Applying fuzzy MCDM for financial performance evaluation of Iranian companies.
Ghadikolaei, Abdolhamid Safaei ; Esbouei, Saber Khalili ; Antucheviciene, Jurgita 等
Introduction
In a competitive environment, characterized by the scarcity of
resources, performance measurement and management play a crucial role
(Amado et al. 2012). Accordingly, an accurate and appropriate
performance evaluation is very crucial.
Financial aspect is one of the main aspects of the organization
performance. Traditionally it should be attractive. Seeing that profit
is the main goal of many companies, financial performance and proper
evaluation is very important. As financial performance indicators
reflect the competitiveness of a company, they must be carefully
identified in the evaluation process (Yalcin et al. 2012).
Most of the economical, industrial, financial or political decision
problems are multi attribute. Multiple Criteria Decision Making (MCDM)
is an advanced field of operation research. It provides decision makers
and analysts with a wide range of methodologies, which are overviewed
and well-suited to the complexity of economical decision problems
(Zavadskas, Turskis 2011). The application of multi-criteria decision
making methods significantly improves the robustness of financial
analysis and business decisions in general (Balezentis et al. 2012).
In the current research a new multiple criteria model, consisting
of Accounting measures and Economic value measures is presented, also a
hybrid approach of MCDM methods in fuzzy environment for financial
performance evaluation of companies is provided. At first FAHP (Fuzzy
Analytic Hierarchy Process) is used to determine the weights of the main
criteria and sub criteria. Then fuzzy VIKOR (Fuzzy VlseKriterijumska
Optimizacija I Kompromisno Resenje), ARAS-F (Fuzzy Additive Ratio
Assessment) and fuzzy COPRAS (Fuzzy Complex Proportional Assessment) are
applied simultaneously for ranking the automotive companies traded on
Tehran stock exchange in 2002-2011. Final ranking of companies is
provided by using mean ranks.
1. Literature review
Several studies on financial performance evaluation are focused on
ranking the alternatives according to their financial performance
measures, included in their comparison environments. Kung et al. (2011)
applied fuzzy MCDM methods for selecting the best company, based on
financial report analysis. The approach used FAHP to select weighting
indicators and fuzzy TOPSIS (Technique for Order Preference by
Similarity to Ideal Solution) for outranking the five major airlines.
Balezentis et al. (2012) used fuzzy TOPSIS, fuzzy VIKOR and ARAS-F
methods for integrated assessment of Lithuanian economy in 2007-2010
periods, based on financial ratios. Ergul and Seyfullahogullari (2012)
applied ELECTRE III for ranking of retail companies trading in Istanbul
stock exchange (ISE), based on their financial performance in 2008-2010.
Lee et al. (2012) performed a comparative study on financial positions
of shipping companies in Taiwan and Korea. At first the study applied
Entropy to find the relative weights of financial ratios of four
companies, and then it used grey relation analysis to rank the
companies. Yalcin et al. (2012) constructed a hierarchical structure of
the financial performance model for ISE's manufacturing company.
The approach used FAHP, VIKOR and TOPSIS. Bayrakdaroglu and Yalcin
(2012) proposed to use MCDM for strategic financial performance
evaluation of ISE. The research applied FAHP for determining the
relative significances of criteria and used VIKOR for best company
selection. Ignatius et al. (2012) surveyed financial performance of
Iran's Automotive Sector based on PROMETHEE II in the study. Cheng
et al. (2012) developed an approach combining fuzzy integral with Order
Weight Average (OWA) method for evaluating financial performance in the
semiconductor industry of Taiwan in 2008. Cement firms are evaluated by
taking into consideration only some of the traditional financial
performance measures.
Recent studies on the subject are summarized in Table 1.
2. Proposed model
A new multi criteria model, consisting of Accounting measures and
Economic value measures is developed with help of the financial experts
and presented in the current study. A combinative approach of MCDM
methods in Fuzzy environment for financial performance evaluation of
companies also provided.
