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

International Journal of Advances in Management Science (IJ‐AMS) Volume 3 Issue 1, February 2014 www.ij‐ams.org DOI: 10.14355/ijams.2014.0301.03

Analysis on Mergers and Acquisitions (M&A) Game Theory of Petroleum Group Corporation Minchang Xin1, Yanbin Sun2 Economic and Management Institute, Northeast Petroleum University (Daqing Heilongjiang)

1,2

dqxinminchang@126.com Abstract Corporation is an economic organization for the purpose of profit whose internal power is the maximization of the interest. The corporation is the basic unit of M&A, so the M&A is feasible only when the expected total revenue is more than the total cost of payment. Namely, the realization of the M&A depends on whether the game equilibrium of interest can be achieved between the corporations participating in the M&A. The paper analyses the M&A game of petroleum group corporations under the complete and incomplete. Keyword M&A; Game; Complete Information Condition; Incomplete Information Condition

Introduction The M&A decision is made based on M&A corporations’ own interest, the industry status and the market information comprehensively. The acquired corporation (or the target corporation) makes the decision whether it accepts the M&A or not also on the basis of overall consideration. Of course, there are the M&A corporation and the potential acquired corporations, namely the competition between the competitors. So the M&A of petroleum group corporations contributes to reduce the competition in the petroleum industry, to increase the scale effect and speed up the development of petroleum industry and even society. The Analysis on the M&A Game of Petroleum Group Corporations under the Complete Information Condition The Static Game Analysis of Complete Information The premise condition: (1) The participants are rational targeted the maximization of interest or the utility. (2) The participants understand fully the strategies and payoff functions each other. (3) All the participants

make decision at the same. (4) The game is done under the perfect competition and fairness. (5) When selecting the strategy, the participants do not affect each other. The result of the complete information static game forms the Nash equilibrium. That is a combination of strategy consisting of the optimal strategies from all the participants. Now suppose the petroleum market only has two corporations of 1 and 2 according to the Cournot model. The costs per unit of them are the same, c1=c2=c, the productions of which are q1 and q2 , and the total production of the market is Q, Q=q1+q2. The demand function is P, P=a‐b*Q a>0 b>0. We can draw the revenue function of the two corporations based on the assumptions 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 optimization 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 2 )  bq 1  c  0     U 2 /  q 2  a  b ( q 1  q 2 )  bq 2  c  0 

According to the equilibrium of Cournot, the equilibrium production is qc, qc=q1=q2= (a‐c)/3b, the equilibrium revenue is Uc, Uc=U1=U2= (a‐c)2/9b. It is promoted to the M&A of n corporations. We can also get the following equilibrium solution: The equilibrium production qi=(a‐c)/b(n+1) (i=1, 2, …, n). The equilibrium revenue Ui= (a‐c)2/b(n+1)2. The total production of the market Q=n(a‐c)/b(n+1). The total n

revenue of the industry U =  Ui  n  a  c  i 1

b  n  1 2

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 enterprise

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assumes the followings.

Ui=(a‐c)2/b(n+1) through mergers and acquisitions, which can be concluded that the M&A is good for the all parties under the static state of complete information.

(1) The both sides of the M&A are the independent, Self‐financing, self‐development, self‐restraint economic subject. Whether the M&A succeed or not only depends on the both sides of the M&A, but the economic system and property relation as the external factors are not considered.

The Dynamic Game Analysis of Complete Information The only difference between both the complete and incomplete is that the participants do not take action at the same time. The later corporation fully understands the actions of the previous corporation. The paper analyzes the M&A by Stan Kerrʹs model.

(2) The participants are rational and pursuit of the maximization of interest, so they have the power of the potential earning by the M&A. (3) The target corporation has the high or low case. The target and the M&A corporations can produce the synergy after the merger. The M&A corporations evaluate the two cases as Vg and Vb. At the same time, the quality information that is the product development capability, the financial situation and the state of production and management and so on are the private. The M&A corporation only knows the pricing of the target corporation and judges the quality of the target enterprise only according to the pricing of the target enterprise, which has incomplete information for the quality of the target corporation.

