The predictive power of financial ratios on bankruptcy : A quantitative study of non-listed limited liability SMEs companies in Sweden

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The predictive power of

financial ratios on bankruptcy

A quantitative study of non-listed limited liability SMEs

companies in Sweden

MASTER THESIS WITHIN: Accounting NUMBER OF CREDITS: 30 ECTS PROGRAMME OF STUDY: Civilekonom AUTHORS: Azra Zubanovic and Laureta Ahmeti TUTOR: Argyris Argyrou

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Master Thesis in Business Administration

Title: The predictive power of financial ratios on bankruptcy Authors: Azra Zubanovic and Laureta Ahmeti

Date: 2020-05-30

Key terms: Bankruptcy, prediction variables, financial ratios, logistic regression

Abstract

Background - Bankruptcy is an issue that not only affects the company that is registered as

bankrupt, but also the society since it has an impact on the economy. Previous studies have been focusing on larger listed companies outside of Sweden hence there is a lack of empirical findings about Swedish companies in this research area. Small and medium companies represent most of the Sweden's labor force and therefore the bankruptcy issue is important to investigate for these companies.

Purpose - The purpose of the thesis is to find out which financial information distinguishes

bankrupt from non-bankrupt companies in Sweden. In other words, which financial ratios have predictive power on bankruptcy. Furthermore, the thesis wants to provide knowledge towards current and future companies so that they can avoid bankruptcy by paying attention to the ratios distinguished in the thesis and keeping the ratios at an acceptable level.

Method – The thesis conducts the research with a quantitative strategy by observing financial

information from companies’ annual reports. The logistic regression model is used to test for the 11 ratios, by matching two samples; bankrupt and non-bankrupt companies, as well as a classification matrix, Pearson correlation matrix and variance inflation factor. The bankrupt companies selected, are classified as bankrupt for the period 2016-2019. The thesis

implements a deductive approach to establish expectation and deduct which financial ratios are predictive.

Conclusion - The thesis ends up with 92 companies, where 46 are bankrupt and 46 are

non-bankrupt. Out of the 11 ratios, three are statistically significant and have predictive power on bankruptcy. These three are; debt rate, gross profit margin and, cash and cash equivalents. The debt rate has a positive effect on bankruptcy, which means that a higher debt rate increases the risk of bankruptcy. Gross profit margin and cash and cash equivalents have a negative effect on bankruptcy; as they increase, the risk of bankruptcy decreases.

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1. Introduction

This section provides a background to the research problem and describes the thesis’ purpose and the chosen research question.

1.1 Background

According to Bernstein, Colonnelli, Giroud, and Iverson (2017), the liquidation of a bankrupt company does not only affect the company, but the society as well. They found that the spillover from the bankruptcy imposes a large negative influence both on the society and economy. Bankruptcy has become part of our economic system and seems to be inevitable, due to the occurring number of bankruptcies (Eklund, Levratto, & Ramello, 2018). Being one of the most well published and influential bankruptcies, the collapse of the Lehman Brothers in 2008 is evidence of how widely bankruptcy can affect not only the local or national economy, but also the global (Sieczka & Sornette, 2011).

Swedish small and medium companies are well integrated into the global economy with their financial markets. These represent the majority of Sweden's labor force, where limited liability companies are included as well. The issue about bankruptcy, becomes highly important to cover among these companies since Sweden's economy depends on their well-being and growth (Öhman & Yazdanfar, 2017).

Swedish legislation, financial/taxation systems, and bankruptcy law differ somewhat from other European countries, and is important to distinguish. In Sweden, there are different legislations depending on the type of enterprise. Limited liability companies have their own legislation, “Aktiebolagslagen”, which defines, for an example, different ways in which the directors should act in situations such as bankruptcy (SFS 2005:551).

By observing the financial situation before the bankruptcy of companies, it is possible to prepare for future distress, since it would be more visible which information is causal towards bankruptcy. According to Swedish bankruptcy legislation “Konkurslagen” (SFS 1987:672), the process towards bankruptcy is not a straight line, rather a number of different criteria and steps that a company encounters before being allowed to go bankrupt. Before a company is considered bankrupt in Sweden, the company reaches a stage where their debt is higher than their assets and have been in this stage up to six months. This stage is called insolvency and is

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when the company files for bankruptcy (SFS 1987:672). A company then closes its bankruptcy in Sweden after the company liquidates all their assets and pays back all their creditors. Altman and Hotchkiss (2005) correspondingly state that bankruptcy is the last stage, the end point of a long process of financial distress. When there are no solutions for financial problems for a company, the financial distress becomes bankruptcy.

Existing literature concentrates much on the investigation of companies outside of Sweden. One of the most researched countries is the United States where different perspectives on bankruptcy and different types of enterprises are analyzed. For instance, Barreda, Kageyama, Singh, and Zubieta (2017), investigate bankruptcy prediction for hospitals within the United States, meanwhile Sissel (2007) investigates bankruptcy filing for a financially distressed company. Except for the United States, other studies such as Pham Vo Ninh, Do Thanh, and Vo Hong (2018), explore prediction of financial distress and bankruptcy for listed companies in Vietnam. Lukason and Laitinen (2019) investigate the company failure processes for 12 European countries, where Sweden is included as well but only as a small segment of the study.

It is stated that the literature in the research area of bankruptcy is divided into two groups: bankruptcy prediction models and bankruptcy prediction variables. Existing literature suggests the following accounting based models for predicting bankruptcy Beaver’s

univariate approach (Beaver, 1966), Altman’s multivariate z-score model (Altman, 1968), Ohlson’s logistic regression analysis (Ohlson 1980), and Zmijewski’s probit regression analysis (Zmijewski, 1984). The literature also emphasizes the market based models by

Shumway (2001), and Hillegeist, Keating, Cran, and Lundstedt, (2004).

Ohlson (1980) not only predicts bankruptcy using a model, but also investigates financial ratios that are influential on bankruptcy by using a logistic analysis. He detects that ratios that represent the financial structure reflect by measurements of leverage, and financial

performance measures have the highest predictive ability on bankruptcy. This is the foundation for the thesis, as well as studies done after Ohlson’s.

1.2 Problem

Sweden is part of previous research in bankruptcy, though it is not the main focus (Lukason, & Laitinen, 2019). This creates a lack of empirical evidence for smaller and medium sized companies in Sweden. It is considered to be a problem, since there is not enough evidence to

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draw a conclusion for only Swedish companies. By investigating the influence on bankruptcy in Swedish companies, the focus is redirected and can potentially reduce the gap.

