Journal of Chemical and Pharmaceutical Research, 2014, 6(7): Research Article

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1 Available online Jornal of Chemical and Pharmacetical Research, 04, 6(7): Research Article ISSN : CODEN(USA) : JCPRC5 A research on IPO pricing model in China's growth enterprise maret-based on analytic hierarchy process and BP Neral networ Wenxi Tang and Xiaoha Zho School of Economics and Bsiness Administration, Chongqing University, Chongqing, China ABSTRACT With the first batch of 8 companies listed on the China's Growth Enterprise Maret (GEM) on October 30, 009, high isse prices, high P/E and high over-raising capital, nown as "Tri-highs" phenomena, have received intensive attention and sspicions from the very beginning of the GEM's establishment in China. The IPO pricing efficiency become the sbect of concern again. In view of the existing problems of IPO pricing in China's GEM sch as deviating from intrinsic vale, high initial retrns and from the point to improve pricing efficiency and effectiveness, this paper combines Analytic Hierarchy Process(AHP) with BP Neral Networ to establish a new IPO pricing model. Firstly, we applies AHP to constrct a comprehensive pricing assessment index system and screens the assessment indexes according to their weights. Then, we carries ot example simlations with BP Neral Networ model. The reslts indicate that the combination model of Analytic Hierarchy Process with BP Neral Networ model is effective in fixing the prices of new isses in China's GEM. Key words: IPO pricing, growth enterprise maret, analytic hierarchy process, BP neral networ INTRODUCTION The IPO pricing is a challenging problem becase ncertainties are always involved in both prodct and stoc marets. Artificial neral networ, as a compting system containing many simple nonlinear compting nits or nodes interconnected by lins, can handle disorderly comprehensive information withot reqiring strong model assmptions, and also has good nonlinear approximation capability, strong self-learning and self-adaptive abilities. The neral networ is a well-tested method for financial analysis on the stoc maret, pattern recognition and optimization. The nonlinear method of artificial intelligence in artificial neral networ is widely sed to predict stoc price and to fix the price for options in financial marets. As for the application of neral networ in IPO research, Robertson et.al(998) constrcted three models to predict the first-day retrn of an initial pblic offering and fond that the neral networ models perform well on both technology and non-technology offerings[]. In fact, many researchers point ot that the price of new isse shares in China's stoc marets deviate from intrinsic vale since the non-maret pricing mechanism redce the efficiency of IPO pricing. Therefore, mltiple reglators start the maret-oriented reform for the pricing mechanism. The inqiry system was introdced in 004 in China's stoc marets, in order to replace the "government pricing" with "maret-based pricing"[]. IPO inqiry system, however, does not fndamentally eliminate the phenomena of high initial retrns and long-term weaness in China's stoc marets. IPO pricing efficiency of China's stoc maret has been the focs of pblic and academic concern again. The first batch of 8 companies listing on the Growth Enterprise Maret (GEM) on October 30, 009, mared the official opening of GEM, which is no dobt of great significance on the development of China's secrities maret. The introdction of the GEM is described as the "booster" and "incbator" for the high-tech, high-growth innovative companies, even if the actal sitation is not satisfactory. "Tri-highs" phenomena (i.e., high isse prices, high P/E 05

2 Wenxi Tang and Xiaoha Zho J. Chem. Pharm. Res., 04, 6(7): and high over-raising capital) have received intensive attention and sspicions from the very beginning of the GEM's establishment in China. The original prpose of the lanch of GEM maret in China is to meet the financing needs in the rapid development of small & medim sized enterprises and to mae social scattered fnds gathered in capital maret. Bt the GEM is still an immatre and emerging maret, whose IPO pricing mechanism is not perfect, cased more serios IPO "Tri-highs" phenomenon than the main board maret. Zhang & Y(0) calclated the inherent vale of listed companies in GEM, and fond that the IPO