Yalcin et al. (2012) constructed hierarchal structure for financial
evaluation of manufacturing company on the ground of value based
financial performance and accounting based financial performance as main
criteria and each having four sub criteria. The model proposed by the
Authors differs from Yalcin et al. (2012) model. The proposed model is
shown in Figure 1. In this model, four Accounting measures are
determined by the finance and Tehran stock exchange expert as the
sub-criteria. These measures are Return On Assets (ROA), Return On
Equity (ROE), Operating Profit Growth (OPG), also ratio of market price
and earnings (P/E). Also, seven Economic value measures are determined
as the sub-criteria. These measures are Economic Value Added (EVA),
Market Value Added (MVA), Refined Economic Value Added (REVA), True
Value Added (TVA), Cash Value Added (CVA), Created Shareholder Value
(CSV) and Tobin's Q. Formulation of these sub-criteria measures are
briefly explained in the Table 2.
[FIGURE 1 OMITTED]
3. MCDM methods
MCDM is an advanced field of Operation Research that provides
decision makers and analysts with a wide range of methodologies,
well-suited to the complexity of economical decision problems. Available
methodologies and their application for economic decisions are broadly
overviewed by Zavadskas and Turskis (2011).
In the presented study four fuzzy MCDM methods were used and
applied for evaluation of TSE's companies. At first FAHP was used
to determine weights of main criteria and sub criteria. Next the
research used fuzzy VIKOR, ARAS-F and fuzzy COPRAS for ranking the
companies according to best financial performance.
3.1. Fuzzy Analytic Hierarchy Process (FAHP)
Analytic Hierarchy Process (AHP) was introduced by Saaty (1971). In
the current research the weights of financial performance criteria are
obtained by using extent FAHP method. That is because of the
computational easiness and efficiency (Yalcin et al. 2012).
Calculation of FAHP can be described as follows.
Assume that O = {[o.sub.1], [o.sub.2],[o.sub.3], ...,[o.sub.n]}, be
an object set, and G = {[g.sub.1], [g.sub.2], [g.sub.3], ...,[g.sub.m]},
be a goal set. Each object is taken and extent analysis for each goal is
performed, respectively. Therefore, m extent analysis values for each
object can be obtained, with the following signs: [MATHEMATICAL
EXPRESSION NOT REPRODUCIBLE IN ASCII], i = 1,2,...,[alpha], where all
the [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (j = 1, 2,...,
m) are triangular fuzzy numbers (TFNs).
The further steps of extent FAHP can be given as follows.
Step 1. The value of fuzzy synthetic extent with respect to the
[i.sup.th] object is defined as:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (1)
perform the fuzzy addition operation of (3 extent analysis values
for particular matrix such that:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)
and to obtain [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII],
perform the fuzzy addition operation of [MATHEMATICAL EXPRESSION NOT
REPRODUCIBLE IN ASCII] (j = 1, 2, ... , [beta]) values such that:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)
Then the inverse of the vector above is computed:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (4)
Step 2. As [[??].sub.1] = ([l.sub.1], [m.sub.1], [u.sub.1]) and
[[??].sub.2] = [l.sub.2], [m.sub.2], [u.sub.2]) are two triangular fuzzy
numbers, the degree of possibility of [[??].sub.2] [greater than or
equal to] [[??].sub.1] defined as:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (5)
and can be equivalently expressed as follows:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (6)
where d is the ordinate of the highest intersection point D between
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and [MATHEMATICAL
EXPRESSION NOT REPRODUCIBLE IN ASCII] (Fig. 2).
[FIGURE 2 OMITTED]
To compare [[??].sub.1] and [[??].sub.2], we need both values of
V([[??].sub.1] [greater than or equal to] [[??].sub.2]) and
V([[??].sub.2] [greater than or equal to] [[??].sub.1]).
Step 3. The degree possibility for a convex fuzzy number to be
greater than k convex fuzzy [[??].sub.1] (i = 1, 2, ... , k) numbers can
be defined by:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (7)
Assume that d'([P.sub.i]) = minV([S.sub.i] [greater than or
equal to] [S.sub.k]) for k = 1, 2,...,n; k [not equal to] i. Then the
weight vector is given by:
W'=[(d'([P.sub.1]),d'([P.sub.2]),
...,d'([P.sub.n])).sup.T], (8)
where [P.sub.i](i = 1,2, ..., n) are n elements.
Step 4. Via normalization, the normalized weight vectors are:
W =([d([P.sub.1]),d([P.sub.2]),...,d([P.sub.n])).sup.T], (9)
where W is a non-fuzzy number.
