Generalized Net Model of the Methodology for Analysis of the
Creditworthiness and Evaluation of Credit Risk in SMEs Financing
George L. Shahpazov
1
, Lyubka A. Doukovska
1
and Krassimir T. Atanassov
2
1
Institute of Information and Communication Technologies, Bulgarian Academy of Sciences,
Acad. G. Bonchev str., bl. 2, 1113 Sofia, Bulgaria
2
Institute of Biophysics and Biomedical Engineering, Acad. G. Bonchev str., bl. 105, 1113 Sofia, Bulgaria
atlhemus@abv.bg, doukovska@iit.bas.bg, krat@bas.bg
Keywords: Generalized Net Model, Small and Medium-Sized Enterprises (SMEs), Credit Risk, Creditworthiness.
Abstract: The launch of the new programming period of the EU in 2014 will lead to many changes in the way the EU
budget is funded. The European Commission is considering various ways to generate their own income to
make it more independent of the Member States. Unfortunately the consequences of the reforms might have
negative influence to European and in particular to the Bulgarian economy and especially for SMEs. The
effective results in these conditions are to ensure financial resources for SMEs beneficiaries - increasing the
amount of advance payments, creating additional financial instruments. Prior to SMEs financing, a
methodology for analysis of creditworthiness and credit risk assessment procedures are applied. The aim of
the methodology is to contribute and establish an unified and systematic approach to analyzing and
assessing credit risk, which is to lead to a more thorough and objective assessment of the credit and
minimize the risk undertaken by the financial institution. The system of credit risk assessment is a
collaboration of estimates of the specified indicators. The final conclusion of the process should result into a
motivated standpoint, based on which, a decision on further conduct of the Bank towards the loan request
will be made (guarantees and other commitments, bearing credit risk), along with periodic risk assessment
procedure on already granted loans. In this paper is provided an analysis using the Generalized Nets. They
are used as a tool for modelling of different processes in industries and medicine. In the present paper, an
application of these nets apparatus for assistive technology and the advantages of using such model, for
SMEs financial support mechanism are discussed.
1 INTRODUCTION
Considering the harder economic conditions, to
which SME’s are exposed, the attitude to external
financing changes. The research of the sector show
that 10 years ago about 7% of enterprises utilized
investment loans, 17% had access to working capital
funds, and 67% didn’t have any access to financing.
The aggressive development of banking system
along with EU structured funds, significantly
increased the accession of SME’s to venture
funding. From year 2010 onwards, about 55% of
companies are able to reach financing of any type.
In 2010 most popular sources of financing
between SME’s was own resources (about 42%),
illegitimate financing from frends and relatives
(close to 17%), and at last EU funds and Bank
financing (near 30%). A year earlier above 50% of
companies are financed with own equity.
Limitations and obstacles in financing occur mainly
due to the reduced investment intentions of SME’s
within the last few years. Main reasons for it are lack
of economic stability within the country and EU,
along with gradual increase of intercompany
leverage. The figures show that, intercompany debp
over the past 3 years has gone up over 100%.At
present time about 83% of all SME’s have
uncollected receivables (Bulgarian Industrial
Association).
One third of all investments made by SME’s are
into new equipment and machinery (about 35%), re
qualification, training and advertisement is the
second investment direction (29%), development of
present and design of additional newer products
(22%), introduction of systems for intercompany
management processes (9%).
Alternative ways of raising funds by SME’s are
via leasing schemes, where at present about 32% of
292
Shahpazov G., Doukovska L. and T. Atanassov K.
Generalized Net Model of the Methodology for Analysis of the Creditworthiness and Evaluation of Credit Risk in SMEs Financing.
DOI: 10.5220/0004776702920297
In Proceedings of the Third International Symposium on Business Modeling and Software Design (BMSD 2013), pages 292-297
ISBN: 978-989-8565-56-3
Copyright
c
2013 by SCITEPRESS – Science and Technology Publications, Lda. All rights reserved
SME’s are able to reach their investment goals,
whereas couple of years earlier the figure is close to
45%.
Due to worsen economic environment and
interbanking debt, weaker turnover and profit
results, most SME’s are unable to rely on own
resources. This is valid to such an extent that the
financing with own funds has decreased 10 times
and in spite of the difficulties, concerning the receipt
of a bank loan, it has turned into the most preferred
source of funds.
The most popular source of financing among
commercial banks and leasing companies is public
procurement. Statistics show that about 15% of
SME’s take advantage of public procurement.