pricing was 50% more than the intrinsic vale[3]. Go & Wan(0) sed the residal income valation model, stochastic frontier model and regression model to test the rationality of IPO isse price in China's GEM. Their reslt showed that IPO isse price in China GEM deviates from intrinsic vale, existing price bbble, and the speclation behavior in secondary maret is the main case of IPO nderpricing [4]. Therefore, the stdy of IPO pricing with Chinese GEM companies has a strong theoretical and practical significance to improve the efficiency of GEM IPO pricing, enhance the efficiency of small and medim enterprises' financing, and ameliorate the operating environment of Chinese capital maret. The companies listed in GEM are small and medim sized enterprises with high growth. Compared with the main board IPO pricing, it is hard to find similar listed companies for reference for the short operating time of GEM. In addition, de to the initial enterprise life cycle stage the new issing companies in, there is not enogh historical operating data to carry on the forecast of ftre development accrately. Traditional methods sch as free cash flow disconted, relative valation and the economic added valation techniqes are no longer applicable to the GEM IPO pricing. Many scholars began to adopt the real option and neral networ methods to fix the IPO prices. Taing advantage of AHP and BP neral networ, this paper tries to resolve the nonlinear and dynamic mathematical problems of the IPO pricing and give reasonable prices of the new isses in China's GEM. ANALYTIC HIERARCHY PROCESS AND BP NEURAL NETWORK.. Analytic Hierarchy Process AHP has been developed and applied to nmeros areas since T. L. Saaty pt forward it first in 980[5]. AHP is an effective way to deal with importance grades with respect to many items. The decision problem is decomposed into a hierarchy of more easily comprehended sb-problems firstly. Once the hierarchy is bilt, the decision maers evalate the factors systematically and compare them to one another in pairs. Among them, for the indexes in the same criteria layer, -9 proportional scaling method (shown in table) is sed to determine the relative weights of each index.then, eigenvale and vector are calclated according to comparison matrix. a = i a = 3 i a = 5 i a = 7 i a = 9 i Table. -9 Proportional scaling method i is as important as i is a little more important than i is obviosly more important than i is strongly more important than i is extremely more important than,4,6,8 are the medians of above dgement Consistency index (C.I.) is introdced to test whether the dgment matrix is consistency. λmax n C. I. = n () Table. The average random consistency index (R.I.) n R.I Consistency Ratio is a comparison between Consistency Index and Random Consistency Index: C. I. C. R. = R. I. () If the vale of consistency ratio is smaller or eqal to 0%, the inconsistency is acceptable. If the consistency ratio is greater than 0%, we need to revise the sbective dgment. 053

3 Wenxi Tang and Xiaoha Zho J. Chem. Pharm. Res., 04, 6(7): BP Neral Networ Statistical and valation methods, sch as discont cash flow model, economic vale added model, comparable company analysis model, mareting retrns model, real options valation model and mltiple factors pricing model, had been proposed to price the new isse stocs. Basically, these conventional methods rely on the restrictive assmptions on linear separability, mltivariate normality, and independence of the variables. Unfortnately, many of the common models of forecasting methods violate these assmptions, and they may not completely reflect actal maret conditions when they are applied to complex real world problems [6]. Seriosly, these methods become more complex if relationships in the inpt/ otpt dataset are nonlinear [7]. Nmeros factors that affect IPO pricing relate to each other and are not independent. They form a complex networ of inflence on IPO pricing. The correlation between inflence factors, the sbective qestion of weight assignment, the difficlty of the qantitative calclation and the noise data of sample will affect the effectiveness of pricing methods. Artificial neral networ has a good ability of falt tolerance and associative memory [8]. The interaction of inpt factors was considered into BP neral networ and a comprehensive analysis was designed to deal with the inflence factors' message. Therefore, it