3.2. Fuzzy MCDM outranking methods
In this study three fuzzy outranking methods are used. Let us
assume the fuzzy decision making matrix [??] = [[??].sub.ij], where i =
1,2,...,m and j = 1,2,...,n represent the number of alternatives and
criteria, respectively. In this study m = 6 and n = 11. The [j.sup.th]
criterion of the [i.sup.th] alternative is represented by triangular
fuzzy number [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. Also
each [j.sup.th] criterion is assigned with respective coefficient of
significance [[??].sub.j], that it obtained by FAHP. Benefit criteria
are members of benefit criteria set B, while cost criteria are members
of respective set C.
3.2.1. Fuzzy VIKOR
Based on crisp VIKOR that was introduced by Opricovic (1998), also
Opricovic and Tzeng (2004), fuzzy VIKOR was developed later and
presented in many studies (Antucheviciene et al. 2011, 2012; Chou, Cheng
2012; Vinodh et al. 2013). VIKOR is based on measuring the closeness to
the ideal alternative according to separate cases of [L.sub.p] metric
(Balezentis et al. 2012). Computing of fuzzy VIKOR consists of following
steps:
Step 1. The fuzzy best values [[??].sup.+.sub.j] and the fuzzy
worst values [[??].sup.-.sub.j] are found:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (10)
Step 2. The distances of each alternative from the ideal one are
determined:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]; (11)
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (12)
Step 3. The reference point is defined by computing values of
[[??].sup.+], [[??].sup.-], [[??].sup.+], and [[??].sup.- ], which, in
turn, enable to obtain the final summarizing ratio [[??].sub.j]:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (13)
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (14)
Step 4. Defuzzifying triangular fuzzy numbers [[??].sub.i],
[[??].sub.i], and [[??].sub.i] into crisp values. A center of area (COA)
defuzzification method is used to determine the best non-fuzzy
performance (BNP). The BNP value of the triangular fuzzy number
([l.sub.i], [m.sub.i], [u.sub.i]) can be found by the following
equation:
BN[P.sub.i] = [l.sub.i] + [m.sub.i] + [u.sub.i]/3, [for all]i. (15)
Step 5. Ranking the alternatives, sorting by the values [S.sub.i],
[R.sub.i] and [Q.sub.i], in decreasing order. The results are three
ranking lists.
Step 6. Proposing as a compromise solution, for given criteria
weights, the alternative (a'), which is the best ranked by the
measure Q if the following two conditions are satisfied:
C1. "Acceptable advantage": Q(a")--Q(a')
[greater than or equal to] DQ, where a" is the alternative with
second position in the ranking list by Q; DQ = [MATHEMATICAL EXPRESSION
NOT REPRODUCIBLE IN ASCII]; m is the number of alternatives (Chou, Cheng
2012).
C2. "Acceptable stability in decision making":
Alternative a' must also be the best ranked by S or/and R. This
compromise solution is stable within a decision making process, which
could be: "voting by majority rule" (when v > 0.5 is
needed), or "by consensus" v [approximately equal to] 0.5, or
"with veto" (v < 0.5). Here, v is the weight of the
decision making strategy "the majority of criteria" (or
"the maximum group utility").
If one of the conditions is not satisfied, then the set of
compromise solutions is proposed, which consists of:
Alternatives a' and a", if only the condition C2 is not
satisfied;
Alternatives a', a", ..., [a.sup.(k)], if the condition
C1 is not satisfied; [a.sup.(k)] is determined by the relation
Q([a.sup.(k)])--Q(a') [approximately equal to] DQ, the positions of
these alternatives are "in closeness".
3.2.2. ARAS-F
The ARAS-F is based on comparing every alternative with the
hypothetic ideal one (Turskis, Zavadskas 2010; Kersuliene, Turskis 2011;
Balezentis et al. 2012). The calculation steps of ARAS-F are as
presented below.
Step 1. In this method the ideal alternative is described in the
following way:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (16)
Step 2. The normalized values [[??].sub.ij] are obtained:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (17)
Step 3. Each [[??].sub.ij] is weighted by computing elements of the
weighted-normalized matrix:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (18)
where [[??].sub.j] is coefficient of significance and [[??].sub.ij]
is the weighted-normalized value of the [j.sup.th] criterion of the
[i.sup.th] alternative.
