跨國合併與購併財務綜效之衡量－或有求償權評價法

行政院國家科學委員會專題研究計畫 成果報告

跨國合併與購併財務綜效之衡量－或有求償權評價法

計畫類別： 個別型計畫 計畫編號： NSC93-2416-H-004-046- 執行期間： 93 年 08 月 01 日至 94 年 07 月 31 日 執行單位： 國立政治大學金融系 計畫主持人： 廖四郎 計畫參與人員： 黃星華；江淑玲 報告類型： 精簡報告 處理方式： 本計畫可公開查詢

中 華 民 國 94 年 10 月 30 日

跨國合併與購併財務綜效之衡量

－或有求償權評價法

摘要

本研究計劃提出一個或有求償權模型來分析跨國合併與購併。在考慮購併者與被 購併者所面臨之利率風險與外匯風險下，本模型最適化購併者，被購併者及購併 後存續公司之資本結構。立基於模型架構下，我們提出跨國合併與購併之純財務 綜效衡量指標與最適換股比例。在數值例子中，本研究發現，二家相對稱(規模 及所面臨之環境皆相同)跨國公司之合併會產生負的財務綜效，而二家不對稱(一 家規模大風險小，而另一家規模小風險高)跨國公司之合併會產生正的財務綜效。 關鍵字: 跨國合併與購併，財務綜效，最適換股比例，利率風險，外匯風險

Measuring Purely Financial Synergies for a Cross-Border

M&A－A Contingent Claims Approach

Abstract

The research provides a contingent claims model to analyze a cross-border M&A. The model makes the capital structures of the acquiring firm, target firm and merger firm to be optimally determined, while taking account of not only the interest rate risks of the acquiring and target firm but also foreign exchange risk. Based on the model, we provide the purely financial synergy measure and the optimal stock for stock exchange ratio for a cross-border M&A. The numerical examples show that the cross-border M&A of two symmetric firms would result in a negative financial synergy, whereas that of two asymmetric firms may lead to a positive financial synergy.

Keywords: Cross-border M&As, Financial Synergies, Optimal Stock Exchange Ratio, Interest Rate Risk, Exchange Rate Risk

1 Introduction

The liberalization of restrictions to international capital flows and the trend toward an integrated world economy have led to increased activity in the global market for cross-border mergers and acquisitions (M&As). Following the rapid increase in international trade and cross-border financial transactions, in most sectors of economic activity, a large share of M&As involve firms operating in different countries. For examples, Deutsche Telekom (Germany) acquired One2One (United States, U.S.) with US$13.629 billion in telecommunication industry announced at July 28, 1999; Deutsche Bank (Germany) acquired Bankers Trust New York Corp. (U.S.) with US$ 9.082 billion in banking industry announced at Nov. 30, 1998; Daimler-Benz (Germany) acquired Chrysler (U.S.) with US$40.467 billion in automobile industry announced at May 7, 1998; Texas Utilities Co. (U.S.) acquired Energy Group PLC (United Kingdom, U.K.) with US$10.947 billion in energy industry announced at Mar. 2, 1998.

Research on international M&As, while growing, has not been as voluminous as the large body of research on both domestic M&A and international alliances. The present research makes an attempt to provide a contingent claims model to quantify the purely financial synergy of a cross-border M&A and provide the optimal stock for stock exchange ratio. The model first constructs the optimal capital structures of the acquiring firm, target firm and merger firm, where the interest rate risks of the acquiring and acquired firm and foreign exchange risk are taken into consideration. Based on the model, we provide the closed-form formulas of the pure financial synergy and optimal stock exchange ratio for a cross-border M&A. The numerical examples show that the cross-border M&A of two symmetric firms would result in a positive financial synergy, whereas that of two asymmetric firms may lead to a negative financial synergy.

2 Model Description

In our model, cross-border M&As are particularly concerned with exchange rate risk, and the present research, therefore, constructs an international dynamic model which takes five kinds of risk factors into consideration, including the risks of unlevered asset values of both acquiring and target firms, the interest rate risks faced by both acquiring and target firms, and the exchange rate risk of acquiring firms. Without loss of generality, the model is initially built in a domestic and foreign risk-neutral framework, while the risk-neutral assumption is not necessary.1 The assumptions of the model are summarized and explained in the following.

Assumption 1 The dynamics of the unleveraged asset value of the domestic acquiring

firm under domestic risk neutrality are given as: ( ) ( ) ( ) ( ) d d Q d d V V d dV t r t dt dW t V t = +σ , given Vd(0)≡Vd (1) where r t is the instantaneous domestic risk-free short rate, _d( ) σ_Vd is the constant volatility of the rate of return of the unlevered asset of the domestic firm, and

d

Q V

W is a Wiener process under domestic risk-neutral filtered probability space.

