the evaluation of the efficiency of listed companies, using nonparametric methods: an empirical...
TRANSCRIPT
-
8/9/2019 The evaluation of the efficiency of listed companies, using nonparametric methods: An empirical analysis of the Gr…
1/18
International Journal of Computer System (ISSN: 2394-1065), Volume 02– Issue 01, January, 2015
Available at http://www.ijcsonline.com/
1 | International Journal of Computer Systems, ISSN-(2394-1065), Vol. 02, Issue: 01, January, 2015
The evaluation of the efficiency of listed companies, using nonparametric
methods: An empirical analysis of the Greek Information Technology sector
Apostolos G. Christopoulos, Ph.D.
[email protected] National and Kapodistrian University of Athens
Faculty of Economics
Abstract
The aim of this study is to evaluate the companies of the IT sector in Greece and to classify them according to their effi-
ciency, using the non-parametric method Data Envelopment Analysis (DEA). The period of investigation covers the
years 2006 - 2010 which is the era of development of IT services, before the beginning of crisis in late 2010 which af-
fected the financial results of these firms. One of the most important questions to be answered by IT firms in recent
years is whether their offered services deliver to them the maximum possible results. Measuring the efficiency of pro-
duction systems is a key problem in this answer. The efficiency concept is related to the ability of a firm to transform theinputs consumed in generated output. The traditional parametric methods for measuring the efficiency are based on a
production function which describes the formation of inputs into outputs in the production system. The DEA is a non-
parametric linear programming method used to measure performance. This method calculates the limit of efficiency of
a set of production units using a function that describes the transformation of inputs into outputs. This method sepa-
rates firms into profitable and non-profitable, while it also calculates the efficiency of each firm using the most favora-
ble conditions for each firm which makes DEA as one of the most popular methods of analysis.
Keywords: DEA, financial ratios, corporate efficiency, linear programming, information technology.
I. I NTRODUCTION AND LITERATURE REVIEW
In order to evaluate the performance of a firm to uti-lize its resources we use two basic measures, productiv-ity and efficiency. The productivity of a firm is given bythe index of the volume of its output production basedon the amount of the employed quantity of inputs. Itmay include either all inputs and outputs or a subset ofthem. Productivity varies depending on the productiontechnology, the technical efficiency of the examinedfirms or the external environment in which these firmsoperate. On the other hand, efficiency is the degree towhich the optimal use of resources for the production ofinputs at a given level is equal to the optimal use ofresources required to produce the output of a given
quality. The examined firm is characterised by the termDMU (Decision Making Unit). This term is used inorder to include under a single framework all kinds of
productive units (firm, region, sector, country). There-fore, a DMU is defined as an entity which transformsinputs N into M final products or outputs at a specifictechnology. The aim of a DMU is to maximize the prof-its of a firm which, inter alia are achieved by improvingits performance.
Measuring the effectiveness of firms within a sectoris a key criterion for the productive performance of theentire industry. In modern economic research, the over-all effectiveness of a production unit consists of three
sub-definitions:
• Technical Efficiency (TE): refers to the ability of
a production unit to operate (or not) at the limit of the possible outcomes of the used production technology.
• Scale (size) Efficiency (SE): expresses the devia-tion of a technically efficient production plant by themost productive scale size (MPSS). MPSS is the pro-duction scale size wherein the average product producesa combination of inputs x becomes maximum. Specifi-cally, is the point of full technical efficiency with con-stant returns to scale. For a given production technologywith production function y = f (x), the SE efficiency is:
where AP is the average product (or the average productivity) of input x and is given by the formula:
• Allocative Efficiency (AE): refers to the ability ofa production unit to use its inputs in optimal quantities,given the market prices of these inputs and the produc-tion technology. In a simple form of a production unitwhich uses an input x (cost price w) and for the quantityof output y, the overall cost effectiveness (total costefficiency) equals to:
-
8/9/2019 The evaluation of the efficiency of listed companies, using nonparametric methods: An empirical analysis of the Gr…
2/18
Apostolos G. Christopoulos et al The evaluation of the efficiency of listed companies, using nonparametric methods: An empirical analysis
of the Greek Information Technology sector
2 | International Journal of Computer Systems, ISSN-(2394-1065), Vol. 02, Issue, 01, January, 2015
Where x * is the amount of inputs when the produc-tion costs is minimize.
Therefore the mathematical formulation of the allo-cation efficiency is:
Combined the technical and the scale efficiencies, theyform the productive efficiency (PE) while the combina-tion of all three efficiencies forms the economic effi-ciency (EE).
To understand the DEA method, it is essential to
make clear the concepts of inputs and outputs in the
implementation of this methodology. To assess the
efficiency of a firm in general, as inputs are considered
the goods or services used for the production of finalgoods or services (raw materials, machinery, capital,
labor, knowledge, energy etc). Inputs are also referred
as factors of production and can be classified into three
broad categories: land (natural resources), labor and
capital. As outputs we consider the produced goods or
services that are either consumed by end user, or arereused in the production process. Depending on the
nature of the investigated sector there are different types
of problems concerning the definition of inputs and
outputs.
The appropriate selection of inputs and outputs toimplement the DEA method is the most important step
to get reliable results. The key questions are whichinputs and corresponding outputs can be used in order
to ensure that the results are comparable. The most
important inputs used for efficiency and productivity
are the capital, labor, energy and raw materials among
which capital and labor are the most usual inputs.
Although such inputs look pretty clear, in real
conditions they become quite complicated. For
example, a firm’s IT division incorporates electronic
data processing and other processes, such as electronic
payments. However, if it these works are given for
management to another firm, then it is involved in more
than one input, such as capital, labor, energy and raw
materials. Labor is usually divided between thenumbers of employees, the hours of work and the labor
cost which includes salaries that vary depending on the
position of employees or even depends on the
geographical location of the firm. Employees are also
divided in skilled and unskilled, experienced and not
experienced etc.
Capital is an equally important input. According to
the literature there are different ways to calculatecapital. Typically, we can take into account the assets,
namely buildings, machineries and equipment. Still,
cash may be included. Very important is the life of the
assets.
From the above we can understand the importance of
outputs and inputs for the calculation of the efficiency
and productivity of the concerned firms. Furthermore,
since firms do not always record a complete and detail
the prices of inputs and outputs, there is a prospect of
forming financial ratios of input/output using more than
one output/input. In more detail, when we examine the
profitability of listed firms, the right selection ofoutputs/inputs becomes very important for shareholders
and investors but also for the lenders of the examined
firms. Such ratios can be derived from the firm’s
financial statements. Therefore, the evaluation of listed
firms is important for both the investors and their
lenders. The most common financial ratios are used dueto the information they provide, concerning the activity,
liquidity, profitability, capital structure, investments and
operating costs of the firm under examination.
To measure correctly the effectiveness we must know
the limit of the production technology on which these
measurements are made. Thus, the primary goal in the
measure of effectiveness is the identification of the
potential limit of production technology. In the last 40years many methods have been developed for assessing
the threshold of production capacity. The two most
basic methods are:- The parametric approach, which uses econometric
techniques for estimating the production technology
threshold, (stochastic frontier),
- The non-parametric approach, which uses linear
programming techniques to determine this threshold
(DEA).Both techniques use a frontier of maximum
production to describe every potentially profitable
combinations of input-output that can produce one unit
at a specific time. The differences between the twocategories mainly concern the assumptions used to
estimate the technological limit production and theexistence of random error. It is worth noting that the use
of different methods leads to differences in measuring
efficiency.
The category of parametric models is referred as the
Stochastic Frontier Analysis (SFA) and was developed
based on the use of econometric techniques to estimate
the frontier of production technology. Such models
were initially developed by Farrell (1957) who also
gave the definition of efficiency for firms. In this study,
Farrell highlighted for the first time, the importance of
assessing the so-called marginal production function(frontier production function). It is also called as the
curve of isoproductivity of the most efficient firm
which is the geometric field of points which reflect the
perfect combination of productive factors among the
sampled firms. Initially, Farrell attempted to measure
the performance of a production unit, by applying a
model of a single input and a single output [1]. He
applied this model to assess the efficiency of American
agriculture compared with other countries. He found out
that aggregation of the various inputs and outputs to a
single input and output, respectively, did not have the
expected outcome. However, after years, his method
was developed and can measure the performance ofoperating units with multiple inputs and outputs based
on linear programming.