According to Altman, Iwanicz-Drozdowska, Laitinen, and Suvas (2017), and Balcaen and Ooghe (2006), prior studies are mainly focused on bankruptcy prediction models on listed companies which means that it has taken over the growing body of literature in this area. Since the larger size companies are required to publish their annual accounts, but the smaller size companies are not always required to do the same, the publicly available information is concentrated on larger listed companies. Balcaen and Ooghe (2006) state that the availability of information is an important factor when conducting research and having restricted

information can make the researcher choose the path that provides more. The problem emerges when smaller and medium companies are less included in the literature because of potential limitations in the data. Although the literature is more extensive regarding larger companies, Gupta, Barzotto, and Khorasgani (2018) show that companies that are larger, are not as affected by bankruptcies as small and medium size companies are.

The division between the two larger groups in bankruptcy literature, also imposes a problem since there is less literature on the prediction variables than the bankruptcy models. To avoid extending the literature gap with more prediction models, the thesis focuses on the prediction variables instead. It is stated that the prediction variables literature incorporates the selection of financial and non-financial variables for the purpose of predicting bankruptcy (Altman, 1968; Ohlson, 1980).

To claim that the factors that affect bankruptcy for newly started companies, are more evident than for the companies that are mature, is incorrect. However, there is evidence that the majority of the companies that become bankrupt in Sweden are newly started (UC AB, 2019). As there has been discussion on why the bankruptcy rate for newly started companies is higher, previous studies show that it may be because of the lack of knowledge of what it means to operate a company, and the responsibilities that comes with it. The main misconception is the time it takes to establish the company in the market, and the high expenses that occur (Hansson & Reinisch, 2007). Compared to historical evidence, the stage in the life cycle of companies has been predominant regarding its survival and a crucial predictor for bankruptcy (Reynolds, 1987). On the contrary, companies that have been established for a longer time and go bankrupt, may not have issues with recent establishment in the market, rather other deeper financial difficulties. The problems that they experience may emerge from internal and external factors that directly affect their finances, for instance

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debt issues. Because of this, there is a need to explore companies that have passed their newly started stage.

When a company in an industry becomes bankrupt, there are a few possible outcomes as far as it comes to its competitors, they either benefit or lose from the situation (Akhgibe, Martin & Whyte, 2005). The competitors may gain the share of sales lost from the bankrupt

company; however the problem arises if there is a so called “negative spillover”. This is caused by mistrust among stakeholders and is problematic to the companies affected by a bankruptcy (Ozturk, Chintagunta & Venkataraman, 2019).

A company that is broadly connected to its suppliers and clients, may have an immediate effect on them in the case of bankruptcy. Sieczka and Sornette (2011) analyze the case of the Lehman Brothers, where they conclude that the bankruptcy of one company had an immense negative effect on their creditors, the companies that partnered with them, and their whole economic network.

1.3 Purpose and research question

Since bankruptcy occurs frequently, it is even more important to look further into the

companies’ financial statements and find a relationship between the bankruptcy and identify the influential factors. The aim of this thesis is to find which ratio/-s have the highest

predictive power on bankruptcy and distinguishes the bankrupt from the non-bankrupt companies. While bankruptcy is present and have already affected multiple companies, the outcome of which ratio/-s are influential, can be used by current and future non-bankrupt companies as guidance and manage similar issues for future companies. The thesis investigates bankruptcies for Swedish small and medium, non-listed, limited liability companies since these companies are a majority in Sweden. The thesis examines what financial ratios have predictive power on bankruptcy.

To find the financial ratios with the highest predictive power, the thesis uses two sample groups: (i) bankrupt companies (sample A), and (ii) non-bankrupt companies (sample B). With help of pair-matched sampling, these two samples are compared. The purpose of including the non-bankrupt companies, is because the comparison of the financial situation with an active company, distinguishes the ratios that differ between them. More information is superior because the thesis wants to expand the findings and to do so, several financial ratios are included.

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The thesis examines these variables with the logistic regression which is a predictive analysis with a dependent variable that takes on a binary value. The regression is used to summarize and describe the data of the bankrupt and non-bankrupt, and explain the correlation that the independent variables, the ratios, may or may not have with bankruptcy.

To accomplish the aim of the thesis, the following research question is of interest:

Which financial information distinguishes bankrupt from non-bankrupt limited liability companies in Sweden?

1.4 Limitations and delimitations of the thesis

There are several limitations connected to the thesis. The limitations include

non-generalization due to country specific legislation and delimitation to one enterprise, a limited selection of financial ratios, and no non-financial variables. Due to limited information on industry classification of the companies used, it is impossible to stratify them by industry. There is also a risk for multicollinearity considering the logistic regression model. The limitations are further discussed in section 7.2.

1.5 Structure of the thesis

The thesis proceeds as follows. Section two, which is the literature review, presents previous studies, different bankruptcy prediction models, prediction variables and an insight into bankruptcy definition in Sweden. The third section presents the research methodology where the thesis discusses the sample of bankrupt and non-bankrupt companies, a selection of financial variables, data collection, model specifications and the classification matrix. The fourth section is where the empirical findings are presented, and in section five these findings are analyzed further. Section six summarize and concludes the thesis and the final section presents an insight into different limitations and also provides recommendations for future research.

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2. Literature Review

The purpose of this section is to provide a deeper understanding about the research area by covering influential studies. Furthermore, the literature review is divided into prediction models and prediction variables with respect to the research area. This section also presents the legislation on bankruptcy that is connected to the purpose.

The existing literature on bankruptcy prediction concentrates on two main areas. First, there is literature on bankruptcy prediction models and secondly on bankruptcy prediction variables. Bankruptcy prediction concentrates on improving the predictive accuracy of the models. On the contrary, bankruptcy prediction variables explore the potential of which variables are significant in the accuracy of the prediction (Altman, 1968; Ohlson, 1984).

There are divided opinions within the group of predictive variables, on whether it is better to include financial variables or non-financial variables, while some agree that a mix of both give more accurate results. This is considered to have higher predictive ability because the results become nuanced and not just from a financial point of view, which is the most common (Tinoco & Wilson, 2013).

Although the thesis investigates which financial variables distinguish bankrupt from non-bankrupt companies, the following section covers both financial and non-financial variables since the literature in this area include information about both.