has been widely sed to deal with complex nonlinear problems and get more reasonable final otpt. This paper analyzes the affecting factors of China's GEM IPO pricing from both internal and external aspects and applies Analytic Hierarchy Process and BP neral networ to constrct a China's GEM IPO pricing model, in order to improve the rationality and reglation of IPO pricing in China's GEM. BP algorithm is mainly divided into two stages: in the first stage, the inpt signal is transmitted forward to the hidden nodes, sing activation fnction to calclate the actal otpt vale of each nit; in the second stage, if the otpt layer fails to achieve the desired otpt vale, the error between actal otpt and desired otpt will be calclated and transmitted step by step bac to hidden and the inpt layers so as to adst the weights and narrow the error. The process of neral networ learning stops when the error satisfies reqirements. As shown in Figre., the Bac-propagation Neral Networ is based on hierarchical strctre, inclding an inpt layer, an otpt layer and one (or more) hidden layer [9-]. Adst weights Bac-propagation process Adst weights x V y W x y o x i y o + o l x n- x n Inpt layer V m y m W l Hidden layer Otpt layer Forward calclation process Figre. The strctre of three-layer BP neral networ X = ( x As shown in Figre., in a three-layer BP neral networ,, x, L, x,, ) T i L xn is the inpt vector; Y = ( y, y, L, y,, ) T L ym O = ( o is the otpt of the hidden layer;, o, L, o,, ) T L ol is the actal otpt of otpt layer and D = ( d, d, L, d,, ) T L dl is the desired otpt vector. There are two weight matrices in a three-layer BP V = ( v, v, L, v, L, vm ) neral networ: is the weight matrix between inpt layer and hidden layer; W = ( w, w, L, w, L, wl ) is the weight matrix between hidden layer and otpt layer. The otpts of all nerons in the hidden layer are calclated by the following calclations: n net = v x, =,, L m, (3) i i i= 0 y = f ( net ), =,, L m. (4) 054

4 Wenxi Tang and Xiaoha Zho J. Chem. Pharm. Res., 04, 6(7): net Here is the activation vale of the th node, activation fnction of a node, sally a sigmoid fnction as follows: y is the otpt of the hidden layer; f ( x ) is called the f ( x) = x ( + e ) (5) The otpts of all nerons in the otpt layer are given as follows: m net = w y, =,, L l, (6) i= 0 o = f ( net ), =,, L l. (7) Error appears when actal otpt and expected otpt trn ot to be neqal. The neral networ is to find the lowest error. E = ( D O) = ( d o ) l = Where E is the error of otpt. To extend the calclation, we get eqation as follow: (8) E = d f net = d f w y = d f w f v x l l m l m n ( ( )) ( ( )) ( i i ) = = = 0 = = 0 i= 0 (9) w v and i. Ths, by correcting weights, the total error of neral networ has Otpt error E is a fnction of been adsted to satisfy the reqirements. The steepest descent method, also nown as the gradient descent method, sed in BP neral networ is a ind of optimization algorithm of differentiable fnction. E w = η, =,, L, m; =,, L, l (0) w E vi = η, i =,, L, n; =,, L, m () vi Where η η is a constant, ( 0,) is the learning rate. Combined E with above two eqations, we get the weights adstment calclation formla of BP learning algorithm as shown below: w = η( d o ) o ( o ) y () l vi = η ( d o ) o ( o ) y ( y ) x (3) i = Above is the algorithm of BP neral networ. All weights are assigned with random vales initially, and then modified by the delta rle according to the learning samples [-6]. Based on the analysis of the present stats of IPO pricing in China's GEM, a model of IPO pricing with AHP-BPNN is introdced. The following steps (as shown in Figre. ) are sed to bild a neral model capable of maing IPO prices of China's GEM. Firstly, IPO pricing factors inclding financial and non-financial factors are pre-selected to constrct the initial index system based on the experiential nowledge of athors. Then, AHP is implemented to calclate the index weights and accordingly screen the indexes in order to amend the index system and to enhance accracy of IPO price maing. Accordingly, three-layer BP Neral Networ is established with sample data from GEM. 055

