A Multi-Criteria Approach

Contemporary Engineering Sciences, Vol. 11, 2018, no. 85, 4203 - 4210 HIKARI Ltd, www.m-hikari.com https://doi.org/10.12988/ces.2018.88456

Ranking of Companies in Colombia Based on Their

Financial Statements: A Multi-Criteria Approach

Mendoza Mendoza Adel Alfonso

3i+d Research Group Universidad del Atlántico, Colombia

Herrera Acosta Roberto José

Gestión de la Calidad Research Group Universidad del Atlántico, Colombia

Cabarcas Reyes Juan Carlos

3i+d Research Group Universidad del Atlántico, Colombia

Copyright © 2018 Mendoza Mendoza Adel Alfonso et al. This article is distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Company’s rankings are usually based on a single criterion, so that results vary according to the criterion used. The objective of this paper is to make a ranking of companies in Colombia in the period from 2012 to 2016 using an approach multicriteria based on their financial statements in a dataset a sample of 40 companies. This classification was carried out by combining two techniques: the fuzzy analytical hierarchy process (fuzzy AHP) and the technique of preference for similarity to the ideal solution (TOPSIS). With the fuzzy AHP the weightings of the selected criteria are obtained, and then with the TOPSIS technique the ratings of the different companies are made.

Keywords: Multicriteria ranking, fuzzy AHP, TOPSIS

1. Introduction

Currently, companies are recognized for its financial results and the position they 4204 Mendoza Mendoza Adel Alfonso et al.

occupy on the market. These financial results of a company are analyzed taking into account different criteria during a specific period of time, from this information a ranking of the companies can be constructed. .Companies ranking is a complex process in which multiple financial criteria are required to be considered simultaneously [1].

The analytical hierarchy process (AHP) introduced by Saaty [2] has been used effective tool for multi-criteria decision-making. This method uses an individual's judgments and preferences to make quantitative comparisons between pairs of elements by constructing matrices from these comparisons and determining the level of importance of each element as a weight or weighting. In this context, comparisons in the AHP are made using a scale of opinions based on human reasoning that represents the measure of preference of one element over another with respect to a given characteristic or attribute. The use of imprecise opinions to express the importance of the criteria offers the possibility of using fuzzy sets or fuzzy numbers, so many authors explored fuzzy AHP. [3]

The analytical hierarchy process (AHP) is one of the multi-criteria analysis tools widely used to model unstructured problems in different areas, such as political, economic, social and management sciences. Many studies have applied AHP and fuzzy AHP for different situations and problems, in the selection of passenger aircraft type [4], to assess the sustainability of a manufacturing plant [5], in the selection of suppliers [6], [7] compare the AHP and fuzzy AHP methods in defining the extent of land use areas in a large-scale urban planning scenario. In classification applications, we can mention some works [8], [9], [10].

The technique for the order of preference of similarity to the ideal solution (TOPSIS), introduced by Hwang and Yoon [11], is a multi-criteria, multi-attribute technique used in decision making processes for the selection of an alternative. The TOPSIS method orders the alternatives taking into account simultaneously the Euclidean distance to the positive ideal solution and the negative ideal solution. This method is based on the fact that it is desirable for a given alternative to be located at the shortest distance from a positive ideal solution (maximizing benefits and minimizing costs) and at the greatest distance from a negative ideal solution (maximizing costs and minimizing benefits). [12]. Like AHP the TOPSIS technique has been used for different applications: evaluated the modes of operation of global positioning systems [13], in the classification of projects in a participatory budget [14], for the selection of wireless mobile communications network interface [15].

2. Methodology

The methodology used in this paper for the ranking of companies is a combination of fuzzy AHP to define the weighting of the hierarchy of criteria and the TOPSIS method to determine the best order of companies. The following are the steps to follow: Ranking of companies in Colombia based on their financial statements 4205

 Selection of companies  Diffuse comparison matrix construction  Logical consistency analysis and determination of matrix weights  Elaboration of the ranking by means of TOPSIS

For the selection of the companies to be considered in the study, it was determined which are the 100 largest companies in Colombia according to the information published in specialized economic and financial magazines in the period 2012- 2016. As selection criteria for the sample, those that present complete information on their financial statements during this period were taken, resulting in 40 companies that are: AES Chivor & Cía, Alpina, Avianca Holdings, Bavaria, Biomax, Celsia, Cementos Argos, Cemex Colombia, Codensa, Colombina, ConConcreto; EAAB, Ecopetrol, Electricaribe, EmCali, Emgesa, EPSA, ETB, Gas Natural Fenosa, Grupo Argos, Grupo EPM, Grupo energía de Bogotá, Grupo Éxito, Grupo Familia, Grupo Nutresa, Grupo Orbis, ISA, Isagen, Odinsa, Organización Terpel, Pacific E&P (Frontera Energy), Postobón, Promigás, Riopaila Castilla, Salud Total, Sodimac Corona, Telefónica Movistar, TGI, Une EPM Telco and Valorem. The companies are randomly ordered from F-1 to F-40 to ensure the confidentiality of the evaluation results. The following criteria were used as criteria for the ranking: Operating Income, Net Profit and Current Assets. Below a short description of every criteria used:

C1 – Operating Income: this is the income derived from the company's main economic activity. C2 – Net Profit: It is the actual profit, and includes the operating expenses that are excluded from gross profit. C3 - Current assets represents the value of all assets that can reasonably expect to be converted into cash within one year

Table 1. Values for each variable of the companies.