Unlike econometric approaches, which attempt to
-
8/9/2019 The evaluation of the efficiency of listed companies, using nonparametric methods: An empirical analysis of the Gr…
3/18
Apostolos G. Christopoulos et al The evaluation of the efficiency of listed companies, using nonparametric methods: An empirical analysis
of the Greek Information Technology sector
3 | International Journal of Computer Systems, ISSN-(2394-1065), Vol. 02, Issue, 01, January, 2015
determine the ultimate effectiveness of a decision-
making unit (DMU) compared with a benchmark set
externally as a standard; non-parametric methods seek
to evaluate the efficiency of a firm in relation with other
firms in the same sector. This class of non-parametric
models is referred as Envelope Data Analysis (DEA)and was developed by using techniques based on linear
programming approaches to the production technology
(Charnes, Cooper and Rhodes, 1978-1979, Banker,
Charnes and Cooper, 1984) [2]. The DEA method does
not require the setting of a specific functional
relationship between inputs and outputs and the total production capacity is determined through a linear
process of integration of the observed input-output
combinations for each decision-making firm together
with assumptions about the scale and availability
inflows and outflows. Farell (1957) ignores the firm’s
internal production process, assuming that this functionis complex and therefore impossible to assess the
overall situation. His method is based only on the
measurements of input and output, which in almost allcases are measurable. He expressed the efficiency of
plants using the TFP index, defined as the ratio of total
outputs to total inputs. In his work for the first time
linear programming techniques are introduced in order
to determine efficiency and to analyze it into individual
compartments.
Successors of Farell were Charnes, Cooper and
Rhodes (1978), who founded the Data Envelopment
Analysis (DEA), introducing a new efficiency valuation
technique [13]. This technique is a non-parametric
method based on linear programming models, which
achieves to quantitatively estimate the maximum value
of the relative efficiency of production units. The DEAmethod assumes the existence of a set of production
units, the Decision Making Units (DMUs), which
operate in a single, comparable and uniform frame and
consume the same multiple inputs and produce the same
multiple outputs. Both inputs and outputs are varied,
usually measured in different measurement scales
depending on the nature of the problem and the
availability of data. The inputs are "goods" to be saved
(thus smaller consumption levels are more desirable),
and the outputs are the "goods" to maximize (hence
larger production levels are more desirable). When
there are several inputs and outputs comparisons of
units become difficult because one unit is very likely totake precedence over other units in an input or output,
but can simultaneously underperform other
inputs/outputs.
Compared with previous methods DEA offers the
chance to manage multiple inputs and outputs withouthaving to put in advance weights in each
inflow/outflow. To proceed to the assessment and
calculations it is not needed to convert the data to a
system of values, to make the summation of inputs /
outputs and valuation. DEA uses ordinary linear
programming methods for the determination andcomparison of similar sets for each system calculates. It
uses similar units as reference system, presenting pricesfor an inefficient unit, which should be amended so that
this unit is effective. Ii even identifies the size of the
required amendments on the basis of the remaining
reference set. Ky Naraini Che Ku Yusof et al. (2010)
Malaysian companies are examined with DEA using as
inputs the operating and financial expenses and other
assets and as outflows the sales [15]. Reza Tehrani et al.
(2012) apply DEA using as inputs the liabilities and
assets and as outputs the performance ratios. Nordin HjMohamad and Fatimah Said (2012) use the operating
expenses and sales, as well as performance ratios [3]
[17]. Kambiz Shahroodi and Fatemeh Feraghnia (2013)
investigate pharmaceutical firms with the use of ROA
to select the proper variables [14].
Banks are always in the center of research with DEA.Specifically, applications of DEA in banks Giokas, D.,
(1990) and Necmi K., (2011) using the cash items, fixed
assets and liabilities as inputs and cash flows, and
liquidity and profitability ratios as outputs. Still, the
man-hour and the operating expenses are used; the
square meters of buildings owned by banks are alsoused as inputs while transactions per branch are
considered as outputs [4-8]. Furthermore, liquidity can
be used as the only output while capital adequacy,efficiency or cash items can be used as the only inputs.
Joe, Z., (2000) uses employees, assets and funds as
inputs and the market value of the firms and the
performance ratios as outputs [9]. In the papers of
Premachandra, I.M., et al. (2011) [5] [18] and
Toshiyuki, S., and Mika, G., (2009) they use the same
inputs and outputs for application to banks [10]. Jose
Humberto Ablanedo and Rosas et al. (2010) evaluate
the ports of Malaysia by using only outputs which are
the liquidity ratios, inventory turnover ratio,
profitability ratios and receivables turnover ratio [11].
Emel, A.B., (2003) follows six steps to select the
appropriate inputs/outputs: Selection of sample andobservations; determination of the main economic
dimensions to consider. The main dimensions to be
examined (liquidity, activity, economic structure,
profitability, growth and investment activity); filtering
of samples depending on the economic dimensions. The
primary economic ratios are restricted to those
expressing more basic economic dimensions. Because
usually ratios are correlated to each other some of them
are excluded as they are expressed by others; use
expertise advices for choosing the most appropriate
economic ratios from the initially selected; application
of DEA using these ratios; verification of results with
the application of other methods, such as regression[12].
During the last decades, the literature on DEA
methods is continuously growing. In his work, Gabriel
Tavaresa presents a large number of works that
implement the DEA method, adjusting them accordingto the applied method and the examined sector. The
large number of published works on DEA points out
that this method has a great research interest [16].
The main aim of this paper is to study the efficiency
of a set of IT firms with of DEA for the period 2006-
2010. This sector was chosen for its vast presence in theGreek economy. The field of Information Technology
and Telecommunications plays arguably one of themost important roles in terms of socio-economic
development, both globally and nationally. The
investigated period was chosen deliberately as it is five
-
8/9/2019 The evaluation of the efficiency of listed companies, using nonparametric methods: An empirical analysis of the Gr…
4/18
Apostolos G. Christopoulos et al The evaluation of the efficiency of listed companies, using nonparametric methods: An empirical analysis
of the Greek Information Technology sector
4 | International Journal of Computer Systems, ISSN-(2394-1065), Vol. 02, Issue, 01, January, 2015
years prior to the economic recession in Greece which
started in late 2010.
In the first section of this thesis efficiency was
explained with the presentation of the mathematical
expression of evaluating a firm. The types of efficiency
and the methods used to measure and evaluate firms based on profitability were also presented with the
analysis of DEA. Also the two key terms of DEA,
inputs and outputs were explained. In the second
section the literature review for DEA is presented with
the two basic models of DEA, the BCC and CCR. The
third section presents specific data on the IT sector and presents the sample of the investigated firms. The
fourth section outlines the variables that will be used to
model and presents the methodology to be followed.
The model chosen in this work is an output oriented
model with three outputs and one input. In the final
section DEA method is applied and the results are presented, based on which the classification of firms
into profitable and not profitable takes place. Last but
not least a comparison of the effects of DEA to theresults of the financial analysis takes place in order to
confirm the efficiency of the applied process.
Using weights and given values for inputs and
outputs, the DEA method calculates the maximum
comparative profitability of each firm in relation to the
other firms of the sample. Also the DEA output is a
threshold that reflects the best combination of
maximum output from the inputs of each module. For
the inefficient firms (technical efficiency
-
8/9/2019 The evaluation of the efficiency of listed companies, using nonparametric methods: An empirical analysis of the Gr…
5/18
Apostolos G. Christopoulos et al The evaluation of the efficiency of listed companies, using nonparametric methods: An empirical analysis
of the Greek Information Technology sector
5 | International Journal of Computer Systems, ISSN-(2394-1065), Vol. 02, Issue, 01, January, 2015
xin, yjn is i input and output of j n DMU
e is infinitesimal positive number
This mathematical problem, when solved, will give
the values of the weights u and v, which will maximize
the efficiency of m DMU. If the rate of return is equal
to one, then the MA is efficient, and will be set on the boundary; otherwise it is relatively non-effective. Still,
it gives the efficiency of a single Unit Decision. In order
to get the rate of return also for other decision units it is
needed to solve more mathematical problems like this
one.
2.2 Input minimizing model
A comparable linear programming typology is
possible to minimize the weighted sums of inputs,
setting the weighted sum of outputs equal to the unit.
This model seeks to minimize the proportion of the
inputs of the evaluated m DMU, based on a weighted
combination of inputs and outputs of other units that
exceed the m DMU. When evaluable m DMU, is
estimated as inefficient, the solution to the dual problem
provides some DMUs (the reference group, the peer
group, or the reference set) estimated as effective
weights of m DMU.
Moreover, the optimal solution of the model provides
a virtual DMU on the frontier, resulting as a linear
combination of all DMUs reference. The m DMU
evaluated, should be transformed to this virtual DMU,
to become effective. This is done by a reduction ofinputs or extension of output.
