The Synergy and Timing of Multi-Firms’ Merges under Uncertainty Kuo-Jung Lee Shih Chien Univeristy, Kaohsiung Campus David S. Shyu* National Sun Yat-sen University Abstract By using real options approach, this paper constructs a model to examine the multi-firms’ merges strategies under stochastic demand shock. The strategies include the benefits and timing of merges. This study derives the synergy effect; timing of multi-firms’ merges and shares between each other under the different market structure. In addition, we find that increasing merger costs and product market uncertainty tend to delay mergers. On the contrary, larger synergies or economy of scale speed up mergers. Keywords: Mergers, Real options, Threshold, Takeover game * Corresponding author. Department of Finance, National Sun Yat-sen University, 70 Lien-hai Rd. Kaohsiung, Taiwan; Tel: +886-7-525-2000 ext. 4814; Fax: +886-7-525-4899. E-mail addresses: leekj@pchome.com.tw (K.J. Lee) dshyu@cm.nsysu.edu.tw (D.S. Shyu), 1 The Synergy and Timing of Multi-Firms’ Merges under Uncertainty 1. Introduction Most successful, large businesses have developed into large, interconnected organizations either through self-development or mergers and acquisitions. Mergers and acquisitions, hence, have been the subject of considerable research in financial economics. The transactions of mergers and acquisitions are larger and strategic. Many mergers are integrated by multi-firms simultaneously. These merging deals consist of tree, four, or even more firms. In Taiwan, for example, Lite-On Electronics, Silitek, Lite-On Technology, and GVC merge and become collectively known as the Lite-On Technology Corporation in2002. In addition, Taiwan International Securities Corporation attempts to merge with First Securities and Far Eastern Securities. This paper structures the model to examine the profits and timing of multi-firms mergers. That is, we study the problem of whether and when to merge when the case is multi-firms merger and not just two firms merger. The traditional approach used to value merger include discounted cash flow model, asset appraisal model, and market comparative approach(Ernst and Young, 1994). These methods, however, ignores the value of timing and operation flexibility(Dixit and Pindyck, 1994; Trigeorgis, 1996). As emphasized by Trigeorgis (1993) and Dixit and Pindyck (1994), among others, the options approach helps explain why actual investment decisions by the business sector cannot be explained by conventional wisdom such as the net present value (NPV) approach. In reality, firms invest only in projects that are expected to yield a return well in excess of the required rate of return. Baba (2001) thank that firms should consider the option to wait until economic conditions improve sufficiently under the assumption of uncertainty and irreversibility. This is a typical setting of a so-called real options approach first applied by McDonald and Siegel (1984) and later extensively reviewed by Dixit and Pindyck (1994). Real options analysis is more focusing on describing uncertainty and in particular the managerial flexibility inherited in many investments. In recent year, some studies applied real options approach to value the project of mergers. The advantage is considering the flexibility value of mergers strategy under uncertainty. Margrabe (1978) is the first to analyze takeovers as exchange options. In his model, the takeover involves a zero-sum game and its timing is exogenous. Shleifer and Vishny (2003) also consider a zero-sum game with exogenous timing. In their framework, the market does not reflect the potential surplus associated with the takeover in the stock market valuations of participating firms. Managers of the firms 2 understand stock market inefficiencies, and take advantage of them, in part through merger decisions. Their model is consistent with available empirical findings about characteristics and returns of merging firms. Herath and Jahera (2002) develop a theoretical model based on option pricing theory to value managerial flexibility arising in stock for stock exchanges. They show how a mergers and acquisition (M&A) deal may be optimally structured as a real options swap by including managerial flexibility of both the acquiring and target firms when stock prices are volatile. As argued by Huisman, Kort, Pawlina, and Thijssen (2004), the real option theory mainly considers single decision maker problems of firms operating in monopoly or perfect competition markets. But capital budgeting decisions can be strongly influenced by existing as well as potential competitors. They conclude this brand new topic requires a merge between game theory and real options. Grenadier (2000) finds that only a few contributions, at present, deal with the effects of strategic interactions on the option value of waiting associated with investments under uncertainty. One of the main