Assessing
the Competitive Ability of companies listed on the Tehran stock exchange based
on Cross Efficiency Model and its Relationship with Cost of Equity

Avaliação da capacidade
competitiva das empresas listadas na bolsa de valores de Teerã com base no
modelo de eficiência cruzada e sua relação com o custo do patrimônio líquido

Faezeh Motamedi Aghkariz

https://orcid.org/0000-0002-4480-0187

Department of Management and Accounting, Karaj Branch, Islamic Azad University, Karaj, Iran. [email-masked].

Bahman Banimahd

https://orcid.org/0000-0001-9554-4091

Department of Management and Accounting, Karaj Branch, Islamic Azad University, Karaj, Iran. [email-masked].

Balal Karimi

https://orcid.org/1234-5678-1234-5678

Department of Mathematics, Karaj
Branch, Islamic Azad University,
Karaj, Iran. [email-masked]

ABSTRACT

This
study aimed to evaluate the relationship between competitiveness score and cost
of equity. To this end, efficiency scores of companies were measured based on
competitiveness using a cross efficiency model in data envelopment analysis
(DEA), and its relationship with the cost of equity was examined using a
multivariate regression model for 19 pharmaceutical companies listed on the
Tehran Stock Exchange during the years 2015 to 2019. The investigation of the
subject was carried out in two stages. In the first stage, assessment of
competitiveness and obtaining the competitiveness efficiency score of companies
were addressed using the mathematical model presented in this study, which was
a secondary goal in cross efficiency. Moreover, the cost of equity was
calculated using the Gordon model. In the second stage, statistical techniques
were exploited to evaluate the competitiveness efficiency score and the cost of
equity. The results achieved from the research indicated that there is a
significant positive correlation between the variables of companies' efficiency
scores based on competitiveness and cost of equity. This means that cost of
equity and dividends will also increase by increasing competitiveness, which
causes an increase in the external financing of companies.

Keywords: assessment of competitiveness; cross-efficiency;
Data Envelopment Analysis (DEA); cost of equity; pharmaceutical companies.

RESUMO

Este estudo teve como objetivo avaliar a relação
entre o escore de competitividade e o custo de capital próprio. Para tanto, os
escores de eficiência das empresas foram medidos com base na competitividade
por meio de um modelo de eficiência cruzada em análise envoltória de dados
(DEA), e sua relação com o custo do capital próprio foi examinada por meio de
um modelo de regressão multivariada para 19 empresas farmacêuticas listadas na Bolsa
de Valores de Teerã, no período entre os anos de 2015 a 2019. A investigação
sobre o assunto foi realizada em duas etapas. Na primeira etapa, a avaliação da
competitividade e a obtenção do escore de eficiência de competitividade das
empresas foram abordadas por meio do modelo matemático apresentado neste
estudo, o que era um objetivo secundário na eficiência cruzada. Além disso, o
custo de capital próprio foi calculado usando o modelo de Gordon. Na segunda
etapa, foram exploradas técnicas estatísticas para avaliar o escore de
eficiência de competitividade e o custo de capital próprio. Os resultados
obtidos na pesquisa indicaram que existe uma correlação positiva significativa
entre as variáveis ​​dos escores de eficiência
das empresas com base na competitividade e no custo de capital próprio. Isso significa que o custo do capital próprio
e dos dividendos também aumentará com o aumento da competitividade, o que
acarreta um aumento no financiamento externo das empresas.

Palavras-chave:
avaliação de competitividade;
eficiência cruzada; Análise Envoltória de Dados (AED); custo de capital próprio;
empresas farmacêuticas.

Recebido
em26/04/2021.  Aprovado em 03/06/2021.
Avaliado pelo sistema double blind peer review. Publicado conforme normas da APA.

https://doi.org/10.22279/navus.2021.v11.p01-15.1592

1 INTRODUCTION

The cost of capital plays an
essential role in financing decisions. In order to determine the financial
resources, the management of the company must identify the expenses of
financing and specify the factors affecting it. Capital cost is regarded as a
measure of performance in the economic value added (EVA) model. The cost of
capital has other applications and is employed as a criterion for the
acceptance of new investment projects and discount rates to calculate market
value added (MVA) (Gupta, 2016). Moreover, the cost of equity is one of the
fundamental concepts in the field of finance literature, which has a major role
in financing and investment decisions. In order to determine the appropriate
financial resources, the management of the company must pay attention to the
cost of equity. Since the cost of equity is based on the rate of return
expected by investors and is linked to the amount of risk accepted by them and
because the bulk of the non-operating expense imposed on the company is
financing costs, the conversion of operating profit into a loss due to the
continuous activities of the company results from the imposition of this type
of costs (Verdi, 2006). The cost of equity primarily reflects the interests of
the original owners in a business institution. The cost of equity is the return
that the investor takes into account on his investment in the company and is
largely exploited in the mere estimation of the investment risk and assessment
of investment projects. Empirical research such as Sharma (2010) demonstrated
that the competitiveness of the product market is among the critical factors
affecting the stock returns.