III. MATHEMATICAL FORMULATION OF THE
DEA MODEL
With the DEA method the decision whether a unit
(DMU) is inefficient is based on the creation of a
complex unit. This composite unit is a linearcombination of inputs and outputs of other units. The
assumption of linearity is equivalent to the assumption
that if two alternative production processes have been
observed in practice, then each output process is a linear
combination of both (wherein each process participateswith a weight), is also feasible (Banker, Morey 1986).
The aim (for the case of reduction of input) is to find
the minimum level of resources required for a unit
operating in a particular environment to produce aspecified level of outputs. Similarly, in the case of
increased output, the aim is to find the maximum levelof output that can be produced by a unit operating in a
particular environment, given a fixed level of inputs.
The efficiency of any unit is calculated by forming the
ratio of the sum of outputs, each of which is assigned
with a weight, to the sum of the input, which are also
assigned with weights. Note that these weights can vary
and are dependent to the decision maker. The
relationship which defines efficiency (Charnes et al,
1978) is therefore:
where,
i: input (i = 1,2,……m)
j : unit (j=1,2,………n)r : output (r= 1,2,…………...s)
Xij : i input of j unit
Υrj : r output of j unit
s : the number of outputs
m : the number of inputs
n : the number of units
The relative efficiency of a particular decision unit
(DMU0) is resulting from the maximization of the
above formula (1). This maximization will take place
under the one limitation for each unit which has the
following form (2):
The efficiency ratio is less than or equal to 1.
So, there will be s + m variables and an equal number
of limitations, as there are units n.
The mathematical formula of this method for assessingthe profitability of DMU0 is therefore summarized as
follows (Charnes et al, 1978):
Where, j = 1,…,n
Ur ≥0, r = 1,…,s Ni ≥0, i = 1,…,m
Where,
i: the input (i = 1,2,……m)
j : the unit (j=1,2,………n)
r : the output (r= 1,2,…………...s)Xij : i input of j unit
Υrj : r output of j unit
s : the number of outputs
m : the number of inputs
n : the number of unitsThe DEA provides an estimate on how efficient each
unit is, based on actual inputs used to produce the
-
8/9/2019 The evaluation of the efficiency of listed companies, using nonparametric methods: An empirical analysis of the Gr…
6/18
Apostolos G. Christopoulos et al The evaluation of the efficiency of listed companies, using nonparametric methods: An empirical analysis
of the Greek Information Technology sector
6 | International Journal of Computer Systems, ISSN-(2394-1065), Vol. 02, Issue, 01, January, 2015
corresponding amounts of costs, without having precise
knowledge of the relationship between inputs and
outputs. The Ur and Ni weights are calculated by DEA
and the values to be assigned to each input and output
in order to maximize the efficiency ratio of the unit are
calculated. This means that the resulting solution is thetotal price of Ur and Ni giving the unit under review the
maximum efficiency ratio, while the efficiency ratio of
the specific values does not exceed 1 for this unit or for
any other unit of the same set of units. Therefore, the
optimal values of Ur and Ni differ for different units,
since they are the solution of (2).
When the evaluated unit is included in the
limitations, we conclude that there is always a solution
to (2), with the value range between 0 and 1. The unit
therefore will be efficient only if the value is 1. If it gets
a value less than 1, then there is a subset of the set of peer data in which the unit belongs, in relation to which
this appears inefficient. To qualify a unit as inefficient,
it should be no other combination of weights such thatthey satisfy the efficiency conditions. Any other choice
of weights than the one that has made by DEA will
further deteriorate the performance of the unit.
For the solution of the problem of valuation units, the
DEA approach is based on creating frontier efficient
units, called effective limit. This is determined by a line
passing through the points P2, P3, P4 and P5. The
technical efficient units are point 1, and any other unit
located on the line segments connecting the turning
points between them.
The term "technical efficiency" has the meaning ofthe failure to reduce the input, without reducing outputs
(or vice versa, failure to increase output without
increasing input). So one unit displays technical
inefficiency in the observed behavior, if the resultsshow that some of the inputs or outputs can be
improved without worsen another input or output
(Charnes, Cooper and Thrall, 1986).
In this sense a unit which is on the efficient frontier
does not necessarily mean that it is efficient. For
example, the unit P5 output (or any other unit that may
be located on the segment P4P5) is equal to that of P4,
but has higher input. Thus the P5 although situated onthe efficient frontier (that has an efficiency ratio 100%
according to DEA), it is not efficient. These cases are
examined by the DEA with control deviation of
variables between inputs and outputs.
3.1 Financial Ratios
Activity ratios express the extent that a production
unit utilizes its assets by converting them into cash;
liquidity ratios determine the short-term economic
ability of a firm to meet its short-term obligations,
considering its current assets and its working capital;
efficiency ratios examine the ability of the firm andtherefore needs to be examined and for possible
correlation between sales, production and profits;
capital structure ratios and sustainability examine the
economic situation of a firm in the long run byanalyzing its capital structure; investment ratios interest
offer information for investors to decide on their
investment in equity securities of the firm; operating
expenditure ratios provide information about the policy
followed by a firm towards its running costs and its
efficiency towards these costs.
The next step is to decide which ratios will be used
for the evaluation of firms by a ranking of these ratios
into inputs and outputs. The ratios of activity, capital
structure and profitability and operating costs can beused to form inputs in a production process, since they
examine the capital activity of these firms, their costs
and the use of their assets. On the other hand, liquidity
ratios, profitability and investment ratios can be used to
form outputs, since they show the financial position of
the company to profitability, performance andinvestment activity.
IV. SELECTION OF THE SAMPLE OF IT AND
TELECOMMUNICATIONS SECTOR
The Information Technology sector in Greece is
among the most growing sectors in the last fifteen
years. The gradual liberalization since 2000 and the
increasing demand for telecommunications services had
a positive impact on the development of the market.
Communications have been one of the sectors that
significantly enhance the economy and have a direct
impact on socio-cultural level of the population. In this
case, the development of communication networks both
for fixed and mobile telephony has been very fast. The
market for fixed and mobile services has broadened
considerably in recent years, mainly after the fully
liberalization of telecommunications on 1st of January2001. Of course the major part of the investments ininformation technology has been undertaken by the
former state monopoly of Hellenic Telecommunications
Organisation (HTO). From the above it is understood
that this sector is very important for the national
economy, which even in the recent years of the
economic crisis in Greece has relatively good performance. The selected companies for our analysis
are as possible homogenous with respect to the products
and services they offer. An important criterion for
selecting companies was to be present in the market for
the entire period under investigation (2006- 2010), and
to be possible to have access to their financialstatements.