2.1 Bankruptcy prediction variables

The selection of which variables to use when wanting to predict bankruptcy is important. Not only which, but also how many, is of interest in this matter (Balcaen & Ooghe, 2006). There are multitude of variables to select from but lack of theoretical framework that explains which ones should be selected, and therefore no unity on which financial variables are the best for distinguishing between bankrupt and non-bankrupt companies. Since the number of variables available is high, the selection of an effective combination is critical (Du Jardin, 2009).

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2.1.1 Financial variables

There is literature on prediction models, but less emphasis put on the selection of variables that these models are dependent on. Financial variables are divided into two categories, accounting based and market based variables (Waqas & Mid-Rus, 2018). In a study by Karas and Reznáková (2017), they state that they collect data on several years prior to the

bankruptcy in order to find which of the variables have the most significant indicators of the bankruptcy (Perry, Henderson & Cronan, 1984). Perry et al. (1984) finds that variables related to liquidity, leverage, and profitability are some of the most beneficial to the prediction of bankruptcy. However, there are also industry/firm specific variables that may be taken into consideration (Waqas & Mid-Rus, 2018). Perry et al. (1984) conclude that by including data for at least four years prior to the bankruptcy, the predictive power of the study increases. As there is no theory that states exactly which financial variables are the most explanatory towards why companies end up in the state of bankruptcy, an ideal selection is usually based on previous studies done in the area (Karels & Prakash, 1987; Horta & Camanho, 2013). It is common that the debt- and asset variable is included, which can be explained by the line of popularity that previous studies follow (Dirickx & Van Landeghem, 1994). It is also

explainable by the fact that variables have been chosen based on the empirical availability of the data needed (Scott, 1981).

Due to the popularity of using certain financial variables in bankruptcy prediction, some risk of choosing non-explanatory variables are avoided in the process, since the used variables have proven to have some predictive power. By using empirically gathered variables, several studies show that it results in sample specific results and therefore non-generalizable

conclusions (Balcaen & Ooghe, 2006; Edmister, 1972). There is, however, evidence that contradicts the claim that financial variables should be chosen deliberately (Dambolena & Khoury, 1980). Thus, later studies use a wider selection of variables with a higher correlation between them (Zavgren, 1985; Hernandez Tinoco, Holmes & Wilson, 2018), which revives the usage and importance of financial variables in bankruptcy prediction.

Multiple studies show that financial variables help predict bankruptcy. In a study done on Romanian companies, the debt ratio is investigated on its ability to predict bankruptcy. Although the study does not provide absolute predictive power, the debt ratio has the ability to predict bankruptcy two years prior to the event of bankruptcy (Brîndescu-Olariu, 2016).

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Debt has been used as a ratio in several other studies (Altman, 1968; Muscettola, 2015; Alifiah, 2014). An Italian study acknowledges the fact that some financial accounting ratios, among them debt coverage ratio, made significant contribution to better predictions on the risk of bankruptcy (Muscettola, 2015).

In a study by Kilborn and Walters (2013), it is shown how important it is to consider debt in bankruptcy, since there are a high number of cases that occur due to issues connected to debt repayment. In the United States, there is an average of 600 bankruptcies that occurs only because the creditors file for it, and demand repayment (Kilborn & Walters, 2013). Despite the fact that debt is a popular variable in previous literature, there are also other financial variables that have turned out to have predictive power on bankruptcy. Charitou and Trigeorgis (2004) uses the option model in their study to test financially distressed companies that have filed for bankruptcy and match these with healthy companies. This study divides the variables into (i) primary option variables, and (ii) extended option motivated, based on different criteria. Their results indicate that the market value of the firm's assets, the book value of total liabilities, and the standard deviation of a firm's value changes, are also

important factors that drive the probability of failure of these companies: the primary option variables. By including extended option variables, they also found that cash flow coverage had incremental explanatory power beyond the primary variables. Similar to previous literature, they also conclude that all of these are affected by higher debt as well.

The cash conversion cycle is also discussed as a accounting based variable that can measure bankruptcy. The study by Szpulak (2016) investigates companies that operate with a negative cash conversion cycle to see how this affects the financial liquidation. The author divides the work by observing into two different financial indicators. Firstly the study looks into invisible debt that is delivered to the company by suppliers or employees (CashOnOWC), and later the study looks at the size of a buffer that the companies have in case of a decrease in sales (operating liquidity margin). The conclusion of the study is that free use of additional cash in invisible debt, increases the risk of bankruptcy for companies that operate under a negative conversion cycle.

A study by Tse and Pak (2011), shows that an inclusion of cash flow statements into the prediction ratios, increases the prediction power on bankruptcy. However, this conclusion is not limited to only cash flow statements. They claim that the ideal way to increase the prediction power is to incorporate the information from the cash flow statements with the

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income statement and balance sheet and convert that information into ratios. Tse and Pak (2011) conclude that long-term profitability as well as short-term liquidity in the company, indicates a higher likelihood to survive bankruptcy.

By using the multiple discriminant model, Gu (2002) detects that companies in the restaurant industry who have low earnings before interest and taxes (EBIT) and have high total

liabilities, have a greater chance to go bankrupt. These companies are still highly burdened by debt, but it is their low EBIT that makes them more sensitive towards bankruptcy. Cultrera and Brédart (2016), add on to this when expanding and developing their bankruptcy

prediction model. They state that profitability ratios and liquidity are excellent predictors of bankruptcy.

Tian and Yu (2017) investigate bankruptcy prediction over international markets and include several countries. In the Japanese market, total assets-, total debt-, and current liabilities ratios were selected as highly predictive when combined. For the European countries, more

specifically Germany, France and the United Kingdom, the equity ratio variable is selected as being the most consistent and highly predictive compared to the rest of the countries tested. However, it needs to be recognized that financial ratios and financial variables are not identical, meaning that they do not exhibit the same information. Beaver (1968) claims that one should not only focus on ratios, since it is the accounting data that has the information and not the ratios. If one makes a comparison between two companies, with the same ratio, it is difficult to know if one or the other is more likely to go bankrupt, since the components of the ratio are not observed immediately. Other studies have also shown the importance of considering the components behind the ratios. Pompe and Bilderbeek (2005) suggests that a decline in profitability of an investment, that is financed by debt capital, should logically coincide with solvency. In this case, bankruptcy is detectable in liquidity ratio due to the liability component, but it was not.