reasons is that the application of game theory to continuous-time models is not well developed and often quite tricky. However, due to the importance of studying the topic of investment under uncertainty in an oligopolistic setting, it can be expected that more publications will appear in the immediate future. Some articles use game theory to investigate the firms’ interaction of mergers. For example, Kwoka (1989) studies the effect of market competition on a merger production and profit. He finds that a merger occurs more easily in more competitive intensity and in which the firm of post-merger makes higher profit. Rodrigues (2001) assumes that merger occurrence is determined by the interplay of the initial number of firms in the industry, the expected competitive intensity, and the possibility of economizing on fixed costs through merger. He shows that the equilibrium market concentration is decreasing in the first of these factors and increasing in the other two. However, these studies are not within the dynamic economic environment and cannot value the flexibility from takeovers. The game-theoretic real options approach is employed to analyze the effects of uncertainty on mergers decisions. These are used to model corporate restructuring as a strategic investment decision under uncertainty. Related papers include Smith and Triantis (1995), Anderson and Sundaresan (1996), Grenadier (1996), Grenadier (1999), Mella-Barral (1999), and Grenadier (2000). There are a number of theoretical papers that have modeled the terms of takeovers under alternative assumptions, but usually not within the dynamic economic environment that is the setting in this paper. A good review of the literature is given by Weston, Chung, and, Hoag (1990) and Weston, Chung, and Siu (1998). A related paper by Smith and Triantis (1995) 3 examines the valuation of strategic options associated with acquisitions. They illustrate how option-pricing theory can be used to value growth, flexibility and divestiture options arising from takeovers. Besides, Morellec (2001) develops an equilibrium framework for the joint determination of the timing and the terms of takeovers. His article analyzes takeovers as exchange options and derives equilibrium restructuring strategies by solving option exercise games between bidding and target shareholders. Lambrecht (2004) thinks that a merger is a cooperative decision where the shares of both firms are determined according to Pareto optimality. So, firms decide on an optimal time first and then share the profits accordingly. In a (hostile) takeover the target first chooses its profit share upon which the acquirer determines the optimal time of takeover. Lambrecht (2004) concludes that M&A activity only takes place during periods of economic expansion. The starting point of the paper is that firms merge to generate a surplus to their shareholders. In the model, the surplus results from synergies arising from increased returns to scale and a reduction in the unit production cost. The surplus is defined as the difference between the market capitalization of the joint (merged) entity and the value of the individual companies. Since the market capitalization of the merged entity and the individual companies are influenced by economic uncertainty, it follows that the surplus is likely to be influenced by economic uncertainty too. In other words the gains from merging depend on the state of the industry or economic environment. In this paper the source of uncertainty considered is the demand shock for the firms' output. Mergers not only generate benefits, however, but also bring with them costs such as legal fees, fees to investment banks and other merger promoters, costs of restructuring and integrating the two companies. These are typically one-off costs that, once incurred, are sunk and irreversible. When merging, both companies therefore have to trade off the stochastic benefit of merging against the cost of merging (Lambrecht, 2004). The companies of mergers have the right (but not the obligation) to exchange their current firm for a share in a new firm with higher returns to scale and lower unit costs. The higher profits they are forgoing by not merging act as an incentive to exercise the merger option. Given that corporate restructurings are (at least partially) irreversible, the merging companies have to decide when it is optimal for them to exercise their option to merge. A key issue in the paper is therefore to examine the optimal timing of corporate restructurings under demand shock uncertainty and irreversibility. We assume that all firms and investors have complete information. The assumption of complete information is an important one as almost all theories on the timing or 4 returns of takeovers are based on asymmetric information arguments. We show that takeovers that increase the firms' returns to scale occur in a rising product market. The