Assumption 2 The dynamics of the price of the domestic zero-coupon bond matured

at T under domestic risk neutrality are given as: ( , ) ( ) ( ) ( , ) d d Q d d B B d dB t T r t dt dW t B t T = +σ , given Bd(0, )T (2)

where σ_Bd is the constant volatility of the rate of return of the domestic zero-coupon bond, and Q_d

B

W is another Wiener process under domestic risk-neutral filtered probability space.

Assumption 3 The dynamics of the exchange rate (in units of foreign currency) under domestic risk neutrality are given as:

(

)

( ) ( ) ( ) ( ) ( ) Q d f X X dX t r t r t dt dW t X t = − +σ , given X(0)≡X (3) where r t is the instantaneous foreign risk-free short rate, _f( ) σ_X is the constant volatility of the rate of return of the exchange rate, and Q

X

W is another Wiener process under domestic risk-neutral filtered probability space.

Assumption 4 The dynamics of the unleveraged asset value of the foreign target firm under foreign risk-neutrality are given as follows:

( ) ( ) ( ) ( ) f f f Q f f V V f dV t r t dt dW t V t = +σ , given Vf(0)≡Vf (4) where f V

σ is the constant volatility of the rate of return of the unleveraged asset of the foreign firm, and f

f

Q V

W is a Wiener process under foreign risk-neutral filtered probability space.

Assumption 5 The dynamics of the price of the foreign zero-coupon bond matured at T under foreign risk neutrality are given as:

( , ) ( ) ( ) ( , ) f f f Q f f B B f dB t T r t dt dW t B t T = +σ , given Bf(0, )T (5) where f B

σ is the constant volatility of the rate of return of the foreign zero-coupon bond matured at T, and f

f

Q B

W is another Wiener process under foreign risk-neutral filtered probability space.2

According to Assumptions 1-5, there are totally five kinds of risk factors in our framework, and the risk factors are mutually correlated. The instantaneous correlation coefficients are assumed to be constant, and are defined in the following: ρ_ijdt=

Q E Q( ) Q( ) i j dW t dW t ⎡ ⎤ ⎣ ⎦ where ,i j V B X V= d, d, , f andBf .

Assumption 6 Assume there would be zero operating synergy, i.e., V t_m( )= ( ) ( ) ( )

d f

V t +V t X t , for all t≥0, where V is the unlevered asset value of the merger _m firm in units of domestic currency, and the initial time zero denotes the time that the merger is determined.

2 _{Note that the maturity of the bond could be various. For notational simplicity, we here assume all the}

Assumption 7 We assume the dynamics of the unleveraged asset value of the acquiring firm under domestic risk-neutrality are as follows:

(

( ) ( )

)

( ) ( ) ( ) ( ) ( ) ( ) f m d d f m d f d V t X t dV t dV t w w V t = V t + V t X t , given Vm(0)≡Vm=Vd +V Xf , (6) where d d m V w V = and f f m V X w V

= are two known constants.

From Assumptions 1, 3, 4 and 7, we can rewrite Equation (6) as ( ) ( ) ( ) ( ) m m Q m d V V m dV t r t dt dW t V t = +σ , (7) where

(

)

(

)

(

)

2 2 2 2 2 2 d f d f d f m d d f f d V f V f X d V f V V V V d V f X V X f V f X V X w w w w w w w w w σ σ σ σ σ ρ σ σ σ ρ σ σ ρ + + + = + + .

Assumption 8 Assume both the domestic and foreign firms have a debt/liability, respectively, with principal value P , discrete constant coupon flows _{i ,}

j

i t

C , and maturity T , where _i i d f= , and j=1,...,n_i . Acquisitions by merger result in combinations of the assets and liabilities of acquired and acquiring firms.

3 Model Derivation

3.1 Preliminary Development

Before we present the model, some preliminary results are provided. First, define the first passage time B inf 0

{

: ( ) ( , ) B

}

i t T V ti i B t T Vi i

τ ≡ < ≤ ≤ , where i d f= , , andm, and

B i

V is a constant. In other words, B i

τ is the first time where the unlevered asset value ( )V t goes down and touches stochastic default barrier _i ( , ) B

i i

B t T V , that is, B i

τ

is the stochastic time that the firm i decide to announce bankruptcy. Equivalently,

B i

τ could be viewed as the first time that the forward unlevered asset value ( , ) ( , )

i i

V t T B t T hits B i

V .

Lemma 1 Using B t T_d( , ) or

(

B t T as the numeraire, all the forward asset _f( , )

)

values in units of domestic (foreign) currency would be martingale processes under domestic (foreign) forward risk-neutral probability measure.