5 Wenxi Tang and Xiaoha Zho J. Chem. Pharm. Res., 04, 6(7): Method Pre-selection and collection of Screen the indexes with AHP Characteristic and present sitation analysis Selection of attribtes Constrction of index system Obtaining of data Application of expert scoring method to gather information on importance of each factor Pair-wise comparison Calclation of priority vector Consistency test Calclating weights and sorting Screening indexes and amending index system Establishing networ architectre Data normalization Modeling and pricing Establishing train and test set Train and test Determination of the model's performance Figre.. Process steps with AHP-BPNN in IPO pricing FACTORS AND INDEX SYSTEM The factors affecting stoc price are often divided into two categories: financial indicators and non-financial indicators. 3. Financial indicators Considering that the GEM is characterized by high growth, we pt the financial factors into five categories as follows: financial fndamentals, debt paying ability, profitability, growth ability and operating ability. Fndamentals -total assets -net assets vale per share -earnings per share -accmlation fnd per share Debt paying ability -debt asset ratio -liqidity ratio -cash to crrent debts ratio -interest cover ratio Profit and Earning ability -retrn on eqity -retrn on total assets -profit rate of sales -srpls cash cover Operating ability -receivables trnover -inventory trnover -crrent assets trnover -total assets trnover Growth ability -growth rate of sales 056

6 Wenxi Tang and Xiaoha Zho J. Chem. Pharm. Res., 04, 6(7): growth rate of net profit -growth rate of sales profit -growth rate of total assets Table 3 The dgment matrix and weights in financial index system the criterion layer C :fndam-entals (0.30) C :debt paying ability (0.6) C 3: profitabilit-y (0.7) C 4: Growth ability (0.8) C 5: operating ability (0.08) Jdge -ment matrix 3 3 / / 3 / /3 /3 /3 / The index layer Comparison matrix Membe-rship weights Synthet-ic weights I :total assets I :net assets vale per share /3 / I 3:earnings per share / I 4:accmlation fnd per share /5 / / I : debt asset ratio I : liqidity ratio I 3: cash to crrent debts ratio I 4: interest cover ratio I 3: retrn on eqity I 3: retrn on total asset I 33: profit ratio of sales I 34: srpls cash cover I 4:average sales growth rate I 4:average net profit growth rate I 43:average sales profit growth rate I 44:average total assets growth rate I 5: receivable trnover I 5: inventory trnover I 53: crrent assets trnover I 54: total assets trnover C.R.=0.0078< /3 /5 / /5 / C.R.=0.005< / / /3 /3 / C.R.=0.0038<0. /7 /3 / /5 /3 5 /3 3 C.R.=0.043< /5 /5 /3 C.R.=0.050< As shown in table3, the paper applies AHP to calclate the weights of all financial factors on the basis of scoring method and pair-wise comparison. To simplify the inpts of BP networ, we exclde the indexes whose weights are less than 0.00, inclding interest cover ratio, srpls cash cover, average sales growth rate and total assets trnover. The exclsion garantee the contribtion rate of the cmlative weight of the remaining 6 indexes is more than 90%, which will not affect the degree of pricing assessment. 3. Non-financial indicators Non-financial factors refer to the elements independent of the enterprise's normal operation, bt reflect its endogenos sstained profitability indirectly, sch as maret interest rate, nexpected events, policy gidance, prodct maret expectations, indstry competition, maret volatility, stoc issance scale and nderwriters' reptation etc. Non-financial factors may have ncertain, nonlinear inflences on the pricing process. According to the existing literatre research, this paper chooses the following factors: index retrns, nderwriter reptation, lottery rate and issing scale. () Index retrns In general, investors can accept higher IPO price in a prosperos capital maret, on the other hand, investors only accept lower new isse price in the decline of the stoc maret [7]. De to imperfect of China's GEM composite index, the Shenzhen composite index retrns (SRET) are sed to measre the maret sentiment instead. Considering IPO price is generally fixed in the two wees before the IPO date, we inclde Shenzhen composite index retrns dring a 30 trading interval from 35 trading days before and 5 trading days before the IPO date into or model. () Underwriter's reptation Underwriters' reptation plays an important role in the IPO nderwriting process. Reptation is the important basic to secrity nderwriters' fnction of "information prodcer" and "certifying agency"[8]. Reptation stands for the nderwriters' behavior featres in the past. Investors have more confidence in the message revealed by higher reptation nderwriters. We se nderwriter raning as or proxy for nderwriter reptation. (3) Issing Scale Generally, the greater isse scale, the greater potential ris of failre. Companies listed in China's main board are divided into large cap stoc issance, mid-cap and small-cap by the bondaries of 00 million and 500 million. However, companies listed on China's GEM are small and medim sized enterprises with high growth and mainly belong to energy, health care, information indstries. Firms with large issing scale are sbect to more strict 057

