Universidade do MinhoEscola de Economia e Gestão

Mara Elisabeth Monteiro Almeida

maio de 2020

Bankruptcy Prediction Models: An Analysis for Portuguese SMEs

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Mara Elisabeth Monteiro Almeida

maio de 2020

Bankruptcy Prediction Models: An Analysis for Portuguese SMEs

Trabalho efetuado sob a orientação daProfessora Doutora Florinda Cerejeira Campos Silva

Projeto de Mestrado Mestrado em Finanças

Universidade do MinhoEscola de Economia e Gestão

ii

DECLARAÇÃO

DIREITOS DE AUTOR E CONDIÇÕES DE UTILIZAÇÃO DO TRABALHO POR TERCEIROS

Este é um trabalho académico que pode ser utilizado por terceiros desde que respeitadas as regras e boas

práticas internacionalmente aceites, no que concerne aos direitos de autor e direitos conexos.

Assim, o presente trabalho pode ser utilizado nos termos previstos na licença abaixo indicada.

Caso o utilizador necessite de permissão para poder fazer um uso do trabalho em condições não previstas

no licenciamento indicado, deverá contactar o autor, através do RepositóriUM da Universidade do Minho.

Licença concedida aos utilizadores deste trabalho

Atribuição-NãoComercial CC BY-NC

https://creativecommons.org/licenses/by-nc/4.0/

iii

Agradecimentos

Assim mais um ciclo se fecha, ciclo este marcado por uma trajetória cheia de obstáculos, incertezas,

tristezas e frustrações mas, sem dúvidas, cheia de alegrias, conquistas, crescimento e experiências que

levarei comigo para a vida.

É com enorme orgulho que concluo o presente projeto de mestrado, e agradeço a todos que, direta

ou indiretamente, me apoiaram na conclusão do mesmo.

Em primeiro lugar, agradeço à minha Orientadora, Professora Doutora Florinda Cerejeira Campos

Silva. Obrigada por toda a disponibilidade, simpatia, paciência e conhecimento demonstrada ao longo deste

percurso, sem a qual a conclusão deste projeto não teria sido possível.

Um especial agradecimento ao Sr. Orlando Costa e toda a esquipa da nBanks, por terem tornado

possível a realização deste projeto bem como, pela confiança, apoio e disponibilidade demonstrada desde o

início.

Agradeço aos pilares da minha vida, meus Pais Elizabete e Manuel, e à minha irmã Lara, por todo

o apoio incondicional e confiança depositada em mim. Obrigada por cada esforço e por toda a motivação,

sem vocês nada disso seria possível. Esta conquista é nossa.

Às minhas irmãs da vida, o presente mais lindo que estes anos me trouxeram. À vocês, Alexandra,

Eliane, Paloma e Grace, um enorme obrigada pela amizade, apoio, motivação e por estarem sempre comigo

nos momentos mais complicados.

Por último, mas não menos importante, agradeço às minhas colegas e parceiras desta experiência

linda que foi realizar este projeto. Sofia, Roxana e Vanise, obrigada pela ajuda, apoio e pelos momentos

fantásticos que vivemos juntas durante esta jornada.

E é com o coração cheio que agradeço a todos os que estiveram envolvidos nestes loucos anos de

viagem. À vocês um enorme obrigada, pois sem cada um de vocês nada disso seria possível.

iv

STATEMENT OF INTEGRITY

I hereby declare having conducted this academic work with integrity. I confirm that I have not used

plagiarism or any form of undue use of information or falsification of results along the process leading to its

elaboration.

I further declare that I have fully acknowledged the Code of Ethical Conduct of the University of

Minho.

v

Modelos de Previsão de Falência: Uma Análise para PMEs Portuguesas

Resumo

Este projeto pretende testar os modelos desenvolvidos por Altman (1983) e Ohlson (1980) e avaliar

a capacidade preditiva desses modelos quando aplicados a um conjunto de dados de PMEs portuguesas.

Este trabalho é resultado de uma parceria com uma startup portuguesa chamada nBanks, que

dedica a sua atividade à prestação de serviços financeiros a seus clientes. Nesse sentido, este projeto

permitirá que a nBanks desenvolva um instrumento novo e inovador que permitirá aos seus clientes

acederem a informação sobre a sua probabilidade de falência ou risco de incumprimento.

Os dados foram coletados na base de dados Amadeus, para o período entre 2011 e 2018. A amostra

é composta por 194.979 empresas, das quais 2.913 empresas estão em dificuldade e as restantes 192.066

são empresas saudáveis. A partir da aplicação dos modelos, concluiu-se que o modelo O-score, utilizando

um ponto crítico de 3,8%, é melhor que o modelo Z’’-score, pois é o modelo que minimiza o erro de uma

empresa em dificuldade ser classificada como uma empresa saudável, embora o Z’’-score apresente, de um

modo geral, melhor precisão. O modelo O-score é melhor que o modelo Z’’-score na previsão de dificuldade

financeira ao considerar o grupo de empresas em dificuldades. Conclui-se também que, quando analisado o

período de até 5 anos antes da dificuldade financeira, a precisão dos modelos diminui à medida que

avançamos no número de anos. Uma análise do Top 25% das empresas classificadas em dificuldade, com

base nos resultados do O-score, mostrou que essas empresas são médias empresas, concentradas no norte

de Portugal e no setor de comércio grossista, exceto veículos automotores e motocicletas.

Palavras-chave: Dificuldade; Modelo O-score; Modelo Z’’-score; Modelos de Previsão de Falência; PMEs.

vi

Bankruptcy Prediction Models: An Analysis for Portuguese SMEs

Abstract

This project intends to test the models developed by Altman (1983) and Ohlson (1980) and assess

the predictive capacity of these models when applied to a dataset of Portuguese SMEs. This work is the result

of a partnership with a Portuguese startup called nBanks, which dedicates its activity to providing financial

services to its customers. In this sense, this project will allow nBanks to develop a new and innovative

instrument that will allow its customers to access their probability or risk of default.

The data were collected from the Amadeus database, for the period between 2011 and 2018. The

dataset consists of 194,979 companies, of which 2,913 companies are in distress and the remaining

192,066 are healthy companies. From the application of the models, it was concluded that the O-score, using

a cut-off of 3.8%, is better than the Z’’-Score as it is the model that minimizes the error of a company in

distress being classified as a healthy company, although the Z’'-score presents the best overall accuracy. The

O-score model is better than the Z’’-Score in forecasting financial distress when considering the group of

companies in distress. It is also concluded that when the period up to 5 years before financial distress is

analyzed, the accuracy of the models decreases as we move forward in the number of years. An analysis of

the top 25% of the companies classified as distressed, based on the results of the O-score, showed that those

companies are medium-sized companies, concentrated in the North of Portugal and the Wholesale trade

sector, except for motor vehicles and motorcycles.

Keywords: Bankruptcy Predicting Models; Distress; O-score model; SMEs; Z’’-score model.

vii

Table of Contents

1. Introduction ................................................................................................................................. 10

2. Terminology and Definitions ..................................................................................................... 11

2.1. Definition of a SME .................................................................................................................. 12

2.2. Default, Failure, Insolvency and Bankruptcy ............................................................................. 13

3. Literature Review ....................................................................................................................... 15

3.1. Evolution of bankruptcy prediction studies ............................................................................... 16

4. Methodology and Sample .......................................................................................................... 22

4.1. Methodology ........................................................................................................................... 22

4.2. Variables ................................................................................................................................. 24

4.3. Dataset ................................................................................................................................... 25

4.4. Descriptive Statistics ............................................................................................................... 27

5. Results .......................................................................................................................................... 31

5.1. General Accuracy of the Models ............................................................................................... 31

5.2. Accuracy of the Models per Group ........................................................................................... 32

5.3. Accuracy of the Models per Period ........................................................................................... 33

5.4. Goals of nBanks ...................................................................................................................... 34

6. Conclusions ................................................................................................................................. 41

References .......................................................................................................................................... 43

Annexes ............................................................................................................................................... 45

viii

Table Index

Table 1 - Simplified classification of micro, small and medium enterprises, according to the European

Commission Recommendation of 2003. ................................................................................................. 12

Table 2 - Description of the Z’’-score model ratios. ................................................................................ 22

Table 3 - Description of the O-score model ratios. .................................................................................. 23

Table 4 - Description of the variables collected from Amadeus. .............................................................. 25

Table 5 - Geographic distribution of non-distressed and distressed companies. ...................................... 26

Table 6 - Descriptive Statistics of the variables, before winsorization. ..................................................... 28