research presented in this paper is motivated by the fact that present takeover projects are more blooming and complicate. A merger project maybe includes tree, four, or possible more firms. The above literatures only analyze the merger case of two firms. To include this kind of mechanism, this paper extends the model of Lambrecht (2004) by incorporating more than two firms in mergers. The main aim of this paper is to provide a theoretical strategy in multi-firms mergers. We, hence, derive closed form solutions for the takeover options, optimal threshold, and acquirer's and acquiree's ownership shares. We also find that increasing merger costs and product market uncertainty tend to delay mergers. From a methodological point of view, this paper also uses continuous-time real options techniques and game theoretical concepts, which enable us to model corporate restructuring as a strategic investment decision under uncertainty. The market structure we assume is an oligopolistic market in which the firms will extend their size, increase market power or improve their efficient by merging. Even by acquiring numerous firms simultaneously the acquirer will be a monopoly in the industry. The remainder of the paper is organized as follows. Section 2 describes the basic theoretical framework of the real options approach. We show that this surplus is a convex increasing function of the output price and that it has option-like characteristics. Section 3 derives the optimal merger timing from a global optimizer’s viewpoint. We show that mergers are optimal in a rising market, causing merger activity to be pro-cyclical. We provide a closed form solution for the merger timing. A closed form solution for the post-merger ownership shares is provided. Section 5 concludes the study. 2. The basic models Consider an oligopolistic industry comprised of n identical firms producing a single, homogeneous good. Firm i produces qi units of output. Output is infinitely divisible. Assume that the market inverse demand function is of a constant-elasticity form: P XQ 1 (1) where P is the price of a unit of output, X is an exogenous shock process to demand, and Q is the industry supply process. We assume that > 1/n to ensure that marginal profits (for any assumed value of n) are increasing in X.1 X represents a multiplicative 1 Concavity of the profit function with respect to each firm’s output is guaranteed for all n > 1. 5 demand shock, and evolves as a geometric Brownian motion: dX X dt X dz (2) where denotes the expected growth rate parameter, the volatility parameter, and dz the increment of the standard Wiener process. Assume that r in order to ensure convergence. In addition, following the setting of Rodrigues (2001), the cost functions of firms are: TCi = cqi + F (3) where F and c are, respectively, fixed and marginal costs, which we assume are identical for all firms, and qi is the quantity i supplied by firm i. Of course, Q = qi + q-i, with q-i representing the quantity supplied by the ith firm (n - 1) competitors. Hence, firms’ profits are: i ( X t ) pi ( X t )qi cqi F (4) Rodrigues (2001) let i dqi / dqi represent firm i’s conjectural variation, i.e. its expectation regarding the change in its competitors production resulting from a change in its own production level, and assume that this conjecture is identical for all firms ( i ). We also use the definition and refer to as the competitive intensity of the industry, with lower values of corresponding to more intense competition. The range of from -1 to n-1 represent, respectively, competitive equilibrium and perfectly collusive one. From the equation (4), the profit maximization requires that i / qi 0 . It is then straightforward to show that, in equilibrium: X qi 1 (5) nc In order to ensure the quality is positive, it requires ( 1) / n . Substituting the equilibrium production into i , each firm’s profit can then be written: 1 n 1 1 1 X 1 i 1 F n n nc 1 (6) One can easy find that the fixed and marginal costs will reduce each firm’s profit. As for the inference of firms’ number among firms in the industry on firm’s profit, we can see from the following equations. 1 X z (1 z ) 2 2 z z 2 1 0 , z 1 n n n c where the third term can be rewritten by [(1 z ) (1 n1 )] , which is positive. 