The overall utility [[??].sub.i] of the [i.sup.th] alternative is
computed in the following way:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (19)
Since [[??].sub.i] = ([s.sub.i1], [s.sub.i2], [s.sub.i3]), i = 0,
1,...,m, is a fuzzy number, the COA method is applied for
defuzzification:
[S.sub.i] = [s.sub.i1] + [s.sub.i2] + [s.sub.i3]/3, [for all]i.
(20)
Finally, the relative utility of the [i.sup.th] alternative
[K.sub.i] is found:
[K.sub.i] = [S.sub.i]/[S.sub.0], [for all]i, (21)
where [K.sub.i] [member of] [0,1]. The best alternative is found by
maximizing value of [K.sub.i].
3.2.3. Fuzzy COPRAS
COPRAS method was first put forward by Zavadskas and Kaklauskas
(1996). Fuzzified COPRAS was presented by Zavadskas and Antucheviciene
(2007). It is used to prioritize the alternatives on the basis of
several criteria along with the associated criteria weights. This method
works on a stepwise ranking and evaluation procedure of the alternatives
in terms of their significance and utility degree. Crisp or modified
method for uncertain environment has been successfully applied in for
maintenance strategy or performance evaluation, for selection of
effective decisions in construction or management (Yazdani et al. 2011;
Kanapeckiene et al. 2011; Fouladgar et al. 2012; Tamosaitiene, Gaudutis
2013; Das et al. 2012; Mulliner et al. 2013; Staniunas et al. 2013;
Palevicius et al. 2013).
Calculations of fuzzy COPRAS can be described as follows:
Step 1. Normalize the values of [[??].sub.ij] by using the
following formula:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (22)
Step 2. Determine the weighted normalized decision matrix:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (23)
where [[??].sub.ij] is the normalized performance value of
[i.sup.th] alternative on [j.sup.th] criteria and [w.sub.j] is the
associated weight of the [j.sup.th] criteria.
Step 3. The sums [S.sup.+.sub.i] and [S.sup.-.sub.i] of weighted
normalized values are calculated for both beneficial and non-beneficial
criteria, respectively. For benefit criteria, higher value is better and
for cost criteria, lower value is better for the attainment of goal.
[S.sup.+.sub.i] and [S.sup.-.sub.i] are calculated using the following
equations:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (24)
Step 4. Determine the relative importance or priorities of the
candidate alternative by the following equation:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (25)
Step 5. Since [[??].sub.i] = ([h.sub.i1], [h.sub.i2], [h.sub.i3]),
i = 0, 1,..., m, is a fuzzy number, the COA method is applied for
deffuzification:
[H.sub.i] = [H.sub.i1] + [h.sub.i2] + [h.sub.i3]/3, [for all]i,
(26)
where the relative importance [H.sub.i] of an alternative shows the
extent of satisfaction attained by that alternative. Among the
alternatives, one with the highest [H.sub.i] value is the best
alternative.
Step 6. Calculate the performance index (P[I.sub.,]) of each
alternative as:
P[I.sub.i] = [H.sub.i]/[H.sub.max]. 100%. (27)
Here [H.sub.max] is the maximum value of relative importance.
P[I.sub.i] value is utilized to get complete ranking of the
alternatives.
4. Applications of the proposed approach
Te aim of this study is to present a fuzzy approach to evaluate the
financial performance of the companies in the Iran, traded on TSE, by
using both Accounting measures and Economic value measures together and
in a fuzzy environment. This approach was applied for evaluation of
automotive companies of TSE in 2002-2011, i.e. in a period of ten years.
Six companies were selected for this study. For this period of the
research, annual financial statements of companies which passed
independent external auditing are considered. Data was gathered from the
TSE's Database and using Rahavard Novin software.
4.1. Determining the weights of criteria
To evaluate the importance of the main criteria and sub-criteria
and compose the fuzzy pairwise matrix, expert group (decision makers)
utilized the membership function of linguistic scale. The scale is
presented in Table 3.
