An Improved PROMETHEE Method Applied in Enterprise's Financial Performance Measurement ZHANG Wei, Zhou Xia School of Business Administration, South China University of Technology, P.R.China, 510640 Abstract: This paper applies an improved PROMETHEE method named multiplication PROMETHEE in enterprise's financial performance measurement for the first time, which is an optimization model built on the basis of PROMETHEE II. The method can solve PROMETHEE II s problem that lacks response sensitivity when the weight of performance index changes and it is also operated easily. Meanwhile, we consider the subective and obective factors that influence the weight of performance index by using synthetic weighted method, and it is beneficial to the accuracy of financial performance measurement. Finally, we illustrate that the new method is practical and scientific by an empirical research on six listed companies financial performance measurement. Keywords: Financial performance, Multiplication PROMETHEE, Synthetic weighted method, PROMETHEE II 1 Introduction Capital operation is in need of enterprise s daily work, and the level of financial performance influences the destiny of the whole enterprise directly. Therefore, the importance of rational measurement on financial performance is self-evident. Domestic and international academicians paid close attention to this field and applied different methods. Brans & Vincke (1985) applied PROMETHEE II to measure financial performance, which brought the distortion phenomena of nonconvex problem into the research. Therefore, the validity of performance measurement needs to be still discussed [1]. Stan Davis & Tom Albright (2004) argued that BSC method is more effective than other methods in enterprise s financial performance measurement field [2]. Wang Yu-Jie (2001) utilized grey relation analysis to cluster financial ratios in order to find representative performance indexes, and then applied fuzzy multi-criteria decision-making (FMCDM) method to measure three airlines financial performance in Taiwan [3]. Nikos Kalogeras, George Baourakis, Costantin Zopounidis & Gert van Dik (2005) measured the financial performance of an agricultural food company based on multi-criteria decision-making method (PROMETHEE II) [4]. Some other scholars also established the measure systems of financial performance according to organization economics theory (Ferrier & Porter, 1991; Porter & Scully, 1987). Liu Jun-qi, Sun Lu, etc. (2001) measured enterprise s financial performance with TOPSIS method synthetically [5]. Li Qing-dong (2005) applied clustering analysis method to consider fifteen indexes in the index measurement system of enterprise s financial performance synthetically, and then took twenty construction enterprises listed on Shanghai Stock Exchange as an example to analyze these enterprises financial performance according to their financial data in 2004 from annual reports [6]. Lu Zheng-fei (1997) adopted twelve financial ratios to do a comparative research on financial performance of listed enterprises in China and in Britain, and stated that the accountant and environment factors make the great difference in financial ratios of these listed enterprises in two countries [7]. However, the evaluation results got by the methods above were not ideal enough because there were some problems such as lacking flexibility, too subective, lacking basis while weighting the financial index, etc. The purpose of this paper is to apply multiplication PROMETHEE method combined with data analysis technology to measure enterprise s financial performance. Multiplication PROMETHEE is more available than original PROMETHEE II in performance measurement, which is capable of solving convex and nonconvex problems easily with finding continuous and discontinuous Pareto fronts quickly, although this new method requires more processing time than original PROMETHEE II. 1139