6 1 z 1 2 1 1 X 0 n c n The increasing firms’ number and competition among firms in the industry will decrease each firm’s profit. This result is the same with that of Kwoka (1989) and Rodrigues (2001). Applying Ito’s lemma, we can get dynamic program of profit function: d i ( X t ) [i 12 i ( i 1) 2 ]dt i dz i (Xt ) (7) The value of the firm, Vi, can be seen as the discounted value of all future profits and is given by: Vi ( X ) i (,n,c) X F n r (8) 1 1 1 1 1 i 1 n n [r g ( )]c 1 where r is the riskless rate, g () 1 [(r ) 12 2 ( 1 1)] , and r 2. Suppose that m + 1 of the n firms comprising an industry merger, i.e. m + 1 firms merger. The new number of firms in the industry will be n’ = n – m. Assume, further, that the merger has no impact on firms’ conjectural variations and marginal costs. The post-merger equilibrium will still be characterized by identical production for each of the n – m firms, with: q m 1 i 1 1 ( nm) X ( n m) c (9) where the superscript, m + 1, denotes that m + 1 firms comprise an industry merger. Similarly, this equation requires ( 1) / (n m) 1 ensuring that the post-merger quality is positive. From the equilibrium production before and after merger, it can be shown that the firm resulting from the merger will produce less than the sum of the pre-merger production of the merged firms, but more than any of them produced separately. Each of the non-merging firms will increase its production, and the overall production level will decrease. This will lead to a price increase that substantiates the market power motive for merger. Using the setting of Rodrigues (2001), the efficiency motive is incorporated in the model through fixed cost economies. Let be a coefficient measuring the degree in which the merger allows such economies, with 0 m . With 0 , fixed costs is usually referred to as the convenience yield. We assume it to be positive, since the problem would otherwise not have a solution. This condition is interpreted in Dixit and Pindyck (1994). 2 7 have a sunk nature, and are not adjustable post-merger: the firm resulting from the merger has the same fixed costs as the whole of the merged firms. At the other extreme, with m , the firm resulting from the merger has the same fixed costs as one of the merged firms. This can happen if those fixed costs result from an indivisibility in the production factors or if the merger is purely anti-competitive, resulting in the closure of all but one of the merged firms. Intermediate cases are, of course, conceivable. When the firm i merges m firms in the industry, the multi-firms merger profit will be: m 1 i 1 1 1 X m 1 1 1 F 1 1 (n m) (n m) (n m)c (10) where the superscript of im 1 denotes that there are m + 1 firms comprising an industry merger. The effect of m on merger profit can be found from the differentiation: im1 X F 1 , z' z ' (1 z ' ) 2 (2 z 'z ' ) 2 1 m 1 ( n m) ( n m) c We can find that the result includes two parts. The second part indicates the effect of fixed cost economies. The increasing will increase a benefit from the number of a merger increasing. If the first part is larger than the second part, the differentiation is positive, increasing number of a merger will increase profit. The sign of this result, however, depends on the third term (i.e. 2 z 'z ' ) of first part. Since the requirement of 1 > z’, the third term is positive when m (n 1) . That is, when the competition intensity is high (i.e. is small) or number of mergers is low, increasing number of a merger will increase profit. Considering these multi-firms that have the option to merge into a new company with value Vm+1. By using the same approach above, we can get the new firm i’s post-merger value: Vi m1 ( X t ) im1 (,n, m,c) where m 1 i X t m 1 F n m ( 1) r (11) 1 1 1 1 1 1 1 (n m) (n m) [r g ( )]c The synergy assumed that comes from scale economy in this paper is the main reason to merge. Considering the synergy of m + 1 firms merger, which can be 8 denoted by the difference between the post- and pre-mergers value: S i Vi m 1 ( X t ) (m 1)Vi ( X t ) m1 (m 1) F (m 1) X n 1 r n m (12) We can check whether the merger of any subset of the n firms in the industry is privately profitable. When 1, equivalent to a competitive industry, the first term in equation (12) is zero. Then, a merger among a subset of the firms in the industry will only be profitable if it allows for fixed cost economies. In fact, even without any merger, the industry profit is already maximized, there being room for no improvement. The merger of all the n firms, creating a multi-plant monopoly, would only maintain the pre-merger industry profit, while the merger of any smaller subset of the firms would imply a loss for the merged firms because, transforming them in a single firm, it would reduce their share in the same industry profit pie. 3. The timing and terms of multi-firms’ mergers 3.1 The timing of multi-firms’ mergers When merging, each firm incurs a fixed cost denoted by I. In considering a merger, firms make a tradeoff between the stochastic benefit of merging and the cost of merging. Since firms have the option but not the obligation to merge, they will do so only when it is in their interest. We use the approach of Lambrecht (2004) and show that firm i’s option value in m + 1 firms merger is given by: Oi ( X t ) max V m1 ( X t ) (m 1)V ( X t ) (m 1) I , 0 m1 (m 1) m a x (m 1) X F (m 1) I , n r ( 1) n m 0 According to the assumption of model, the demand shock follows geometric Brownian motion. The partial differential equation of mergers option is(see Dixit and