The pairwise comparison scores have been carried out by financial
experts. Experts were asked to make pairwise comparisons for all
evaluation criteria based on Table 2. In this study for testing the
consistency ratio (CR) of fuzzy pairwise matrix, Lin (2010) approach was
used. If the CR is greater than 0.1, the result is not consistent, and
the pair-wise comparison matrix must be revised by the evaluator. Let
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] be a fuzzy judgment
matrix with triangular fuzzy number [[??].sub.ij] = ([l.sub.ij],
[m.sub.ij], [u.sub.ij]) and form R = [[m.sub.ij]]. If R is consistent,
then [??] is consistent (Lin 2010).
After computing the result of each evaluator's assessment, Lin
(2010) approach was used to obtain the consistency ratio of each
expert's pare wise matrix. Consistency ratio values are less than
the acceptable threshold value (i.e. CR < 0.1).
The overall results were obtained by taking the geometric mean of
individual evaluations. Combined pairwise matrix of main criteria with
their weights from FAHP is shown in Table 4.
With respect to the results, Economic value measures are more
important than Accounting measures in financial performance evaluation
of TSE's companies. Table 5 shows the weights of the sub criteria
were obtained by FAHP. CVA, TVA, REVA have highest weight among sub
criteria, respectively, so TSE's companies should Pay special
attention to this measures about their financial performance.
4.2. Ranking the alternatives
The following approach was used for convert crisp numbers of
financial measures into fuzzy numbers. As for time series data, when
[x.sub.ij] is the value of [j.sup.th] criterion of [i.sup.th]
alternative in each year (2002-2011), a fuzzy number can represent the
dynamics of certain indicator during past t = 10 periods (Balezentis et
al. 2012):
(Min([x.sub.ij]), [10.summation over (i=1)] [x.sub.ij]/10,
Max([x.sub.ij])), [for all]i, [for all]j. (28)
Let us assume [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
are the initial values of each criterion, obtained using Eq. (28). As
some of values in each criterion were negative, for preventing of any
problem in computation, all the values in each criterion are transformed
to positive values by the following equation:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (29)
Indeed the above equation is the same as [MATHEMATICAL EXPRESSION
NOT REPRODUCIBLE IN ASCII] in the computation steps of methods.
As it was mentioned, six Iranian automotive companies are analysed.
Initial data on their financial performance measurements is presented in
Annex 1.
At first fuzzy VIKOR is used to rank the companies. Usually in
other studies, the value of v is considered 0.5, but in this study
different values of v are considered and ranking of Q was obtained from
average of different values of [Q.sub.i]. Table 6 shows the results of
fuzzy VIKOR with different values of v.
As one can see from the Table 6, RENA has the minimum score with
respect to the Q values, also conditions of Acceptable advantage and
Acceptable stability in decision making are satisfied by this
alternative. Accordingly, RENA is chosen as the best company in terms of
financial performance among other companies.
Table 7 shows the results obtained from ARAS-F and fuzzy COPRAS
together. In this proposed model all the criteria are of benefit, while
for applying COPRAS a cost criterion is necessary. Hence values of one
criterion (OPG) for all alternatives have been reversed for feasibility
of using fuzzy COPRAS method for this study.
As it shown, RENA is the best company with respect to the financial
performance among automotive companies traded on TSE in 2002-2011.
Finally, for composing the final order of priority among all
alternatives, average of obtained ranks of the three methods has been
considered. Table 8 shows the final ranks of the companies.
Conclusions
Financial ratios provide useful quantitative financial information
about performance of a company. In this context, this study displays a
fuzzy hybrid approach for the financial performance evaluation of
companies.
In the proposed approach, at first FAHP is used to determine the
weights of the main-criteria and also sub-criteria. Then fuzzy VIKOR,
ARAS-F and fuzzy COPRAS are used for ranking the companies based on
financial performance, simultaneously. Finally, by combining the results
of these three methods via mean ranks, final ranking of the companies
can be presented.
In today's world economy, good financial situations provide
company's competitive advantage. Many studies in the literature
involving MCDM procedures use only the traditional financial ratios. In
this study both of Accounting measures and Economic value measures have
been used for financial performance evaluation. Results showed that
Economic value measures are more important than Accounting measures for
companies' evaluation. Also, to achieve better performance
evaluation, companies should pay more attention to CVA, TVA, REVA and
other measures in line with calculated their relative significances.
A case study of automotive parts producer companies traded on TSE
in 2002-2011 is presented. The proposed approach is applied for
measuring financial performance of companies in uncertain environment
with respect to multiple criteria.