7 Wenxi Tang and Xiaoha Zho J. Chem. Pharm. Res., 04, 6(7): verification of the government and reglators, ths the IPO price is often redced to a lower level by nderwriters and issers [9]. It is consistent with "small company effect" in China's stoc marets that small-cap stocs have higher retrns than large-cap stocs. (4) Lottery Rate The price for new isse was determined by taing into accont the maret demand factors. If the aggregate demand in the boo-bilding process was great, the offer price cold be increased. Conversely, if there is little demand for the new isse, nderwriter and isser shall lower the offer price in order to ensre the sccess of IPO. It is the essence of the inqiry system. So, Lottery rate is selected to measre the maret demand in this paper. IPO PRICING MODEL BASED ON AHP-BPNN 4.. The strctre of AHP-BPNN Three-layer networ is adopted in this paper. We select and screen the variables to constrct the GEM IPO pricing index system. The pricing assessment index system inclding 0 variables cold serve as the inpts of AHP-BPNN, as shown in Table4. Table 4. The inpts of AHP-BPNN C fndamentals C debt paying ability C 3 profitability I :total assets I :net assets vale per share I 3: earnings per share I 4:accmlation fnd per share I : debt asset ratio I : liqidity ratio I 3: cash to crrent debts ratio I 3: retrn on eqity I 3: retrn on total asset I 33: profit ratio of sales C 4 growth ability C 5 operating ability Non-financial factors I 4:average net profit growth rate I 43:average sales profit growth rate I 44:average total assets growth rate I 5: receivable trnover I 5: inventory trnover I 53: crrent assets trnover index retrns nderwriter's reptation issing scale lottery rate Lei(003), Zhao(008) pt forward the idea of constrcting neral networ to price the new isse, bt withot empirical research for frther spport. The ey of designing otpt layer is to choose an appropriate variable for "target-price". Bt so far there is no definition of reasonable price for IPO. Hang(008) point ot that the sccessfl price is the highest acceptable price which ensre the sccess of the isse. Based on the actal sitation, it is inappropriate to tae the first day opening/closing price as the reasonable price. For the prpose of narrowing the gap between IPO price and first day opening price, we adopt the method of Hang(0) and tae the average vale of IPO price and the first opening price is selected as the expected otpt of the pricing model [0-]. The selection of hidden layer generally is often decided on experience. One hidden layer is selected to constrct networ when the problem is not very complex and the nmber of nerons in hidden layer is decided by the following formla: m + n m + n + 0 (4) Where m is the nmber of neron in inpt layer, n is the nmber of neron in otpt layer, is the nmber of neron in hidden layer. We choose one hidden layer in ot pricing model and get the nmber of neron [0, 0] in hidden layer with formla (4). The precise is determined throgh debgging and comparing in the training. The ANP-BPNN model of China's GEM IPO pricing is implemented throgh the neral networ toolbox of MATLAB 03a. Twenty-five samples are sed to train the networ. In the training process, the parameters set are adsted continosly ntil the error satisfies the reqirements. 4.. Simlating and testing Different indstries have different potential profitability. Expectations of investors on companies' vale vary among firms with different growth abilities in different indstries. Considering new shares' pricing of the same indstry has greater similarity, firms of electronic information technology indstry with the important characteristic of innovation, are selected as a representative of new isses of GEM in this paper. Thirty new isses listed from Oct. 009 to Jn. 00 are involved. The first 5 samples are sed to train the networ and the last 5 samples are taen as a test set. There are twenty nodes in inpt layer and one node in otpt layer. The data is normalized before training and the following parameters are applied in the model: performance goal 0.00, training epochs 000. We set the nmber of 058