Pindyck, 1994): 1 2 2 X t2 O' ' ( X t ) (r ) X t O' ( X t ) rO ( X t ) 0 (13) As suggested by Dixit and Pindyck (1994), in such a case, the solution has a form3: 3 Strictly speaking, one must write the solution as 9 O( X t ) AX , 0 (14) where A and β are constants to be determined. The expression for β > 0 can be found by solving the following fundamental quadratic equation: Q 12 2 ( 1) ( r ) r 0 (15) We consider the boundary conditions4 that must be satisfied at a threshold value for entry to close the model: (16) (m 1)V ( X ) O( X ) V m ( X ) ' (m 1)V ' ( X ) O ' ( X ) V m ( X ) (17) where X is the threshold to merge. Equation (16) is referred to as the value-matching condition. The second boundary condition, equation (17), is called the high-order contact or smooth-pasting condition. According to the boundary condition above, the parameter A can be solved as: m1 (m 1) A (m 1) X F (m 1) I X n r ( 1) n m (18) Concerning existence and uniqueness of X t , we were able to show the following results. The merger takes place the first time when the state variable Xt hits the threshold X from below. The value of firm's option to merge is given by: m1 X (m 1) O( X t ) (m 1) X F (m 1) I t , X t X (19) n m n r ( 1 ) X Under the condition of O( X ) / X 0 , we can get the threshold X to merge: 1 (m 1) I ((m11) ) Fr X m 1 n m (m 1) n (20) Using the threshold, a firm’s manager has the principal to deal with the problem of mergers. The optimal timing, T, to multi-firms merge is: T inf[ t 0 : X (t ) X ] . The optimal merger threshold without concern as to how the merger option is divided between the firms of two parts. The above expressions for the value of the merger options, Equation (19), have a simple and intuitive interpretation. The first factor represents the surplus, S(Xt), generated at the time of the merger. The factor O( X t ) A1 X 1 A2 X 2 , 1 0; 2 0 4 Generally speaking, the value-matching and smooth-pasting conditions consist of so-called boundary conditions. 10 ( X t / X ) is a discount factor that discounts the surplus back to the present. Lambrecht (2004) thinks that the discount factor can also be interpreted as the probability of the state variable ever hitting the merger threshold X given the current level, Xt, of the state variable. From the merger threshold in equation (20), we can find that the larger merger costs, I, and hysteresis factor, /( ) , delay merger. This is in line with the predictions of real options theory. On the contrary, larger synergies including m 1 nm ( m 1) F 1 r and (m 1) n speed up mergers. For each firm of multi-firms merger, the cumulative return, R, at X is given by: O( X ) R (m 1)V ( X ) m 1 X m11 Fr (m 1) I nm m 1 n X (m 1) Fr 1 (21) From the cumulative return of multi-firms merger, we can see the return of merger will increase when merger effect, m1 , increases and merger cost, I, decreases. Besides, the return of merger will increase through parameter of fixed cost economies, , increasing. 3.2 The terms of multi-firms’ mergers In a merger the equity of the individual merging companies is exchanged for a fraction of the equity in the newly created firm. We assume that the acquirer consists of m firms in the merger with m + 1 firms. This acquire is denoted by V am and the acquiree in the merger with m + 1 firms is denoted by Ve1 . In a stock offer the acquirer buys the shares of the target and gives a fraction of its own shares in exchange. So similar to a merger both the acquirer and the acquiree hold shares in the restructured company. We model mergers as the outcome of a Cournot-Nash game in which both firms determine simultaneously the timing and the terms of the merger. We study further the options value from individual firm’s merging. The payoff to each firm has the option to exchange its own shares for shares in a new company. Oa ( X t , s a ) max[ s aV m 1 ( X t ) Vam ( X t ) I a , 0] , 11 Xt X Oe ( X t , s e ) max[ s eV m 1 ( X t ) Ve1 ( X t ) I e , 0] , Xt X (22) where Vm+1 is a new company value after merging. Besides, Ij (j = a, e) is firm j’s cost incurred in merger and Ia + Ie = I. Besides, sj denotes the fraction of the new equity capital owned by firm j and sa + se = 1. Hence, at the time of the stock offer, the payoff of acquirer and acquiree can be written as: s jV m1 ( X t ) V j ( X t ) , j = a, e. The acquirer constructs a new company with value Vm+1, but has to offer a fraction 1-sa. The firm’s option of merger is: O j ( X t , s j ) s jV m 1 X Vj I j t , X j = a, e and X t X (23) Let X a X e X and the conditions: O j ( X t , X j , s j ) 0 (j = a, e) and sa + se = 1 X j X j X Hence, the ownership structure of post-merger firm (sa, se) ensures that both firms want to execute the merger at the efficient threshold (i.e. X a X e X ) and that the total merger surplus gets divided (i.e. sa + se = 1). The ownership structures of the post-merger firm are: sa Va n X I a m 1 V m 1 n m X , (24) Ve n m1 X I e m and se (25) m 1 V m1 n m X The optimal merger threshold is: X nm1 n I m 1 nm F 1 r m 1 (26) The implication of threshold is similar to that in equation (20). The main difference is synergy, the second term of threshold. 