Analysis on Mergers and Acquisitions (M&A) Game Theory of Petroleum Group Corporation

Transcription

1 DOI: /ijams Analysis on Mergers and Acquisitions (M&A) Game Theory of Petroleum Grou Cororation Minchang Xin 1, Yanbin Sun 2 1,2 Economic and Management Institute, Northeast Petroleum University (Daqing Heilongjiang) dqxinminchang@126.com Abstract Cororation is an economic organization for the urose of rofit whose internal ower is the maximization of the interest. The cororation is the basic unit of M&A, so the M&A is feasible only when the exected total revenue is more than the total cost of ayment. Namely, the realization of the M&A deends on whether the game equilibrium of interest can be achieved between the cororations articiating in the M&A. The aer analyses the M&A game of etroleum grou cororations under the comlete and incomlete. Keyword M&A; Game; Comlete ; Incomlete Introduction The M&A decision is made based on M&A cororations own interest, the industry status and the market information comrehensively. The acquired cororation (or the target cororation) makes the decision whether it accets the M&A or not also on the basis of overall consideration. Of course, there are the M&A cororation and the otential acquired cororations, namely the cometition between the cometitors. So the M&A of etroleum grou cororations contributes to reduce the cometition in the etroleum industry, to increase the scale effect and seed u the develoment of etroleum industry and even society. The Analysis on the M&A Game of Petroleum Grou Cororations under the Comlete The Static Game Analysis of Comlete Information The remise condition: (1) The articiants are rational targeted the maximization of interest or the utility. (2) The articiants understand fully the strategies and ayoff functions each other. (3) All the articiants make decision at the same. (4) The game is done under the erfect cometition and fairness. (5) When selecting the strategy, the articiants do not affect each other. The result of the comlete information static game forms the Nash equilibrium. That is a combination of strategy consisting of the otimal strategies from all the articiants. Now suose the etroleum market only has two cororations of 1 and 2 according to the Cournot model. The costs er unit of them are the same, c1=c2=c, the roductions of which are q1 and q2, and the total roduction of the market is Q, Q=q1+q2. The demand function is P, P=a bq a>0 b>0. We can draw the revenue function of the two cororations based on the assumtions above as follows. U 1 q 1 ( a bq 1 bq 2 c ) U 2 q 2 ( a bq 1 bq 2 c ) Solving the otimization is the first to find out the Nash Equilibrium, which means the two revenue functions take the first derivative of q and make q zero. U 1 / q 1 a b ( q 1 q U 2 / q 2 a b ( q 1 q 2 ) 2 ) bq 1 c bq 2 c According to the equilibrium of Cournot, the equilibrium roduction is q c, q c =q1=q2= (a c)/3b, the equilibrium revenue is U c, U c =U1=U2= (a c) 2 /9b. It is romoted to the M&A of n cororations. We can also get the following equilibrium solution: The equilibrium roduction qi=(a c)/b(n+1) (i=1, 2,, n). The equilibrium revenue Ui= (a c) 2 /b(n+1) 2. The total roduction of the market Q=n(a c)/b(n+1). The total n revenue of the industry U= Ui nac 2 bn1 2 i1 Thus it can be seen that the industryʹs total revenue after mergers and acquisitions, U= n(a c) 2 /b(n+1) 2, is greater than the equilibrium revenue of each enterrise