Table 7 - Descriptive Statistics, after winsorization. ................................................................................ 29

Table 8 - Results from the T-test performed to test the difference between the means of the two groups. 30

Table 9 - Overall accuracy of the models. .............................................................................................. 32

Table 10 - Accuracy of the models by group. ......................................................................................... 33

Table 11 - Accuracy of the models up to 5 years before the financial distress. ....................................... 33

Table 12 - Evolution of the ratios mean for the companies classified as distressed for the period under

analysis. ................................................................................................................................................. 38

Table 13 - Evolution of the variables mean for the companies classified as distressed for the period under

analysis. ................................................................................................................................................. 39

Table 14 - Evolution of the financial autonomy ratio for the companies classified as distressed. ............. 40

Table 15 - Evolution of the bank debt ratio for the companies classified as distressed. ........................... 40

ix

Figure Index

Figure 1 - Geographic distribution of the Top 25% of companies in distress. ........................................... 35

Figure 2 - Distribution of the Top 25% of companies in distress by sector. .............................................. 36

Figure 3 - Distribution of the Top 25% of companies classified as distressed by size. .............................. 37

10

1. Introduction

Financial distress is the term used to indicate a condition when the promises made to creditors of a

company are broken or honored with difficulty. If the financial distress cannot be relieved, it can lead to

bankruptcy so, it is valid to say that financial distress may be one of the reasons a company goes bankrupt.

Global financial crises contributed to the failures of many vulnerable institutions and corporate scandals in

recent years and these events justify the need for deepened and extended research on financial distress and

the probability of default. Considering the Portuguese context, this is not an exception once the number of

insolvencies, mainly for SMEs, has increased due to the hard times experienced in the country. This means

that there are more and more companies that do not have enough economic and financial resources to fulfil

the commitments to which they are linked with creditors, shareholders, suppliers and employees. Thus, the

relevance of this topic lies in the fact that anticipating events such as financial distress or bankruptcy is very

important, since it allows, for both creditors, shareholders and employees, the minimization of possible losses

when measures are taken in a timely manner.

The choice of this topic for my project arose through the interest of a startup called nBanks to develop

a new project in a partnership with students from the School of Economics and Management of the University

of Minho. nBanks is a Portuguese fintech company that provides financial services. It has an innovative

business model that allows the optimization of the banking relationship with all its clients namely, companies,

professionals and individuals, and also all types of financial institutions. nBanks provides a platform that

aggregates banking services, focusing on the interests of its users by offering services related to portfolio

management, the search for banking products, index of banking potential, document management,

communication hub, dashboards, and media center. In other words, nBanks provides a global set of financial

services that gives its clients the possibility to improve the accounting and banking procedures, the search

for banking products in a very interactive way and also, to determine the banking risk that they are exposed

to. All these services make the communication between the clients, the accounting and financial professionals

easier. However, nBanks is equally interested in developing a new service that gives their clients the possibility

to know their probability or risk of default or bankruptcy by comparing with other companies of their

benchmark based on some variables such as dimension, sector, and geographical position of the companies.

This service will be a predictive model for the risk of default or bankruptcy for Portuguese SMEs.

11

Many models of bankruptcy prediction were developed over the years so, it is important to study these

models and test how they behave in a Portuguese context. Thus, the main objective of this project is to test

the accuracy of models such as the Z’’-score (Altman, 1983) and the O-score (Ohlson, 1980) to come to

conclusions about their ability to predict financial distress for Portuguese SMEs. With this project, it is also

expected to achieve some goals proposed by nBanks, which will, consequently, be very useful for the

development of a new and differentiating approach that will help their clients to make the best financial

decisions. The proposed goals are:

1. Obtain the percentage of companies in distress in the period under analysis by sector, dimension,

and location;

2. Identify reasons that may have led to the distress of the companies analyzed;

3. Assess the weight of bank debt and the weight of equity in companies in distress in the period under

analysis.

This project is organized into six sections. The first section presents the introduction. The second

section presents some important concepts for the development of this project. In the third section, a brief

literature review about the models for forecasting bankruptcy of companies is elaborated. The fourth section

contains a description of the methodology used, the variables, as well as the sample composition. The fifth

section presents the results obtained from the application of the models, as well as answers to the questions

proposed by the company. Finally, the sixth section presents the conclusions, the limitations of the study

found during the development of the project, as well as the perspectives of future investigations.

2. Terminology and Definitions

In this section, I present a brief description of relevant topics that will be approached in presentation

of this project.

12

2.1. Definition of a SME

The concept of a small and medium enterprise (SME) is not the same for all countries. The definition

of a SME varies from country to country, according to the characteristics assumed by each country for this

type of company.

According to the European Commission Recommendation of 6 of May of 20031 relative to the

definition of micro, small and medium-sized companies, a company is any entity that, regardless of its legal

form, carries out an economic activity. Besides that, according to the same recommendation, the SME’s are

defined considering the number of effective workers, annual turnover and/or the annual balance sheet of the

companies. Given that, a microenterprise is a company that employs less than 10 employees and whose

annual turnover or total annual balance sheet doesn’t exceed 2 million euros. A small enterprise is defined

to be a company that employs less than 50 employees and whose annual turnover or total annual balance

sheet doesn’t exceed 10 million euros. Lastly, a medium-sized enterprise is defined to be a company that

employs less than 250 employees and whose annual turnover doesn’t exceed 50 million euros or whose total

annual balance sheet doesn’t exceed 43 million euros. Table 1 summarizes these definitions of SMEs.

SMEs Number of Employees Turnover Total Balance Sheet

Micro < 10 employees ≤ 2 million € ≤ 2 million €

Small < 50 employees ≤ 10 million € ≤ 10 million €

Medium-sized < 250 employees ≤ 50 million € ≤ 43 million €

Table 1 - Simplified classification of micro, small and medium enterprises, according to the European Commission Recommendation of 2003.

1“Recomendação da Comissão de 6 de Maio de 2003 relativa à definição de micro, pequenas e médias empresas,” 2003

13

2.2. Default, Failure, Insolvency and Bankruptcy

To develop models capable of forecasting bankruptcy of companies, it is important to understand the

definition of bankruptcy. Consequently, over the years, many bankruptcy definitions have been assumed by

the authors, with the main goal of being able to respond to the necessity of forecasting bankruptcy. On the

other hand, we can find in the existing literature a set of other different concepts used to describe business

failure. In general, four generic terms are usually used and found in the literature namely: default, failure,

insolvency, and bankruptcy. Some of these concepts can somehow be mistaken or used in the wrong context,

and that’s why it is important to understand the difference between these terms. In this section, I will briefly

address some of the many definitions that have been adopted.

When it comes to the discussion of this topic, the book ‘’Corporate Financial Distress and

Bankruptcy’’ published by Altman and Hotchkiss (2005) is a good reference. The authors underline the

importance of understanding the difference between these terms.

The default term is associated with the terms of failure, insolvency, and bankruptcy. In other words,

we can say that a situation of default can be seen as a booster, leading a company to end up a failure,

insolvency or bankruptcy situation. According to Altman and Hotchkiss (2005) the term default always

involves the relationship between a debtor and a creditor and it can be technical and/or legal. Technical

default usually happens when the debtor violates the condition of an agreement with a creditor. On the other

hand, the authors illustrate the situation when a company misses a scheduled loan or a bond payment as a

legal default. Failure of companies, by economic criteria, occurs when the realized rate of return on invested

capital is significantly and continually lower than prevailing rates on similar investments (Altman & Hotchkiss,

2005). Beaver (1966) presents a different perspective by defining the term failure as the inability of

companies to pay its financial obligations when due. Situations like bankruptcy, bond default, an overdrawn

bank account, or non-payment of a preferred stock dividend, can lead a company to failure (Beaver, 1966).

Scott (1980) highlights the usefulness of the appropriate definition of failure, contradicting the studies that

used the term failure as the same as bankruptcy. The failure of a company does not always lead to

bankruptcy.

Insolvency is another term that is commonly used to classify a company facing financial difficulties.

In general, this term is defined by its technical form assuming that it occurs when a company cannot meet

its current obligations, resulting in a lack of liquidity (Altman & Hotchkiss, 2005). Altman and Hotchkiss

14

(2005) also define insolvency in a bankruptcy sense as another possible condition. According to them, this

condition is more critical, resulting in a more chronic rather than a temporary condition as in the first one. A

company is susceptible to this condition when its total liabilities exceed a fair valuation of its total assets. The

authors claim that, differently from technical insolvency that is easily detectable, an insolvency in a bankruptcy

sense condition requires a comprehensive valuation analysis.