-
8/9/2019 The evaluation of the efficiency of listed companies, using nonparametric methods: An empirical analysis of the Gr…
7/18
Apostolos G. Christopoulos et al The evaluation of the efficiency of listed companies, using nonparametric methods: An empirical analysis
of the Greek Information Technology sector
7 | International Journal of Computer Systems, ISSN-(2394-1065), Vol. 02, Issue, 01, January, 2015
V. SAMPLE AND METHODOLOGY WITH THE USE OF
RATIOS
The selected firms are listed in the Athens Exchange
in the sector of information technology: ALT; COCON;
BYT; ILI; PROF; PCSYST; INTR; PLAIS; INF; MSL;
The model that is implemented in our analysis uses
only outputs. Following it will be explained how anoutput turned into input in order to avoid errors in the
application of the method. Since our sample is
relatively small, we will apply 4 ratios in order to
receive secure results. The outputs selected:
1. ROΑ = 100* (EBIT / total assets)
2. Receivables Turnover Ratio = net sales / average
account of receivables
3. Days’ inventory on hand (average) = days in year /
inventory turnover
4. Current Ratio = (cash items + receivables +
inventories) / short term liabilities
In this paper we apply the DEA using an inputs and
outputs method. We apply DEA on the 10 selected
firms for five years (2006- 2010). Next we assess the
progress of the firms during these five years. The stepswe follow are:
selection and presentation of ratios
testing correlation of ratios
financial analysis of firms on the basis of
selected ratios
application of DEA
comparing the results of DEA with the results
of the financial analysis
conclusions
TABLE 1. R ATIOS FOR 4 OUTPUTS FOR THE 10 FIRMS FOR 5 YEARS
2006 2007 2008 2009 2010
Χ1 Χ2 Χ3 Χ4 Χ1 Χ2 Χ3 Χ4 Χ1 Χ2 Χ3 Χ4 Χ1 Χ2 Χ3 Χ4 Χ1 Χ2 Χ3 Χ4
Ε1 1.36% 0.84 1.65 1.26 1.52% 0.91 1.52 2.94 1.59% 0.55 1.27 1.67 1.12% 0.32 1.42 2.78 1.41% 0.1 1.52 1.19
Ε2 2.24% 0.26 1.47 2.1 2.70% 0.69 1.8 2.53 7.35% 0.44 1.53 2.11 3.21% 0.32 1.94 1.45 3.65% 0.46 1.24 1
Ε3 7.67% 2.21 7.76 1.79 7.71% 2.53 5.89 1.71 6.68% 2.37 7.82 1.8 1.94% 1.92 6.61 1.69 6.41% 1.59 5.35 1
Ε4 9.21% 1.76 10.01 2.43 8.85% 1.75 11.25 2.82 7.33% 2.17 8.62 3.41 6.97% 1.29 9.83 1.5 8.09% 1.45 11.46 1.46
Ε5 6.72% 2.29 11.14 1.75 7.78% 1.77 15.05 1.51 4.58% 1.38 13.97 1.98 3.24% 1.05 11.65 1.33 1.51% 1.9 14.56 1.4
Ε6 8.06% 1.38 5.15 1.92 4.78% 1.54 4.26 1.46 1.58% 1.34 5.96 1.71 4.88% 1.19 6.45 1.64 5.15% 0.74 2.54 1.54
Ε7 1.02% 0.23 1.95 4.69 1.07% 0.22 1.26 2.23 1.80% 1.18 1.96 1 2.62% 0.17 1.89 2.57 1.96% 0.15 2.54 1.96
Ε8 6.68% 9.46 6.29 1.48 6.86% 8.33 6.01 1.44 2.64% 9.75 5.76 1.19 3.14% 8.66 5.67 1.36 1.93% 8.89 6.33 1.55
Ε9 4.32% 2.03 11.3 3.62 3.89% 1.82 9.65 1.73 4.04% 2.85 11.88 1.42 2.46% 2.31 10.79 2.03 1.92% 1.91 11.54 1.96
10 3.88% 2.7 2.9 2.53 5.87% 3.48 0.91 3.89 6.38% 5.03 1.69 2.28 11.73% 3.66 1.4 1.92 7.48% 3.78 1.69 2.15
Where,
X1= return on asset
Χ2 = receivables turnover ratio
Χ3 = inventories turnover ratio in days
Χ4 = current ratio
Ε1= ALT
E2=COCON
E3=BYT
E4=ILIE5=PROF
E6=PCSYST
E7=INTR
E8=PLAIS
E9=INF
E10=MSL
-
8/9/2019 The evaluation of the efficiency of listed companies, using nonparametric methods: An empirical analysis of the Gr…
8/18
Apostolos G. Christopoulos et al The evaluation of the efficiency of listed companies, using nonparametric methods: An empirical analysis
of the Greek Information Technology sector
8 | International Journal of Computer Systems, ISSN-(2394-1065), Vol. 02, Issue, 01, January, 2015
TABLE 2. R ATIOS WITH 3 OUTPUTS AND 1 INPUT FOR THE 10 FIRMS FOR 5 YEARS
2006 2007 2008 2009 2010
Χ1 Χ2 Χ3 Χ4 Χ1 Χ2 Χ3 Χ4 Χ1 Χ2 Χ3 Χ4 Χ1 Χ2 Χ3 Χ4 Χ1 Χ2 Χ3 Χ4
1 1.36% 0.84 221.21 1.26 1.52% 0.91 240.13 2.94 1.59% 0.55 287.4 1.67 1.12% 0.32 257.04 2.78 1.41% 0.1 240.13 1.19
2 2.24% 0.26 248.3 2.1 2.70% 0.69 202.78 2.53 7.35% 0.44 238.56 2.11 3.21% 0.32 188.14 1.45 3.65% 0.46 294.35 1
3 7.67% 2.21 47.04 1.79 7.71% 2.53 61.97 1.71 6.68% 2.37 46.68 1.8 1.94% 1.92 55.22 1.69 6.41% 1.59 68.22 1
4 9.21% 1.76 36.46 2.43 8.85% 1.75 32.44 2.82 7.33% 2.17 42.34 3.41 6.97% 1.29 37.13 1.5 8.09% 1.45 31.85 1.46
5 6.72% 2.29 32.76 1.75 7.78% 1.77 24.25 1.51 4.58% 1.38 26.13 1.98 3.24% 1.05 31.33 1.33 1.51% 1.9 25.07 1.4
6 8.06% 1.38 70.87 1.92 4.78% 1.54 85.68 1.46 1.58% 1.34 61.24 1.71 4.88% 1.19 56.59 1.64 5.15% 0.74 143.7 1.54
7 1.02% 0.23 187.18 4.69 1.07% 0.22 289.68 2.23 1.80% 1.18 186.22 1 2.62% 0.17 193.12 2.57 1.96% 0.15 143.7 1.96
8 6.68% 9.46 58.03 1.48 6.86% 8.33 60.73 1.44 2.64% 9.75 63.37 1.19 3.14% 8.66 64.37 1.36 1.93% 8.89 57.66 1.55
9 4.32% 2.03 32.3 3.62 3.89% 1.82 37.82 1.73 4.04% 2.85 30.72 1.42 2.46% 2.31 33.83 2.03 1.92% 1.91 31.63 1.96
10 3.88% 2.7 125.86 2.53 5.87% 3.48 401.1 3.89 6.38% 5.03 215.98 2.28 11.73% 3.66 260.71 1.92 7.48% 3.78 215.98 2.15
Where,
X1= return on assetΧ2 = receivables turnover ratioΧ3 = inventories turnover ratio (in days)
Χ4 = current ratio
Ε1= ALT
E2=COCON
E3=BYT
E4=ILIE5=PROFE6=PCSYST
E7=INTR
E8=PLAIS
E9=INF
E10=MSL
TABLE 3. DESCRIPTIVE STATISTICS OF RATIOS FOR ALT
Χ1 Χ2 Χ3 Χ4
Mean 1.410 0.470 256.170 2.145
Standard Error 0.103 0.173 11.145 0.425
Median 1.465 0.430 248.131 2.225
Mode 240
Standard Deviation 0.207 0.346 22.290 0.851
Sample Variance 0.040 0.11 496.870 0.724
Kyrtosis 1.500 -0.314 1.124 -4.320
Skewness -1.293 0.509 1.335 -0.237
Range 0.47 0.81 47.27 1.75
Minimum 1.12 0.10 240.13 1.19
Maximum 2 1 287 3
TABLE 4. DESCRIPTIVE STATISTICS OF RATIOS FOR COCONΧ1 Χ2 Χ3 Χ4
Mean 4.227 0.48 230.959 1.772
Standard Error 1.058 0.077 23.636 0.340
Median 3.430 0.450 220.669 0.340
Mode
Standard Deviation 2.117 0.154 47.272 0.680
Sample Variance 4.484 2.013 2234.700 -2.464
Kyrtosis 3.358 2.013 -0.052 -2.464
Skewness 1.799 1.016 0.974 1.530
Range 4.65 0.37 106.21 1.00
Minimum 2.70 0.32 188.14 1.00
Maximum 7 1 294 3
-
8/9/2019 The evaluation of the efficiency of listed companies, using nonparametric methods: An empirical analysis of the Gr…
9/18
Apostolos G. Christopoulos et al The evaluation of the efficiency of listed companies, using nonparametric methods: An empirical analysis
of the Greek Information Technology sector
9 | International Journal of Computer Systems, ISSN-(2394-1065), Vol. 02, Issue, 01, January, 2015
TABLE 5. DESCRIPTIVE STATISTICS OF RATIOS FOR BYT
Χ1 Χ2 Χ3 Χ4
Mean 5.720 2.102 58.022 1.752
Standard Error 1.288 0.214 4.521 0.030
Median 6.615 2.145 58.594 1.755
Mode
Standard Deviation 2.577 0.428 9.242 0.061
Sample Variance 6.644 0.183 85.424 0.003
Kyrtosis 3.224 -2.738 -0.840 -5.348
Skewness -1.730 -0.368 -0.303 -0.068
Range 5.77 0.94 21.55 0.12
Minimum 1.94 1.59 46.68 1.69