Now assume that the market exists n enterprises, and there are the M&A of corporations from the first to the m enterprise (1<m<n). The new corporation after the M&A is named as corporation 1, the others is corporation m+1 m+2…n. At this point, corporation 1 is the market leader, other corporations are the follower. So corporation 1 decides q1 that is the production of corporation, other corporations decide qi(i=m+1 m+2 …n)that are their own productions when they know corporation 1 has taken action. So the total production of the market is Q, Q=q1+qm+1+…+qn. Each corporation’s revenue function is as follows: U1 =q1  a  c  bQ  U m 1  qm 1  a  c  bQ    U n  qn  a  c  bQ  We make the first derivative zero for the optimization:

(4) All optional strategies of the M&A corporation include mergers and acquisitions or not mergers and acquisitions. All optional strategies of the target corporation include high pricing or low pricing that are represented by Ph and Pl respectively, and Ph>Pl. The fair value of the net asset for the target corporation is Vh and Vl when the quality is high or low. The target corporation choose to set high price or low price when the quality is high, while choose to set high price or low price when the quality is low. C1 is the bankruptcy loss when the target enterprise with low quality doesn’t merger and acquisition; C2 is the packaging cost when the low quality of target enterprise chooses to set the high price. C3 is the market additional penalty cost after the M&A corporation is identified when the low quality of target enterprise chooses to set the high price.

qm 1  qm  2    qn   a  c  b  q1  n  m  1

When corporation 1 knows the choices of the others, we put qi (i=m+1, m+2, …n) into its revenue function and the best production of the enterprise can be got, q1* =(a‐c)/2b. At this time, the other corporations can calculate the production, qm* 1 = qm*  2 =…= qn* = (a‐c)/2b (n‐m+1), based on the q1* in order to find out the total production of industry Q* = (2n‐2m+1) (a‐c)/2b (n‐m+1) after the M&A. The earning of corporation 1 is U1* =(a‐c)2/4b(n‐m+1)2, and the other corporations’ * * * = U m+2 =∙∙∙= U m+n = (a‐c)2/4b(n‐m+1)2. is U m+1

(5) The M&A corporation cannot bargain, either accepting the target corporation pricing or refusing. There is no anti‐takeover risk for the M&A corporation.

The Analysis on the M&A Game of Petroleum Group Corporations under the Incomplete Information Condition

(6) The indicators of net earnings are used to measure the earnings. If the M&A succeeds, when the quality of the target corporation is high, the earnings of the M&A and target corporation are Vg‐Ph and Ph‐Vh if the target corporation chooses to set a high price. The earnings of the M&A and target corporation are Vg‐Pl

The Basic Assumptions In the actual economic activities, most of the game does not meet the premise condition of the game static complete information, which is called of the incomplete information dynamic game. This article

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high, which is named the corporation with a poor economic situation. Assume p(g) stands for the probability that the quality of the target corporation is high and p(b) stands for the probability that the quality of the target corporation is low, which meet P(g)+ p(b)=1.

and Pl‐Vh if the target corporation chooses to set a low price; when the quality of the target corporation is low, the earnings of the M&A and target corporation are Vb‐Ph and Ph‐Vl‐C2 if the target corporation chooses to set a high price. The earnings of the M&A and target corporation are Vb‐Pl and Pl‐Vl if the target corporation chooses to set a low price. If the M&A fails, the target corporation with low quality that sets a high price doesn’t be accepted by the buyout corporation, so there will be the loss, C=C1‐C2‐C3. The target corporation with low quality that sets a low price doesn’t be accepted by the buyout corporation, so there will be the loss, ‐C1. The earnings of the both sides in other cases are all 0.

On the second stage, the target corporation selects the pricing household as the signal according to the choice of the natural person N. the signal space is p= (Ph Pl), the Ph is to set high price and the Pl set low price. On the third stage, the M&A corporation doesn’t know the types of the target corporation, but only knows it belongs to the probability distribution of household. When the target corporation sets the signal household, the M&A corporation applies the Bayes Law to fix the prior probability and get the posteriori probability of target corporation 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 corporation, and a1 means the M&A, a2.

(7) To simplify the analysis, we assume that Vg‐Ph>Vb‐Pl>0>Vb‐Ph, the earning of the M&A from the target corporation of high quality with a high price is higher than that from the target corporation of low quality with a low price. While the earning of the M&A from the corporation of low quality with a low price is not negative. If the target corporation of low quality is bought with a high price, the earning of M&A corporation are negative. The target corporation of high quality is bought with a low price; the earning of M&A corporation is highest. At this time, there may be the value of the target corporation undervalued by the market or the possibility of some related transaction.

The game above is extended as follows in the game tree: in the figure 1, the number in the ending bracket’s top is the earning of the target corporation, the one at the bottom of which is the earning of the M&A. Generally, as the target corporation has the probability to set a high price or low price in the two cases of high quality and low quality, it can’t simply judge the quality of the target corporation only through the pricing of the target corporation. So the M&A corporation make right judgment of target enterprise quality by Bayes Law and referring to the price of the stock market based on the pricing of the target corporation and their own past experience.

Based on the assumptions above, the expected earnings of M&A corporation 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 probabilities are the conditional probability of the high quality of the target corporation setting a high price, the low quality of the target corporation setting a high price, the high quality of the target corporation setting a low price and the low quality of the target corporation setting a low price. Obviously, when E(V)>0, the M&A corporation take action; when E(V)<0 , it doesn’t.