2 Establish a index system of financial performance measurement 2.1 Choose the indexes of financial performance measurement Financial management is fundamental to enterprise s success, and a complex accounting system is in need of enterprise s financial management information. Considering this fact, financial ratios can aid in converting the mass of data, which is common in an effective and well-structured accounting system, into meaningful information. Nowadays, ratio analysis is an efficient tool commonly used to measure financial performance. It provides valuable comparisons in financial analysis. Therefore, on one hand, we cluster a large number of financial performance indexes based on financial ratio analysis (Courtis, 1978) [7], and on the other hand, we took Enterprise s Performance Measurement System promulgated by the Ministry of Finance as a reference, in order to divide financial performance into four kinds of indexes: debt-paying ability index, earning capacity index, growth capacity index and operating capacity index, the concrete indexes are as shown in Table.1. Debt-paying capacity X 1 Earning capacity X 2 Table1 The Index System of Enterprise s Financial Performance Measurement Asset-liability ratio X 11 Maor business revenue growth rate X 31 Growth capacity Current ratio X 12 Net profit growth rate X 32 Quick ratio X 13 X 3 Total assets expansion rate X 33 Return on net assets X 21 Total assets turnover X 41 Return on total assets X 22 Operating Net assets turnover X 42 capacity Maor business gross profit X 23 Inventory turnover X 43 Maor business profit Rate X 24 X 4 Receivables turnover X 44 From Table 1, we realize that ratio analysis may simplify the complexity of enterprise's financial performance, and these four kinds of financial performance indexes are key indexes often used by enterprise, which are apt to get from enterprise s financial statement. Except that asset-liability ratio, current ratio and quick ratio included in debt-paying capacity index have to reach one suitable value, the bigger other index value is, the better financial performance is. Generally, it is appropriate that asset-liability ratio s level is 40%-60%, current ratio is 2 and quick ratio is 1 [8]. 2.2 Financial performance indexes non-dimension and positive orientation According to the description of each financial ratio s characteristic 或 (2) in chapter 2.1, this paper divides these fourteen indexes into two groups for positive orientation. (1)Benefit index We adopt half ladder-shaped function to settle this sort of indexes as shown in formula(1). 0, b x< a ( x a) a x< b R( x), ( b a) 1, b x (2)Neutral index In this group, we adopt triangular distribution function to settle this kind of indexes as shown in formula(2). ( x b)( a b), b x< a R( x) ( c x)( c a), a x< c 0, c x x< b The value of parameter a, b, c in formula (1) and (2) are assigned respectively according to every index s characteristic. The formula for non-dimension of indexes can be expressed as: (1) 1140
p i ( xi x ) s Therein, x,s are the mean and standard deviation of index respectively. Because of the need of calculating logarithm, we translate p i for avoiding negative number and zero. According to 3δ principle, we order p i p i + 4 to get a decision matrix of performance indexes after translation, therein, pi is the weight of index under proect i. 2.3 Establish a weight calculation method How to calculate the weight of index is significant to the whole measurement result, therefore, we should select the calculation method cautiously. Entropy method can fully reveal the information from initial data and get the obective result, so we use this method to calculate the weight of index system in this paper. The concrete calculation process can be shown as follows. Based on entropy theory, the entropy of index can be defined as: (3) (4) (5) (6) Therein, Pi, a i n a 1 i n H k P ln P 1 i i 1, 2,..., m 1 K ln n Therefore, the entropy weight w of index can be expressed as: 1 H w m i 1 ( 1 H ) We assume that, when p i,ln 0 p i p i 0, and w is the obective weight of H. Meanwhile, we consider that entropy method cannot reflect expert's knowledge or experience and decision maker s opinion, sometimes even get the contrary result that does not consistent with the real situation. Due to the strong relevance among those four kinds of financial performance indexes above, we decide to apply ANP method to remedy the deficiency of entropy weight method in order to describe the connection of obective things accurately and combine data, expert s opinion with analyst s udgment effectively. It is a more effective and more practical decision-making method developed by AHP method. Therefore, the weight of index, which calculated by ANP, is w, and the synthetic weight w of index can be expressed as: ( 1 ) w β w + β w 0 β 1 The synthetic weight w of index is alterable with parameterβ. Literatures [10] and [11] have made a sensitivity analysis of β by measuring the proportion change of the subective and obective weight of each index. Considering the literatures conclusion and the actual condition of financial performance measurement system in this paper, we believe that 0.5 β is suitable. 1141