2.1.2 Non-financial variables

Before defining non-financial information, it is of relevance to demonstrate the limitations with financial information to further understand the importance of implementing non-financial information. As early as in 1990, instability of non-financial ratios over time was detected due to changes in external affecting factors such as interest rates (Platt & Platt, 1990). The predictive ability of financial variables in traditional bankruptcy models is also

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higher the first year, but then slowly loses its ability over time (du Jardin and Severin 2011; du Jardin 2015). These setbacks make it more important to not only rely on financial information, such as debt and asset ratios, but also on non-financial information, such as corporate governance indicators (Platt & Platt, 1990; Liang, Lu, Tsai & Shih, 2016).

Developing an effective prediction model for several years is challenging, especially since the financial ratios can be unstable. Despite the instability of ratios, other factors such as

fluctuations alongside the economic cycle and inflation are considered. It is often smaller and medium sized companies that are affected by these fluctuations since they can be more sensitive to changes, and it is not certain that the information that is provided is reliable. All of the above is why non-financial variables have become very important to include (Balcaen & Ooghe 2006; Altman & Sabato, 2007; Altman, Sabato, Wilson, 2010).

Keasey and Watson (1987) state the importance of non-financial information, since

historically it is known that financial ratios in the financial statements of a company do not provide all the information. The qualitative information that could be gathered from these non-financial variables were less exposed to manipulation, in comparison with financial ratios. Keasey and Watson (1987) conclude that better predictions about failure can be made considering smaller companies, if one used non-financial information. The same cannot be said about larger companies, since the study tests only smaller companies. Examples of non-financial variables that are used in the study are the age of the company, number of current directors, how long the directors have been working, change of auditors, relationship to the bank, etc.

Factors such as corporate governance indicators, are mentioned as influential. It is shown that the performance of bankruptcy prediction using corporate governance indicators, such as board structure and ownership structure, improves the bankruptcy prediction significantly (Liang, Lu, Tsai & Shih, 2016). Kim (2019), adds on by stating that ownership concentration as a governance mechanism, and higher institutional quality reduces the risk of bankruptcy. The different examples of non-financial variables demonstrate that there is not one clear definition of a non-financial variable. Dhaliwal, Li, Tsang, and Yang (2011), state that any information that is disclosed by management and that is beyond mandatory financial reporting, is voluntary disclosure. The information can consist of product, customer, environmental, social and competition information, as well as corporate governance mechanisms (Li & Yang, 2016; Meek, Roberts & Gray, 1995; Rezaee, 2016).

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Altman, Sabato and Wilson (2010), tests the study of Altman and Sabato’s (2007) SME-model for a different sample in the United Kingdom, by including non-financial information in their study to expand it further. The first study, Altman and Sabato (2007), investigate United States companies, without any non-financial information. The non-financial

information added is internal auditing, trade credit relationships and reporting compliance as predictive variables (Altman et.al., 2010). They find that by including non-financial

information it is expected that the prediction accuracy of the model would improve up to 13%. The limitation is that this non-financial information is not available for all companies. They conclude that non-financial variables are important for predicting failure for both large and small and medium companies, but especially for the latter. Small and medium size companies run a higher risk of missing financial information, or not having it available which larger companies do not have a problem with. If some of the financial information is not available, the non-financial information can be helpful. Considerable information that the authors conclude is that non-financial information can be updated frequently, which is beneficial because the information is up to date (Altman et.al., 2010).

Another unexplored area when it comes to non-financial information is according to Süsi and Lukason (2019), corporate governance variables. In their study they examine how corporate governance variables are interconnected with company bankruptcy, for small and medium companies. The variables used are seven different corporate governance variables. Examples of some variables are manager’s age, board size, board tenure, multiple directorships, and board gender. They conclude that there is a higher risk for bankruptcy when larger boards and managers have directorships in more than one firm, but the risk reduces when the manager’s age and presence of managerial ownership grows. These findings are limited to one country. Ciampi (2015), states that there are limited studies that include corporate variables into their research. Variables such as ownership and board characteristics are not always included when investigating bankruptcy risks, but they should be. Since the area is an unexplored area it is hard to conclude the effectiveness of the variables for the small and medium companies’ segment.

Non-financial variables are somewhat harder to get access to regarding private companies than for public ones. These limitations are the reason why this area does not have as much attention as financial variables. A study in Italy (Wang, 2019) focuses on private companies and combines financial and non-financial variables. By analyzing the variables for over a year, the study concludes that the shareholders have the strongest impact on private

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companies, then the number of subsidiaries followed by industry and company age.

Companies that are owed by more shareholders show lower risk for failure. These findings were limited to one country (Wang, 2019). Süsi and Lukason (2019), and Wang (2019) therefore agree with their findings when it comes to corporate governance variables.

2.2 Bankruptcy prediction models

The accounting based models are based on financial ratios and information that can be observed from financial statements of companies. Literature suggests a number of models for bankruptcy prediction; (i) univariate analysis (Beaver, 1966), (ii) multivariate discriminant analysis (Altman, 1968), (iii) logistic regression analysis (Ohlson, 1980), and (iv) probit regression analysis (Zmijewski, 1984).

2.2.1 Accounting based models

Beaver (1966) introduce a univariate analysis to predict bankruptcy and investigate companies that are: bankrupt; have bond default; have an overdrawn bank account; and non-payment of a preferred stock dividend. This is a univariate approach that suggests that the financial ratios have predictive ability of bankruptcy, by observing the effect of each financial variable at a time. 79 randomly chosen bankrupt companies are matched to healthy companies and divided into groups depending on industry and asset size. A set of 30 financial ratios are included in the analysis over a five-year period. Beaver shows that for the majority of the companies investigated, the financial ratios show indications of bankruptcy in the last five years prior to filing for bankruptcy, therefore he concludes that the ratios can acknowledge early signs of bankruptcy.

However, the univariate model received criticism because of its irrelevant application to practice. Altman (1968) states that a univariate approach on bankruptcy prediction is

inaccurate, partly because of the assumed linear relationship between the financial ratios and bankruptcy prediction. Altman also states that the univariate ratios may display different results depending on which company it is applied to, that the assumptions are sample specific.

Altman (1968) extends Beaver’s univariate model by using multivariate discriminant analysis, an improvement of the accounting based prediction, which investigates the possibility of multiple independent variables affecting bankruptcy. The z-value in this model is the score which predicts bankruptcy, where Altman chooses a certain point: a higher z-value, which

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means a non-bankrupt company; and a lower z-value which means a bankrupt company. The range for a company is clearly defined as bankrupt when z < 1,81, and the range for it being clearly defined as non-bankrupt is z > 2,99. However the area in between is defined as

ambiguous, where the definition of bankruptcy is declared to be uncertain. A z-value of 2,675 means a 50% chance of a company being bankrupt and 50% of being non-bankrupt.

