The evaluation of the efficiency of listed companies, using nonparametric methods: An empirical analysis of the Greek Information Technology sector

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International Journal of Computer System (ISSN: 2394-1065), Volume 02– Issue 01, January, 2015

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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:


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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


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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


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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


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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


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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.


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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


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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


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


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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


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


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


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


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Mode


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


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


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


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


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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


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


12/18




Where,

X1= return on asset



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


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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


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



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


15/18




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


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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.


17/18




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.

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Documents

The evaluation of the efficiency of listed companies, using nonparametric methods: An empirical analysis of the Greek Information Technology sector