8 Wenxi Tang and Xiaoha Zho J. Chem. Pharm. Res., 04, 6(7): nodes in hidden layer from 0 to 0 and train the networ with calling program. After debgging and comparing, forteen nodes of the hidden layer are determined de to the least mean sqare error it has. Table 5. The comparison of rnning reslts and expected reslts Stoc code Expectation price Normalized data of expected price Otpt data Error % % % % % After rnning the program, we obtain the following otpt: Y =0.363, Y =0.765, Y 3 =0.48, Y 4 =0.4999, Y 5 =0.8348, as shown in Table 5. Considering the sitation of China's GEM, we hold that error below 0% is acceptable. So, we accept the reslts for the average error is 6.58% which verifies the validity of the model. From the reslts, we also find that the bigger the expectation data, the greater the error, which is coincide with the research reslts of Hang(0). CONCLUSION IPO pricing is one of the most basic and important theme relative to the profit of the issing firm and investors in the stocs offerings plan, and it also affect the stocs' real performance after coming into the stoc maret. If the offering price is too low, it is difficlt to satisfy the capital demand of issing firm and may inre the original shareholders' profits. On the other hand, if the offering price is too high, it will enlarge the nderwriters' isse ris and investors' investment ris. Based on the analysis of the crrent sitation of IPO pricing in China's GEM and the characteristics of the capital maret and companies, we obtain the IPO pricing factors of the GEM from both financial and non-financial aspects. Both theoretical and empirical findings sggest that combining different methods can improve the efficiency and effectiveness of maing price of new isses. This paper presents an AHP-BPNN model for IPO pricing by combining Analytic Hierarchy Process with BP Neral Networ. In the AHP-BPNN IPO pricing model, AHP is sed to filter ot the nrelated variables and eep only those variables, which have significant weights to the IPO price. Then a comprehensive and clear index system based on AHP was constrcted and taen as the inpt variables of BP Neral Networ. In order to improve the normativeness of GEM IPO pricing in China, reasonable IPO price was defined and calclated as the expected otpt of the networ based on the crrent sitation of China's GEM. After training and testing, the reslt we have obtained shows that the combination model of Analytic Hierarchy Process with BP Neral Networ model (AHP-BPNN) is effective in pricing new isses in China's GEM. REFERENCES [] SJ Robertson; BL Golden; GC Rnger; EA Wasil. Nerocompting, 998, 8(), [] SW Hang; GP H. Jornal of Changchn University of Science and Technology (Social Sciences Edition). 0,5(7),9-95. [3] JF Zhang; J Y. Jornal of Shenyang University(Social Science). 0,4(6),0-. [4] HX Go; WD Fang.China Soft Science.0,9, [5] H Jiang; JH Ran. Jornal of networs, 00,4(5). [6] B Lo; WJ Hang; S Yang. Jornal of Chongqing University (Natral Science Edition), (), [7] HX Lin. Jornal of Miniang University, 004,. 5(),7-75. [8] XH Tan; YP Bai. Economist, 009,, [9] SL Y; XC Qi. Jornal of Tsingha University (Science & Technology), 0,5(), [0] YANG Gelan; Ye WU; Hixia JIN. Jornal of Comptational Information Systems, 0, 8(0): [] L Han;R Li;HL Zh. Chinese Society of agricltral machinery.0,4(7), [] HY Shen; ZX Wang; CYGao. Jornal of Tianin University of Technology. 008, 4(5),3-5. [3] K Horni; M Stinchcombe; H White. Neral Networs, 989.(5), [4] JF Ci; JX Qi; SD Yang. Jornal of Central Soth University (Science and Technology), 009,40(), [5] RG Ibbotson..Jornal of Financial Economics, 975,,35-7. [6] P Anna;I Vong; N Zhao. Applied Financial Economies, 008, 8: [7] MK Henry; YV Hi. Pacific- Basin Finance Jornal, 998, 6(5), [8] XZ Steven; AS David. Financial Management, 008, 36(), l- 0. [9] WW Hang. Soth China University of Technology 0. [0] G Yang; X X; G Yang; J Zhang. Models and Applications, 00,

9 Wenxi Tang and Xiaoha Zho J. Chem. Pharm. Res., 04, 6(7): [] GL Yang; Q He; XJ Deng. International Jornal of Advancements in Compting Technology(IJACT), 0,3(0), [] ML Zhao. Lanzho Academic Jornal.00, 7,