When it comes to bankruptcy, we can find different definitions adopted by authors over the years.

Altman (1968), defines bankruptcy as a situation in which a company is not capable of paying off its debts

or obligations and, consequently the company cannot keep on with its operating activities anymore. In the

study of Gordon (1971), bankruptcy is defined as a reduction of the profiting power of companies that causes

the increase of the inability of companies in paying its expenses and other obligations. Blum (1974) uses the

term bankruptcy as the inability of companies to pay their debts and therefore, manage to get a debt reduction

arrangement or enter an insolvency process. Altman and Hotchkiss (2005) consider that the term bankruptcy

doesn’t precisely means that the company no longer exists. In other words, a company can go bankrupt and

still exist in the market. According to the authors, it is important to look at the investment rate of return and

profits of the companies. Legal bankruptcy or disappearance of a company only occurs when it can’t settle

its legal responsibilities.

In general, the economic and financial literature provides three different definitions of bankruptcy

namely, economic bankruptcy, technical bankruptcy, and legal bankruptcy. The economic bankruptcy is

justified by the inability of the company to pay its expenses due to low profitability. In other words, the costs

of the company are higher than the profits. The technical bankruptcy happens when a company presents a

negative liquid situation, this means that the liabilities of the company are higher than the assets and

consequently, the company is not capable to deal with its obligations. This can lead to several negative results

during the years of activity of the company.

In Portugal, the term bankruptcy is not so relevant. This is a result of the introduction of a new code

in 2004 that rules the insolvency and restructuring processes of Portuguese companies called the Insolvency

and Corporate Recovery Code (CIRE)2. Since then the term bankruptcy has no longer been used, giving rise

to term of insolvency. From a legal point of view, this means that what matters is to detect if a company is in

an insolvency situation or not. According to article 3 of CIRE, a company is declared insolvent when it is

2 “Código da Insolvência e da Recuperação de Empresas (CIRE),” 2004

15

unable to fulfil its overdue obligations, or also when its liabilities exceed its assets and any individual can

respond personally and unlimitedly, directly or indirectly for its debts. In other words, we can say that

bankruptcy is a state in which a company’s debts are greater than the assets to pay them, therefore being

an irreversible situation, whereas insolvency is a state in which the company’s debts are greater than the

resources to pay them in time, thus a reversible situation.

In this project, three different states will be considered to define the situation of the companies under

analysis, namely active, insolvency proceedings and liquidation. According to the database used in this

project, Amadeus, an active company is active or in other words healthy. When it comes to the state of

insolvency proceedings the company is declared insolvent but still active. During this period of insolvency,

the company is usually placed under the protection of the law and continues operating and repaying creditors

and tries to reorganize and return to normal operating. In the end, the company will either return to normal

operating, which means that the default of payment was thus temporary, or will be reorganized, or will be

liquidated. Lastly, a company is in liquidation when all of its assets are being sold. The next step will be that

the company will be dissolved and will no longer exist. However, the reason why the company is in liquidation

is not known. The reason for the liquidation can be the termination of the company as per the company

status, voluntary dissolution, or another reason that is not related to payment or credit difficulties.

As we can see, over the years many different definitions of bankruptcy, insolvency, failure, and default

were used. Given that, we can conclude that it is important to understand the meaning of these terms thus

avoiding their misuse.

3. Literature Review

Over the years many models have been developed to predict the bankruptcy of companies. These

models primarily use financial ratios computed and based on accounting information from the companies

contained in their financial statements. Financial ratios can be good predictors of bankruptcy given that they

are likely to reveal strong differences between bankrupt and non-bankrupt companies. These models became

very important and famous, especially in the academic world, as they prove strong evidence of success to

predict financial distress. This section presents a brief description of the existing literature about the

bankruptcy of companies, since the first approaches to the most recent ones.

16

3.1. Evolution of bankruptcy prediction studies

The bankruptcy of companies is not a recent issue and it has been addressed in many studies over

the years, contributing to the existence of many approaches that differ at the level of variables and

methodologies used to predict the probability of bankruptcy of a company.

The literature identifies the study carried out by Beaver in 1966, as the first study of bankruptcy

forecast. Beaver used a univariate analysis, based on a separate analysis of many financial ratios and on the

determination of a value by which one can say that a company is in a critical situation. The sample consisted

of 158 industrial and publicly traded companies, located in the USA and for the period between 1954 and

1964. Initially, the author computed 30 ratios selected using three criteria: the popularity of the ratios in the

literature, the performance of the ratios in previous studies and the definition of the ratios in terms of ‘’cash-

flow’’. However, from this initial list of 30 ratios, only the ratios with the best discriminatory ability were

selected. In total, six ratios were selected namely:

Cash flow/Total debt;

Working capital/Total assets;

Net income/Total assets;

Total debt/Total assets;

Current assets/Current liabilities

No-Credit Interval.

After the comparison of the ratios for both groups, failed and non-failed companies, Beaver

concluded that non-failed companies present, on average, much better results for the selected ratios, except

for the total debt/total assets ratio. According to the author, this happens because failed companies tend to

incur more debt than healthy companies, although they are less likely to honor their obligations (Beaver,

1966). The author also concluded that the ratio cash-flow/total debt was the ratio responsible for the correct

classification of 87% of the companies, for one year before bankruptcy, and it classified correctly 73% of the

companies, four years before the bankruptcy.

This model provides us with a methodology for the financial analysis of companies, being possible to

predict the bankruptcy of a company up to five years before the event. However, this approach has a big

limitation, which is the fact that the analysis of each ratio is done individually, not allowing the study of the

relation between the ratios.

17

To overcome the limitations of the univariate analysis, Altman (1968) proposed the Z-Score model

based on a multiple discriminant analysis (MDA), which allows distinguishing, on a statistical basis, two or

more groups using many variables simultaneously to predict bankruptcy of companies. MDA is generally used

to classify a dependent variable in a qualitative form, for example, bankrupt or non-bankrupt. Altman (1968)

used a sample of 66 North American publicly-traded manufacturing companies, divided into two groups,

where 33 were bankrupt companies and 33 were non-bankrupt or ‘’healthy’’ companies during the period of

1946 to 1965. It is important to say that the healthy companies were selected according to similarities in

terms of sector, size and years of the sample, with the bankrupt companies. Because of the existence of a

large number of potential indicators of corporate difficulties, Altman defined a list of 22 potential variables

(ratios). Those variables were classified into 5 ratio categories reflecting the liquidity, profitability, leverage,

solvency and activity situation of the companies. The ratios were chosen given two important factors, their

popularity in the literature and the potential relevancy to the study. From the list of the 22 possible ratios,

only five proved to be statistically significant, and were therefore the chosen ones:

Working capital/Total assets;

Retained Earnings/Total assets;

EBIT/Total assets;

Market value of equity/Book value of total liabilities;

Sales/Total assets.

A linear combination of the five variables, through a discriminant function, allowed the development

of the so-called Z-score whose values allow us to distinguish the bankrupt companies from the normal/healthy

ones.

The model was able to predict bankruptcy for 95% of the companies, for one year before the event,

and for 83% of the companies, two years prior to the bankruptcy. The author also tested the model for three,

four and five years before the event, and concluded that the accuracy of the model fell consistently over the

years of analysis.

However, the model showed some limitations, such as:

The model was only tested for publicly held corporations, whose market value could be known;

There was no theoretical basis that would justify the selection of the ratios;

The model assumed that the variables followed a normal distribution and equal variance-

covariance matrices for both groups (failed and non-failed companies).

18

Altman (1983), estimated a new version of the model substituting the market value for the book value

of equity. This revised version of the original Z-score model was named Z’-score model.

In this study the accuracy of a four-variable model called Z’’-score model was also analyzed. This new

version of the model excluded the ratio Sales/Total assets from the original model because it is a very volatile

ratio from industry to industry which could influence the results of the model. It is important to note that the

results in terms of the classifications obtained by the Z’’-score model were identical to the Z’-score model.

The Z’’-score model also has the advantage of being wider, given the fact that it is intended for both listed

and unlisted companies, and is also not only for manufacturing companies. Over the years, the models

developed by Altman (1968, 1983) have been adapted to other contexts, updated and improved by several

authors (Deakin, 1972; Altman et al.,1977; Taffler, 1982).