2012-2016 2012-2016 Company Operating Current Company Operating Current Net Profit Net Profit Income Assets Income Assets F1 $ 23.477.720 $ 397.920 $ 13.903.355 F21 $ 2.479.219 $ 986.302 $ 2.392.987 F2 $ 61.605.866 $ 6.775.517 $ 24.121.137 F22 $ 2.633.202 $ 36.092 $ 272.803 F3 $ 10.068.269 $ 558.952 $ 4.474.728 F23 $ 2.331.083 $ 353.942 $ 834.109 F4 $ 13.613.261 $ 144.579 $ 1.404.447 F24 $ 1.922.749 $ 267.859 $ 625.431 F5 $ 12.950.886 $ 1.574.910 $ 5.871.079 F25 $ 1.922.970 $ 147.533 $ 783.376 F6 $ 10.058.247 $ 108.594 $ 2.518.714 F26 $ 1.860.244 $ 238.183 $ 542.128 F7 $ 5.846.787 $ 895.045 $ 4.858.574 F27 $ 1.485.643 $ 14.936 $ 454.479 F8 $ 6.857.611 $ 386.765 $ 2.168.986 F28 $ 1.599.307 $ 213.620 $ 856.108 F9 $ 6.316.215 $ 396.396 $ 2.235.711 F29 $ 1.551.810 $ 48.127 $ 347.273 F10 $ 5.577.505 $ 1.579.201 $ 4.102.245 F30 $ 1.508.723 $ 58.560 $ 458.332 4206 Mendoza Mendoza Adel Alfonso et al.

Table 1. (Continued): Values for each variable of the companies.

F11 $ 3.320.264 $ (137.309) $ 1.120.070 F31 $ 1.618.957 $ 188.351 $ 1.925.330 F12 $ 4.478.480 $ (162.415) $ 1.214.807 F32 $ 1.987.724 $ 47.576 $ 1.116.774 F13 $ 3.579.463 $ (22.495) $ 1.498.331 F33 $ 1.426.251 $ 281.556 $ 469.192 F14 $ 7.517.922 $ (1.691.886) $ 3.124.575 F34 $ 1.115.199 $ 104.828 $ 350.711 F15 $ 3.538.892 $ 521.078 $ 1.019.065 F35 $ 1.466.159 $ 14.424 $ 1.331.490 F16 $ 2.741.384 $ 475.197 $ 1.991.106 F36 $ 905.751 $ 207.720 $ 771.582 F17 $ 2.123.016 $ 37.981 $ 671.696 F37 $ 1.009.124 $ 73.024 $ 1.004.027 F18 $ 2.896.036 $ 178.871 $ 1.216.123 F38 $ 1.045.498 $ 257.173 $ 341.860 F19 $ 2.792.802 $ 861.651 $ 1.096.435 F39 $ 1.013.735 $ 150.971 $ 830.154 F20 $ 2.889.894 $ 129.843 $ 714.058 F40 $ 800.258 $ 21.938 $ 269.668

2.1 Construction of the fuzzy matrix of comparison For the construction of the matrix four experts were consulted and each one gave a hierarchy in order to achieve a consensus among them. The result was an application of fuzzy logic to find the order of preferences of the experts [16]. Finally, these data were collected and the fuzzy matrix of comparison between the criteria shown in Table 3 was created taking into account the values of the fuzzy scale used in Table 2 [17].

Table 2. Fuzzy scale

Linguistic scale Numeric scale Triangular fuzzy scale Just equal 1 (1,1,2) Weakly more important 3 (2,3,4) Strongly more important 5 (4,5,6) Very strongly more important 7 (6,7,8) Absolutely more important 9 (8,9,9) Intermediate values 2, 4, 6, 8 (1,2,3) (3,4,5) (5,6,7) (7,8,9)

Table 3. Fuzzy matrix of comparison criteria

C1 C2 C3 C1 1 1 1 1/2 2/3 1 1 3/2 2 C2 1 3/2 2 1 1 1 3/2 2 5/2 C3 1/2 2/3 1 2/5 1/2 2/3 1 1 1

2.2 Logical consistency analysis and calculation of matrix weights Consistency refers to the congruence of the judgements established by the experts, through the process of peer comparison. In the case of diffuse AHP, it is necessary to convert the diffuse matrices into matrices with real numbers using a defuzzification method and then calculate the ratio of consistency (RC) with the traditional AHP method, if CR ≤ 0.1, the level of inconsistency can be accepted. Table 4 shows the value of CR for this case. Ranking of companies in Colombia based on their financial statements 4207