Corollary 1 According to assumptions 1-7 and Lemma 1, together with Ito sˆ '

Lemma, the processes that we need to derive the formulas are summarized in the following.

(

)

2 ln ( ) ( , ) 0.5 d ( ) d d d d d d B d d V B V B V B d V t B t T = − σ dt+σ dW t , (8)

(

)

2 ln ( ) ( , ) 0.5 f ( ) f f f f f f B f f V B V B V B d V t B t T = − σ dt+σ dW t , (9)

(

)

2 ln ( ) ( , ) 0.5 d ( ) m d m d m d B m d V B V B V B d V t B t T = − σ dt+σ dW t , and (10)

(

)

(

2

)

ln ( ) ( , ) 0.5 f ( ) m d m d m d m d B m d V B V B V B V B d V t B t T = µ − σ dt+σ dW t . (11) where 2 2 ₂ d d d d d d d d V B V B V B V B σ = σ +σ − σ σ ρ , 2 2 ₂ f f f f f f f f V B V B V B V B σ = σ +σ − σ σ ρ ,

(

)

2 2 ₂ m d m d d d d d f f d d V B V B B wd V V B wf V V B wf X XB σ = σ +σ − σ σ ρ + σ ρ + σ ρ , and

(

)

(

)

(

)

(1 ) (1 ) (1 ) . m d d d f f f f f d d f f f f f f d d d d f f d d f d f V B X d V V X f V V X f X B XB B d V V B f V V B f X XB B B d V V B f V V B f X XB B B B w w w w w w w w w µ σ σ ρ σ ρ σ σ ρ σ σ ρ σ ρ σ ρ σ σ σ ρ σ ρ σ ρ σ ρ = + − − − + + − − − − + − − −

In our framework, the distributions of the first passage time B i

τ under domestic and foreign forward martingale measure are quiet essential. The distribution of the stopping time of a standard Brownian motion with drift and diffusion could be found in Harrison (1985), and we summarize the result in the following.

Lemma 2 Let dln ( )B t =adt bdB t+ ( ) and τ =inf

(

t>0 : ( )B t ≤c

)

, where a, b

and c are three positive constants, and B is a standard Brownian motion, and then

(

)

(

)

(

)

2

(

)

2 ln (0) ₍₀₎ ln (0) ; , , Pr a b B c at _B B c at F t a b c t N N c b t b t τ − ⎛ + ⎞ _{⎛ ⎞} ⎛− + ⎞ ⎜ ⎟ ⎜ ⎟ ≡ > = _{− ⎜ ⎟} ⎜ ⎟ _{⎝ ⎠} ⎜ ⎟ ⎝ ⎠ ⎝ ⎠  _  , where N( )⋅ is the cumulative normal distribution.

Corollary 2 By Corollary 1 and Lemma 2, the distributions of the first-passage times B inf 0

(

: ( ) ( , ) B

)

d t T V t B t Td d d Vd τ = < ≤ ≤ , B inf 0

(

: ( ) ( , ) f t T V t B t Tf f f τ = < ≤ ≤

)

B f V , B inf 0

(

: ( ) ( , ) B

)

m t T V t B t Td m d Vm τ = < ≤ ≤ , B inf 0

(

: ( ) ( , ) m t T V t B t Td m d τ = < ≤ ≤

)

B m

V with respect to the processes of Equations (8)-(11) can be derived.

Due to stochastic interest rates, the risk-neutral pricing method is changed to the forward risk neutral pricing method. The pricing methodology is summarized in the following.

Lemma 3 Any domestic (foreign) contingent claim Y (d Y ) under stochastic interest f

rates can be priced by changes of probability measure as below.3

[

]

0 (0) E exp ( ) ( ) (0, )E d ( ) T B Q d d d d Y = ⎡⎢ ⎛⎜− r s ds Y T⎞⎟ ⎤⎥=B T Y T ⎢ ⎝ ⎠ ⎥ ⎣

∫

⎦ , and 0 (0) E exp ( ) ( ) (0, )E ( ) (0, )E ( ) ( ) . f f d T Q B f f f f f B d f XY X r s ds Y T XB T Y T B T X T Y T ⎡ ⎛ ⎞ ⎤ ⎡ ⎤ = _{⎢ ⎜}− _{⎟ ⎥}= _{⎣ ⎦} ⎢ ⎝ ⎠ ⎥ ⎣ ⎦ ⎡ ⎤ = _{⎣ ⎦}

∫

3.2 Optimal Capital Structure Model

To derive the optimal capital structures for the domestic acquiring firm, foreign target firm, and the merger firm, we firstly price their outstanding debts. For domestic acquiring firm, by Lemma 3, the forward risk neutral pricing method, we can derive the capital structure of the acquiring firm as below.