Deakin (1972) proposed a model based on a discriminant analysis to predict bankruptcy. The author

criticizes Altman (1968) because of the abrupt decrease of the forecasting ability when considering more

distant years. The dataset consisted of 32 failed and non-failed companies, all from the same sector and

asset size, between the years 1964 and 1970. Through a linear combination of the ratios proposed by Beaver

(1966), 14 ratios were selected, namely:

Cash flow/Total debt;

Net income/Total assets;

Total debt/Total assets;

Current assets/Total assets;

Quick assets/Total assets;

Working capital/Total assets;

Cash/Total assets;

Current assets/Current liabilities;

Quick assets/Current liabilities;

Cash/Current liabilities,

Current assets/Sales;

Quick assets/Sales;

Working capital/Sales;

Cash/Sales.

19

The model provided a success rate of 97%, 95%, 95%, 80% and 83% for one, two, three, four and

five years before the bankruptcy, respectively.

Altman, Haldman and Narayanan (1977), along with a private company called Zeta Services, Inc.,

developed another model that allowed its application to companies of a bigger dimension and from different

sectors and also, considered the changes in accounting standards (Cristina, 2019). The sample was

composed of 53 failed companies and 58 non-failed companies or the so-called ‘’standard’’ companies.

Initially, the model considered 27 possible ratios but only 7 ratios were selected given their statistical

significance. In general, the model classified correctly more than 90% of the companies for a year prior to the

bankruptcy and about 70% of the companies up to five years before the bankruptcy. Given these results, we

can conclude that this model provided better results than the Z-score model. Unfortunately, the equation for

the discriminant function of this model wasn’t disclosed.

Taffler (1982) developed a model using discriminant analysis and financial ratio data to measure the

solvency of companies. To do that he considered a sample of 46 failed companies and 46 non-failed

companies. The author selected companies that had failed over the past 6 years and the non-failed companies

were randomly selected according to their good financial situation, dimension, and sector. From an initial list

of 80 possible ratios, only four ratios were selected. Taffler developed what we can call the ‘’Solvency

Thermometer’’, which allows classifying the companies as solvent or not solvent, according to a predefined

solvency threshold.

As already mentioned above, the MDA assumes that independent variables follow a normal

distribution and also assumes equal variance-covariance matrices for both groups of failed companies and

non-failed companies. These are some of the limitations of the method that may influence the results of the

model. In this sense, a new method has emerged, called the Logit method. The Logit method emerged as a

way to overcome the limitations of the MDA method by allowing the use of dummy variables as independent

variables.

Ohlson (1980) was one of the pioneers in the development of a probabilistic model called O-score,

by using the logistic regression to analyze the bankruptcy of companies. The use of a conditional logit analysis

avoids the problems that can be caused by the MDA method. The final sample was made up of 2,058 non-

bankrupt companies and 105 bankrupt companies, for a period of time between 1970 and 1976.

The O-score showed ability to predict correctly at about 96.12% one year before bankruptcy, 95.55%

for two years before bankruptcy and 92.84% between one and two years before the bankruptcy. This study

20

shows that the predictive power of any model depends on the timing in which each financial and accounting

information is made available to the economic agents. This fact is a distinguishing feature from other studies,

since they do not consider this timing issue. Most of the studies presume that the financial and accounting

information is available at the fiscal year-end date. However, Ohlson (1980) emphasize that if the purpose is

to evaluate bankruptcy forecasting ability, this kind of assumption is inadequate because it may be possible

that a company files for bankruptcy at some point in time after the fiscal year, but before releasing the

financial and accounting statements. The study also considered that the results provided by the discriminant

analysis are less intuitive than the results obtained with the logistic regression, once that the logistic

regression had managed to determine the bankruptcy probability of a company.

There are other methods that can be used in the prediction of bankruptcy, like the Probit Model and

the Neural Networks. Zmijewski (1984) was one of the first studies to apply the Probit model. The Probit

model is very similar to the Logit model, however, it considers a normal cumulative distribution function.

Zmijewski (1984) used a sample of 40 insolvent companies and 800 non-insolvent companies, between the

period of 1970 and 1978. All the companies were publicly traded companies. The model was built by using

three independent variables, reflecting the assets profitability, the liquidity and debt ratio.

Neural Networks is the most recent methodology and because of its increasing popularity this

methodology is still under investigation and development. The literature identifies Dumontier (1996) as the

first author to develop this method in the evaluation of the risk of failure. The analysis was carried out between

the period of 1988 and 1990, where he analyzed 2,736 French companies from the transport sector. From

this group of companies, 114 were bankrupt companies.

Altman, Marco and Varetto (1994) compare the neural networks with the Logit analysis and the

results showed a balanced degree of accuracy between the neural networks and the Logit analysis. Both

techniques provided over 90% accuracy, suggesting that further studies using these two techniques would be

very interesting in the future. However, Altman, Marco and Varetto (1994) highlight the existence of some

type of behaviors that are not accepted by the network and also that the neural networks are hard to

understand and to apply.

Altman and Sabato (2007) developed a study where the main goal was to analyze a group of financial

ratios characteristic of SMEs. One of the features of this study is that it recognizes the importance of SMEs

in the economy of many countries, especially for the members of OCDE (Altman & Sabato, 2007). The sample

was collected for the period between 1994 and 2002, and it was constituted by 2,010 from which 120 were

21

bankrupt companies. The authors applied the Logit analysis to develop the model and initially selected 17

financial ratios that reflect the liquidity, profitability, coverage, leverage, and activity of the companies. These

ratios were selected according to their success ability in predicting companies’ bankruptcy in the literature.

Basing on the accuracy ratio, two ratios with the highest accuracy for each category were arbitrarily selected.

The next step was to apply a statistical forward stepwise selection procedure to the 10 selected ratios and

then, estimate the complete model by excluding the less efficient ones, which means the ones which their

significance level was below the chosen critical level. After all these procedures, five ratios remained to

compute the model, namely:

Short term debt/Equity book value;

Cash/Total assets;

EBITDA/Total assets;

Retained earnings/Total assets;

EBITDA/Interest expenses.

In the first stage, logistic regression was applied to the model without any treatment of the data. The

model provided a forecasting ability of 75%. This result is clearly below the ones shown in previous studies.

In this sense, the logarithmic transformed variables were used to compute a new model with the aim to

increase the accuracy of the model. This new model achieved an accuracy of 87%. Besides that, the authors

also tested a generic corporate model (Z’’-score) which presented an accuracy of 69%. After that, they

compared the results provided by the logistic model developed with the logarithmic transformed variables,

the logistic model developed with the original variables (with no logarithmic transformed variables) and the

Z’’-score model. The conclusion was that the logistic model developed with logarithmic transformed variables

presented a higher forecasting ability. For comparison purposes, a multivariate discriminant analysis (MDA)

was tested using the same five logarithmic transformed financial ratios as the ones used for the logistic

model. The main conclusion was that the Z”-score performed better than the MDA.

Altman et al. (2017) studied financial distress prediction in an international context by using Altman’s

Z-score model. The study shows evidence that, in general, the Z-score model works for the major part of the

countries and the accuracy of the forecast increases as more variables of the countries are added for more

specific estimations. The methodology was, in the first stage, to test how the original model would perform

in different countries and then, in a second stage, re-estimate the original Z-score model by using a different

statistical approach, the LRA (Logistic Regression Analysis). The LRA method is different from the MDA

22

because it is based on less restrictive statistical assumptions. Altman et al. (2017) concluded that the original

Z-Score model performs very well when considering an international context, and the same conclusion holds

for the re-estimation of the model using the LRA method. The study proved that the results in terms of

performance of the LRA method were very similar to the performance of the original one.

4. Methodology and Sample

In this section we describe the selected models, variables and sample.

4.1. Methodology

The revised Z’’-score model developed by Altman (1983) and the logit analysis or O-score developed

by Ohlson (1980) are the selected models and therefore the ones to be tested.

The revised Z’’-Score model takes the form of a discriminant function with four variables given by:

Z’’ = 6.56X1 + 3.26X2 + 6.72X3 + 1.05X4

Table 2 summarizes the description of each ratio.

Variable Ratio Description

X1 Working Capital / Total Assets Measures the net liquid assets of a company relative to the total number of its assets.

X2 Retained Earnings / Total Assets Measures the accumulation of profits of a company.

X3 EBIT / Total Assets Measures the operating profitability of a company's total assets, excluding any tax or leverage factors.

X4 Book value of equity / Book value of total liabilities

Indicates how much the company’s assets can decrease before the company goes bankrupt.

Table 2 - Description of the Z’’-score model ratios. Working Capital=Current Assets - Current Liabilities; Retained Earnings=Other shareholders’ funds + Net income - Dividends; Total Liabilities= Total Assets – Equity.