Table 1

Altman’s z-function and variables

Altman (1968)

The multivariate approach has received criticism because of its diminishing predictive power when the horizon of forecasting is extended in time, as well as the assumption of normally distributed independent variables. Literature has documented that the independent variables are not normally distributed in an abnormal setting, therefore the limitation (Barnes, 1982). Altman has himself developed his own model (1968) further several years later (Altman, 1997).

Ohlsson (1980) introduces the conditional logistic regression analysis as a development of multivariate discriminant analysis. However, compared to the other predictive models, Ohlson also investigates financial ratios that affect bankruptcy. A significantly larger sample of 2000 companies are included, compared to Altman that uses 66 companies. Ohlson claims that his model is more generalizable because the assumptions of the logistic regression is not as restrictive as those of the multivariate. This model uses the same idea as the z-score, but it has another limit (o-score), where companies with a value below or above are considering to be non-bankrupt or bankrupt respectively. Logit regression analysis also combines several

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characteristics of the companies compared and uses a function of probability to calculate the likelihood of a company going bankrupt.

Table 2

Ohlson’s function

Ohlson (1980) Although the prediction rate may be higher with the logistic regression than it is with the z-score model, it attracts some criticism because of its use of values on the dependent variable. The limit of the o-score is based on the range from 0 to 1, in which the problem of companies that take on the value of 0, are bankrupt from the beginning (Abdullah, Ahmad & Rus, 2008). However, the logistic model’s main criticism, is about its sensitivity to multicollinearity, the assumption of logistic probability distribution, and sensitivity to missing values and outliers (Balcaen & Ooghe, 2006).

The probit regression model, which is introduced by Zmijewski (1984), investigates the same prediction as the logistic regression, in which the value of the dependent variable is either bankrupt or non-bankrupt. The difference between Ohlson’s and Zmijewski’s model, is that logistic regression uses cumulative function of the logistic distribution, while the probit regression uses the cumulative function of the standard normal distribution (Zmijewski, 1984).

Table 3

Zmijewski’s function

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This model is different from the previously mentioned models, as Zmijewski choses to define bankruptcy with the p-value as the determinant. In cases where the p-value is lower than 0,5, a company is seen as non-bankrupt, and if it is equal and higher than 0,5, it is seen as bankrupt. Zmijewski also introduces variables as size and industry, meaning external factors, and are considered being crucial for bankruptcy prediction (Zmijewski, 1984).

2.2.2 Market based models

Market based models are based on market information and data, such as interest rates, stock-market security or risk of investment. According to Agarwal and Taffler (2008), models that are based on market information, provide a sound theoretical model for bankruptcy. Agarwal and Taffler (2008) also confront the criticism that accounting based models have received, since market based models claim that stock prices reflect all the information in financial statements in efficient markets, which accounting based models do not take into

consideration.

The discrete-time hazard model by Shumway (2001), states that many ratios used in

accounting based models do not bring much value when trying to predict bankruptcy. Instead, Shumway (2001) combines variables from Altman (1968) and Zmijewski (1984) with market based variables such as firm size compared to the market size, and the idiosyncratic standard deviation of each firm’s stock returns.

As far as the discrete-time hazard model, Shumway (2001) argues that these are more appropriate when trying to predict bankruptcy, due to the consideration of multiple-periods, than other methods that only consider single-time period.

The second market based bankruptcy prediction model is a model by Hillegeist, Keating, Cram and Lundstedt (2004) which is based on Black-Scholes-Merton (BSM) option-pricing. The choice of using option-pricing as a foundation for bankruptcy prediction is motivated by the fact that they give guidance about theoretical determinants of bankruptcy risk but may be difficult when it comes to the assumptions and implementing them in practice. One of the restrictive assumptions is that the bonds are considered as zero-coupon bonds, but in practice bonds do have interest (Hillegeist et. al, 2004)

Hillegeist et al. (2004) claim that accounting based models do not provide relevant

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that are prepared under the historical cost convention. They do not provide as relevant information when it comes to trying to predict bankruptcy in the future.

2.3 Bankruptcy definition in Sweden

The definition of bankruptcy is inconsistent in the literature and can both cause biased results and/or definition-related results (Balcaen & Ooghe, 2006). It is therefore necessary to

consider the appropriate and necessary legislation for the country that is at focus. In this case, the definition of bankruptcy in Sweden needs to be explained to avoid these biased results (Dirickx & Van Landeghem, 1994). As some studies are based on bankruptcy (Keasey & Watson, 1991) other focuses on the legislation (Hanson & Reinisch, 2007). The thesis takes the direction of legislation-based bankruptcy definition and uses it to further understand the term “bankruptcy” for the Swedish companies that are investigated.

According to the Swedish legislation on bankruptcy, the so called “Konkurslag” 1st chapter 2nd § (SFS 1987:672), a company is considered insolvent when their debt exceeds their assets, and when their liquidity issues are not only temporary. The companies that find themselves in this state, must apply for bankruptcy to the district court.

According to the 1st chapter 1st §, in the state of bankruptcy, the company is obligated to liquidate their property/possession, to be able to pay back its creditors (SFS 1987:672). In Sweden, the company as well as the creditor can file for bankruptcy on the company’s behalf, if there is not a clause or paragraph that states otherwise on the rights of application of

bankruptcy (1:2, SFS 1987:672). Further, the legislation also states that the creditor can forcibly use the debtor’s aggregate assets to pay their debts (1:1, SFS 1987:672). After the decision of bankruptcy is made by the district court, the debtor (the company) is no longer granted possession of its property and can no longer make decisions in the name of the company (3:1, SFS 1987:672).

2.3.1 Company reconstruction

Before applying for bankruptcy, a company has, according to the law on company

reconstruction (SFS 1996:764), the opportunity to apply for a reconstruction instead. This option applies given that the company has difficulties or is expected to have difficulties in the near future with paying its creditors. This is the main difference between applying for

bankruptcy and applying for company reconstruction, difficulties versus insolvency (2:6, SFS 1996:764). To be approved for reconstruction, the company must have a plan of potential

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future growth (2:3, SFS 1996:764). In difference to the bankruptcy regulations, a company reconstruction can only be granted if the debtor (the company) also approved of it (2:6, SFS 1996:764). The reconstruction shall be registered in the “Aktiebolagsregistret” which is the limited liability companies’ register (25:48, SFS 2005:551).