3.3 The terms of hostile takeovers In acquisition, we assume the first firm in the industry is acquiring firm and the 12 mth firm is the target firm. We follow Lambrecht (2004) to assume that the process of acquisition is described by Stackelberg leader-follower game. The target first decides on the terms, s, at which it is prepared to offer its shares, and the acquirer subsequently decides on the timing (i.e. when to make the offer). That is, the timing and terms decisions are not made simultaneously. This situation is similar to a hostile takeover where the target management dictates the minimum terms required for relinquishing control. Lambrecht (2004) thinks that the costs of renegotiating the terms demanded by the target are prohibitively high and the target can make a take-it-or-leave-it offer with respect to the takeover terms. The target's and the acquirer's optimization problem can be formulated respectively as: max Oe ( X t , X ( s a ), s a ) and max Oa ( X t , X , s a ) sa X By using similar method above one can show that takeover options value and threshold. The acquirer’s takeover option value is: Oa ( X t , X , s a ) s aV m 1 X ( X ) Va ( X ) I a t , X Xt X s aV m 1 ( X ) Va ( X ) I a , Xt X (27) Besides, the target’s takeover option value is: Oe ( X t , X , s a ) (1 s a )V m 1 X ( X ) Ve ( X ) I e t , X (1 s a )V m 1 ( X ) Ve ( X ) I e , The post-takeover ownership shares are given by: ( )Va m1 Fr I a sa and se 1 s a ( )V m 1 m11 Fr Xt X Xt X (28) (29) However, we cannot find the closed form of takeover threshold. For simply, we assume a firm’s fixed cost F = 0. The post-takeover ownership shares then are given by: ( )Va I a and se 1 s a (30) sa ( )V m1 The optimal takeover threshold is given by X 1 m nm1 n I a I e m 1 nm (31) 13 From the threshold above, we can also find that the increasing takeover costs, Ia and Ie, and hysteresis factor, /( ) , will delay mergers. On the contrary, larger synergies m 1 nm nm1 n speed up mergers. m 4. Extension: merger to monopoly Mergers within an industry, horizontal mergers, can increase concentration within an industry. According to Demsetz (1973), high market concentration helps firms in a particular industry to reach collusive agreement, thus increasing the degree of monopolization within that industry and creating monopolistic profits. Assuming there is an industry with n firms originally. The acquirer plants to merge the remainder (i.e. n –1 firms) in the industry. The acquirer’s value is denoted by V1 and the value of remainder entirely is denoted by Vn-1. The merger of all the n firms creates a multi-plant monopoly with the new value Vn. When merging to monopoly, the option to merge is given by: O( X t ) max[ V n ( X t ) V 1 ( X t ) V n 1 ( X t ) I , 0] (32) where I is the cost incurred in merger. For all the n firms, the optimal threshold X for merger to monopoly is: I X n n 1 1 1 2 n F 1 r 1 (33) Similarly, from the threshold above, we find that the increasing takeover costs, I and hysteresis factor, /( ) , will delay mergers. On the contrary, larger synergies including F 1 r n 1 and n 2 n speed up mergers. For merger to monopoly, the firm’s cumulative return, R, at X is given by: R n X n1 Fr nI 1 X n Fr (34) From this cumulative return of multi-firms merger above, we can find that the return of merger will increase when synergy effect, n , increases and merger cost, I, decreases. Besides, the return of merger will increase through parameter of fixed cost economies, , increasing. If the fixed cost F = 0, we can see the return more clearly. The cumulative return in this time is: 14 Ri n I 1 Vi ( X ) Then the firm’s cumulative return is synergy effect minus merger cost rate and firm’s value. 5. Conclusion Owing to there are multiple firms participating in a merger sometimes and they want to merge together. This study therefore develops a model for the timing and terms of multi-firms mergers in a dynamic economic environment where the firm’s demand shock is stochastic. We model mergers as the outcome of a Cournot Nash game where the timing and terms of the takeover are simultaneously determined, whereas tender offers result from a Stackelberg leader follower game where the target decides first on the terms and the acquirer subsequently on the timing. This paper, hence, obtain closed form solutions for the takeover synergy, options, optimal threshold, and acquirer's and acquiree's ownership shares. We find that the expected time to merge is inversely related to the magnitude of the synergies generated. That is, increasing merger costs, product market uncertainty and decreasing scale economy tend to delay mergers. 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