In the opinion of Sarkar (2013), as
the company's ability in the competitive market increases, then this will
affect decisions regarding capital structure, including the cost of capital.
Competitiveness is equivalent to the economic power of a unit against its
competitors in a market where goods, services, skills, and ideas are easily
offered across geographical boundaries. Barecly,
Holderness and Sheelan (2006) introduced a framework
consisting of three elements of competitive performance, competitive potential,
and management processes called the performance process asset approach to
assessing the competitiveness of an enterprise. However, some experts also consider
competitiveness to depend on the competitiveness of the firm. This T approach
is a resource-based or capability-based approach. They emphasized the role of
internal factors of the organization on its competitiveness (Towit, & Mendelson, 2013). Porter (1990) on the other
hand, considers the competitiveness of a firm to be more influenced by the
firm's position in the market. This approach is also called the market-based
approach. But Schumpeter (1950) and von Bern (1999) employed the discussions
associated with knowledge for the assessment of competitiveness. This is also
called the knowledge-based approach (McGuane, &
Zhou, 2016).

In this study, the competitiveness
assessment of pharmaceutical companies listed on the Tehran Stock Exchange will
be discussed using mathematical models. With regard to the importance of equity
costs for investors' decisions, after calculating the efficiency score of
companies based on competitiveness using a cross-efficiency model, its
relationship with the cost of equity will be paid.

2 THEMATIC LITERATURE RESEARCH

2.1 Competitive Ability

Based on the views of Hitt (1995), competitiveness is the amount of producing
goods and services that can enter the international markets by a country while
simultaneously increase the real income of its citizens and at least prevent to
reduce it. Siggel & Cockburn (1995) consider
competitive ability as a condition that enables a firm to offer their products
with higher quality by employing superior methods and provide more profits for
firms in competition with rivals (Siggel, 2000).
Indeed, the competitiveness is efforts and activities of a firm for profitable
sales of its products. In other words, if a firm could have a competitive
ability, it should supply its products with lower prices and higher quality. In
1993, Siggel in an article addressed the theoretical
study of international competitiveness and provided a framework to assess
competitiveness and its constituent resources through economic and mathematical
relations. In 1995, in collaboration with Cockburn, he presented two papers.
They addressed different aspects of competitiveness in one of these articles.
In another article, they provided indicators for competitive ability and
thoroughly explained their resources. In 1997, they employed their method for
assessing the competitiveness of industries in Mali against the industries in
Ivory Coast, which is the main rival of Mali. In 1999, they employed the same
approach in the form of a research project to study the competitiveness of industries
in Uganda and Kenya to the country joining regional and international
associations and calculated indicators of competitiveness for the industry of
the two countries. In 2000, Siggel applied his method
for India with a slight modification through which he evaluated the effect of
economic policies of the country on the competitiveness of industries.
Furthermore, researchers such as Gaspar & Massa (2006), Pepall,
Richards and Norman (2008), Choua, Ng, Sibilkov, Qinghai et al. (2011), and Leventis
and Weetman (2011) take into account one of three
ratios: one minus the cost ratio of goods sold to sales, one minus the ratio of
fixed assets to total assets, and the ratio of sales of each company to the
total sales of the industry as indicators of competitiveness.