The companies are classified according to the three zones of discrimination defined by Altman:

Z > 2.6 – ‘’Safe’’ Zone

1.1 < Z > 2.6 – ‘’Grey’’ Zone

Z < 1.1 – ‘’Distress’’ Zone

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On the other hand, the O-score model is a result of a linear combination of 9 independent variables,

where two are dummy variables and the other variables are business ratios that can be obtained from the

financial statements of the companies. The calculation of the O-score is given by the following formula:

y = - 1.32 – 0.407(SIZE) + 6.03 (TLTA) – 1.43 (WCTA) + 0.0757 (CLCA) – 2.37 (NITA) – 1.83 (FUTL) +

0.285(INTWO)-1.72 (OENEG) – 0.521 (CHIN)

The description of the ratios of the model is summarized in table 3 below.

Variable Ratio Description

SIZE Log ( Total Assets / GNP price-level index)

It indicates the company’s size measured as its total assets adjusted for inflation.

TLTA Total Liabilities / Total Assets Measures the company's long term leverage.

WCTA Working Capital / Total Assets Measures the company's liquidity indicating the weight of the working capital on its total assets.

CLCA Current Liabilities / Current Assets Measures the company's short term leverage.

OENEG 1 if total liabilities exceeds total assets, 0 otherwise

Leverage measure by assessing if a company has negative net book value or not.

NITA Net Income / Total Assets Measures the profitability of a company by assessing the return the company makes on its assets.

FUTL Funds provided by operations / Total Liabilities

Measures the company's liquidity through the degree by which it can finance its liabilities with its operational income.

INTWO 1 if net income was negative for the last two years, 0 otherwise

Indicates the profitability of a company by analyzing whether the company had losses for the last two years.

CHIN ( NIt + NIt-1 )/(|NIt| + |NIt-1|) Measures the change in the net income.

Table 3 - Description of the O-score model ratios.

To calculate the probability of bankruptcy of a company, Ohlson (1980) uses a logistic function

given by:

P = 1 / (1 + exp (-y))

To classify the companies we consider the cut-off of 3.8% used by Ohlson (1980) given that,

companies with a P>3.8% are classified as distressed and companies with P

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off of 50%. For this research we test the O-score model using the cut-off point of 3.8% and also the cut-off of

50%, to analyze which cut-off provides better accuracy for the model.

Regarding the general accuracy of the models, this is calculated by the sum of the total number of

correct classifications divided by the total number of companies. The accuracy of the model in classifying a

distress situation is calculated by the sum of the total number of correct classifications of distressed

companies divided by the total number of distressed companies. Thus, the accuracy of the model to classify

the active or non-distressed companies is given by the sum of the total number of correct classifications of

non-distressed companies divided by the total number of non-distressed companies.

We also consider two types of errors namely Type I error and Type II error, according to each one of

the models since each model defines this type of error differently. When using the Z’’-score model, the Type

I error happens when the model classifies a distressed company as non-distressed and when a non-distressed

company is classified as distressed, we are in presence of a Type II error. When using the O-score model the

definitions of the errors are different. Thus, the Type I error happens when a non-distressed company is

classified as distressed and Type II error occurs when a distressed company is classified as non-distressed.

For nBanks the most serious error would be classifying a distressed company as non-distressed (Type

I error for the Z’’-score model and Type II error for the O-score model). Given such analysis, the best model

is the one that minimizes this type of error.

4.2. Variables

Since one of the objectives of this research is to test the models developed by Altman (1983) and

Ohlson (1980), the variables used are the ratios defined by the authors for the respective models. Even so,

to calculate each of the ratios, a set of variables is necessary and all of them were collected from the Amadeus

database, except the GNP (Gross National Product) price-level index variable used to calculate the SIZE ratio.

To calculate this variable the GNI (Gross National Income), previously known as GNP, was taken from the

Bank of Portugal website. The variables collected from Amadeus are presented in table 4.

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Variables Amadeus Definitions

Total Assets Total assets (Fixed assets + Current assets)

Current Assets Total amount of current assets (Stocks + Debtors + Other current assets)

Current Liabilities Current liabilities of the company (Loans + Creditors + Other current liabilities)

Shareholders’ Funds Total equity (Capital + Other shareholders funds)

Other Shareholders Funds All Shareholder funds not linked with the Issued capital such as Reserve capital,

Undistributed profit, include also Minority interests if any.

Net Income Net income for the Year before deduction of Minority interests if any (Profit after

taxation + Extraordinary and other profit).

EBIT All operating revenues - all operating expenses (Gross profit-Other operating expenses

Cash flow Profit for period + Depreciation

Operating Revenue (Turnover) Total operating revenues (Net sales + Other operating revenues+ Stock variations)

Number of Employees Total number of employees included in the company's payroll

Table 4 - Description of the variables collected from Amadeus.

4.3. Dataset

The sample consists of 194,979 Portuguese SMEs, divided into two groups: the group of active

companies, representing healthy companies, and the group of companies in financial difficulty. Within this

latter group are companies that are in a situation of insolvency proceedings or liquidation situation. Since for

companies in liquidation it is not possible to know the reason that justifies this situation, only those for which

information about the previous status was insolvency proceedings were collected. These companies, as well

as their financial data, were collected from the Amadeus database.

From this group of companies, only unlisted companies were collected and companies from the

financial sector, which correspond to CAE 64, 65, 66 and 68, were excluded. When it comes to financial data

of the companies, data corresponding to the period of 2010 to 2018 were collected.

To obtain a sample consisting only of SMEs, the statistical program STATA was used to proceed with

the elimination of companies that, according to the previously defined criteria, do not fit the definition of

SMEs. Therefore, the only companies selected were those whose number of employees was more than 9 and

26

less than 250 and whose annual turnover did not exceed 50 million euros or whose total annual balance

sheet did not exceed 43 million euros.

Still using the STATA program, an adequate cleaning of the data was carried out to avoid possible

bias in the results. This cleaning process consisted of the following points:

Exclusion of companies with no identification (BvD ID number);

Elimination of the years of observations that did not present data that would allow the

calculation of the ratios;

Exclusion of companies that didn’t present at least 3 years of activity (startups founded in

2016);

Elimination of data with possible errors (negative total assets, negative current assets,

negative total liabilities, and negative current liabilities);

Exclusion of companies with less than 3 years of consecutive data.

Thus, the final sample consists of Portuguese SMEs not listed on the stock exchange, distressed and

non-distressed and distributed geographically as follows:

Current Situation Region Number of Companies

Non-distressed

North 68620 Lisbon Metropolitan Area 53227 Centre 42232 Alentejo 12308 Algarve 8948 Autonomous Region of Madeira 3932 Autonomous Region of Azores 2799

Non-distressed Total

192066

Distressed

North 1292 Lisbon Metropolitan Area 691 Centre 586 Alentejo 142 Algarve 82 Autonomous Region of Madeira 70 Autonomous Region of Azores 50

Distressed Total

2913

Table 5 - Geographic distribution of non-distressed and distressed companies.

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As we can see from table 5, both distressed and non-distressed companies are mostly located in the

North of Portugal, Lisbon, and the Centre of Portugal.

4.4. Descriptive Statistics

Table 6 presents the descriptive statistics of the ratios for each one group of companies: distressed

and non-distressed. The variables often present extreme values or outliers sometimes due to some data errors

so, it is important to analyze the existence of possible outliers to avoid possible bias in the results.

According to Loeffler and Posh (2007), a good indicator of the existence of outliers is the excess

kurtosis (defined as kurtosis minus 3). Assuming as a benchmark of normal distribution, and knowing that a

normal distribution has an excess kurtosis of 0, we can see that most of the variables present very high

kurtosis values ranging from 1.67 to 992 191.50. This means that, compared to a normal distribution, there

are many observations far outside the mean. Looking at the skewness of the variables, we can conclude that

these are also skewed meaning that, for the variables with a negative skewness, the outliers or extreme values

are concentrated on the left and, for the variables with positive skewness, the extreme values are concentrated

on the right.

The elimination of the extreme values would lead to a reduction of the sample so, to avoid this, the

winsorization technique is used as it allows the correction of the outliers without a reduction of the sample.

The winsorization controls the influence of outliers by pulling the extreme values to less extreme ones, using

a certain level of winsorization. All variables were winsorized at the 1% level, which mean that values below

the percentile 1 of the values of the distribution are set equal to the value of percentile 1, and values above

percentile 99 are set equal to the value of percentile 99. The descriptive statistics for the winsorized variables

are presented in table 7.