We can know that signaling game is Stan Kerr Game in the incomplete information circumstance which means the sender is the leader and the receiver is the follower,. When setting the signal that is the price, the participant 1(the target corporation) predicts that the participant 2(the M&A corporation) revises the judgment for its own type according to the signal, so the choice of an optimal type depends on the signal strategy; as well the participant 2(the M&A corporation) knows the participant 1(the target corporation) chooses the given types and the optimal strategy with the information effect, so they use the Bayes Law to revise the judgment for the type of the participant 1(the target corporation) in order to choose its own optimal strategy, namely whether the M&A happens or not.

The Game Analysis On the first stage, the natural person 0 selects the type of the target corporation. We assume that the types of the target corporation only are the two cases of high quality and low quality for simplicity. θ= {g b} stands for the corporation type set. g means the quality of target corporation is high, which is named the corporation with good earning and development prospect. b means the quality of target corporation is

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the target corporation: p(g|h)= p(g) p(b|h)=p(b). The two cases are considered. When (Ph‐Vl‐C2)>(Pl‐Vl) and p(g) is large enough, making E(V)>0: no matter the quality of the corporation is high or low, the target corporation choose the high pricing. the M&A corporation make the following judgment based on Bayes Law and the strategy of the target corporation: p(g) is large enough, p(b|h) =p(b)>0 p(g|l)=0 p(b|l)=0. The M&A corporation choose the M&A.

FIG 1 GAME TREE OF GAME

The Separating Equilibrium

The separating equilibrium is the signal that the target corporation transfers can reflect its real type and provide sufficient information and basis for the judgment of the M&A corporation. When Ph‐Vl‐C2<Pl‐Vl, the M&A game of the corporation realizes the separating equilibrium. The corporation with high quality chooses to set the high price and the one with low quality sets the low price. The M&A corporation makes the following judgment based on Bayes Law and the strategy of the target corporation: P(g|h)=1 P(b|h)=0 P(g|l)=0 P(b|l)=1. The M&A corporation should select the target corporation.

When p(g) is large enough, it shows that there are many target corporations with high quality in the M&A market and M&A is beneficial. The return from the M&A of the target corporation with high quality as the price of PA can make up for the loss from the M&A of the target corporation with low quality (certainly, if the M&A doesn’t be chosen, its expected return is 0), choosing the M&A is the best policy balance of the M&A corporation. For the target corporation, when the quality is high, it should choose the high pricing because of Ph>Pl; when the quality is low, it still choose the high pricing because of (Ph‐Vl‐ C2)> (Pl‐Vl).

The M&A corporation choose the expected return of M&A based on its own judgment: p

 g  p h

 g  p h g



p b



 p h





p g   g   p b 

When (Ph‐Vl‐C2)> (Pl‐Vl) and p(b) is larger enough, making E(V)<0, the M&A market will break down if the M&A corporation don’t choose the mergers and acquisitions when the target corporation choose the high pricing. Namely, in the M&A market, there are a large number of the low quality of corporations with a high pricing making the expected earning of the M&A corporation less than 0 when it choose the M&A (their expected earning is 0 if it don’t choose the M%A). Therefore, it this case, the merger and acquisition enterpriseʹs optimal choice is not merger and acquisition certainly. The target corporation is difficult to sell in order that the M&A market will break down completely.

p b  , p g l   0 , p b l   1 。  g   p b  The expected return of the M&A corporation from the target corporation is:

p b h



E V

p g  p b  V g  Ph   V b  Ph   V h  Pl p  g   p b  p b h   p b 



Obviously, the earning is higher than the former, so the mergers and acquisitions is the best policy for the M&A corporation. For the target corporation, when the quality of the corporation is high, it is better to choose the high pricing because Ph>Pl; when the quality of the corporation is low, it is reasonable to choose the low pricing because Ph‐Vl‐C2<Pl‐Vl. So under the condition of separating equilibrium, price signals can truly reflect the quality of target enterprise, namely the target corporation with high quality can choose the high pricing, the one will automatically choose the low pricing. 2)

Conclusions Analysis on Mergers and Acquisitions (M&A) Game Theory of Petroleum Group Corporation can help petroleum corporations know the revenue after the M&A and maximize the earning by the pricing strategy. So this game analysis is very important for making the M&A strategy and development of petroleum.

The Pooling Equilibrium

The pooling equilibrium is that the target corporation whose quality is high or low chooses the same signal of high pricing. At this time, the price has no the function conveying information. In this case, the M&A corporation make the following judgment based on Bayes Law and the strategy of

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