2.2  Cost of Equity

Cost of equity is the
minimum rate of return required by investors in order to finance the company,
which relies on the assumption that the company aims to maximize shareholder
wealth. If a connection is established between the cost of equity and maximization
of shareholder wealth, with the assumption of a fixed value of other variables,
one can say that the cost of equity is the minimum rate of return that would
maintain the value of companies (Munteanu, 2011). Each company has its own risk
and return. Each group of investors (bondholders, common stock, and preferred
stock) want to measure the rate of return that is commensurate with the risk.
Estimating the cost of equity is among the major matters associated with
investment decisions, which are used by firms and stakeholders to evaluate and
assess investment opportunities, especially when the cost of equity represents
the return rates expected by investors. In previous studies, many researchers
employed the capital asset pricing model (CAPM) to calculate the cost of equity
(Chen, 2013). The basis for the development of this model was named by Harry
Markowitz (1959) and Tobin (1958). Then, Sharpe (1964), Lintner (1964), and
Black (1972) were among the persons who have attempted to use the theory of
Markowitz for the pricing mechanism of market securities effectively. This is a
one-factor model, which was tested repeatedly and the latest amendments on this
model were applied; however, the use of the CAPM model was not free of
criticism in spite of the development and widespread (Chen, 2013). Fama & French (2013) found ambiguities and inaccuracies
in assessing the cost of equity on the basis of the CAPM model. They indicated
that these ambiguities are because of the difficulty in identifying the correct
model, ambiguity caused by assessing the susceptibility of factors that cause
their differentiation over time, as well as the evaluation of the risk premium.
Fama & French model has more explanatory power.
Later, Carhart in 1997 offered a four-factor model by adding a new variable to Fama & French three-factor model as a momentum, which
had better performance relative to the Fama &
French three-factor model. Eventually, with the development of their
three-factor model to five-factor model, Fama &
French attempted to increase the explanatory power of their model (Fama & French, 2013, Fama & French 2015).

2.3  Competitive Ability and Cost
of Capital

Zhang (2005) studied the
competitive behavior of companies and capital structure. They revealed that
equity financing has a direct relationship with companies' competitiveness.
They considered the issue due to shareholders' expectations and pressure on
managers to achieve their expected profits, which is a stimulus to improve
competition in the product market.

Aggarwal & Kyaw (2010),
in examining the relationship between capital structure in multinational
corporations, found that as the activity and competitiveness of companies
abroad increase, they use less debt in the capital structure compared to
companies operating in the country. Sharma (2010) studied the impact of product
competition structure in the market with stock returns. The results of this
study represented that firms in centralized industries earn lower returns.
Meanwhile, companies with high substitution ability of goods earn higher
returns compared to companies with less substitution ability. Jiang, Kim, Nofsinger & Zhu (2015), in a study, investigated the
relationship between product market competition and investment in companies
using a sample of Chinese manufacturing companies from 1999 to 2010. The
achieved results indicate a positive relationship between competition and
investment. Besides, it was found that high investment is under the influence
of high competition. On the basis of the investigations conducted in this
survey, the impact of market competitiveness on the cost of equity of
pharmaceutical companies listed on the stock exchange in Iran is explored. In
accordance with the definition of equity cost, i.e., the rate of return
expected by investors, dividends among investors and consequently the cost of
equity seem to be increased by increasing the efficiency of companies based on
competitiveness.

2.4  Data Envelopment Analysis
(DEA)

Data Envelopment Analysis
(DEA) is a nonparametric method to evaluate relative efficiency for a number of
decision-making units (DMUs). The method does not need to estimate the
production function for measuring the efficiency (Liu, Lin, & Shu, 2017). Charnes, Cooper & Rhodes proposed this method for the
first time in 1978. Before that, Farrell in 1957 initially raised estimation of
efficiency with non-parametric methods. A sample considered by Farrell to
evaluate the efficiency contained an input of an output. After that, in 1978, Charnes, Cooper & Rhodes developed Farrell perspective
and offered a fractional and nonlinear programming model. This model has the
ability to measure the efficiency with multiple inputs and outputs. This model
was named DEA or CCR model (Charnes et al., 1978). By
changing the model, in 1984, Banker, Charnes &
Cooper proposed a new model that became known as BCC, which was capable of
measuring the efficiency in the mode of varying return to scale. However, the
nature of self-evaluation in the DEA (evaluation at best) is criticized a lot.
That's why cross efficiency evaluation method was introduced in DEA. In this
method, we calculate the efficiency of other units using the weights obtained
from the evaluation of DMU_j (j=1,…,n),
and form a matrix known as the cross efficiency matrix. Ultimately, we will pay
the rating of DMUs by obtaining the cross-efficiency index from this matrix
(Sexton, Silkman, Hogan, 1986).Because the basic DEA models have multiple
optimal solutions, the cross-efficiency matrix gained from it varies concerning
the type of software exploited. This lack of uniqueness of the cross-efficiency
matrix was the first problem with the cross-efficiency method. In order to
overcome the problem, models with secondary goals were presented. For example,
Duel and Green (1994) for the first time presented optimistic and pessimistic
secondary models with respect to the maximization and minimization of the
efficiency of other DMUs, respectively. Moreover, Liang, Wu, Cook and Zhu
(2008) presented other models for secondary goals by the concepts of deviation
from efficiency. Moeini, Karimi and Khorram (2015) suggested a multi-objective model for
secondary goals and turned it into a linear programming model using
multi-objective methods. In addition to the above-listed approaches, other
models have been proposed for secondary goals in cross-efficiency (Moeini et al., 2015, Davtalab Olyaie, 2019).