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Non-distressed Mean Standard Deviation

Percentile 1

Minimum Percentile 99

Maximum Skewness Kurtosis

X1 (Working Capital / Total Assets)

0.12 7.12 -3.59 -4981.90 0.96 4.46 -592.96 382532.60

X2 (Retained Earnings / Total Assets)

-0.12 8.08 -7.82 -5269.65 1.13 106.40 -504.94 305624.80

X3 (EBIT / Total Assets) -0.01 0.81 -1.52 -165.90 0.59 464.37 120.24 96817.95 X4 (Book value of equity

/ Book value of total liabilities)

14.64 5178.76 -0.85 -0.99 47.89 4511452 732.56 580068.30

SIZE 5.29 0.70 3.84 1.19 7.14 8.68 0.37 3.27 TLTA 0.92 7.36 0.02 0 6.67 4981.96 539.30 335571.50 WCTA 0.12 7.12 -3.59 -4981.90 0.96 4.46 -592.96 382532.60 CLCA 1.46 81.52 0.01 0 13.90 85966.48 983.42 1031886 NITA -0.03 0.77 -1.55 -165.98 0.50 380.32 55.71 59232.18 FUTL 1.49 788.35 -1.06 -126691 5.12 822775.10 955.45 992191.50 CHIN 0.02 323.89 -10.01 -299293.50 9.64 70717.10 -680.94 621222.20

INTWO 0.15 0.36 0 0 1 1 1.91 4.65 OENEG 0.17 0.37 0 0 1 1 1.77 4.15

Distress Mean Standard Deviation

Percentile 1

Minimum Percentile 99

Maximum Skewness Kurtosis

X1 (Working Capital / Total Assets)

-0.36 21.18 -5.74 -2591.83 0.89 1 -118.80 14495.97

X2 (Retained Earnings / Total Assets)

-0.82 21.76 -11.37 -2637.82 0.79 3.26 -115.43 13935.40

X3 (EBIT / Total Assets) -0.14 1.10 -2.14 -55.68 0.36 5.66 -30.97 1264.31 X4 (Book value of equity

/ Book value of total liabilities)

0.39 4.18 -0.89 -1.00 5.40 422.72 72.60 6904.11

SIZE 5.71 0.71 4.07 4.07 7.42 7.42 0.07 2.65 TLTA 1.48 21.24 0.16 0.00 9.02 2592.83 117.77 14327.09 WCTA -0.36 21.18 -5.74 -2591.83 0.89 1 -118.80 14495.97 CLCA 3.08 81.17 0.05 0 23.06 9437.21 104.13 11860.03 NITA -0.16 1.13 -2.17 -59.30 0.29 4.77 -31.70 1327.21 FUTL -0.04 0.88 -0.87 -65.13 0.73 40.22 -32.90 2751.73 CHIN 0.07 39.33 -8.82 -1510.01 8.22 3832.03 69.14 6720.51

INTWO 0.25 0.44 0 0 1 1 1.13 2.27 OENEG 0.31 0.46 0 0 1 1 0.82 1.67

Table 6 - Descriptive Statistics of the variables, before winsorization.

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Non-distressed Mean Standard Deviation

Percentile 1 Minimum Percentile 99 Maximum Skewness Kurtosis

X1 (Working Capital / Total Assets)

0.19 0.66 -3.59 -3.59 0.96 0.96 -3.03 16.18

X2 (Retained Earnings / Total Assets)

0.00 1.24 -7.82 -7.82 1.13 1.13 -4.12 23.32

X3 (EBIT / Total Assets) 0.01 0.27 -1.52 -1.52 0.59 0.59 -2.95 16.74

X4 (Book value of equity / Book value of total

liabilities)

2.30 6.42 -0.85 -0.85 47.89 47.89 5.25 33.69

SIZE 5.29 0.69 3.84 3.84 7.14 7.14 0.34 2.89

TLTA 0.82 0.92 0.02 0.02 6.67 6.67 4.13 23.75

WCTA 0.19 0.66 -3.59 -3.59 0.96 0.96 -3.03 16.18

CLCA 1.04 1.92 0.01 0.01 13.90 13.90 4.72 28.28

NITA -0.02 0.26 -1.55 -1.55 0.50 0.50 -3.33 18.60

FUTL 0.28 0.77 -1.06 -1.06 5.12 5.12 3.91 22.31

CHIN 0.31 2.09 -10.01 -10.01 9.64 9.64 -0.62 13.26

INTWO 0.15 0.36 0 0 1 1 1.91 4.65

OENEG 0.17 0.37 0 0 1 1 1.77 4.15

Distress Mean Standard Deviation

Percentile 1 Minimum Percentile 99 Maximum Skewness Kurtosis

X1 (Working Capital / Total Assets)

-0.06 0.88 -5.57 -5.74 0.89 0.89 -3.90 22.81

X2 (Retained Earnings / Total Assets)

-0.44 1.58 -10.68 -11.37 0.79 0.79 -4.70 29.05

X3 (EBIT / Total Assets) -0.10 0.33 -2.07 -2.14 0.36 0.36 -3.73 20.10

X4 (Book value of equity / Book value of total

liabilities)

0.27 0.84 -0.88 -0.89 5.37 5.40 3.46 19.73

SIZE 5.72 0.72 4.07 4.07 7.41 7.42 0.06 2.65

TLTA 1.14 1.14 0.16 0.16 8.56 9.02 4.73 29.30

WCTA -0.06 0.88 -5.57 -5.74 0.89 0.89 -3.90 22.81

CLCA 1.56 2.92 0.05 0.05 22.44 23.06 5.46 36.42

NITA -0.12 0.33 -2.07 -2.17 0.29 0.29 -3.80 20.41

FUTL -0.02 0.21 -0.84 -0.87 0.71 0.73 -0.55 7.68

CHIN -0.22 1.85 -8.39 -8.82 8.19 8.22 -0.02 11.39

INTWO 0.25 0.43 0 0 1 1 1.14 2.31

OENEG 0.30 0.46 0 0 1 1 0.87 1.76

Table 7 - Descriptive Statistics, after winsorization.

Analyzing Tables 6 and 7, we can observe that the winsorization allowed the elimination of the existent

outliers. Table 7 allow us to conclude that there is a clear difference between the average values of the

distressed and non-distressed companies. The distress group of companies presents negative values for

almost all of the variables, mainly for the ones that reflects the profitability situation of the companies, which

30

is not surprising if we consider that the incidence of financial distress in companies with negative profits is

more likely to occur.

The means of the variables for each group of companies and respective t-tests and p-values are

shown in table 8 below:

Ratios Non-distressed Group Mean

Distress Group Mean

T-test P-value

X1 ((Working Capital / Total Assets)) 0.19 -0.06 45.6198 0.00 X2 (Retained Earnings / Total Assets) 0.00 -0.44 41.5811 0.00

X3 (EBIT / Total Assets) 0.01 -0.10 45.8035 0.00 X4 (Book value of equity / Book

value of total liabilities) 2.30 0.27 37.2305 0.00

SIZE 5.29 5.72 -73.4007 0.00 TLTA 0.82 1.14 -41.4266 0.00 WCTA 0.19 -0.06 45.6198 0.00 CLCA 1.04 1.56 -31.6262 0.00 NITA -0.02 -0.12 47.2122 0.00 FUTL 0.28 -0.02 46.7638 0.00 CHIN 0.31 -0.22 29.8492 0.00

INTWO 0.15 0.25 -31.4342 0.00 OENEG 0.17 0.30 -41.1278 0.00

Table 8 - Results from the T-test performed to test the difference between the means of the two groups.

The performed t-test indicates that the means of the two groups are not equal, at a significance level

of 5%. This means that there is a significant difference between the two groups. Looking to the means

presented by the ratios for both groups, we can conclude that, in general, the non-distressed group presents

better values for the ratios, as we would expect. For example, ratio X1 (Working capital/Total assets) is a

liquidity ratio that reflects the liquidity level and the financial power of a company. In general, the higher the

value of this ratio, the higher is the liquidity of the company which means that the value of the current assets

of the company is higher than that of current liabilities. Although the non-distressed group presents a low

value for this ratio (0.19), it still shows a better value than the distressed group that presents a negative value

(-0.06). This negative value is a sign of the financial distress of the companies and reflects the lack of liquid

assets to pay their current liabilities as they mature.

The ratio X2 (Retained earnings/Total assets) is seen as a cumulative profitability over time. According

to Altman (1968), the age of a company is implicitly considered in this ratio, assuming that a younger

company will probably present low values for this ratio since it has not had enough time to build up its

cumulative profits. In addition, this ratio tells us what the leverage level of a company is. High values of this

31

ratio indicate that assets of a company are essentially funded from internal resources of the company. In

other words, the higher this ratio means that a company is less reliant on other common types of financing

such as external debt and capital injections. Comparing the two groups, once again the non-distressed group

shows a better value.