2 International Journal of Advances in Management Science (IJ AMS) Volume 3 Issue 1, February 2014 Ui=(a c) 2 /b(n+1) through mergers and acquisitions, which can be concluded that the M&A is good for the all arties under the static state of comlete information. The Dynamic Game Analysis of Comlete Information The only difference between both the comlete and incomlete is that the articiants do not take action at the same time. The later cororation fully understands the actions of the revious cororation. The aer analyzes the M&A by Stan Kerrʹs model. Now assume that the market exists n enterrises, and there are the M&A of cororations from the first to the m enterrise (1<m<n). The new cororation after the M&A is named as cororation 1, the others is cororation m+1 m+2 n. At this oint, cororation 1 is the market leader, other cororations are the follower. So cororation 1 decides q1 that is the roduction of cororation, other cororations decide qi(i=m+1 m+2 n)that are their own roductions when they know cororation 1 has taken action. So the total roduction of the market is Q, Q=q1+qm+1+ +qn. Each cororation s revenue function is as follows: U1= q1 Um 1 qm1acbq Un qnacbq We make the first derivative zero for the otimization: qm1 qm2 qn ac bq1 nm1 When cororation 1 knows the choices of the others, we ut q i (i=m+1, m+2, n) into its revenue function and the best roduction of the enterrise can be got, q 1 =(a c)/2b. At this time, the other cororations can calculate the roduction, qm 1 = q m 2 = = q n = (a c)/2b (n m+1), based on the q 1 in order to find out the total roduction of industry Q = (2n 2m+1) (a c)/2b (n m+1) after the M&A. The earning of cororation 1 is U 1 =(a c) 2 /4b(n m+1) 2, and the other cororations isu m+1 = U m+2 = = U m+n = (a c) 2 /4b(n m+1) 2. The Analysis on the M&A Game of Petroleum Grou Cororations under the Incomlete The Basic Assumtions In the actual economic activities, most of the game does not meet the remise condition of the game static comlete information, which is called of the incomlete information dynamic game. This article assumes the followings. (1) The both sides of the M&A are the indeendent, Self financing, self develoment, self restraint economic subject. Whether the M&A succeed or not only deends on the both sides of the M&A, but the economic system and roerty relation as the external factors are not considered. (2) The articiants are rational and ursuit of the maximization of interest, so they have the ower of the otential earning by the M&A. (3) The target cororation has the high or low case. The target and the M&A cororations can roduce the synergy after the merger. The M&A cororations evaluate the two cases as Vg and Vb. At the same time, the quality information that is the roduct develoment caability, the financial situation and the state of roduction and management and so on are the rivate. The M&A cororation only knows the ricing of the target cororation and judges the quality of the target enterrise only according to the ricing of the target enterrise, which has incomlete information for the quality of the target cororation. (4) All otional strategies of the M&A cororation include mergers and acquisitions or not mergers and acquisitions. All otional strategies of the target cororation include high ricing or low ricing that are reresented by Ph and Pl resectively, and Ph>Pl. The fair value of the net asset for the target cororation is Vh and Vl when the quality is high or low. The target cororation choose to set high rice or low rice when the quality is high, while choose to set high rice or low rice when the quality is low. C1 is the bankrutcy loss when the target enterrise with low quality doesn t merger and acquisition; C2 is the ackaging cost when the low quality of target enterrise chooses to set the high rice. C3 is the market additional enalty cost after the M&A cororation is identified when the low quality of target enterrise chooses to set the high rice. (5) The M&A cororation cannot bargain, either acceting the target cororation ricing or refusing. There is no anti takeover risk for the M&A cororation. (6) The indicators of net earnings are used to measure the earnings. If the M&A succeeds, when the quality of the target cororation is high, the earnings of the M&A and target cororation are Vg Ph and Ph Vh if the target cororation chooses to set a high rice. The earnings of the M&A and target cororation are Vg Pl 12

3 and Pl Vh if the target cororation chooses to set a low rice; when the quality of the target cororation is low, the earnings of the M&A and target cororation are Vb Ph and Ph Vl C2 if the target cororation chooses to set a high rice. The earnings of the M&A and target cororation are Vb Pl and Pl Vl if the target cororation chooses to set a low rice. If the M&A fails, the target cororation with low quality that sets a high rice doesn t be acceted by the buyout cororation, so there will be the loss, C=C1 C2 C3. The target cororation with low quality that sets a low rice doesn t be acceted by the buyout cororation, so there will be the loss, C1. The earnings of the both sides in other cases are all 0. (7) To simlify the analysis, we assume that Vg Ph>Vb Pl>0>Vb Ph, the earning of the M&A from the target cororation of high quality with a high rice is higher than that from the target cororation of low quality with a low rice. While the earning of the M&A from the cororation of low quality with a low rice is not negative. If the target cororation of low quality is bought with a high rice, the earning of M&A cororation are negative. The target cororation of high quality is bought with a low rice; the earning of M&A cororation is highest. At this time, there may be the value of the target cororation undervalued by the market or the ossibility of some related transaction. Based on the assumtions above, the exected earnings of M&A cororation is when it takes action: E V =P(g h)(vg Ph)+P(b h)(vb Ph)+P(g l)(vg Pl)+P(b l)(vb Pl) The four robabilities are the conditional robability of the high quality of the target cororation setting a high rice, the low quality of the target cororation setting a high rice, the high quality of the target cororation setting a low rice and the low quality of the target cororation setting a low rice. Obviously, when E(V)>0, the M&A cororation take action; when E(V)<0, it doesn t. The Game Analysis On the first stage, the natural erson 0 selects the tye of the target cororation. We assume that the tyes of the target cororation only are the two cases of high quality and low quality for simlicity. θ= {g b} stands for the cororation tye set. g means the quality of target cororation is high, which is named the cororation with good earning and develoment rosect. b means the quality of target cororation is high, which is named the cororation with a oor economic situation. Assume (g) stands for the robability that the quality of the target cororation is high and (b) stands for the robability that the quality of the target cororation is low, which meet P(g)+ (b)=1. On the second stage, the target cororation selects the ricing household as the signal according to the choice of the natural erson N. the signal sace is = (Ph Pl), the Ph is to set high rice and the Pl set low rice. On the third stage, the M&A cororation doesn t know the tyes of the target cororation, but only knows it belongs to the robability distribution of household. When the target cororation sets the signal household, the M&A cororation alies the Bayes Law to fix the rior robability and get the osteriori robability of target cororation quality P(θ P). It decides whether it does the M&A or not. A= (a1 a2) stands for the action set of the M&A cororation, and a1 means the M&A, a2. The game above is extended as follows in the game tree: in the figure 1, the number in the ending bracket s to is the earning of the target cororation, the one at the bottom of which is the earning of the M&A. Generally, as the target cororation has the robability to set a high rice or low rice in the two cases of high quality and low quality, it can t simly judge the quality of the target cororation only through the ricing of the target cororation. So the M&A cororation make right judgment of target enterrise quality by Bayes Law and referring to the rice of the stock market based on the ricing of the target cororation and their own ast exerience. We can know that signaling game is Stan Kerr Game in the incomlete information circumstance which means the sender is the leader and the receiver is the follower,. When setting the signal that is the rice, the articiant 1(the target cororation) redicts that the articiant 2(the M&A cororation) revises the judgment for its own tye according to the signal, so the choice of an otimal tye deends on the signal strategy; as well the articiant 2(the M&A cororation) knows the articiant 1(the target cororation) chooses the given tyes and the otimal strategy with the information effect, so they use the Bayes Law to revise the judgment for the tye of the articiant 1(the target cororation) in order to choose its own otimal strategy, namely whether the M&A haens or not. 13