3 METHODOLOGY

This is a descriptive
survey study with a practical nature and is cross-sectional research in terms
of time. In this study, a survey method will be exploited to collect data.
Hence, it can be placed in the group of field research. The statistical population
of this research included pharmaceutical companies listed on the Tehran Stock
Exchange. The data associated with active pharmaceutical companies were
collected from sites related to the Tehran Stock Exchange. Indicators of
efficiency evaluation and dividend were proposed by studying and searching in
the valid books and papers, and some of them were considered by academic
experts and the Tehran Stock Exchange, and the rest of the indicators were
eliminated. After data collection, the data analysis was performed. Library
studies and internet searches and articles and books were exploited to collect
preliminary data. We gathered information to answer the research questions in a
field method. Data collection tools were documents and statistical data in the
yearbook of the Tehran Stock Exchange. Data associated with research variables
were collected during the five years of 2015 and 2019. Eventually, the
competitiveness assessment of pharmaceutical companies listed on the Tehran
Stock Exchange was studied using the cross-efficiency method in data
envelopment analysis (DEA) and the relationship between this efficiency score
and cost of equity was examined.

3.1 How to Calculate Variables

In this section, research
variables will be introduced and how their operational calculation will be
expressed. These variables are as follows:

- Competitive Ability

Competitive ability is the
company's share of industry sales. That is, this ratio is as follows (Leventis & Weetman, 2011).

- Calculating the Efficiency of Competitive Ability:

With
regard to the concept of efficiency, which evaluates the comparison of the
obtained outputs with the consumed inputs, the competitive ability can be used
as an output factor, and some variables related to competitive ability can be employed
as input factors to calculate the competitiveness efficiency of companies.
Indeed, competitiveness was regarded as output, and the following variables
were considered as inputs of the cross-efficiency model in data envelopment
analysis (DEA) to calculate the efficiency competitive ability.

1.
Number of employees

2.
Company size (total assets)

3.
The cost price of the goods sold

4.
Sales and administrative costs.

However,
the cross-efficiency method in data envelopment analysis exploited in this study
is as follows.

- Cross Efficiency

One of the ranking methods
of efficient units is to use the "cross-efficiency" model, which has
high power in distinguishing efficient units (Bazrkar
& Iranzadeh, 2017). As previously mentioned,
efficiency in data envelopment analysis (DEA) is calculated by the ratio of
"weighted sum of outputs" to "weighted sum of inputs". The
choice of weights in the DEA linear programming model is such that it allows
the unit under study to maximize its efficiency size compared to other units.
Evaluating the efficiency of each unit with the best set of weights calculated
by the model is called "simple efficiency".

The cross-efficiency of
data envelopment analysis (DEA) was first proposed by Sexton et al. (1986) and
further developed by Doyle and Green (1994). The basic idea of cross-efficiency
is to use DEA as a reference evaluation for the mere evaluation model
(self-evaluation). The two main advantages of cross-efficiency evaluation are
as follows:

Cross-efficiency provides
an efficiency ranking among all decision-making units (DMUs) to distinguish
between best and worst performance.

The cross-efficiency can
eliminate the need for weight constraints for a variety of applications and
thus violate the DEA unrealistic weighting method (Anderson et al., 2002; Liang
et al., 2008).

In DEA, we have the
following classic symbols: Suppose there is a set of DMUs. Each DMUj has m distinct input x_ij (i=1,.., m) and s distinct output y_rj (r=1,…,s).

Cross-efficiency of DEA is
a traditional extension in a two-step process. More specifically, in step 1,
the self-evaluation efficiencies of each DMU will be calculated based on the
DEA model of constant returns to scale (CRS) developed by Charans,
Cooper, & Rhodes (1978) (hereinafter CCR). In Step 2, the weights obtained
from Step 1 will be employed for each DMU in order to obtain a score,
hereinafter referred to as the cross-efficiency evaluation score. Then, a
mathematical model for the two-step process described above will be provided.

Step
1: Self-evaluation efficiency from DMU_d using the
CCR model in DEA will be displayed as follows:

(1)

Where

and

are the
representations of the weights of r-th output and i-th input from

,
respectively. For each

, we obtain
a set of optimal weights

،

،.... ،

،

،

،.... ،

by solving
the model in step 1.

Step 2: The cross-efficiency of each

using the optimal weights

i.e.,

can be calculated as follows:

(2)

Therefore, we form a cross-efficiency
matrix (CEM) using the above equation.