TLTA (Total liabilities/Total assets) and CLCA (Current liabilities/Current assets) reflect the long-

term and short-term leverage levels of a company, respectively. These ratios indicate the proportion of a

company’s assets which are financed through debt. High values of these ratios reflect high levels of leverage

of companies. Looking at both groups in analysis, we can conclude that the distressed group presents higher

levels of leverage.

NITA (Net income/Total assets) is a profitability ratio, which measures how profitable a company is

relative to its assets. In other words, this ratio indicates the efficiency of a company at using its assets to

generate profits. The higher this ratio, the more efficient the company at generating income through its assets.

Comparing both groups, we can see that both show negative values for this ratio, reflecting negative net

income of the companies.

As mentioned before, we can verify a significant difference in the mean value of the variables between

non-distressed and distressed companies, with the distressed group of companies presenting a negative

mean for almost all of the ratios, and the non-distressed group of companies presenting a positive mean for

the ratios.

5. Results

This section presents the analysis of the financial distress prediction ability of the Altman (1983)

and Ohlson (1980) models.

5.1. General Accuracy of the Models

Using the STATA statistical program, the Z’’-score model, the O-score with the original cut-off of 3.8%

and the O-score with the cut-off of 50% models were applied. The scores for each company for each year of

observation were calculated, so that it was possible to classify the companies according to the cut-offs

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previously defined. As mentioned before, the accuracy of the models is calculated from the total number of

companies correctly classified by the models divided by the total number of companies. After making the

necessary calculations, the accuracy for each model was obtained as well as the percentage of type I and II

errors as shown in table 9 below:

Models Accuracy Type I Error Type II Error

Z-score 79.88% 63.06% 14.99%

O-score (cut-off 3.8%) 23.13% 77.72% 3.56%

O-score (cut-off 50%) 57.43% 42.77% 25.75%

Table 9 - Overall accuracy of the models. For the Z’’-score model, the Type I error happens when the model classifies a distressed company as non-distressed and when a non-distressed company is classified as distressed we are in presence of a Type II error. For both O-score models the Type I error happens when a non-distressed company is classified as distressed and Type II error occurs when a distressed company is classified as non-distressed.

As we can see, the Z’’- score model has a better overall accuracy. This means that Z’’- score is the

best model in forecasting financial distress from the dataset under analysis. However, we must look at type I

and II errors, since from the perspective of nBanks the best model is the one that best minimizes the error

of a company being classified as healthy or non-distressed when, in reality, it is a distressed company. In this

sense, we must look at type I errors of the Z’’-score and type II errors of the O-score models. Thus, it is

concluded that the best model is O-score with a cut-off of 3.8% since it presents a lower percentage of the

type II error (3.56%). The O-score model with the 50% cut-off comes next with a percentage of the type II error

of 25.75%% and, finally, the Z’’-score model with a percentage of 63.06% of the type I error.

5.2. Accuracy of the Models per Group

For a more detailed analysis of the results of the models, we also analyze the accuracy per group. In

other words, we analyze the model’s ability to correctly classify the non-distress group and the model’s ability

to correctly classify the distress group of companies. The accuracy is calculated as before, dividing the total

number of correct classifications by the total number of companies in each group. The following results were

obtained:

33

Non-distressed Distress

Models Z’’-score O-score (cut-off 3.8%)

O-score (cut-off 50%) Z’’-score

O-score (cut-off 3.8%)

O-score (cut-off 50%)

Accuracy (%) 80.48% 22.28% 57.23% 28.33% 96.44% 74.25%

Table 10 - Accuracy of the models by group.

Considering the non-distress group, the best model is the Z’’-score with an accuracy of 80.48%. This

means that the model correctly classified 80.48% of non-distressed companies. Taking into account the group

of companies in distress, the best model is O-Score with a cut-off of 3.8%, with an accuracy of 96.44%. This

means that 96.44% of companies in distress were correctly classified. This result strengthens the previous

conclusion that the O-score is better than the Z’’-score for predicting financial distress.

5.3. Accuracy of the Models per Period

We also analyze the predictive ability per period to know the length of time, i.e. up to how many years

before financial distress, the models can predict the event. The following table contains the accuracy of each

model up to five years before financial distress (t-1, t-2, t-3, t-4 and t-5). The accuracy is calculated by dividing

the total number of correct classifications by the total number of companies for each period.

It can be concluded that as we move forward in the number of years before financial distress, the

predictive ability of the models decreases. The Z’’-score model is better at predicting financial distress up to

1 year before, with a sharp drop in the t-2 period and gradual declines in the others.

Models t-1 t-2 t-3 t-4 t-5

Z’’-Score 53.67% 37.32% 30.34% 25.38% 22.97%

O-score (cut-off 3.8%)

98.34% 97.53% 96.75% 96.61% 96.16%

O-score (cut-off 50%)

88.56% 82.36% 76.77% 74.00% 71.14%

Table 11 - Accuracy of the models up to 5 years before the financial distress.

34

These results are consistent with the results obtained in the study by Altman (1968). His study proved

that the model's accuracy decreases over the years, with the model showing greater accuracy for the first

two years. According to the author, the most logical reason for this result is that, after the second year, the

model becomes less reliable in terms of its predictive capacity. The O-score model with a cut-off of 3.8% is

undoubtedly the best. We can't compare these results with those obtained in the original study since Ohlson

(1980) only tested the model for one year before, two years before and for one to two years before the event

occurred.

Although accuracy gradually decreases, the model presents a very high predictive ability for all

periods, which may lead us to question the accuracy of the model mainly for periods t-4 and t-5. The use of

the 3.8% cut-off may be one of the reasons that could justify these very high values for all years. It is extremely

important to remember that this cut-off was selected because it minimized both types of classification errors

taking into account a specific sample. Therefore, given that the sample of the present study is quite different

from that used by Ohlson (1980), both in terms of the number of countries and the period under analysis,

3.8% is a very small cut-off and may have influenced the results presented above. Another reason has to do

with the year in which companies' financial distress are declared. Looking at the insolvent and liquidating

companies in my sample, which make up the group of companies in financial distress, there are many cases

where companies are declared as distressed in a given year but already had evidence or had already been in

difficulty during previous years. This is because many times, such insolvency or liquidation processes take

years, which means that these companies will only be declared as distressed later than the actuality. This

can justify high accuracy during all periods under analysis. The O-score model with a 50% cut-off also has

high predictive ability, predicting financial distress up to three years before.

5.4. Goals of nBanks

As mentioned at the beginning of this research, nBanks is interested in developing a new service that

gives their clients the possibility to know their probability or risk of default or bankruptcy by comparing with

other companies of their benchmark based on some variables such as dimension, sector, and geographical

position of the companies. In this sense, nBanks proposes some goals by which it expects that this research

will be able to achieve and thus help in the development of a new differentiating service. Basing on the O-

35

score model or, in other words, considering the companies classified as distressed by the model, this section

aims to answer the questions underlying each goal.

1. Obtain the percentage of companies in distress in the period under analysis by sector, dimension,

and location.

The main idea of this analysis is to identify the percentage of companies in distress by sector, size,

and location. For this, we consider the O-score model with a cut-off of 3.8% since based on the analysis

above, it is the model that presents a higher predictive ability. After ordering the scores3 obtained with

the model, the Top 25% of companies in distress was analyzed, that is, those with the worst results4.

Then the percentage of these companies by sector, size, and location was calculated, obtaining the

following results.

Figure 1 - Geographic distribution of the Top 25% of companies in distress.

Figure 1 gives us the percentage of companies in distress by location. We can see that these

companies are located mainly in 3 regions: North, Lisbon Metropolitan Area and Center with 45.88%, 25.10%,

and 16.47%, respectively. The region with the lowest incidence of these companies is the Autonomous Region

3 Scores were ordered from the largest to the smallest values. 4 Very high scores indicate a higher level of distress.

45.88%

25.10%

16.47%

4.71%

3.53%

2.35%

1.96%

North

Lisbon Metropolitan Area

Centre

Alentejo

Algarve

Autonomous Region of Azores

Autonomous Region of Madeira

Region

36

of Madeira with 1.96% of companies in distress. This distribution is in line with the initial distribution of

companies in distress, which shows once again that the O-score model is able to forecast financial distress.

Figure 2 - Distribution of the Top 25% of companies in distress by sector.