Maximum 8 3 68 2
TABLE 6. DESCRIPTIVE STATISTICS OF RATIOS FOR ILI
Χ1 Χ2 Χ3 Χ4
Mean 7.810 1.665 35.940 2.297
Standard Error 0.417 0.193 2.438 0.487
Median 7.710 1.600 34.787 2.160
Mode
Standard Deviation 0.835 0.386 4.877 0.974
Sample Variance 0.698 0.149 23.790 0.949
Kyrtosis -1.707 -0.559 -1.066 -4.243
Skewness 0.506 0.768 0.876 0.306
Range 1.88 0.88 10.49 1.95
Minimum 6.97 1.29 31.85 1.46
Maximum 9 2 42 3
TABLE 7. DESCRIPTIVE STATISTICS OF RATIOS FOR PROF
Χ1 Χ2 Χ3 Χ4
Mean 4.277 1.525 26.690 1.555
Standard Error 1.325 0.193 1.598 0.146
Median 3.910 1.575 25.598 1.455
Mode
Standard Deviation 2.651 0.386 3.184 0.292
Sample Variance 7.031 0.149 10.140 0.085
Kyrtosis 0.679 -2.295 2.854 2.708
Skewness 0.739 -0.495 1.663 1.633
Range 6.27 0.85 7.08 0.65
Minimum 1.51 1.05 24.25 1.33
Maximum 8 2 31 2
TABLE 8. DESCRIPTIVE STATISTICS FOR RATIOS FOR PCSYST
Χ1 Χ2 Χ3 Χ4
Mean 4.097 1.202 86.803 1.587
Standard Error 0.842 0.170 20.010 0.050
Median 4.830 1.265 73461.000 1.590
-
8/9/2019 The evaluation of the efficiency of listed companies, using nonparametric methods: An empirical analysis of the Gr…
10/18
Apostolos G. Christopoulos et al The evaluation of the efficiency of listed companies, using nonparametric methods: An empirical analysis
of the Greek Information Technology sector
10 | International Journal of Computer Systems, ISSN-(2394-1065), Vol. 02, Issue, 01, January, 2015
Mode
Standard Deviation 1.685 0.340 40.020 0.109
Sample Variance 2.841 0.12 1601.626 0.012
Kyrtosis 3.837 1.232 1.756 -2.051
Skewness -1.947 -0.981 1.455 -0.098
Range 3.57 0.80 87.11 0.25
Minimum 1.58 0.74 56.59 1.46
Maximum 5 2 144 2
TABLE 9. DESCRIPTIVE STATISTICS OF RATIOS FOR INTR
Χ1 Χ2 Χ3 Χ4
Mean 1.860 0.430 203.182 1.940
Standard Error 0.318 0.250 30.830 0.337
Median 1.880 0.195 189.670 2.095
Mode
Standard Deviation 0.636 0.500 61.668 0.674
Sample Variance 0.405 0.25 3803.040 0.455
Kyrtosis 1.202 3.929 2.309 1.721
Skewness -0.161 1.979 1.224 -1.208
Range 1.55 1.03 145.98 1.57
Minimum 1.07 0.15 143.70 1.00
Maximum 3 1 290 3
TABLE 10. DESCRIPTIVE STATISTICS OF RATIOS FOR PLAIS
Χ1 Χ2 Χ3 Χ4
Mean 3.642 8.907 61.530 1.385
Standard Error 1.100 0.303 1.501 0.075
Median 2.890 8.775 62.050 1.400
Mode
Standard Deviation 2.201 0.606 3.003 1.151
Sample Variance 4.847 0.37 9.021 0.022
Kyrtosis 3.070 1.707 -1.149 0.381
Skewness 1.696 1.164 -0.725 -0.530
Range 4.93 1.42 6.71 0.36
Minimum 1.93 8.33 57.66 1.19
Maximum 7 10 64 2
TABLE 11. DESCRIPTIVE STATISTICS OF RATIOS FOR INFO
Χ1 Χ2 Χ3 Χ4
Mean 3.077 2.222 33.501 1.785
Standard Error 0.525 0.234 1.581 0.137
Median 3.175 2.110 32.728 1.845
Mode
Standard Deviation 1.050 1.469 3.162 0.275
Sample Variance 1.102 0.22 10.003 0.075
Kyrtosis -4.630 -0.396 0.522 -0.506
Skewness -0.200 0.979 1.113 -0.920
Range 2.12 1.03 7.10 0.61
-
8/9/2019 The evaluation of the efficiency of listed companies, using nonparametric methods: An empirical analysis of the Gr…
11/18
Apostolos G. Christopoulos et al The evaluation of the efficiency of listed companies, using nonparametric methods: An empirical analysis
of the Greek Information Technology sector
11 | International Journal of Computer Systems, ISSN-(2394-1065), Vol. 02, Issue, 01, January, 2015
Minimum 1.92 1.82 30.72 1.42
Maximum 4 3 38 2
TABLE 12. DESCRIPTIVE STATISTICS OF RATIOS FOR MSL
Χ1 Χ2 Χ3 Χ4
Mean 7.865 3.987 273.441 2.560
Standard Error 1.331 0.352 43.839 0.449
Median 6.930 3.720 215.976 2.215
Mode
Standard Deviation 2.662 0.705 87.68 0.899
Sample Variance 7.090 0.5 7687.628 0.808
Kyrtosis 2.669 3.431 2.710 3.494
Skewness 1.640 1.816 1.680 1.834
Range 5.86 1.55 185.12 1.97
Minimum 5.87 3.48 245.98 1.92
Maximum 12 5 401 4
TABLE 13. AVERAGES OF RATIOS FOR EACH FIRM FOR THE PERIOD 2006-2010
Χ1 Χ2 Χ3 Χ4
Ε1 1.4% 0.54 248.3 1.96
Ε2 3.83% 0.43 229.56 1.83
Ε3 6.11% 2.12 53.21 1.76
Ε4 8.09% 1.68 35.68 2.32
Ε5 4.76% 1.67 27.51 1.59
Ε6 4.89% 1.23 74.95 1.65
Ε7 1.69% 0.39 190.1 2.49
Ε8 4.21% 9.01 60.73 1.4
Ε9 3.32% 2.18 33.09 2.15
Ε10 7.06% 3.73 213.45 2.55
Where,
X1= return on asset
Χ2 = receivables turnover ratioΧ3 = inventories turnover ratio in days
Χ4 = current ratio
Ε1= ALT
E2=COCON
E3=BYT
E4=ILI
E5=PROF
E6=PCSYST
E7=INTRE8=PLAIS
E9=INFE10=MSL
TABLE 14. R ATIO AVERAGE PER YEAR
Χ1 Χ2 Χ3 Χ4
2006 5.09% 2.31 61.24 2.35
2007 5.10% 2.3 63.37 2.22
2008 4.41% 2.7 60.43 1.85
2009 4.13% 2.08 63.37 1.822010 3.95% 2.09 62.18 1.6
Average 4.54% 2.3 62.12 1.97
-
8/9/2019 The evaluation of the efficiency of listed companies, using nonparametric methods: An empirical analysis of the Gr…
12/18
Apostolos G. Christopoulos et al The evaluation of the efficiency of listed companies, using nonparametric methods: An empirical analysis
of the Greek Information Technology sector
12 | International Journal of Computer Systems, ISSN-(2394-1065), Vol. 02, Issue, 01, January, 2015
Where,
X1= return on asset
Χ2 = receivables turnover ratio
Χ3 = inventories turnover ratio in days
Χ4 = current ratio
In our analysis we make an assumption concerning
the ratios’ prices when they are either zero or negative.
In order to properly use these ratios, we took accepted
these prices as positive, under the limitation that they
are smaller compared to the relevant prices of the other
firms for the particular year. This assumption ensuresthat we will have measurable values for all ratios and
that the transformed values will not lead to wrong
conclusions.
VI. R ATIOS’ CORRELATION
In order to come to a final decision for the selectedratios we applied correlation tests for every one of
them. Specifically, we examined for each firm the
existence of correlation for ratios by testing these ratios
pairwise with the Spearman correlation coefficient
which is a non-parametric measure of statisticaldependence between two variables and is denoted by p.
The Spearman ratio evaluates how well the relationship
between two variables is described using a monotonic
function. If there are no repeated data values, a perfect
Spearman correlation by +1 or -1 is the case where each
of the variables is a perfectly monotonic function of the
other. The Spearman correlation coefficient is defined
as the Pearson correlation coefficient between the rating
variables. The n scores Xi, Yi converted into rankings
xi, yi, and p is calculated by the formula:
Where,
If p = ±1 there is perfect linear correlation.
If−0,3≤ p < 0,3 there is no perfect linear
correlation.
If −0,5 < p ≤ −0,3 ή 0,3≤ r < 0,5 there is weak
linear correlation. If −0,7 < p ≤ −0,5 ή 0,5 ≤ r < 0,7 there is
average linear correlation.
If −0,8 < p ≤ −0,7 ή 0,7 ≤ r < 0,8 there is a
strong linear correlation.