For each

, the
average of all

(d=1,…,n)

(3)

is expressed as the
cross-efficiency score for DMU_j. Cross-efficiency
can also be referred to as the cumulative score with the same weight  1⁄n. The existence of multiple optimal
solutions in the model (1) causes the lack of uniqueness of the
cross-efficiency matrix (CEM) and cross-efficiency score. To fix this problem
in data envelopment analysis (DEA), the secondary goal method was introduced
(Liang et al., 2008; Roeder and Rutcher, 2011, 2012; Moeini et al., 2015, Davtalab Olyaie, 2019). In the continuation of this subsection, we
will present a linear programming model for secondary goals in data envelopment
analysis.

- A Linear Model for the Secondary Goal

In this subsection, a
secondary model for cross efficiency will be provided. The purpose of the
secondary model is to obtain the most appropriate weight among the optimal
weights in order to have the best efficiency index. Initially, the CCR model of
DMU_d is implemented, and it is assumed that E_dd^* is the amount of efficiency obtained for DMU_d. Now, we will have the following linear programming
model:

(4)

s.t.

Where

is the value of the efficiency obtained for

(

) and the
constraint

is the normalizing constraint, which is used
to prevent the optimal zero solution. Suppose that

is the optimal weight vector for model (4). In
this case, the following theorem states that the optimal solution of the model
(4) is zero.

Theorem 1: The value of the optimal
objective function of model (4) is zero.

Conclusion: According to the above
theorem, one can conclude that the efficiency index obtained for the CCR
multiplicative model is equal to the efficiency index obtained by the model (4).

In order to select a weight from the
optimal weights, the following multi-objective model as a secondary goal is
presented.

s.t.

(5)

In which

is the value of the efficiency index achieved
using the CCR model in

. The
purpose of the above model is to obtain the optimal weight among the optimal
weights in

so that the efficiency of this unit remains
constant and the efficiency of other decision-making units is maximized. This
multi-objective model can be solved using a variety of methods in the
multi-objective domain (For example, Ehrgott, 2005, Karimi & Karimi, 2017). One of the methods exploited in this
paper is the max-min method, which is in the following form:

s.t.

(6)

Actually, model (6) maximizes the minimum
of the goals and thus a single-objective linear programming model is achieved
and it can be easily solved. After solving this model, assume that

،

، .... ،

،

،

، .... ،

is the optimal solution of the model. In this
case, the cross-efficiency score of each company can be calculated using
equations (2) and (3).

- Cost of Equity

On the other hand, we intend to examine the relationship between
cross-efficiency and cost of equity. How to calculate the cost of equity
through Gordon Growth Model (GGM) (Davtalab Olyaie, 2019) is as follows:

In this model, the cost of equity can be achieved from the following
equation:

In the above model:

(7)

D1: Dividend paid at
the end of the first year,

P0: Price
per share at the beginning of the year

g: The
dividend growth rate obtained from the following equation.

(8)

3.2 Statistical
Model of the Research

In order to
test the research hypothesis, the following regression model is exploited.

(9)

In which

Y: Cost of equity

:
Competitiveness efficiency score of each company in each year

: The
company size, which is equal to the natural logarithm of the total assets of
the company.

: The ratio
of debt to total assets

: The ratio
of profits to total assets

: Sales
growth

In fact, in this model, the variable of
equity cost is the dependent variable, the competitive ability efficiency score
variable is the independent variable, and the variables of company size, the
ratio of debt to total assets, the ratio of profit to total assets, and sales
growth are considered as control variables.

4 RESULTS

4.1 Research
Data

The
statistical population of this research consisted of pharmaceutical companies
listed on the Tehran Stock Exchange. These companies must have the following
characteristics in the five-year period 2013 and 2017:

1- Their
fiscal year leads to the end of the fiscal year

2- During the
period in question, their shares have been actively traded on the stock
exchange.

3- To be among
the profitable companies

4- To be among
the companies that have distributed their profits

In fact, 19
companies apply in this situation. Moreover, because we have 5 financial years
for study, the data of this research include 95 years of the company.

4.2
Calculation of Cross- Efficiency and Evaluation of Competitiveness Efficiency
of Companies in the Statistical Sample

In this
subsection, the calculation of the competitive ability efficiency score using
the cross-efficiency model presented in this paper is addressed. In fact, the
following procedure is carried out to evaluate the efficiency score of
companies' competitiveness. Initially, evaluating the efficiency of companies
using model (1) provided in the previous section is dealt with. The executive
results of the model are given in Table (1) below.