Further study can include some other Economic value measures like
shareholder value added (SVA), equity economic value added (EEVA) and
other for performance measures. In addition to the proposed methods in
this study, some other MCDM methods can be used in this area.
ANNEX 1.
Initial data for fuzzy MCDM implementation for financial
performance measures of companies
Companies Economic value measures
CVA (mln. IRR *) EVA (mln. IRR)
IKCO (1; 6676345; 19386085) (1151005; 5814877;
10735632)
KAV (1141978; 2726328; 4233550) (649871; 1348592; 2065734)
PKO (1466459; 3214814; 4296745) (704625; 948637; 1215284)
SIPA (4011568; 10796070; (438828; 2403779; 4797621)
17324195)
RENA (2698054; 16835140; (1; 958242; 1455259)
73758751)
BHMN (727230; 5754355; 26599228) (472085; 825119; 1647045)
REVA (mln. IRR) TVA (mln. IRR)
IKCO (7306087; 9610754; (5423593; 21322844;
12755448) 27770850)
KAV (6636993; 8610637; 9253876) (29576630; 31134860;
33655814)
PKO (8013380;8896032;9381532) (29109228; 30410458;
32000762)
SIPA (1; 5325172; 9706911) (1; 14918929; 31757275)
RENA (5798266; 8419043; 9614870) (27594800; 29824510;
31821233)
BHMN (6222600; 8853049; (19911498; 27440943;
10683371) 34812535)
Accounting measures
ROE ROA
IKCO (122.11; 143.86; 158.48) (9.63; 13.38; 16.89)
KAV (1.00; 130.45; 202.82) (1.00; 12.16; 17.10)
PKO (114.39; 181.40; 382.74) (9.54; 16.04; 26.26)
SIPA (122.63; 168.24; 363.51) (10.34; 26.65; 40.13)
RENA (115.26; 142.75; 204.92) (15.64; 29.64; 50.75)
BHMN (124.67; 136.57; 176.48) (17.39; 22.34; 31.99)
Companies Economic value measures
MVA (mln. IRR) Tobin's Q
IKCO (2995114; 10991575; 23923765) (1.03; 1.21; 1.64)
KAV (3360439; 4718970; 6528396) (1; 1.16; 1.51)
PKO (3391226; 4489809; 5998817) (1.11; 1.34; 1.75)
SIPA (1; 11296067; 25376019) (1.22; 1.76; 3.29)
RENA (3268146; 5332461; 7218471) (1.22; ; 2.43; 5.80)
BHMN (3706467; 2726328; 10928858) (1.57; 2.23; 3.76)
CSV (mln. IRR)
IKCO (47094486; 63223227; 131121457)
KAV (56091123;58005205; 61485912)
PKO (52998354; 57440769; 59821396)
SIPA (1; 54554376; 119760813)
RENA (54197129; 58614863; 64847896)
BHMN (50904915; 59186347; 76083196)
Accounting measures
P/E OPG
IKCO (1.55; 3.72; 8.51) (3.40; 4.04; 5.72)
KAV (1.00; 3.65; 9.30) (2.87; 3.77; 4.41)
PKO (1.34; 5.30; 13.71) (1.00; 3.62; 4.83)
SIPA (1.32; 3.01; 7.16) (3.02; 4.09; 6.22)
RENA (1.60; 3.74; 7.26) (3.27; 3.94; 5.75)
BHMN (1.34; 3.29; 9.65) (3.05; 3.90; 6.33)
* (1 EUR = 16280 IRR).
doi: 10.3846/20294913.2014.913274
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Abdolhamid SAFAEI GHADIKOLAEI (a), Saber KHALILI ESBOUEI (a),
Jurgita ANTUCHEVICIENE (b)
(a) Faculty of Economic and Administrative Sciences, University of
Mazandaran, P. O. Box 416, Babolsar, Mazndaran, Iran
(b) Faculty of Civil Engineering, Vilnius Gediminas Technical
University, Sauletekio al. 11, 10223, Vilnius, Lithuania
Received 02 July 2013; accepted 13 July 2013
Corresponding author Abdolhamid Safaei Ghadikolaei
E-mail: ab.safaei@umz.ac.ir
Abdolhamid SAFAEI GHADIKOLAEI. PhD in Operation Management,
Assistant Professor at the Department of Industrial Management in
University of Mazandaran. He is working as head of Khazar Nonprofit
institution of higher education. His scientific interests cover areas of
OR, decision-making theory, sustainable development, supply chain
management, performance evaluation.