2.3.2 Payment priority

When a company is either in bankruptcy or in financial distress, the creditors of the company get paid what they are owed according to the law of payment priority, “Förmånsrättslag” (SFS 1970:979). This regulates the order that the creditors will get paid, meaning which of the creditors’ payment right is prioritized, after the property of the company is sold in conjunction with the bankruptcy (1§, SFS 1970:979). The order of payment to the creditor is divided into two categories of priority: special and general, which depends on the type of claim that the creditor has on the company. The special priority is associated with a specific property, and usually goes in front of the general (15§, SFS 1970:979).

2.3.3 Limited liability company legislation

Considering that the thesis focuses on limited liability companies, it is compelling to include the additional legislation on bankruptcy for this type of enterprise. The importance of this addition is the connection between the general Swedish bankruptcy legislation and the specific legislation on limited liability companies. There are different aspects, such as owner responsibility and owner rights, that guides the company in the bankruptcy process, therefore the importance to include this legislation.

Before a limited company is registered it cannot acquire rights or undertake obligations. (2:25, SFS 2005:551). The responsibility will pass to the company as soon as it is registered, but before the registration the individual has a personal payment responsibility (2:26, SFS

2005:551). There are exceptions where the responsibility is on the individual and that is if, for example, that the individual has knowledge that the company is required to go into liquidation but still participated in decisions to continue operating the business (25:19, SFS 2005:551). In a study done by Tinoco and Wilson (2013), it is found that some companies stop presenting their annual accounts up to three years before they become registered bankrupt, considering the fact that the financial issues usually start earlier. The Swedish limited liability company legislation, however, states that the assignment by the auditor does not end by the company going into liquidation. The auditor shall still state in the audit report whether the liquidation is

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unnecessarily delayed or not. The chosen liquidator for the company shall prepare an annual report for each financial year. The annual general meeting establishes the balance sheet and income statement (25:31 & 37, SFS 2019:1264).

There are two different definitions of liquidation. Either the liquidation is done on a voluntary basis or in some cases it is forced into liquidation by law or other provision. According to the 25th chapter 2nd § (SFS 2005:551), the majority of the shareholders, with more than half of the votes cast, who attends the annual meeting need to vote for liquidation for it to be valid. If the decision to go into liquidation goes through this way, it is on voluntary basis. However, this does not apply if otherwise is stated in the articles of the association. If the articles state different rules regarding the rights to vote for bankruptcy, the general court decides on the liquidation (25:12, SFS 2005:551).

There are also other ways that decide if a company needs to have forced liquidation. In some cases, the “Swedish Companies Registration Office” (Bolagsverket) can decide for the company, if the company has not registered correct information about the CEO, the board members or if they have not provided correct information in their annual reports. This is called forced liquidation (25:11, SFS 2005:551).

Also, the company can face forced liquidation due to lack of capital. If the company's equity is calculated to be less than half of the registered share capital, the board of directors shall immediately provide a control balance sheet (25:13, SFS 2005:551). If the balance sheet is not controlled within eight months after the first control meeting, the general court can decide about the company's liquidation (25:17, SFS 2005:551).

When the company later on is in bankruptcy, and there is no surplus left, the company is dissolved, and the bankruptcy is closed (25:50, SFS 2005:551).

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3. Research Methodology

The purpose of this section is to explain the methodology and theoretical framework that the thesis has and why it is chosen. The section provides a detailed description of the data collection and the criteria that are included when selecting the relevant information for the two samples and how these are stratified. The independent and dependent variables are further explained, and the construction of the logistic regression model, the classification matrix, and the Pearson correlation matrix are also presented.

3.1 Theoretical framework

The cause-and-effect relationship between bankruptcy and the variables that affect the bankruptcy, depends on several factors which makes it challenging for one theory to answer the research question of the thesis. A theory can have difficulties with the identification of all possible and relevant connections between bankruptcy and ratios, which can lead to some of the actual influencing ratios being omitted or misspecified (Dietrich, 1984). This also adds on the difficulties by, for an example, being qualitative and quantitative, thus creating a

measurement problem. The measurements can also be affected by time periods. A bankruptcy in 1960 and one in 2019 may differ somewhat. Real companies are analyzed when looking at bankruptcy prediction, thus the analysis of the cause-and-effect relationship is often damaged by these difficulties above (Mckee, 2000). Factors like all of these, contributes to the fact that there is not a single theory that can be used for bankruptcy prediction, instead there are different perspectives to look at the problem.

Even though there are limitations regarding the choice of a theory for predicting bankruptcy, the thesis has chosen to follow Ohlson’s logistic regression as the framework. This framework is mainly chosen since it is appropriate considering the area of research and the non-restrictive assumption that it has compared to previous models. The restrictive assumptions of previous studies have affected the results of the studies since the results have relied on the assumptions. On the contrary, the result of the logistic regression analysis will be determined by the

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The logistic regression simultaneously has the possibility of including several different characteristics of the companies in the regression analysis and can provide a more diversified picture, since it can include several variables. As it is a function of probability, it does not assume a linear relationship between the independent variables (Laitinen & Kankaanpaa, 1999), which can be relieving towards the problematic condition of multicollinearity. Since the thesis is highly focused on the relationship between the financial ratios (i.e. the

independent variables) and their effect on the probability of bankruptcy (i.e. the dependent variable), it is particularly important to consider that the independent variables are not dependent of each other.

Ohlson’s logistic regression divided the ratios into four categories: (i) the size of the

company, (ii) a measure(s) of the financial structure, (iii) a measure(s) of performance, (iv) a measure(s) of current liquidity (Ohlson, 1980). These categories included ratios with

components such as assets, liabilities, and net income, to mention a few. The information used for his study, was gathered from financial statements of companies, which also sets the

foundation for gathering the financial information for the thesis.

3.2 Research approach

To make sense of the empirical findings, researchers may need a research approach. It helps researchers choose how the data will be collected and later analyzed. There are three

approaches to consider: the inductive approach; the deductive approach; and the abductive approach (Saunders, Lewis & Thornhill, 2016). The inductive approach is more focused on developing a theory to try and make sense of the findings, while the deductive approach emphasizes a theory or previous research to try and explain the findings. The abductive approach is a combination of the two, where both qualitative and quantitative methods are adopted (Saunders et al., 2016; Bryman & Bell, 2015).