Efficiency
value

for 2019

Efficiency
value

for 2018

Efficiency
value

for 2017

Efficiency
value

for 2016

Efficiency
value

for 2015

Company

1

1

1

1

1

1

0.75

0.82

0.68

0.83

0.70

2

0.73

0.89

0.81

0.82

0.78

3

0.78

0.69

0.72

0.73

0.73

4

0.72

0.74

0.79

0.84

0.77

5

0.82

0.89

0.98

1

0.92

6

1

0.87

0.88

0.97

1

7

0.75

0.78

0.75

0.78

0.75

8

1

1

0.76

1

0.86

9

1

1

1

1

1

10

1

0.71

1

0.78

1

11

0.75

0.66

0.78

0.76

0.73

12

0.51

0.72

0.48

0.79

0.58

13

0.65

0.76

0.89

0.90

0.59

14

1

1

1

1

1

15

1

1

1

1

1

16

0.72

0.78

0.79

0.74

0.69

17

0.83

0.82

0.86

0.90

0.86

18

1

1

1

1

1

19

Table 1.  Efficiency of pharmaceutical
companies listed on the stock exchange using model (1)

Source:  Research Results (2021).

Note that the amount of efficiency

can be the basis for ranking the
competitiveness of companies. However, many companies have an efficiency score
of 1 per year, which means that these companies are efficient. Concerning this
model, they do not have a priority relative to each other and a unique ranking
of companies for each year cannot be provided. This is because cross efficiency
model is employed.

Subsequently, the presented secondary goal model (6)
is exploited, and the efficiency of each

using the optimal weights

, i.e.,

is calculated and cross efficiency matrix is
formed from Equation (2). This continues for each year until five
cross-efficiency matrices are achieved. Ultimately, using the average column, i.e. equation (3), the cross-efficiency score is calculated.
The results are provided in the following Table (2).

Cross
efficiency score in 2019

Cross
efficiency score in 2018

Cross
efficiency score in 2017

Cross
efficiency score in 2016

Cross
efficiency score in 2015

Company

0.52

0.57

0.60

0.88

0.97

1

0.66

0.72

0.93

0.64

0.56

2

0.61

0.71

0.85

0.68

0.68

3

0.57

0.61

0.79

0.65

0.69

4

0.56

0.61

0.76

0.76

0.72

5

0.60

0.70

0.87

0.86

0.80

6

0.30

0.34

0.25

0.73

0.86

7

0.61

0.71

0.86

0.66

0.64

8

0.53

0.58

0.62

0.95

0.80

9

0.52

0.57

0.59

0.96

0.91

10

0.52

0.57

0.59

0.70

0.85

11

0.78

0.88

0.55

0.59

0.53

12

0.79

0.89

0.52

0.57

0.49

13

0.78

0.90

0.52

0.64

0.51

14

0.56

0.62

1

0.70

0.67

15

0.40

0.44

0.38

0.84

0.74

16

0.64

0.69

0.96

0.62

0.62

17

0.48

0.51

0.95

0.63

0.82

18

0.58

0.63

0.80

0.89

0.94

19

Table 2. Cross efficiency score of pharmaceutical companies listed on the stock
exchange

Source:  Research Results (2021).

The cross-efficiency score for pharmaceutical
companies is represented in Table (2). With respect to this obtained
cross-efficiency score, the ranking of companies can be considered. Here, any
company that has a higher cross-efficiency score has a better ranking in terms
of competitiveness (competitive ability) than other companies. Besides,
companies with lower cross-efficiency scores have worse ranking in terms of
competitiveness compared to other companies.

4.3 The Relationship
between Cross-Efficiency with Cost of Equity

In
order to examine the relationship between the competitiveness efficiency of
pharmaceutical companies listed on the stock exchange and the cost of equity,
the multivariate regression method is exploited. The regression model used in this
study was presented as Equation (9) in the previous section. Table (3) contains
descriptive statistics of research variables.

Standard
Deviation

Mean

Maximum

Minimum

Range

0.160

0.677

1

0.25

0.75

Competitive
ability efficiency score

X1

0.255

6.29

6.76

5.95

0.81

Company
size

X2

0.162

0.355

0.64

0

0.64

Debt to
asset ratio

X3

0.099

0.185

0.37

0.02

0.34

Profit to
asset ratio

X4

0.167

0.141

0.3

-0.23

0.96

Sales
growth

X5

Table 3. Descriptive
statistics

Source:  Research
Results (2021).

4.3.1 Pre-tests

-Test for
Normality

Before checking the research hypotheses, the
normality of the research variables should be initially examined by one-sample
Kolmogorov-Smirnov test. The hypotheses of this test are as follows.

: The variable
under study has a normal distribution.

: The variable
under study has no a normal distribution.