Raising funds via government programs was used by
2.9% of the companies, and access to financing via
programs of non-government organizations has a
share of 2%. Financing via EU structured funds had
an insignificant portion (1.6%) up until few years
ago. Nowadays the percentage has increased
considerably and 45% of SME’s is making efforts to
receive the embedded financing and grant schemes,
(Bulgarian Small and Medium Enterprise Promotion
Agency).
Regardless of the above mentioned statistics
there hasn’t been any considerable changes in
regards to the specific difficulties, with which SME
are confronted upon the receipt of a bank loan. Most
of which they encounter are:
• Considerableinterest rates and requirements for
sufficient loan collateral. Often companies do not
dispose with the necessary real estates, and the
interest rates are close to the profitability of their
assets.
• Lacking or insufficient credit history (valid to an
even greater extent for the new companies). The
reason for this often is the concealing of tax,
despite the decrease in the tax and social security
burden in the last years.
• The relatively low economic and legal general
knowledge of the owners of SMEs.
• Incapacity for the preparation of a long-term plan
for the development of business. This is the
result of the unstable economic environment, as
well as of the incapacity of SMEs to prepare
reliable long-term financial forecasts.
• High fees, “hidden” interest and the heavy
paperwork, associated with loan granting/project
financing.
• Requirements for minimum equity and minimum
turnover.
2 SHORT REMARKS ON
GENERALIZED NETS
Generalized Nets (GN) (Atanassov, 1991,
Atanassov, 2007) are extensions of Petri nets and
other modifications of them. They are tools intended
for the detailed modelling of parallel processes.
A GN is a collection of transitions and places
ordered according to some rules (see Figure 1). The
places are marked by circles. The set of places to the
left of the vertical line (the transition) are called
input places, and those to the right are called output
places. For each transition, there is an index matrix
with elements called predicates. Some GN-places
contain tokens – dynamic elements entering the net
with initial characteristics and getting new ones
while moving within the net. Tokens proceed from
an input to an output place of the transition if the
predicate corresponding to this pair of places in the
index matrix is evaluated as “true”. Every token has
its own identifier and collects its own history that
could influence the development of the whole
process modelled by the GNs.
Two time-moments are specified for the GNs:
for the beginning and the end of functioning,
respectively.
A GN can have only a part of its components. In
this case, it is called reduced GN. Here, we shall
give the formal definition of a reduced GN without
temporal components, place and arc capacities, and
token, place and transition priorities.
Formally, every transition in the used below
reduced GN is described by a three-tuple:
Z =
L
, L
, r
(1)
where:
Figure 1: A GN transition.
(a) L and L are finite, non-empty sets of places (the
transition’s input and output places, respectively),
for the transition these are:
Generalized Net Model of the Methodology for Analysis of the Creditworthiness and Evaluation of Credit Risk in SMEs
Financing
293
L = {
m
lll ',...,','
21
} and L = {
n21
"l,...,"l,"l
};
(b) r is the transition’s condition determining which
tokens will pass (or transfer) from the
transition’s inputs to its outputs; it has the form of
an Index Matrix (IM):
)1,1(
)(
'
...
'
...
'
"..."..."
,
,
1
1
njmi
predicater
r
l
l
l
lll
r
ji
ji
m
i
nj
where r
i,j
is the predicate that corresponds to the i
-th
input and j
-th
output place.
When its truth value is “true”, a token from the
i
-th
input place transfers to the j
-th
output place;
otherwise, this is not possible.
The ordered four-tuple:
E = A, K, X,
(2)
is called a reduced Generalized Net if:
(a) A is the set of transitions;
(b) K is the set of the GN’s tokens;
(c) X is the set of all initial characteristics which
the tokens can obtain on entering the net;
(d)
is the characteristic function that assigns
new characteristics to every token when it makes the
transfer from an input to an output place of a given
transition.
Many operations (e.g., union, intersection and
others), relations (e.g., inclusion, coincidence and
others) and operators are defined over the GNs.
Operators change the GN-forms, the strategies of
token transfer and other. There are six types: global,
local, hierarchical, reducing, extending and dynamic
operators.
3 GENERALIZED NET MODEL
A GN model is described in In this paper will be
used GN shown on Figure 2. Five types of tokens
move in this GN.
The tokens from the first type are
1
and
2
, and
they represent bank-administrators. The tokens have
the initial and current characteristics: “Credit
specialist at branch level” in place l
8
and “Experts
at Headquarters level” in place l
15
.
The tokens from the second type are the
-tokens
that permanently enter place l
1
with initial char-
acteristic “Potential SME Borrower”.