If −1< p ≤ −0,8 ή 0,8 ≤ p
-
8/9/2019 The evaluation of the efficiency of listed companies, using nonparametric methods: An empirical analysis of the Gr…
13/18
Apostolos G. Christopoulos et al The evaluation of the efficiency of listed companies, using nonparametric methods: An empirical analysis
of the Greek Information Technology sector
13 | International Journal of Computer Systems, ISSN-(2394-1065), Vol. 02, Issue, 01, January, 2015
TABLE 18. R ATIOS CORRELATION OF ILI
Χ1 Χ2 Χ3 Χ4
Χ1 1
Χ2 0.06 1
Χ3 0.36 0.2 1
Χ4 0.1 0.36 0.25 1
TABLE 19. R ATIOS CORRELATION OF PROF
Χ1 Χ2 Χ3 Χ4
Χ1 1
Χ2 0.36 1
Χ3 0.03 0.01 1
Χ4 0.37 0.18 0.01 1
TABLE 20. R ATIOS CORRELATION OF PCSYST
Χ1 Χ2 Χ3 Χ4
Χ1 1
Χ2 0.01 1
Χ3 0.23 0.55 1
Χ4 0.4 0.19 0.45 1
TABLE 21. R ATIOS CORRELATION OF INTR
Χ1 Χ2 Χ3 Χ4
Χ1 1
Χ2 0.02 1
Χ3 0.43 0.03 1
Χ4 0.42 0.06 0.06 1
TABLE 22. R ATIOS CORRELATION OF PLAIS
Χ1 Χ2 Χ3 Χ4
Χ1 1
Χ2 0.24 1
Χ3 0.24 0.03 1
Χ4 0.31 0.09 0.2 1
TABLE 23. R ATIOS CORRELATION OF INFO
Χ1 Χ2 Χ3 Χ4
Χ1 1
Χ2 0.22 1
Χ3 0.11 0.59 1
Χ4 0.29 0.36 0.09 1
TABLE 24. R ATIOS CORRELATION OF MSL
Χ1 Χ2 Χ3 Χ4
Χ1 1
Χ2 0.24 1
Χ3 0.49 0.27 1
Χ4 0.49 0.24 0.38 1
-
8/9/2019 The evaluation of the efficiency of listed companies, using nonparametric methods: An empirical analysis of the Gr…
14/18
Apostolos G. Christopoulos et al The evaluation of the efficiency of listed companies, using nonparametric methods:
An empirical analysis of the Greek Information Technology sector
14 | International Journal of Computer Systems, ISSN-(2394-1065), Vol. 02, Issue: 01, January, 2015
Where,
X1= return on asset
Χ2 = receivables turnover ratio
Χ3 = inventories turnover ratio in days
Χ4 = current ratio
From the above tables which are in line with the
ratios’ theory of when two variables are correlated and
what kind of relationship they have with each other, wecan conclude that the selected ratios have low
correlation between them. The values of p range from
0.01 up to 0.56. Therefore, we can go to our
calculations, using their values. The financial analysis
of the examined firms based on the selected ratios is
presented in the following section.
VII.
FINANCIAL ANALYSIS OF FIRMS BASED ONTHE SELECTED RATIOS
In this section we can see the performance of the ten
selected firms by using the four ratios, following with
the conclusions for the examined firms. In our analysiswe examine every firm for each ratio for the period of
five years (2006-2010). Initially, firms are examined for
each year, and then they are compared based on the
average rate of the ten firms for the particular year,
which is considered as the average rate of the sector.
Then we find the overall averages of firms for the entire
period of the five years.
According to the first ratio, which is the asset
efficiency, we test the ten firms for their efficiency. As
already mentioned, the efficiency of a company is its
ability to generate profits. It shows how efficient is the
firm’s management to utilize its assets in an appropriate
manner to produce revenues. The higher the index, the
better is for the firm which can go on and to attract new
capitals for investment.
The firm with the highest profit for 2006 was ILI
with ratio 9.21%, much higher than the industry
average, which is 5.09%. The lower profit ratio was for
INTRA, at 1.02%. For 2007 ILI holds the primacy in
the industry, with 8.85%, while INTRA notes a slight
increase in profits with a ratio of 1.07%, but stillremains last in the sector (sector is relatively steady at
5.1%). In 2008 COCON manages to be first with
7.35%, while ALT notes the smaller profits in the
sector, with 1.59%, but at the same time the sector to
fall to 4.41%. In 2009 the presence of MSL is dynamic,with a ratio 11.73%, much higher than the 4.13% of the
sector, while the last in the sector is still ALT with a
ratio of 1.12%. In 2010, the higher profits are again for
ILI with a ratio of 8.09%, and the lower profits are for
ALT by 1.41%, while the average of the sector are
further reduced to 3.95%.
Then, we calculated the averages of ratios for each
firm for the five years period. Overall in these five years
we see that ILI manages the have the largest profit, with
an average for the five years at 8.09%, followed by
MSL with 7.06%. Last on the scale is ALT with 1.4%.
The receivables turnover ratio shows how many
times on average a firm collects its receivables duringthe accounting year. It is therefore desirable to have a
higher ratio which means that the firm’s sales are higher
than its receivables.
For 2006, PLAIS is the firm that manages to collect
the receivables better than the rest of the sector, with a
ratio 9.46, compared to the sector’s average 2.31, while
the lowest percentage of receivables are collected by
INTRA, with a ratio of 0.23. In 2007 PLAIS is again
first with a downward trend at 8.33, while INTRA
continues steadily to 0.22, and the average of the
examined firms in the sector to be 2.3. In 2008 PLAIS
notes a further increase with a ratio of 9.75, whileCOCON show a decrease in its ability to collect
receivables with a ratio 0.44 while at the same time theaverage for the ten firms is 2.7. In 2009 PLAIS remains
on the top although with a decrease to 8.66, and INTRA
is last with a ratio 0.17, while the industry is on average
2.08. The best performance to collect receivables is
therefore PLAIS for the five years period from 2006 to
2010 with an average ratio of 8.89, while ALT is lastwith a ratio 0.1 and the sector’s average to be at a ratio
of 2.09. For the total period of investigation the average
receivables turnover ratio is greater for the firm PLAIS
(9.01), while the lower ratio is for COCON (0.43)
The use of inventories turnover ratio offers
significant findings relevant to the ability of a firm to
manage its inventories efficiently.
For 2006 the firm which managed to sell inventories
in hand in the best way was INFO, with a ratio of 11.3
and an average number of 32.3 days to sell inventories
in hand, while on the other hand inventories of COCON
had an average 248.3 days for this year and a ratio of
inventories turnover ratio at 1.47, while for the sector
the average ratio of inventories turnover ratio was 5.96
and the period of inventories in hand to sell was 61.24
days. For 2007, PROF’s average number of days takento sell its inventories on hand was better than the other
firms, with an average ratio of 24.25 days and a ratio of
inventories turnover ratio at 15.05, much lower than the
sector’s average of 63.37 days and inventories turnoverratio 5.76). At the same time MSL does not do so well,
with an average time to replace its inventories of 401.1
days and ratio of inventories turnover ratio. 0.91. In
2008 PROF holds the lead with an average time to
replace its inventories of 26.13 days and ratio
inventories turnover ratio 13.97 (compared to 60.43days and inventories turnover ratio 6.04 of the sector).
The worse average number of days taken to sell
inventories on hand for 2008 is ALT with a ratio of
inventories turnover ratio 1.27 and an average of 287.4
days. In 2009 PROF notes a decrease, but still remains
-
8/9/2019 The evaluation of the efficiency of listed companies, using nonparametric methods: An empirical analysis of the Gr…
15/18
Apostolos G. Christopoulos et al The evaluation of the efficiency of listed companies, using nonparametric methods: An empirical analysis
of the Greek Information Technology sector
15 | International Journal of Computer Systems, ISSN-(2394-1065), Vol. 02, Issue, 01, January, 2015
high compared to the sector average, with an average
time of 31.33 days and a ratio of inventories turnover
ratio 11.65, while the sector is at 63.37 days and a.
Social Insurance Fund 5.76 and last is the MSL, with an
average residence time of the stock 260.71 days and
inventories turnover ratio is 5.76 and at the end is MSLwith an average of 260.71 days and inventories turnover
ratio 1.4. In 2010 PROF closes the five years period
with an average time to replace its inventories 25.07
days and inventories turnover ratio 14.56, while
COCON notes a lower ratio with an average time to
replace its inventories 294.35 days and inventoriesturnover ratio 1.24. The sector’s average in the
respective year is 62.18 days and inventories turnover
ratio 5.88. In 2010 PROF closes five years with an
average time to replace its inventories 25.07 days and
inventories turnover ratio 14.56, while COCON has a
lower ratio with an average time to replace itsinventories 294.35 days and inventories turnover ratio
1.24. At the same year the sector’s average is 62.18
days and the ratio inventories turnover ratio 5.88.
From the averages of the time to replace its
inventories for each firm for the entire period of the fiveyears, we found that the lower average time to replace
its inventories is for PROF, with 27.51 days and a ratio
of inventories turnover ratio 13.27, followed by INFO,
with 33.09 days and inventories turnover ratio 11.03.