The deductive approach is appropriate, since it uses previous findings to establish hypotheses which later are tested through and concluded through the empirical analysis (Bryman & Bell, 2015). The thesis similarly uses this approach towards the bankruptcy literature on financial ratios, to establish expectations and deduct which financial ratios are predictive towards bankruptcy. After a set of ratios are chosen, the thesis then tests these ratios using the logistic regression, to either verify the significance of previous findings in the bankruptcy literature or reject that the ratios chosen affect bankruptcy. Depending if the ratios are either verified or

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rejected as significant, the thesis then analyses the outcome with what has been previously stated.

3.3 Research strategy

The two research strategies to consider are the qualitative and the quantitative, where the thesis uses a quantitative method to align with the explanatory nature of the research. Bryman and Bell (2015) state that a qualitative method mostly reflects the inductive and exploratory approach, where focus is put on finding out why conditions are constructed the way they are. However, the quantitative method is commonly used when the research aims to analyze tangible data from either collecting data through surveys and/or questionnaires, or by

observing and deducing previous statistical data (Bryman & Bell, 2015). A quantitative study is therefore argued to be the most suitable approach to satisfy the purpose of the thesis, which is to understand the predictive power that the independent variables have on the dependent variable. To understand the independent variables’ (ratios’) relationship to the dependent variable (bankruptcy), the thesis collects the data from the companies’ financial statements and test these with the logistic regression. A quantitative research strategy is also suitable since the thesis wants to include a larger sample which, according to Gheondea-Eladi (2014), is not the case with a qualitative method. A qualitative method often fails to be generalizable, due to the focus being on gaining further understanding and not generalizing the findings to the population (Gheondea-Eladi, 2014). On the contrary, the quantitative method qualifies for obtaining generalizable data if the sample is representative (Bryman & Bell, 2015). Since the thesis has a deductive approach, and is applying measurements to test the previously existing literature through a set of ratios, it also obtains objectivity since it is analyzing the data as an external reality (Bryman & Bell, 2015).

3.3.1 Research purpose

Exploratory, explanatory, and descriptive researches are the three main classifications of a research purpose. Exploratory research search to understand more about a specific

phenomenon that has been observed and seeks to get familiar with the data, whereas the explanatory research is conducted for an issue that exists in a less explored area. The explanatory purpose also creates guidance to find the underlying problem that was not investigated in-depth before. The descriptive research however tries to both describe what is happening in a more detailed way, but at the same time fill the missing gap in the research area (Saunders et al., 2016).

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Since the research purpose of the thesis is to find out what ratios have predictive power on bankruptcy and can distinguish a bankrupt company from a non-bankrupt company, the thesis has an explanatory research purpose. Saunders et al. (2016), states that an explanatory

research implements a sort of relationship between the included variables, which supports the purpose of the thesis.

The data that is collected in the thesis, is not analyzed in-depth for each company individually but instead taken into consideration for the overall sample size. The quantitative strategy is also connected to the explanatory research purpose since the thesis aims to include as many companies as possible to fill the literature gap that exists for Swedish SME, non-listed, limited liability companies.

3.4 Data collection and sample design

The thesis chooses to carry out the research by observing financial information from the annual reports for each company that is selected. Pre-chosen ratios are used to select only the information that is relevant for this thesis. This way of collecting the data is selected since it can answer the research question in the most effective and specific way.

Since the thesis investigates bankrupt companies that are no longer in operation, interviewing or sending questions to the board and/or owners may be difficult and the probability of receiving answers is low. Annual reports are more effective to gather since they are publicly available and can all be collected at the same place. Considering that the purpose of this thesis is to answer which financial ratios have predictive power on bankruptcy, it is more accurate to use existing numbers rather than try to find new information. The thesis is interested in

previous events that may have caused bankruptcy and therefore no new information is needed, only the historical information that is available in the financial reports.

This section presents the use of a database in selecting the bankrupt and non-bankrupt companies, the criteria for selecting the samples and the stratification process.

3.4.1 Data collection

The thesis first selects a total of 200 bankrupt companies from the Swedish database “Business Retriever” according to the following criteria:

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(i) Limited liability companies denoted by AB (aktiebolag).

Non-listed limited liability companies are chosen since there must be some limitation in the research to reduce the sample. If several types of enterprises are included, there is a risk that the findings cannot be concluded. Since different enterprises, for example limited liability and sole proprietorship, have different bankruptcy regulation in Sweden, the sample selection would be very complex and problematic when it comes to the matching and stratification of the companies.

(ii) Time of registration.

The time of registration is selected to make sure that the companies have been active more than three years before going bankrupt to avoid selecting companies that were newly started ones. A random selection of 50 companies for each year between the years 2016-2019 is made.

(iii) The bankruptcy is established

The most important criteria is making sure to choose “bankruptcy closed” and not “in liquidation” in the database. The main role of the data collection is to gather financial statements of bankrupt companies, it would not add value if companies in liquidation were included.

(iv) Financial statements

Statements that belong to the companies are downloaded, not for the whole group. The companies have different financial statement periods, thus there is a requirement that only December-to-January period statements be included. The last financial statement for every company is accounted for when analyzing the information, not the year of bankruptcy. This is because there is a gap between the last financial statement and the year of bankruptcy, due to omitted financial statements in Business Retriever. The gap exists because of the time period between the liquidation process and the closed bankruptcy. An issue emerges from a practical point of view, since the years that are without statements affects the results of thesis. The gap has a negative impact on the results since the variables from the lacking years do not have a value of more than zero. By including these values in the thesis, it does not give a fair judgement of the years that the companies are in business. All this considered, although the thesis includes 50 companies for each year, for example 2019, the years analyzed are those with available and tangible information.

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Further about the data collection, there is no limitation about the number of employees or sales for the company, which means that the bankrupt companies consist of different sizes at this stage when selecting criteria in the database. The reason behind this choice is that the thesis wants to include as many companies as possible to limit the risk of not finding enough data because of too many limitations. The stratification process filters and categorizes the information that is found.

3.4.2 Sample selection and stratification

The thesis uses two different samples, sample A which represents bankrupt companies, and sample B which represents non-bankrupt companies. The process is different for collecting the samples. Initially the bankrupt companies are collected because there is a risk that the information can be limited. After finding all the available information for bankrupt

companies, they are matched with non-bankrupt companies. By gathering the relevant data for the bankrupt companies first, the matching process becomes more effective since the

probability of the information for non-bankrupt companies being available is high.

3.4.2.1 Sample stratification bankrupt companies (sample A)

After selecting all the bankrupt companies for sample A by following all the criteria, the thesis stratifies the collected data based on one of the requirements regarding size: the amount of net sales.