Saber KHALILI ESBOUEI. Master of Science of Operation Management at
the Faculty of Economic and Administrative Sciences of University of
Mazandaran. His scientific interests cover areas of OR, sustainable
development, Decision-making theory, Supply chain management, financial
performance evaluation.
Jurgita ANTUCHEVICIENE. Doctor, Assoc. Professor at the Department
of Construction Technology and Management, Vilnius Gediminas Technical
University, Lithuania. Research interests: sustainable development,
construction business management and investment, multiple criteria
analysis, decision-making theories and decision support systems.
Table 1. Comparison of the previous studies that have used MCDM
methods for financial performance evaluation
Study Objectives Methods used
Kung et al. Select the best FAHP, fuzzy
(2011) company, based TOPSIS
on financial report
analysis
Balezentis et al. Integrated assessment Fuzzy TOPSIS,
(2012) of Lithuanian economy fuzzy VIKOR,
ARAS-F
Ergul and Ranking of retail ELECTRE III
Seyfullahogullari companies trading
(2012) in ISE
Yalcin et al. Financial performance FAHP, VIKOR,
(2012) evaluation of Turkish TOPSIS
manufacturing
company
Bayrakdaroglu and Strategic financial FAHP, VIKOR
Yalcin (2012) performance
evaluation of ISE
Ignatius et al. Financial performance PROMETHEE II
(2012) of Iran's automotive
sector
Cheng et al. Evaluating of financial Fuzzy
(2012) performance in Integral, OWA
the semiconductor
industry of Taiwan
Lee et al. Survey of financial Entropy,
(2012) positions of shipping Grey Relation
companies in Taiwan Analysis (GRA)
and Korea
Study Approach used
Kung et al. Used FAHP to determine
(2011) indicators' weights and the fuzzy
TOPSIS method for outranking
the five major airlines
Balezentis et al. Applied fuzzy TOPSIS, fuzzy
(2012) VIKOR and ARAS-F together for
evaluation of economic sector
Ergul and Used ELECTRE III for ranking
Seyfullahogullari five retail companies in Turkey
(2012)
Yalcin et al. Combined FAHP to determine the
(2012) weights of criteria, also VIKOR
and TOPSIS for comparatively
ranking of companies
Bayrakdaroglu and Used FAHP for calculate the
Yalcin (2012) relative importance measures and
VIKOR to select the best company
Ignatius et al. PROMETHEE II was used to
(2012) select the best company
Cheng et al. Combined fuzzy integral with
(2012) Order Weight Average for
financial evaluation
Lee et al. Used Entropy for determining the
(2012) weights of criteria and GRA to
rank the company
Table 2. Formulation of financial performance evaluation measures
Financial Formula Study
performance
measures
Return On ROA = Net income available to Yalcin et
Assets (ROA) common stockholder/Total assets al. (2012
Return On ROE = Net income available to Yalcin et
Equity (ROE) commmon stockholder/Stockholder's al. (2012)
equity
Operating OPG = [(Operationg profit).sub.t] Ergul and
Profit - [(Operationg profit).sub.t-1]/ Seyfullahogullari
Growth (OPG) [(Operationg profit).sub.t-1] (2012)
P/E P/E = Market price per share/ Yalcin et
Earning per share al. (2012)
Economic [EVA.sub.t] = Net operating profit Yalcin et