The highest average ratio for the entire period of five
years is for ALT, with 248.3 days and a ratio ofinventories turnover ratio 1.47, followed by COCON,
with 229.56 days and inventories turnover ratio 1.59.
The current ratio defines the financial position of afirm in the short run and therefore its ability to meet its
short-term liabilities. Specifically, we can see howmany times a firm covers its current liabilities by its
current assets. The higher this ratio is the better in terms
of liquidity is the position of this firm.
Better liquidity for 2006 presented by INTRA, with a
ratio of 4.69 and the lower for ALT, with a ratio of
1.26, while the average for all firms is 2.35. The 2007
MSL displays liquidity 3.89, higher than the 2.22
average of the sector, while PLAIS has a liquidity ratio
of 1.44. In 2008 ILI notes the highest of 3.41 and
INTRA the lowest ratio of 1.0, while the sector shows a
decrease in liquidity with 1.82. In 2010, the five years
period ends with ALT showing the highest liquidity
ratio between the ten examined firms, with a ratio of
2.78 and COCON the lowest one with a ratio of 1.0while the sector’s average is at 1.6.
From the averages of the current ratios for the ten
firms for the entire five years period, we can see that the
highest liquidity on average for the five years is for the
company MSL, with a ratio of 2.55, followed byINTRA, with 2.49. The lower average ratio for the five
years is for PLAIS with 1.4, followed by PROF, with
1.59.
A remarkable conclusion, based on the averages of
the four ratios for all ten firms per year, is thedownward trend which is noted in all four ratios over
the examined years. The sector seems to fall in profits,
starting from an average return on assets at 5.09% in2006 and ending at 3.95% in 2010. It also seems that
the average receivables turnover ratio was reduced from
2.31 in 2006 to 2.09 in 2010. Downward is also the
average inventories turnover ratio, which starts from
5.96% in 2006 and ends at 5.87% in 2010. The average
time to replace its inventories has increased over the
years, from 61.24 days in 2006 to 62.18 days in 2010.
Last but not least, the liquidity of the examined firms
of the sector is also declining, with the ratio to start in
2006 from 2.35 and to reach 1.6 in 2010. This
downward trend in the examined ratios for the sector
which are related with the outputs of our model showsthe overall downward trend in the sector of Information
Technology for the years 2006 to 2010, when the crisis
period started in Greece.
VIII. APPLICATION OF DEA
To implement the DEA method, we applied the
program DeaOS and the results from this application for
the ten examined firms for the five years ofinvestigation (2006-2010) are presented in Table 25.
TABLE 25. CORPORATE PERFORMANCE RESULTS FOR 2006-2010
2006 2007 2008 2009 2010 Average
Ε1 0.05 0.14 0.07 0.18 0.08 0.1
Ε2 0.07 0.14 0.18 0.15 0.07 0.12
Ε3 0.7 0.47 0.87 0.51 0.41 0.59
Ε4 1 1 1 1 1 1
Ε5 0.93 1 1 0.83 1 0.95
Ε6 0.45 0.24 0.37 0.6 0.2 0.37
Ε7 0.22 0.9 0.08 0.22 0.22 0.33
Ε8 1 1 1 1 1 1
Ε9 1 0.64 1 1 1 0.93
Ε10 0.23 0.12 0.24 0.27 0.23 0.22
Average 0.57 0.57 0.58 0.58 0.52 0.56
-
8/9/2019 The evaluation of the efficiency of listed companies, using nonparametric methods: An empirical analysis of the Gr…
16/18
Apostolos G. Christopoulos et al The evaluation of the efficiency of listed companies, using nonparametric methods: An empirical analysis
of the Greek Information Technology sector
16 | International Journal of Computer Systems, ISSN-(2394-1065), Vol. 02, Issue, 01, January, 2015
Where,
Ε1= ALT
E2=COCON
E3=BYT
E4=ILI
E5=PROF
E6=PCSYST
E7=INTR
E8=PLAIS
E9=INF
E10=MSL
TABLE 26. DESCRIPTIVE STATISTICS FOR PERFORMANCE
2006 2007 2008 2009 2010
Mean 0.622 0.565 0.581 0.576 0.521
Standard Error 0.127 0.122 0.134 0.113 0.133
Median 0.700 0.555 0.620 0.555 0.320
Mode 1 1 1 1 1
Standard Deviation 0.383 0.388 0.424 0.360 0.422
Sample Variance 0.147 0.151 0.179 0.129 0.178
Kyrtosis -1.935 -2.084 -2.298 -1.959 -2.174
Skewness -0.305 0.019 -0.098 0.093 0.323
Range 0.93 0.88 0.93 0.85 0.93
Minimum 0.07 0.12 0.07 0.15 0.07
Maximum 1 1 1 1 1
IX. GENERAL CONCLUSION
From Table 20 with the efficiency scores for the ten
firms for the five years period, we can draw conclusions
from the implementation of the method. Resulting
conclusions on which firms managed to qualify as
efficient (efficiency is equal to 1), and which firms werenon-profitable firms. We can draw conclusions aboutwhich firms are close to be characterized as efficient
and which are very low in efficiency in relation to the
other firms of the sector. Conclusions can be made
comparing all the firms for each year, but also for each
company within the period of the five years (2006-
2010).
8.1 Conclusions for the per year effiiciency of firms
Specifically, for 2006 only three firms (E4, E8, E9)
are efficient, i.e. only the 30% of the sample, while the
average efficiency for this year is 0.57. From the non-
efficient firms, E1 (0.05), has the lower efficiency whileat the same levels we find also E2, E3. Very close to be
characterized as efficient is firm E5 while moderate
efficiency is presented for E6.
For the year 2007, efficient are three firms (E4, E5,
E8), i.e. 30% of the sample while E7 (0.9) is very close
to efficiency (close to 1). The average efficiency for theyear is 0.57. From the inefficient firms, E10 (0.12), E1
(0.14) and E2 (0.14) show low efficiency.
In 2008 four firms manage to have efficiency equal to
1 (E4, E5, E8, E9) so 40% of the sample is efficient
while the average for 2008 is equal to 0.58. The lower
efficiency is for the firms E1 and E7, while relatively
high (close to 1) is the efficiency of E3 (0.87).In 2009 the efficient firms are again three (E4, E8,
E9), so 30% of the sample is efficient, while the
average for this year is 0.58. From the inefficient firms
E2 (0.15) has the lower efficiency followed by E1
(0.18), while E5 is approaching to become efficient
with 0.83.In 2010 efficiency firms are four (E4, E5, E8, E9),
which represents the 40% of the sample, while the
average efficiency is equal to 0.52. From the inefficient
firms, E6 (0.02) shows the lower efficiency, followed
by E2 (0.07) and E1 (0.08).
8.2 Conclusions for each firm for the five years period
The firms E4 and E8 are efficient for the entire
period of the five years. As far as the other five firms,
the best efficiency score is achieved by the firm E5,
with an average of 0.95 in five years, followed by the
firm E9 with an efficiency score of 0.93. The firm E3
has a relatively low efficiency score (0.59), while E6
and E7 are following with even lower efficiency scores
(0.37 and 0.33 respectively) and in the last position we
find the firm E10 with a score of 0.22, the firm E2 witha score of 0.12 and the firm E1 with a score of 0.1.
The firm E1 has very low efficiency scores in the
period of the five years, ranging from 0.05 up to 0.18,
presenting the lowest efficiency scores in all the years
compared to the other firms of the sample. The firm E2
is moving in the same context with the E1, with an
average of five years slightly higher than E2, (0.12
compared to the 0.1 of E1). The firm E3 presents high
variation in the rates of return for the period of the five
years, with values ranging from 0.07 in 2006 to 0.87 in
2008. The average rate of efficiency for the firm E3 is
0.59, which means that it cannot be characterized as
particularly efficient during this five years period.The firms E4 and E8 are efficient for the entire
period of the five years according to the DEA method.
-
8/9/2019 The evaluation of the efficiency of listed companies, using nonparametric methods: An empirical analysis of the Gr…
17/18
Apostolos G. Christopoulos et al The evaluation of the efficiency of listed companies, using nonparametric methods: An empirical analysis
of the Greek Information Technology sector
17 | International Journal of Computer Systems, ISSN-(2394-1065), Vol. 02, Issue, 01, January, 2015
The firm E5 is efficient for the three of the five
examined years, while for two years it is not efficient
although its scores are quite high (0.93 and 0.83). The
firm E6 has relatively low efficiency in the five years,
with an average of 0.37. Its higher efficiency score 0.6
is in 2009 and its lower efficiency score 0.2 is in theyear 2010, while the firm E7 is also equally inefficient
to E6. The average of the firm E6 for the examined
period is 0.33 with its higher score of efficiency to be in
the year 2007 (0.9) and lower efficiency score in 2008
(0.08). The firm E9 is almost in the same level with the
firm E5, being efficient for four of the five years of theinvestigated period, while for one year it is inefficient,
with a score of efficiency 0.64 and an average
efficiency score for the five years 0.93. Finally, the firm
E10 has a low efficiency scores, with an average of 0.22
for the five years period with its highest efficiency score
to be in the year 2009 (0.27) and its lowest in 2007(0.12).