3 Apply multiplication PROMETHEE method in financial performance measurement (1)The basic information needed in measurement problem We assume that all indexes of measurement problem are benefit indexes and the index set can be i I : I 1, 2,..., m. The synthetic weight of index set is defined by calculating as expressed as I, ({ }) { 1, 2,..., } ( 0) w w w w m w >. (2)The calculation of preference function In order to simplify the calculation of preference function, Brans & Vincke proposed six kinds of general criterions (Usual, U-shape, V-shape, level, linear and Gaussian) [3]. We choose Gaussian criterion (people may define other general criterions according to their needs). It is a general form of other five criterion forms, and only requires the use of parameter σ. Brans, Vincke & Mareschal (1986) proposed that this criterion has important contributes to the stability and the robustness of the obtained results in practice. Gaussian criterion can be expressed as follows: 2 d 1 exp, ( ) p d 2 2s d > 0 0, d 0 (7) In this criterion, s is the distance between the origin and the inflexion point of the curve p ( d ) P (d ) a 1 s (1) d Fig. 1. Gaussian preference function p a, b is associated to each arc, as p ( a,b) b p ( b,a) Fig.2. Arcs symbolizing the preference relations Therefore, considering the graph, the net flow under criterion is defined as follows: ψ ( a ) p ( a, b ) p ( b, a ) b A Definition 1: The net flow ψ ( a) satisfies the following three criterions: m w ( a ) ( a ) 1 ψ ψ (in Fig. 1). PROMETHEE II and multiplication PROMETHEE are very similar. Both of them start with the specification of preference function for each criterion. However, their differences are the way they calculate the net flow and define the outranking relation. In multiplication PROMETHEE, there is no need to calculate all the preference indexes while calculating the net flow. Indeed, there are two arcs between each pair of nodes (a, b), and preference function value ( ) shown in Fig. 2. (8) 1142
(2) (3) ( ( n ψ a) 0 1 ψ + a) p ( a, b) ψ b A The proving process is omitted., ( a) p ( b, a) b A Based on Gaussian criterion and the synthetic weight w of index, a new outranking index O( a) aggregates the net flow values of each alternative and gives a global idea of how much each alternative is preferred to the others, taking into account the importance weight of each criterion: m w O( a) Φ ( a) 1 In this formula, Φ ( a) is defined as ψ ( a ) ψ min assumed by ψ ( a). As ( a ) min +, therein, ψ min is the minimum value ψ may assume negative values and 0 < w i < 1, the addition of ψ is essential to avoid complex values in the outranking index ( ) O a. It is worth noting that O( a ) assumes only nonnegative values and it is null if O( a ) 0 for at least one criterion. Finally, the alternatives can be ranked by formula(9): If O(a) O(b), then a is indifferent to b; If O(a) > O(b), then a outranks b. 4 Numerical Example We take six enterprises listed on Shanghai and Shenzhen Stock markets as a numerical example to prove altogether how the measurement method we created above used. Their stock codes are 600462, 600984, 600499 and 000605, 000669, 000545 respectively, and their financial data are chosen at one time point in the 2005 financial statements. We analyze and calculate these sample data and get the concrete financial performance indexes we need as shown in Table 2. (9) Table 2 The financial performance indexes of six sample enterprises X11 X12 X13 X21 X22 X23 X24 X31 X32 X33 X41 X42 X43 X44 600462 0.73 0.71 0.55-0.28-0.12 0.067-0.24-0.24-10.29-0.032 0.32 0.45 4.38 4.96 600984 1.44 1.32 0.65-0.12-0.07 0.13-0.12-0.29-3.72 0.018 0.45 0.58 1.28 2.31 600499 0.45 1.36 0.79 