Status

Significance

Kolmogorov-Smirnov
statistic

Normal

0.20

0.105

Competitive
ability efficiency score

X1

Normal

0.21

0.103

Company
size

X2

Normal

0.2

0.108

Debt to
asset ratio

X3

Normal

0.2

0.1

Profit to
asset ratio

X4

Normal

0.051

0.107

Sales
growth

X5

Normal

0.173

0.121

Cost of
equity

Y

Table 4. One-sample Kolmogorov-Smirnov test for the research
variables

Source:  Research Results (2021).

On the basis of the results
in Table (4), all variables are normal. Thus, parametric tests such as
regression can be exploited.

- Unit Root Test (Augmented Dickey Fuller (ADF))

The augmented
Dickey-Fuller test was used to test the stationary of the variables.

Status

Significance

Augmented
Dickey-Fuller statistic

stationary

0.000

-4.81

Competitive
ability efficiency score

X1

stationary

0.000

-5.754

Company
size

X2

stationary

0.000

-10.395

Debt to
asset ratio

X3

stationary

0.000

-5.346

Profit to asset
ratio

X4

stationary

0.000

-6.115

Sales
growth

X5

stationary

0.000

-5.853

Cost of
equity

Y

Table 5. The augmented Dickey-Fuller test

Source:  Research Results (2021).

In accordance with the
results of Table (5), all research variables are at the stationary level and
there is no need to differentiate from the variables, so we will not face the
spurious regression and the estimation results will be reliable.

- Estimation of the
Research Model

To estimate the model, the multivariate regression method
was used. The results are provided in Table (6).

Probability

t
statistic

Standard
Deviation

Coefficients

Variables

0.233

-1.214

0.738

-0.896

Fixed
coefficient

C

0.002

3.369

0.174

-0.589

Competitive
ability efficiency score

X1

0.123

1.581

0.113

0.180

Company
size

X2

0.04

2.139

0.123

0.263

Debt to
asset ratio

X3

0.001

-3.575

0.273

-0.978

Profit to
asset ratio

X4

0.425

-0.807

0.114

-0.092

Sales
growth

X5

0.757

Coefficient
of determination

0.569

Mean of
the dependent variable

0.719

Adjusted
coefficient of determination

0.213

Standard
deviation of the dependent variable

0.112

Standard
deviation of regression

-1.381

Akaike
Information Criterion (AIC)

0.407

Residual
sum of squares (RSS)

-1.123

Schwartz
criterion

32.255

Log
likelihood

-1.289

Hannan-Quinn
criterion (HQ)

20

F
statistic

2.06

Durbin-Watson
statistic

0.000

Probability
(F statistic)

Table 6. Model
coefficients

Source:  Research Results (2021).

With regard to the estimation results in Table (6),
the influence of the competitive ability efficiency score variable on the cost
of equity is 0.589, which is statistically significant at the 95% confidence
level (p <0.05). Thus, the cost of equity will increase at a rate of 0.589
by one unit increase in the competitiveness efficiency score. Besides, the
effect of control variables on the debt-to-assets ratio was significant to the
amount of 0.263. Moreover, the effect of the profit-to-assets ratio on the dependent
variable, i.e., cost of equity was significant at a rate of -0.978.

The impact of company size and sales growth on the
cost of equity in the period under study was not significant (p> 0.05). The
coefficient of determination, adjusted coefficient of determination, the
standard deviation of regression, residual sum of squares, Akaike's information
criterion, Hannan Quinn criterion, and Schwartz criterion represent good fit so
that as the coefficient of determination and the adjusted coefficient of
determination are higher and the other criteria introduced are lower, the model
will have a better fit.

4.3.3 Diagnostic
Tests for Validity of the Model

- Autocorrelation Test

To investigate the absence
of autocorrelation for the disturbing elements of the first hypothesis
regression, Glejser test was exploited. The null
hypothesis of this test is the absence of autocorrelation in the disturbing
elements.

F Probability (5.32)

F statistic

Coefficient of determination

0.989

0.107

8.16

Table 7. Breusch–Godfrey test of the
first hypothesis

Source:
Research Results (2021).

According to the results of
Table (7), the F-statistical probability is obtained to be 0.989, which is more
than 0.05. Thus, the null hypothesis, indicating the absence of autocorrelation
in the disturbing elements of research regression is accepted and the existence
of autocorrelation is rejected. Therefore, the regression results are reliable.

- Collinearity
Test

In this section, the VIF test is exploited for the
co-linearity test in the model.

Central VIF

-

Fixed coefficient

1.594

Competitive
ability efficiency score

2.464

Company
size

1.163

Debt to
asset ratio

2.138

Profit to
asset ratio

1.061

Sales
growth

Table 8. Co-linearity test

Source:
Research Results (2021).