The tokens from the third type are
1
,
2
and
3
,
representing Bank management. They have the
initial and current characteristics: “Credit Council”
in place l
18
, “Management Board” in place l
21
and
“Supervisory Board” in place l
24
.
In some time-moments, some token
will split
to the original token
and a token
, while some
-token and the
3
-token will split to the original
-
or
3
-token and a
-token. These new types of
tokens will be discussed below.
114132341
{, , },{ , , },
Z
lll lll r
(3)
234
44,24
1
,
1
3
13
,
lll
r
l false false true
lWWtrue
l false false true
where:
W
4,2
= “There is a SME client that has prepared a
project”,
W
4,3
= “There is an answer from the SME client to a
question from the credit specialist at branch level”.
Token
enters place l
4
without a new
characteristic.
Token
4
enters place l
4
and unites with token
,
staying there.
If W
4,2
= true, then token
splits to the original
token
and token
. The second one enters place l
2
and there it obtains the characteristic “Loan
application, based upon a prepared project”. If
W
4,3
= true, then token
splits to the original token
and token
1
. The second one enters place l
3
and
there it obtains the characteristic “Requested
additional information in regards to submitted
project”. This token is generated in a result of token
4
that enters place l
4
.
2 25814 5678 2
{ , , , },{ , , , },
Z
llll llll r
(4)
5678
2
55,5 5,6 5,7
8,7
8
1
2
4
,
llll
r
l true false false false
l W W W false
W
l
f
alse false true
f
alse false truel
false
Third International Symposium on Business Modeling and Software Design
294
Figure 2: Generalized net model.
where:
W
5,5
= „By the moment, there is not a solution for
the project”,
W
5,6
= “Project rejected at first level (at branch
level)”,
W
5,7
= “Project accepted at branch level, sent to
Headquarters for further detailed research”,
W
8,7
= “There is an answer of a question initiated
by Headquarters experts in regards to the submitted
project”.
Token
enters place l
5
without any new char-
acteristic. Token
5
enters place l
8
and unites with
token
1
.
When W
5,5
= true, token
continues to stay in
place l
5
without a new characteristic. When W
5,6
=
true, token
enters place l
6
with a characteristic
“Project rejected (due to specific motives)”. When
W
5,7
= true, token
enters place l
7
with a
characteristic “Project accepted (due to specific
motives)”. If W
8,7
= true, then token
1
splits to the
original token
1
and token
2
. The second one
enters place l
7
and there, it obtains the characteristic
“Answer from branch level”.
3 3 7 9 5 22 9 10 11 12 13 14 15 3
{, , , },{, , , , , , },
l
Z
lllll lllllll r
(5)
9 101112131415
3
3
77,9 7,15
9 9,9 9,11 9,12
15 15,10 15,13 15,14
22
ll ll l l l
r
l false false false false false false true
l W false false false false false W
l W false W W false false false
l false W false false W W true
l false false false false false f
,
alse true
where:
W
7,9
= “The current token is from
-type”,
W
7,15
= “The current token is from
5
-type”,
W
9,9
= „By the moment, there is not a solution for the
project”,
W
9,11
= “Rejected at Headquarters level”,
W
9,12
= “Accepted and prepared for loan granting”,
W
15,10
= “An inquiry is initiated and addressed to
the Supervisory Board”,
W
15,13
= “An inquiry is initiated and addressed to
the SME Client-borrower”,
W
15,14
= “An inquiry is initiated and addressed to
branch level”.
Token
1
enters place l
15
and unites with token
2
.
When W
7,9
= true, token
enters place l
9
without
a new characteristic.
When W
9,15
= true, token
2
enters place l
15
and
unites with token
2
, that obtains the above
mentioned current characteristic.
When W
9,9
= true, token
contains to stay in
place l
9
without a new characteristic.
Generalized Net Model of the Methodology for Analysis of the Creditworthiness and Evaluation of Credit Risk in SMEs
Financing
295
When W
9,11
= true, token
enters place l
11
with a
characteristic “Project rejected at Headquarters
level (due to specific motives)”.
When W
9,12
= true, token
enters place l
12
with a
characteristic “Project accepted at Headquarters
level (due to specific motives)”.
When W
15,10
= true, token
2
splits to the original
token
2
and token
3
. The second one enters place
l
10
and there, it obtains the characteristic “An inquiry
is addressed to the Supervisory Board for specific
project” or “An answer of Head quarters level to
the Supervisory Board”
When W
15,13
= true, token
2
splits to the original
token
2
and token
4
. The second one enters place
l
13
and there, it obtains the characteristic “An inquiry
is addressed to the SME Client-borrower in regards
to a specific detail of the project”.