X.
COMPARISON OF DEA RESULTS WITH FINANCIAL
ANALYSIS
Comparing the efficiency scores of DEA for the
firms with the results of the financial analysis of thesame firms several interesting conclusions are
generated.
Starting from the two firms E4 and E8 which are
characterized as efficient for the entire period of the five
years, we see that for E4 efficiency is established also
by the DEA method, since E4 has managed the highest profits for the five years and has on average the highest
asset efficiency. On the other hand, firm E8 notes the
highest average of turnover receivables ratio but at thesame time it is the firm with the lower liquidity
compared to the other firms for the period of the five
years. Therefore, we can see that at a high percentage,the results of DEA are in line with the results of the
financial analysis for both firms E4 and E8.
Continuing with the examination of the inefficient
firms, E9 shows quite low average turnover inventories
ratio which means that it manages to sell inventories on
hand in less days and also has quite good liquidity
performance. Also the firm E5 has the greatest turnover
inventories ratio with the highest average rate among
the firms of the examined sample. However, E5
presents a low current ratio for the period of five yearswhich allows us to conclude again that DEA method is
at a high percent in line with the results of the financial
analysis for the examined firms.
The firm E3 has an average efficiency ratio 0.59 for
the five years, which places it in a fair condition of the
efficiency scale. This is confirmed also by its financial
situation, since in the average ratios for the period of the
five years the efficiency score is close to the overall
averages of the sector. In particular, the profitability of
its assets is 6.11 slightly higher than the sector’s
average (for five years is 4.53, Tables 13 and 14) the
receivables turnover ratio is 2.12, slightly lower than
the average of the sector, which is 2.3 while the currentasset ratio for E3 is averaged again near the average of
the sector, i.e. 1.76 compared to 1.97. Finally, the
average inventories turnover ratio is lower than the
sector’s average which is 53 days compared with 62
days respectively. In this case we can conclude that
financial analysis for E3 is in line with the result of the
DEA.
As far as the firms E6 and E7 are concerned, they are
the firms with the lower efficiency, followed by E10which is close to them. More specifically efficiency for
E6 is on average equal to 0.37 while according to the
financial analysis the receivables turnover ratio is half
(1.23) compared to the sector’s average (2.3), and the
days taken to sell inventories on hand is on average 74
days for the five years period, much longer than theaverage of the sector (62 days). Also with the DEA
method firm E7 is ranked as inefficient, with an
efficiency ratio of 0.33. From the financial analysis we
can see that the return on asset efficiency is 1.69 on
average for the five years, compared to the sector’s
average 4.5, while its receivables turnover ratio is alsolow (0.39). Nevertheless, the current ratio average is
just above the sector’s average (2.49), but its number of
days to sell inventories on hand is very high (190 days).The firm E10 is also low in terms of efficiency (0.22).
In more detail, the return on assets, the receivables
turnover ratio and the current ratio are lower than the
sector’s averages, while the average number of days to
sell inventories on hand is also lower. Therefore, the
results of DEA are in line with the results of the
financial analysis for the two of the three examined
firms.
Finally, the firms with the lowest efficiency are E1
and E2. The firm E1 has the lowest efficiency score of
0.1, while E2 is inefficient with efficiency score equal
to 0.12. The firm E1 according to the financial analysis
has the lowest profits in the period of five years, thelowest return on assets ratio, and relatively low
receivables turnover ratio. On the other hand, E2 shows
very low ratio for the five years both in terms of asset
efficiency and for the average number of days taken to
sell inventories on hand and also lower current ratio
compared to the other firms. Therefore, also in this case
of the DEA method the results are in line with the
results of the financial analysis.
In conclusion, we can say that for nine of the ten
firms the results of DEA are in line with the conclusions
resulting from the financial analysis for the sample of
firms. Therefore, we can say with certainty that the
evaluation of the ten firms of the informationtechnology sector is satisfactory and to draw reliable
conclusions about their efficiency.
REFERENCES
[1] Timothy J. Coelli, D.S. Prasada Rao, Christopher J. O’Donnell,George E. Battese, (2005). “An Introduction to Efficiency and
Productivity Analysis”. Springer.
[2] Reza Tehrani et al. (2012). “A Model for Evaluating Financial
Performance of Companies by Data Envelopment Analysis: A Case
Study of 36 Corporations Affiliated with a Private OrganizationInternational”. Business Research Vol. 5, No. 8; 2012
[3] Joseph C. Paradi et al. (2004). “Using DEA and Worst PracticeDEA in Credit Risk Evaluation”. Journal of Productivity Analysis
Vol. 21 Issue 2, p153.
-
8/9/2019 The evaluation of the efficiency of listed companies, using nonparametric methods: An empirical analysis of the Gr…
18/18
Apostolos G. Christopoulos et al The evaluation of the efficiency of listed companies, using nonparametric methods: An empirical analysis
of the Greek Information Technology sector
[4] Giokas, D., (1990). “Bank branch operating efficiency: A
comparative application of DEA and the loglinear model”. Omega
Volume 19, Issue 6, 1991, Pages 549–557
[5]Joe Zhu (2000). “Multi-factor performance measure model with
an application to Fortune 500 companies”. European Journal ofOperational Research Volume 123, Issue 1, 16 May 2000, Pages
105–124.
[6] Jose Humberto Ablanedo –Rosas, Hongman Gao, Xiaochuan
Zheng, Bahram Alidaee and Haibo Wang (2010). “A study of the
relative efficiency of Chinese ports: a financial ratio- based data
envelopment analysis approach”. Expert Systems Volume 27, Issue
5, pages 349–362.
[7] Necmi K.Avkiran (2011). “Association of DEA super-efficiency
estimates with financial ratios: Investigating the case for Chinese
banks”. Omega Volume 39, Issue 3, June 2011, Pages 323–334
[8]Quey-Jen Yeh, (1996). “The Application of Data Envelopment
Analysis in Conjunction with Financial Ratios for Bank PerformanceEvaluation”. The Journal of the Operational Research Society, Vol.
47, No. 8., pp. 980-988.
[9] Toshiyuki Sueyoshi, Mika Goto (2009). “Methodological
comparison between DEA (data envelopment analysis) and DEA–
DA (discriminant analysis) from the perspective of bankruptcyassessment”. European Journal of Operational Research Volume 199,
Issue 2, 1 December 2009, Pages 561–575.
[10] Emel A.B., M. Oral, A.Reisman and R.Yolalan (2003). “A
Credit Scoring Approach For the
Commercial Banking Sector”. Socio-Economic Planning Sciences,37 (2003), 103-123.
[11] Simak, P.C., (1997). “DEA Based Analysis of CoporateFailure”. Graduate Department of Mechanical and Industrial
Engineering University of Toronto, National Library of Canada.
[12] Vassiloglou, M., & Giokas, D. (1990). “A study of the relative
efficiency of bank branches: an application of data envelopment
analysis”. Operation Research Society, 41, 591-597.
[13] Charnes, A., Cooper, W. W., & Rhodes, E. (1978). Measuring
the efficiency of DMUs. European Journal of Operational Research,2, 429-444.
[14] Kambiz Shahroodi, Fatemeh Feraghnia (2013). “Benchmarking
of Pharmaceutical companies
accepted in Tehran Stock Exchange using DEA”. Science Road
Publishing Corporation Trends in Social Science.
[15] Ky Naraini Che Ku Yusof (2010). “An Evaluation of CompanyOperation Performance Using Data Envelopment Analysis (DEA)
Approach: a study on Malaysian Public Listed companies”.
International Business Management Volume: 4 Issue: 2 Page No.:47-52.
[16] Maryam Zohdi, (2012). “Data envelopment analysis (DEA) based performance evaluation system for investment companies:
Case study of Tehran Stock Exchange”. African Journal of Business
Management Vol. 6(16), pp. 5573-5577, 25 April, 2012.
[17] Nordin Hj Mohamad and Fatimah Said (2012). Using super-
efficient DEA model to evaluate the business performance in
Malaysia. World Applied Sciences Journal, Vol. 17(9), p1167-1177.
[18] Premachandra, I.M. and Yao Chen, J. (2011). “DEA as a toolfor predicting corporate failure and success: A case of bankruptcy
assessment”. Omega, 32, pp. 620–626.