Table 4. Consistency parameters

λ máx. IC IR RC

3,036 0,018 0,99 0,018

To determine the weights of the fuzzy comparison matrix, follow the steps for the application of this method [18]. It begins with the calculation of the synthetic fuzzy degree, comparison of fuzzy numbers to determine the degree that a fuzzy number can be better than others, thus obtaining the weight vectors, finally, normalization is performed to obtain the normalized weight vector of this matrix.

Table 5. Weighting of the criteria

C1 (Income) C2 (Profit) C3 (Assets) 0,345 0,558 0,097

3. Results

Once the weights have been obtained, the TOPSIS methodology is used to establish the ranking of the companies. For each company and its respective assessment, the expert group considered different factors that meet all the criteria.

Table 6. Qualification of the companies in each criterion

C1 C2 C3 C1 C2 C3 C1 C2 C3 C1 C2 C3 F1 38 14 57 F11 5 1 4 F21 4 36 9 F31 2 6 7 F2 100 100 100 F12 7 1 5 F22 4 2 1 F32 3 2 4 F3 16 20 18 F13 5 1 6 F23 3 13 3 F33 2 10 1 F4 22 5 5 F14 12 1 12 F24 3 9 2 F34 1 3 1 F5 21 58 24 F15 5 19 4 F25 3 5 3 F35 2 2 5 F6 16 4 10 F16 4 17 8 F26 3 8 2 F36 1 7 3 F7 9 33 20 F17 3 2 2 F27 2 2 1 F37 1 3 4 F8 11 14 8 F18 4 6 5 F28 2 7 3 F38 1 9 1 F9 10 14 9 F19 4 31 4 F29 2 2 1 F39 1 5 3 F10 9 58 17 F20 4 4 2 F30 2 3 1 F40 1 2 1

According to [19].the second step in the technique is the normalization of the matrix of qualifications and then determine the positive and negative ideal solutions (D+, D-), determine the Euclidean distance of each company to the ideal solutions and from these values the relative proximity Ri, finally, will be ordered in decreasing order the companies. In this way, the ranking is obtained that prioritizes the companies according to the importance established for the criteria considered. This ranking is the final result of the proposed methodology.

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Table 7. Final ranking of companies

D+ D- Ri Ranking D+ D- Ri Ranking D+ D- Ri Ranking D+ D- Ri Ranking F1 0,37 0,13 0,26 5 F11 0,47 0,01 0,02 30 F21 0,38 0,13 0,26 4 F31 0,46 0,02 0,04 24 F2 0,00 0,48 1,00 1 F12 0,46 0,02 0,04 25 F22 0,47 0,01 0,02 31 F32 0,47 0,01 0,02 35 F3 0,39 0,08 0,18 8 F13 0,47 0,01 0,03 29 F23 0,44 0,05 0,09 15 F33 0,45 0,03 0,07 16 F4 0,43 0,06 0,13 10 F14 0,46 0,03 0,07 17 F24 0,45 0,03 0,06 18 F34 0,47 0,01 0,02 34 F5 0,29 0,22 0,44 2 F15 0,42 0,07 0,14 9 F25 0,46 0,02 0,03 26 F35 0,47 0,01 0,01 37 F6 0,44 0,05 0,09 14 F16 0,42 0,06 0,12 11 F26 0,45 0,03 0,06 20 F36 0,46 0,02 0,05 22 F7 0,37 0,12 0,25 6 F17 0,47 0,01 0,01 36 F27 0,47 0,00 0,01 38 F37 0,47 0,01 0,02 33 F8 0,42 0,06 0,12 12 F18 0,46 0,02 0,04 23 F28 0,46 0,02 0,05 21 F38 0,45 0,03 0,06 19 F9 0,42 0,06 0,12 13 F19 0,39 0,11 0,22 7 F29 0,47 0,00 0,01 39 F39 0,46 0,01 0,03 27 F10 0,32 0,21 0,40 3 F20 0,46 0,01 0,03 28 F30 0,47 0,01 0,02 32 F40 0,47 0,00 0,01 40

Conclusions

The ranking of companies is an analysis that must be approached from a multi- criteria point of view, since in this way many financial items can be taken into account for its preparation. The use of fuzzy AHP in conjunction with TOPSIS is proposed as an appropriate strategy for this situation, since it allows the opinions of different experts to be combined in a consistent and coherent manner, achieving a robust result that satisfies all the criteria. A real-world application study of the largest Colombian companies was presented.

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Received: September 3, 2018; Published: September 26, 2018