On the basis of the results
of Table (8), the VIF statistic for all research variables is less than 10.
Hence, one can conclude that the fitted model has no co-linearity and the
results of estimating the coefficients are reliable.

5 CONCLUSIONS &
SUGGESTIONS

Overall, this article aimed to evaluate companies
based on competitive ability using cross-efficiency in data envelopment
analysis (DEA) and its relationship with the cost of equity. In this survey,
the information of pharmaceutical companies listed on the stock exchange was
exploited. In accordance with Table (2), the cross-efficiency score for
pharmaceutical companies was provided. With regard to these cross-efficiency
scores obtained, the ranking of companies was performed. Here, any company with
a higher cross-efficiency score has more competitive ability compared to other
companies with a lower cross-efficiency score.

Generally, there is a significant relationship
between the competitiveness efficiency score obtained using the
cross-efficiency model and the cost of equity in pharmaceutical companies
listed on the Tehran Stock Exchange. Taking into account the research results,
there is a positive relationship between the level of efficiency of the company
in competitiveness and the cost of equity. In other words, the higher the level
of competitiveness of the company, the more the cost of equity will increase.
This means that companies that have higher efficiency in the competitive
ability can share greater profits, therefore increasing the cost of capital. On
the basis of the findings of Linter (1956), Rozeff (1992), Beiner
(2001), the factors affecting dividend policy can be generally divided into
four groups:

1) Legal factors 2) Contractual factors 3) Internal
factors of the company 4) Macroeconomic and market factors. Accordingly,
competitiveness as one of the market factors also affects dividend policy.

This finding of
the current study theoretically matches the existing theories about dividend
(hunting theory). Based on the hunting theory, corporate governance mechanisms
encourage managers of companies that are more vulnerable to being hunted to pay
fewer dividends, so that the manager's performance is consistent with the
interests of the company and shareholders.

Eventually, the relationship between the efficiency
score of companies' competitive ability and cost of equity was specified. Based
on the results of model estimation using the multivariate regression method, it
was found that the influence of the competitive ability efficiency score
variable on the cost of equity is 0.589, which is statistically significant at
the 95% confidence level (p <0.05). Thus, the cost of equity will increase at
a rate of 0.589 by one unit increase in the competitiveness efficiency score.

The result obtained in terms of the significance of
the relationship between competitiveness efficiency score and equity cost is
consistent with the results obtained in the research of Jiang et al. (2015).
The results of the present study and previous research indicate that the higher
the efficiency score of competitive power; the cost of equity also increases.

Besides, the
effect of control variables on the debt-to-assets ratio was significant to the
amount of 0.263. Moreover, the effect of the profit-to-assets ratio on the
dependent variable, i.e., cost of equity was significant at a rate of -0.978.
The impact of company size and sales growth on the cost of equity in the period
under study was not significant (p> 0.05). In other words, this study
demonstrated that increasing the efficiency score of competitive ability will
increase the cost of equity (increase the ratio of dividends to the price per
share). Hence, a question raised in this study was answered. The results
obtained in relation to the relationship between debt to asset ratio, profit to
asset ratio with variable equity cost with the results obtained in the research
of Smith, Chen and Anderson (2008), Kohansal, Dadrasmoghaddam, Karmozdi, & Mohseni (2013), Chaharmahali,
Zahedi and Mohammadi (2019) has it. Based on the results, the role of both
ratios on the variable cost of equity can be evaluated; however, the effect of
earnings-to-assets ratio on equity is more significant.

The results obtained in relation to the relationship
between firm size and equity were consistent with the results obtained in the
study of Zhou, Keng, Faff & Zhu (2016). This
indicates that in many studies, the relationship between firm size and cost of
equity is typically a negative or inverse relationship, meaning that larger
firms have lower equity costs.

The obtained results can be considered by the
supervisory boards on the performance of managers, including the general
meetings of shareholders and major shareholders, and the board of directors of
listed companies. On the one hand, the dividend is a factor affecting the
investments made by companies. The more profits are distributed, the less
company's internal resources for investment projects, and the company will
require greater financing outside the company. This factor affects the stock
price in the future and increases the cost of equity. On the other hand, many
shareholders of the company want to increase dividends. Thus, managers must
always establish a balance between the different interests of shareholders in
the distribution of dividends, while increasing the competitive ability of the
company. Furthermore, it is recommended that investors who want more dividends
choose companies that have a higher cross-efficiency score in competitive
ability that, of course,  have a higher
financial risk as well.

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