Value after [tax.sub.t] - ([Weighted al. (2012)
Added (EVA) average cost of capital.sub.t] x
[Capital employed.sub.t-1])
Market Value MVA = Total market value - Total Bayrakdaroglu
Added (MVA) capital employed and Yalcin
(2012)
Cash Value CVA = Gross Cash flows - Economic Yalcin et
Added (CVA) depreciation - Capital charge al. (2012)
True Value TVA = Free cash flow + Capital Bayrakdaroglu
Added (TVA) gains - Market value x (1 + and Yalcin
Weighted average cost of capital) (2012)
Refined [REVA.sub.t] = [Net operating Hajiabasi et
Economic profit after tax.sub.t] - Weighted al. (2012)
Value Added average cost of capital
(REVA) ([Mcapital.sub.t-1])
Tobins Q Tobin's Q = Market value + Book Jones et
value of Liabilities/Book value al. (2011)
of assets
Created CSV = Market value of equity x Largani et
Shareholder (Shareholder return - Cost of al. (2012)
Value (CSV) equity)
Table 3. Membership function of linguistic scale (Chou, Cheng 2012)
Linguistic scale Positive triangular Positive reciprocal
fuzzy numbers triangular fuzzy
numbers
Absolutely importance (8, 9, 10) (1/10, 1/9, 1/8)
Intermediate (7, 8, 9) (1/9, 1/8, 1/7)
Very strongly (6, 7, 8) (1/8, 1/7, 1/6)
Intermediate (5, 6, 7) (1/7, 1/6, 1/5)
Strong (4, 5, 6) (1/6, 1/5, 1/4)
Intermediate (3, 4, 5) (1/5, 1/4, 1/3)
Weakly (2, 3, 4) (1/4, 1/3, 1/2)
Intermediate (1, 2, 3) (1/3, 1/2, 1)
Equally importance (1, 1, 1) (1, 1, 1)
Table 4. The fuzzy evaluation matrix with respect to the goal
Accounting Economic value Weights
measures measures
Accounting measures (1, 1, 1) (0.3102, 0.4518, 0.2332
0.8409)
Economic value (1.1892, 2.2134, (1, 1, 1) 0.7668
measures 3.2237)
Table 5. Weights of sub criteria obtained from FAHP
Sub criteria Local Weights Total Weights Rank
ROA 0.2431 0.0567 10
ROE 0.2089 0.0487 11
OPG 0.2689 0.0627 9
P/E 0.2791 0.0651 8
EVA 0.1040 0.0797 6
MVA 0.1359 0.1042 4
CVA 0.1823 0.1398 1
TVA 0.1764 0.1353 2
REVA 0.1668 0.1279 3
Tobin's Q 0.1031 0.0791 7
CSV 0.1315 0.01008 5
Table 6. The results of fuzzy VIKOR
Company v = 0 v = 0.25 v = 0.5 v = 0.75
[Q.sub.1] [Q.sub.1] [Q.sub.1] [Q.sub.1]
IKCO 0.8853 0.7994 0.7134 0.6275
KAV 1.3953 1.4116 1.4279 1.4442
PKO 1.3705 1.3155 1.2604 1.2054
SIPA 1.1878 1.1183 1.0488 0.9793
RENA 0.0021 0.0022 0.0023 0.0024
BHMN 0.7393 0.7493 0.7593 0.7693
Company v = 1 Average
[Q.sub.1] Rank
IKCO 0.5415 2.4
KAV 1.4604 6
PKO 1.1503 5
SIPA 0.9098 4
RENA 0.0026 1
BHMN 0.7793 2.6
Ranking results
Company Rank [S.sub.i] Rank [R.sub.i] Rank
obtained
from [Q.sub.i]
IKCO 2 1.4078 2 0.8199 3
KAV 6 1.9485 6 0.8634 4
PKO 5 1.7295 5 0.8780 5
SIPA 4 1.7112 4 0.8901 6
RENA 1 0.8693 1 0.2764 1
BHMN 3 1.4827 3 0.6463 2
Table 7. The results of ARAS-F and fuzzy COPRAS
Company [K.sub.i] Rank [H.sub.i] [PI.sub.i] Rank
IKCO 0.3251 2 0.2384 57.05 2
KAV 0.0760 5 0.0772 18.48 5
PKO 0.0624 6 0.0734 17.56 6
SIPA 0.2118 3 0.1834 43.90 4
RENA 0.4104 1 0.4178 100.00 1
BHMN 0.1706 4 0.1930 46.19 3
Table 8. Final Rankings of the companies
Company Fuzzy ARAS-F Fuzzy Average Final
VIKOR COPRAS Rank Ranks
IKCO 2 2 2 2 2
KAV 6 5 5 5.33 5
PKO 5 6 6 5.67 6
SIPA 4 3 4 3.67 4
RENA 1 1 1 1 1
BHMN 3 4 3 3.33 3
