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
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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
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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.
29
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.
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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