4 International Journal of Advances in Management Science (IJ AMS) Volume 3 Issue 1, February 2014 the target cororation: (g h)= (g) (b h)=(b). The two cases are considered. E FIG 1 GAME TREE OF GAME 1) The Searating Equilibrium The searating equilibrium is the signal that the target cororation transfers can reflect its real tye and rovide sufficient information and basis for the judgment of the M&A cororation. When Ph Vl C2<Pl Vl, the M&A game of the cororation realizes the searating equilibrium. The cororation with high quality chooses to set the high rice and the one with low quality sets the low rice. The M&A cororation makes the following judgment based on Bayes Law and the strategy of the target cororation: P(g h)=1 P(b h)=0 P(g l)=0 P(b l)=1. The M&A cororation should select the target cororation. The M&A cororation choose the exected return of M&A based on its own judgment: g h g g g h g b h b g b b b h, g l 0, b l 1 g b The exected return of the M&A cororation from the target cororation is: g b V V g Ph V b Ph V h Pl g b b h b Obviously, the earning is higher than the former, so the mergers and acquisitions is the best olicy for the M&A cororation. For the target cororation, when the quality of the cororation is high, it is better to choose the high ricing because Ph>Pl; when the quality of the cororation is low, it is reasonable to choose the low ricing because Ph Vl C2<Pl Vl. So under the condition of searating equilibrium, rice signals can truly reflect the quality of target enterrise, namely the target cororation with high quality can choose the high ricing, the one will automatically choose the low ricing. 2) The Pooling Equilibrium The ooling equilibrium is that the target cororation whose quality is high or low chooses the same signal of high ricing. At this time, the rice has no the function conveying information. In this case, the M&A cororation make the following judgment based on Bayes Law and the strategy of When (Ph Vl C2)>(Pl Vl) and (g) is large enough, making E(V)>0: no matter the quality of the cororation is high or low, the target cororation choose the high ricing. the M&A cororation make the following judgment based on Bayes Law and the strategy of the target cororation: (g) is large enough, (b h) =(b)>0 (g l)=0 (b l)=0. The M&A cororation choose the M&A. When (g) is large enough, it shows that there are many target cororations with high quality in the M&A market and M&A is beneficial. The return from the M&A of the target cororation with high quality as the rice of PA can make u for the loss from the M&A of the target cororation with low quality (certainly, if the M&A doesn t be chosen, its exected return is 0), choosing the M&A is the best olicy balance of the M&A cororation. For the target cororation, when the quality is high, it should choose the high ricing because of Ph>Pl; when the quality is low, it still choose the high ricing because of (Ph Vl C2)> (Pl Vl). When (Ph Vl C2)> (Pl Vl) and (b) is larger enough, making E(V)<0, the M&A market will break down if the M&A cororation don t choose the mergers and acquisitions when the target cororation choose the high ricing. Namely, in the M&A market, there are a large number of the low quality of cororations with a high ricing making the exected earning of the M&A cororation less than 0 when it choose the M&A (their exected earning is 0 if it don t choose the M%A). Therefore, it this case, the merger and acquisition enterriseʹs otimal choice is not merger and acquisition certainly. The target cororation is difficult to sell in order that the M&A market will break down comletely. Conclusions Analysis on Mergers and Acquisitions (M&A) Game Theory of Petroleum Grou Cororation can hel etroleum cororations know the revenue after the M&A and maximize the earning by the ricing strategy. So this game analysis is very imortant for making the M&A strategy and develoment of etroleum. REFERENCE Baoming Li, Jiazhuang Liu. The Utility Function and the 14

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