0.088 0.069 0.24 0.072 0.034-0.21 0.025 0.72 0.12 2.10 5.75 000605 0.67 0.65 0.61-0.22-0.10 0.54-0.41-0.37-3.75-0.026 0.16 0.22 3.07 1.84 000669 0.61 1.12 0.95 8.41 7.32 0.41 0.13 0.12 2.86 0.073 0.23 0.31 1.49 1.81 000545 0.89 0.58 0.34-0.06-0.02 0.53-0.34-0.10 0.28 0.062 0.24 0.30 1.23 1.27 From formula (4), (5) and (6), we calculate the weight of these financial indexes and get the results as shown in Table 3. Table 3 The weight of financial performance indexes X11 X12 X13 X21 X22 X23 X24 X31 X32 X33 X41 X42 X43 X44 Weight 0.05 0.072 0.070 0.131 0.120 0.082 0.084 0.10 0.134 0.042 0.025 0.023 0.04 0.027 Then, from formula (7) and (8), we get the outranking index value as shown in Table 4. 1143
Table 4 The outranking index value pi ( a, b) 600462 600984 600499 000605 000669 000545 Ψ + 600462-0.20 0.045 0.159 0.203 0.082 0.689 600984 0.32-0.009 0.003 0.17 0.369 0.871 600499 0.587 0.253-0.575 0.026 2.31 3.751 000605 0.155 0.324 0.33-0.158 0.644 1.611 000669 0.22 0.119 0.048 2.716-0.151 3.254 000545 0.408 0.218 0.505 1.039 1.671-3.841 Ψ - 1.69 1.114 0.937 4.492 2.228 3.556 - From the results of Φ ( a) above and definition 1, we can get the rank of financial performance among these six sample enterprises by outranking indexes O( a ), that is: 000669> 600499> 000545> 600984> 600462> 000605. This rank is identical with the rank calculated by PROMETHEEII. Also, the result calculated by TOPSIS method is: 000669>600499 >000545>600984>000605>600462, basically identical with the results above. Therefore, the good result indicates that multiplication PROMETHEE method is an effective multi-criteria decision-making method of financial performance measurement. 5 Conclusion Based on rich literature researches, this paper creates a new multiplication PROMETHEE method which is developed from PROMETHEEII method and modifies the deficiency of PROMETHEEII in financial performance measurement process. Meanwhile, the synthetic weighted method based on ANP method ensures the accuracy of measurement. Also, the empirical research proves that this method enables the measurement process easily-operated and the result more effective and creditable. As to investors and managers, multiplication PROMETHEE will have great reference and be benefit to their decision Reference [1] Brans, J. P.& Vincke,ph. A preference ranking organization method: the PROMETHEE method for multiple criteria decision making. Management Science, 1985, Vol.31. 647~651. [2] Wang Yuie. Applying FMCDM to measure financial performance of domestic airlines in Taiwan. Expert Systems with Applications.2007. 1~5. (in Chinese) [3] Nikos Kalogeras, George Baourakis, Costantin Zopounidis & Gert van Dik. Evaluating the financial performance of agri-foodfirms: a multicriteria decision-aid approach. Journal of Food Engineering. 2005. 365~ 367. [4]Liu Junqi, Sun Lu, Liu Bing. Application and Practical Research of TOPSIS in Evaluation of Enterprises Financial Performance. Journal of Sichuan University (Social Science Edition). 2001 No.3.42~43.(in Chinese) [5]Li Qingdong. Financial Performance Evaluation and Cluster Analysis of Listed Company. Industrial Technology & Economy. 2005.8. Vol.24, No.8. 146~147.(in Chinese) [6]Lu Zhengfei. Comparative research of Listed Company s Financial Performance between China and England. Accounting Research. 1997.10 37~38.(in Chinese) [7] Courtis, J. K. Modeling a financial ratio categoric framework. Journal of Business Finance and Accounting. 1978.Vol.5 371~379. [8]Stephen A. Ross, Randolph W. Westerfield & Bradford D. Jordan. Fundamentals of Corporate Finance(6th Edition).35~43. [9]Wang Juying, Wang Bo, Zhao Quanchao. Application of Balanced Scorecard and Analytic Network Process to Enterprise Performance Evaluation.Industrial Engineering Journal. 2006,7.Vol.9, No.4. 60~63.(in Chinese) [10]Tao Juchun, Wu Jianmin. New Study on Determining the Weight of Index in Synthetic Weighted Mark Method. 1144
Systems Engineering -Theory & Practice. 2001.8. 43~48.(in Chinese) [11]Fan Zhiping, Zhao Xuan. An Obective and Subective Synthetic Approach to Determine Weights for Multiple Attribute Decision Making. Journal of Decision Making And Decision Support Systems. 1997, Vol.7 No.4. 87~ 91.(in Chinese) The author can be contacted from e-mail : zw_hawk@163.com 1145