The thesis chooses companies with net sales in the range between 10 000 000 - 49 999 999. It is one of the possible criteria to choose from the database Business Retriever and is also classified within the small to medium criteria in Sweden (table 4).

According to the legislation on the annual accounts “Årsredovisningslag” (SFS 1995:1554), there are two different ways to classify the business size in Sweden. The first one states that if the company is listed, it is automatically classified as large. The other way to decide the size is by observing at the net sales, employees, and total liabilities/assets of the company. According to the Swedish Tax Agency “Skatteverket”, the required values for the

classification of size are important in the Accounting Act “Bokföringslag” when it comes deciding whether certain companies are required to prepare annual reports. The values also affect what additional information is required by the company to provide in their annual report (Skatteverket.se, 2020).

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For large companies, if one of the following criteria is met, they are considered large (1:3:4, SFS 1995:1554): (i) if the average number of employees in the company has been more than 50 during each of the last two years; (ii) the company for the two last financial years has reported total assets to more than 40 million SEK; (iii) the company reported net sales of more than 80 million SEK for the past two financial years.

Small and medium companies are in the same category and are classified when the criteria for large companies is not met.

The following table shows the criteria for stratification of company size according to Årsredovisningslag:

Table 4

Classification of business size

(SFS 1995:1554)

3.4.2.2 Selecting non-bankrupt companies (sample B)

The thesis selects non-bankrupt companies based on the same criteria as bankrupt companies, except one. The main difference between the sample selection is the factor of bankruptcy, where in this sample “bankruptcy closed” is not selected. The non-bankrupt companies therefore have similar criteria compared to the bankrupt companies. The matching process is done automatically, by having met the same criteria and merging the data from the two samples in SPSS.

3.5 Independent variables

The independent variables consist of financial ratios. In this section the variables are

explained and why the thesis determines to include these. The calculation behind the ratios in the financial variables is also stated in this section.

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3.5.1 Financial variables

The financial variables that the thesis selects, consist of 11 financial ratios as described in table 5. These are based on: (i) previous literature where these variables have presented themselves to be useful (Tian and Yu, 2017); (ii) from our own observations of the existing completed researches; and (iii) the predictive power in previous studies (Altman, 1968; Gu, 2002; Muscettola, 2015; Szpulak, 2016). The chosen variables are a big part of the accounting research area and are not only useful for bankruptcy prediction. They help internal and

external parties to receive necessary information about the company's well-being.

Due to the difference in the value of the components of the ratios, depending on the size of the companies, it is much more fare to compare the companies between each other using ratios. Even though the total equity may be the same between two companies, if the total assets and total liabilities are not equal between the companies, they will not end up with the same equity ratio. These 11 are tested later to see if they are statistically significant or not.

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The 11 financial ratios

Note: The calculations are retrieved from the database Business Retriever.

3.6 Dependent variable

The dependent variable is a binary variable which means that it can only take on two values, 1 or 0. The bankrupt companies takes on the value of 1 and the non-bankrupt companies takes on the value of 0. The definition of bankruptcy in Sweden, as explained in the literature review, has shaped the meaning of the dependent variable in this thesis.

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Since the Swedish legislation does not regulate bankruptcy as mutually exclusive variables, meaning that the bankruptcy process does not immediately place the company in one category, bankruptcy, or the other, non-bankruptcy. This implies that the several stages between the company being healthy and later registered bankrupt, are not accounted when the binary variables are selected for the thesis. The different stages, for instance, the liquidation process or company reconstruction, are not considered in either of the categories. The dependent variable does therefore not represent any other stage other than a company being non-bankrupt (healthy) or bankrupt (not active).

3.7 Constructing the logistic regression model

The thesis tries to find out whether one can see if a company is likely to be bankrupt or not, thus both of the possible outcomes have to be defined separately in the regression analysis, since they are mutually exclusive (table 6).

Since the dependent variable of the logistic regression is represented by a logit score, the logit score is the natural logarithm of the odds, therefore the natural logarithm of either being bankrupt or non-bankrupt. For the logit score to be in between the numbers 1 and 0 a transition must be made, therefore the use of logarithms (Ohlson, 1980).

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The logistic regression

(Ohlson, 1980)

3.8 Classification matrix

The thesis includes a classification matrix, because of the benefit of being able to locate the possible errors that comes with trying to predict the results. In terms of the thesis, it shows the risk of classifying a non-bankrupt company as bankrupt (type I error), and a bankrupt

company as a non-bankrupt one (type II error).

To be more specific, the classification matrix is a 2x2 formatted table, which illustrates the two possible outputs of the predictions taking the form of either a bankrupt company (denoted 1) or a non-bankrupt company (denoted 0). By doing so, it becomes apparent how and if the model the thesis uses, misclassifies the companies (Hair, 1992).

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Notation to classification matrix

(Hair, 1992)

The true positive is when a bankrupt company is being correctly classified as a bankrupt company, while the true negative is when a non-bankrupt company is correctly classified a non-bankrupt. The false positive stands for the companies that are non-bankrupt but are being misclassified as bankrupt, similarly to the false negative that is the bankrupt companies being misclassified as non-bankrupt (Hair, 1992).

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Performance measures

(Hair (1992)

The correct classification rate is according to Hair (1992) the most common performance measure. It calculates the percentage of companies that are being classified in the correct category, either bankrupt or non-bankrupt companies. However, the missing percentage from the correct classification, which is the misclassification rate, is disregarded. Although it is one of the most used performance measures, it does not distinguish between false positive (type I error) and false negatives (type II error).

The true positive rate is the percentage of the companies that are bankrupt and are being correctly classified as bankrupt. Correspondingly, the true negative rate calculates the correct percentage of non-bankrupt companies being classified as non-bankrupt. The type I error, in other words the false positive rate, describes the percentage of the non-bankrupt companies being misclassified as bankrupt companies. The type II error, the false negative rate, is the percentage of bankrupt companies in the sample being misclassified as non-bankrupt

(Altman, 1997). Misclassification is calculated because of the risk of over- or underestimating the predictive ability of a model. It has been found that the misclassification can be correlated to the independent variables, and therefore crucial to include (Hu, 2008; Feng & Hu, 2013).

3.9 Pearson correlation matrix

The thesis uses the Pearson correlation matrix to detect the potential collinearity between the independent variables, the financial ratios. Since the risk for multicollinearity exists when including the logistic regression model, the thesis investigates the correlation to get a deeper understanding of the underlying results in the regression, and to increase the reliability of the

The predictive power of financial ratios on bankruptcy : A quantitative study of non-listed limited liability SMEs companies in Sweden