to 72.3% and 72.8% for UTADIS and MHDIS as opposed to 68.3% and 69.2% for DA

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and LA, respectively.14 It should also be mentioned that the models developed through UTADIS and MHDIS achieve satisfactory classification accuracies (i.e., above 60%) both for firms with qualified reports as well as for the unqualified ones, in almost all cases, while only the last DA and LA models can classify correctly above 60% of the unqualified observations. A direct comparison with the results of previous studies is inappropriate because of differences in the datasets (Kocagil et al., 2002; Gupton and Stein, 2002), the country under investigation, the variables employed and the classification methods. Nevertheless, a tentative comparison provides two interesting conclusions relative to the level of accuracy of our models with respect to those achieved by other studies. First, the results of the present study support the findings of studies in Greece that compared auditing models developed with multicriteria decision aid and multivariate techniques (Spathis et al., 2002, 2003). Second, the range of accuracy in our study 14 The cut-off probability point was set equal to 0.5 in both discriminant and logit analysis as in many previous studies. Hence, financial statements with estimated probability higher than 0.5 are classified as qualified, while those with estimated probability lower than 0.5 are classified as unqualified. One should be aware that the choice of cut-off point typically involves a trade-off between the magnitude of type I and type II errors. The proper selection of a cut-off point requires knowledge of prior probabilities and cost of type I and type II errors. The determination of the actual prior probability of qualified audit reports in the population requires historical data for many years while it might also depend upon the sector, whether the firms are listed or not, etc. Hence, it is difficult to be estimated with confidence. Furthermore, as Bartley and Boardman (1990) mention, when firms from the two groups are unequal in number, the use of actual prior probabilities will result in a large percentage of the firms from the group with the large proportion being classified in this group irrespective of the statistical fit of the model. They point out that the solution to this problem is to compare classification accuracy using equal probabilities, as was suggested by Morrison (1969) and Pinches (1980). The issue of model error is also a complex one as different users may have different cost structures. Consequently, most of the previous studies (including the present study) have assumed that costs are equal to avoid an arbitrary selection. Palepu (1986) proposes the empirical determination of the optimum cut off point. Under this classification rule, the cut-off point is where the conditional marginal probability densities for firms of the two groups are equal and is equivalent to minimizing the total error probabilities. Barnes (1998) proposes the use of a maximization of returns cutoff or a weighted cut-off point based on historical data. However, the results of Barnes do not indicated any superiority of these alternative classification rules when compared to the ones of Palepu. In general, both approaches have resulted in rather unbalanced classification accuracies.

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is comparable to other studies in auditing. Spathis (2003) reports in sample (i.e., training) overall classification accuracies equal to 75% and 78% in Greece, similar to Ruiz-Barbadillo et al. (2004) in Spain that report an in sample overall classification accuracy equal to 79.7%. The results are not significantly different in studies that used re-sampling techniques or holdout samples to test the models such as Spathis et al. (2002, 2003) in Greece, Welch et al. (1998) and Anandarajan and Anandarajan (1999) in the US and report overall classification accuracies between 69.10% and 86.91%. Laitinen and Laitinen (1998) in Finland report that the total error rate in classification can be as low as 5.4% (depending on the selection of the cut-off point), however this is due to the ability of their model to classify correct unqualified financial statements (94.6%), although it classifies correct a quite smaller proportion of qualified financial statements15 (62.5%). Consequently, our study supports the capability of multicriteria decision aid techniques in the classification of financial statements in qualified or unqualified ones. 4. Conclusions and further research The present study explored the development of auditing decisions models using two multicriteria methodologies (UTADIS and MHDIS) based on a sample of UK manufacturing firms. Four financial variables were selected for inclusion on the models based on a combination of an auditor’s opinion, a correlation analysis and a univariate statistical test. An additional variable, indicating the probability of default was also employed, however in contrast to the majority of previous studies that used the z-score we relied on the risk estimates of a credit agency. Furthermore, while previous studies relied on the use of specific training and holdout samples, the analysis performed in this study was based on a thorough model development and testing methodology that enabled the analysis of the out-of-time and outof-sample performance of the proposed approaches. For comparison purposes the MCDA models were compared with models developed through discriminant and logit analysis. According to the 15 This is due to the performance measure that is affected by positive prevalence in unbalanced samples. The average classification accuracy (similar to the overall in an equal matched sample) would had been equal to 78.55%, hence similar to the one obtained in our study.

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Table 5 Classification results Panel A: In sample (training) UTADIS (%)

Model 1 Model 2 Model 3 Model 4 Average

MHDIS (%)

Unqualified

Qualified

Average

Unqualified

Qualified

Average

82.1 73.5 86.6 66.8

72.3 75.6 60.6 76.6

77.2 74.6 73.6 71.7 74.3

82.1 72.7 89.5 88.6

68.8 69.2 56.5 57.9

75.5 70.9 73.0 73.3 73.2

75.4 76.6 63.2 54.7

71.3 70.3 75.2 74.5 72.8

84.4 81.1 79.1 73.6

71.7 69.4 63.8 71.7 69.2

Panel B: Out of time and out of sample (validation) UTADIS (%) 1 2 3 4 Average

66.4 57.7 81.6 67.9

MHDIS (%)

82.0 78.3 69.3 75.5

74.2 68.00 75.5 71.7 72.3

84.4 78.9 79.8 71.7

70.5 68.6 63.5 70.8 68.3

DA (%) 1 2 3 4 Average

56.6 58.3 47.2 69.8

67.2 64.0 87.1 94.3 LA (%)

obtained classification results, UTADIS and MHDIS achieved higher classification accuracies on average than the other two techniques. Both UTADIS and MHDIS outperform chance assignments and achieve satisfactory classification accuracies that are above 70% on average. Hence, the models can be used to discriminate between financial statements that should receive qualified opinions from the ones that should receive unqualified opinions. While there are no empirical studies demonstrating the extent of the benefits from using such models, either in terms of time or money, researchers point out a number of additional advantages. For example, Laitinen and Laitinen (1998) and Ramamoorti et al. (1999) among others point out that classification models that employ financial variables can provide the basis for a decision tool for auditors when predicting what opinion other auditors would issue in similar circumstances, when evaluating potential clients, in determining the scope of an audit for existing clients, in peer reviews, to control quality within firms and as a defence in law suits, as well as to avoid difficulties in analysing large quantities of data. Bell and Tabor (1991), as well as Chen and Church (1992), mention that auditors can use such models to plan specific auditing procedures that can be applied to achieve an acceptable level of audit risk, while Calderon and Cheh

59 57.7 48.5 69.8

(2002) argue that advanced technologies are required to signal critical incidents such as management fraud and going-concern problems that could if not detected, derail an audit. Spathis (2002) also points out that the model could assist auditors in identifying ‘‘red flags’’ that substantially differ from the norms of the industry. The current research could be extended towards several directions. First of all, alternative classification techniques, such as nearest neighbours and support vector machines could be employed and compared with the developed models. Furthermore, the results of the different methods could be combined in an integrated model, an approach that has yielded promising results so far in bankruptcy prediction, credit risk assessment and acquisitions prediction. Third, the development of multicriteria decision support systems (MCDSSs) could be of particular use to auditors in their daily practice regarding the assessment and monitoring of their clients. Fourth, the research could be extended towards the inclusion of additional, non-financial variables such as auditor’s size, auditing fees, managers’ experience, and firm’s market share. Finally, once the International Accounting Standards will be implemented, a sample pooled across several countries could be used, allowing us to consider country-specific variables as well.

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