Analyzing the distribution of companies in distress by sector (Figure 2), we can see that the Wholesale

trade sector, except for motor vehicles and motorcycles presents the highest percentage (18.04%) of

companies classified as distress companies. The sectors with the lowest percentages are Warehousing and

support activities for transportation and Legal and accounting activities, with 0.39% and 0.78%, respectively.

From this analysis, we can say that there is no sector with a very high incidence of companies in distress.

Regarding the size of the companies (Figure 3), we observe that they are all medium-sized

companies.

18.04%

10.98%

7.45%

3.92%

2.35%

1.96%

1.57%

1.18%

0.78%

0.39%

Wholesale trade, except of motor vehicles and motorcycles

Retail trade, except of motor vehicles and motorcycles

Food and beverage service activities

Manufacture of leather and related products

Manufacture of fabricated metal products, except machinery and…

Advertising and market research

Office administrative, office support and other business support…

Services to buildings and landscape activities

Legal and accounting activities

Warehousing and support activities for transportation

Sector

37

Figure 3 - Distribution of the Top 25% of companies classified as distressed by size.

The same analysis was made for bottom 25% of the O-scores for companies in distress, and the

results obtained were very similar to the ones obtained with the top 25%.

For comparison purposes, the same analysis was carried out for the non-distressed companies. After

ordering the scores, the bottom 25% of the companies classified as non-distressed by the O-score model was

analyzed, that is, those with the best results5. The statistical composition of these companies by region, sector

and size is presented in annexes 1, 2 and 3, respectively. In general, we concluded that these companies

are medium-sized companies, concentrated in the Lisbon Metropolitan Area and the Human health activities

sector.

2. Identify reasons that may have led to the distress of the companies analyzed.

In this analysis, we look at the evolution of the mean of the ratios, as well as for the variables to

identify possible reasons that justify the distress situation of the companies. The results are shown in

tables 12 and 13.

Looking at the working capital ratio (X1 and WCTA), as these are companies in financial difficulty, it

would be expected that they would present negative values of these ratios for almost all years of analysis

with the exception of years 2011 and 2012.

5 Very low scores indicate low levels of distress.

Medium Enterprise

100%

Dimension

Medium Enterprise

38

Ratios 2011 2012 2013 2014 2015 2016 2017 2018

X1 (Working Capital / Total

Assets)

0.08 0.02 -0.05 -0.09 -0.13 -0.15 -0.25 -0.56

X2 (Retained Earnings / Total

Assets)

-0.12 -0.24 -0.41 -0.51 -0.59 -0.68 -0.96 -1.53

X3 (EBIT / Total Assets)

-0.04 -0.07 -0.09 -0.11 -0.11 -0.13 -0.18 -0.29

X4 (Book value of equity / Book

value of total liabilities)

0.40 0.34 0.28 0.24 0.21 0.18 0.11 0.11

SIZE 5.89 5.82 5.75 5.69 5.62 5.56 5.47 5.30

TLTA 0.92 0.99 1.12 1.19 1.26 1.32 1.47 1.90

WCTA 0.08 0.02 -0.05 -0.09 -0.13 -0.15 -0.25 -0.56

CLCA 1.22 1.36 1.53 1.68 1.74 1.80 1.87 2.90

NITA -0.06 -0.10 -0.12 -0.14 -0.14 -0.15 -0.20 -0.31

FUTL 0.02 -0.02 -0.02 -0.03 -0.03 -0.04 -0.05 -0.11

CHIN 0.05 -0.23 -0.27 -0.26 -0.25 -0.28 -0.44 -0.74

INTWO 0 0.22 0.31 0.34 0.33 0.32 0.33 0.38

OENEG 0.17 0.23 0.29 0.33 0.36 0.39 0.46 0.57

Table 12 - Evolution of the ratios mean for the companies classified as distressed for the period under analysis.

This reflects the difficulty of these companies over the following years in balancing short-term assets

with short-term liabilities, translating into current liabilities higher than current assets. This may justify the

recurrence of these companies to long-term financing to settle their short-term obligations.

These companies present negative operating results for all years under analysis, which consequently

translates into a negative X3 profitability ratio (EBIT / Total assets). These are companies with low profitability

levels since their operating activities do not contribute sufficiently to compliance with the obligations of the

companies and once again, the demand for external financing appears as a solution to meet the obligations.

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Variables 2011 2012 2013 2014 2015 2016 2017 2018

Current assets 1858756 1588049 1422336 1220585 1054432 938237 810755 623931

Current liabilities 1455135 1339160 1294701 1179858 1041219 921922 879825 548491 Total assets 2926192 2606599 2342349 2059712 1887129 1670221 1397903 972233

Total liabilities 2355771 2209313 2118563 1952154 1799467 1695388 1559247 1044687

Equity 570421 397286 223786 107559 87662 -25167 -161344 -72454

EBIT -50619 -119215 -100024 -124662 -95888 -161105 -113721 -93655

Net income -119494 -182520 -150166 -169506 -133727 -189811 -137698 -104590

Working Capital 403622 248890 127635 40726 13214 16315 -69070 75440

Retained Earnings 129265 -100210 -230782 -361780 -329236 -475176 -534935 -357647

Cash flow -53212 -126038 -95423 -127467 -95558 -152025 -94344 -84786

Table 13 - Evolution of the variables mean for the companies classified as distressed for the period under analysis.

These companies have shown negative net income over the years, which indicates that the losses are

greater than the earnings. Consequently, these companies have a negative return on assets (ROA) as we can

see when analyzing the values for the NITA ratio which reflects how profitable the company is relative to its

assets. In this sense, we can say that these companies are not efficient at generating income through their

assets.

With negative net income, it would be expected that these companies would present negative values for

retained earnings over the years since the retained earnings can be analyzed as the profit of the companies

after deducting all obligations and which is usually reinvested in the company itself. Negative retained earning

means that the company has an accumulated deficit which means that the company has more debt than it

has earned. This can be proved if we take a look at X2 (Retained earnings / Total assets). This ratio presents

negative values for all years, indicating that these companies are more reliant on other common types of

financing such as external debt and capital injections than from internal resources.

3. Assess the weight of bank debt in companies in distress and the weight of equity in companies in

distress in the observed period.

The weight of equity in a company determines its level of financial autonomy, measured by the ratio

equity to total assets. This ratio gives the percentage of assets of the company that is being financed by

equity. Very low values (usually less than 1/3) of this ratio reveal a difficult situation for the company in

depending excessively on debt financing.

40

2011 2012 2013 2014 2015 2016 2017 2018

Financial Autonomy

0.02 -0.05 -1.23 -0.37 -0.46 -0.56 -0.78 -3.92

Table 14 - Evolution of the financial autonomy ratio for the companies classified as distressed.

Analyzing the evolution of this ratio in the years under analysis, it can be seen that it has always

presented negative values except for the year 2011. These very low values reflect the strong dependence on

debt financing of companies in distress. Concluding that these companies finance their assets mainly through

debt, it would be of interest to analyze the extent to which these companies finance their assets through bank

financing. To do that analysis, and given that the Amadeus database does not have information on banks

loans, we use as a proxy of bank financing the following ratio:

Bank Debt = (Long term debt + Loans)/Total Assets

An approximation formula was used in cases when the companies did not present values for long

term debt:

Banking Debt = (Non-current liabilities + Loans)/Total Assets

2011 2012 2013 2014 2015 2016 2017 2018

Bank Debt 0.33 0.34 0.36 0.40 0.41 0.41 0.434 0.48

Table 15 - Evolution of the bank debt ratio for the companies classified as distressed.

The higher this ratio, the greater the degree of financing through bank debt. Analyzing this ratio over

the years, it can be seen that it has been increasing, revealing an increase in the demand of these companies

for bank financing. In 2018 the value of this ratio was 0.48, reflecting that almost half of the companies'

assets were financed by loans.

After analyzing these two scenarios, it can be concluded that these companies are heavily dependent

on external capital, with a considerable proportion of their assets being financed through banking debt.

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6. Conclusions

The increase in the number of insolvencies in Portugal, mainly for SMEs, due to the financial crisis

has further increased the interest of creditors as well as the companies themselves in anticipating events

such as default and bankruptcy thus making it possible to take avoidance measures promptly.

The contribution of this project is reflected in the intention to help nBanks, a Portuguese fintech

company that provides financial services, in the development of a tool that allows its customers to assess

their risk or probability of default.

The dataset under analysis consists of 194,979 Portuguese SMEs over the period 2011 to 2018.

The data was collected from the Amadeus database. Of the final dataset, 2,913 companies are companies

in distress and 192,066 healthy or non-distressed companies. The methodology used was the application of

bankruptcy forecasting models such as the r