When W
15,14
= true, token
2
splits to the original
token
2
and token
5
. The second one enters place
l
14
and there, it obtains the characteristic “An inquiry
is addressed to Branch level in regards to specific
details of the project”.
124181617184
{,},{, ,},
Z
ll lll r
(6)
16 17 18
4
12 12,16 12,17
18 18,18
,
lll
r
lW W true
lfalsefalseW
where:
W
12,16
= “There is a positive decision by Credit
council in regards to specific project”,
W
12,17
= “There is a negative decision by Credit
council in regards to specific project”,
W
18,18
= “There is a token in place l
12
”.
When W
12,16
= true, token
enters place l
16
with
a characteristic “The project is voted and accepted
for financing by the Credit council under the
original or new updated parameters”.
When W
12,17
= true, token
enters place l
17
without any characteristic.
5 1621 192021 5
{, },{, , },
Z
ll lll r
(7)
19 20 21
5
16 16,19 16,20
21 21,21
,
lll
r
lW W true
lfalsefalseW
where:
W
16,19
= “The Project receives affirmative decision
when voted by Management Board”,
W
16,20
= “The Project receives negative decision
when voted by Management Board”,
W
21,21
= “There is a token in place l
16
”.
When W
16,19
= true, token
enters place l
19
with
a characteristic “The project is voted and accepted
for financing by the Management Board under the
original or new updated parameters”.
When W
16,20
= true, token
enters place l
20
without any characteristic.
6 101924 222324 6
{, , },{, , },
Z
lll lll r
(8)
22 23 24
6
10
19 19,23
24 24,22 24,24
,
lll
r
l false false true
l false W false
l W false W
where:
W
19,23
= “Final decision by Supervisory Board”,
W
24,22
= “There is an answer of the Supervisory
Board to the Management Board level or there is an
answer of the Supervisory Board to a question from
the Credit council ”,
W
24,24
= “There is a token in place l
19
”.
Token
3
enters place l
24
and unites with token
3
.
When W
19,23
= true, token
enters place l
23
with
a characteristic “Final decision (positive or nega-
tive) of the Supervisory Board about the project”.
When W
24,22
= true, token
3
splits to two tokens
– the original token
3
and token
6
that obtains the
characteristic “Answer of the Supervisory Board”.
4 CONCLUSIONS
The so constructed GN model describes the most
important steps of the process of evaluation of a
business project proposal intended for financing
. In
a next research, the authors plan to elaborate the
model in the aspect related to the process of decision
making within the frames of the bank
administration.
First, the model can be used for real-time control
of the processes, flowing in a particular bank. If this
is the case, the databases of the model will
correspond to the real databases of that bank, and the
process of adding new characteristics of the
respective GN-tokens will correspond to the process
of inputting new information in the bank's databases.
The tokens, representing the bank's clients, will have
Third International Symposium on Business Modeling and Software Design
296
as initial characteristics their specific parameters and
with their real project proposals intended for
financing
. The movement of these real projects will
be observed and information for the current status of
each of them can be obtained from the model.
Practically, the GN-model will synchronize the real
processes, related to the above described procedure.
Second, it can be a tool for prognostics of
different situations, related to the modeled
processes, for example in a given moment of time, a
large number of projects may be submitted, and
these have to be evaluated in parallel or compete for
a limited amount of funding.
Third, on the basis of the model, some changes
of the process of evaluation can be simulated and the
results can be used for searching the optimal
scheduling of the separate steps of this process.
ACKNOWLEDGEMENTS
The research work reported in the paper is partly
supported by the project AComIn “Advanced
Computing for Innovation”, grant 316087, funded
by the FP7 Capacity Programme (Research Potential
of Convergence Regions) and partially supported by
the European Social Fund and Republic of Bulgaria,
Operational Programme “Development of Human
Resources” 2007-2013, Grant № BG051PO001-
3.3.06-0048.
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Bulgarian Small and Medium Enterprise Promotion
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2012.
European Commission, “SEC (2011) 876 final/2”,
Brussels, 27.10.2011.
The Global Competitiveness Report 2011, www.ced.bg.
Atanassov K. - Generalized Nets. World Scientific,
Singapore, New Jersey, London, 1991.
Atanassov K. - On Generalized Nets Theory, “Prof. M.
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Financing
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