Proposition 1 The debt value, total firm value and equity value of the domestic firm are given as:

( )

(

)

(

)

(

)

2 , , 1 2 , (0, ) (1 ) ; 0.5 , , (0, ) ; 0.5 , , (0, )(1 ) ; d d d d d d d d d n B B B d d d d d d d d V B V B d d d i d i i B B d i V B V B d d d d d D V B T P V F T V B t C F t V B T V α σ σ σ σ α = = − − ⋅ − + − + −

∑

( )

(

)

(

)

(

)

2 , , , 1 2 (0, ) ; 0.5 , , (0, ) 1 ; 0.5 , , ; d d d d d d d d d n B B d d d d d i d d i d i V B V B d i B B d d d d d V B V B d v V V B t C F t V B T V F T V δ σ σ α σ σ = = + ⋅ − − ⋅ − −

∑

( )

B

( )

B

( )

B d d d d d d

E V =v V −D V , where δ_d is the domestic corporate tax rate Proof By Corollary 1 and Lemma 2.

By the same token, the debt value, total firm value, and equity value of the foreign target firm, in units of foreign currency, can be expressed as follows.

Proposition 2 The debt value, total firm value and equity value of the foreign target firm are given as:

( )

(

)

(

)

(

)

2 , , 1 2 , (0, ) (1 ) ; 0.5 , , (0, ) ; 0.5 , , (0, )(1 ) ; f f f f f f f f f n B B B f f f f f f f f V B V B f f f i f i i B B f i V B V B f f f f f D V B T P V F T V B t C F t V B T V α σ σ σ σ α = = − − ⋅ − + − + −

∑

( )

(

)

(

)

(

)

2 , , , 1 2 (0, ) ; 0.5 , , (0, ) 1 ; 0.5 , , ; f f f f f f f f f n B B f f f f f i f f i f i V B V B f i B B f f f f V B V B f v V V B t C F t V B T V F T V δ σ σ α σ σ = = + ⋅ − − ⋅ − −

∑

( )

B

( )

B

( )

B f f f f f f

E V =v V −D V , where δ_f is the foreign corporate tax rate. Proof By Corollary 1 and Lemma 2.

For simplifying the following analysis about the merger firm, without loss the generality, we further assume: 1) T_f <T_d; 2) The proportional bankruptcy of the target firm is also a value-weighted combination of the individual bankruptcy costs, i.e., α_m =w_dα_d +w_fα_f . The explicit formulas of the merger firm’s debt value, total firm value, and equity value are provided in the following.

Proposition 3 The debt value, total firm value and equity value of the merger firm are given as:

( )

(

)

(

)

(

)

(

)

2 2 2 , , 1 (0, ) ; 0.5 , , (0, ) ; 0.5 , , (0, ) ; 0.5 , , m d m d m d m d m d d m d m d B B m m d d d d V B V B m B f f f f V B V B V B m n B d d i d i d V B V B m i D V B T P F T V XB T P F T V B t C F T V σ σ µ σ σ σ σ = = ⋅ − + ⋅ − +

∑

⋅ −

(

)

(

)

(

)

(

)

2 , , , 1 2 (0, ) ; 0.5 , , (0, )(1 ) 1 ; 0.5 , , ; f m d m d m d m d m d n B f f i f i f i V B V B V B m i B B d d m m d V B V B m X B t C F t V B T V F T V µ σ σ α σ σ = + ⋅ − + − − −

∑

( )

(

)

(

)

(

)

(

)

(

)

2 , , 1 2 , , , 1 2 (0, ) ; 0.5 , , (0, ) ; 0.5 , , (0, ) 1 ; 0.5 , , ; d m d m d f m d m d m d m d m d n B B m m m d d i d d i d V B V B m i n B f f i f f i f i V B V B V B m i B B d d m m d V B V B m V V V B t C F T V X B t C F t V B T V F T V δ σ σ δ µ σ σ α σ σ = = = + ⋅ − + ⋅ − − − −

∑

∑

( )

B

( )

B

( )

B . m m m m m m E V =V V −D V

Proof Again by Corollary 1 and Lemma 2.

Until now the bankruptcy triggers of the domestic firm, foreign firm and merger firm are exogenous constant. We are now making an attempt to endogenously determine those bankruptcy strategies, *

d V , * f V and * m V by the following smooth-pasting conditions: B * 0 d d d d d V V V E V _{= =} ∂ ∂ = , B * 0 f f f f _{f V V V} E V = = ∂ ∂ = and * 0 B m m m m m V V V E V _{= =}

∂ ∂ = . The intuition behind these three conditions is that the equityholders of the acquiring firm, target firm, and merger firm, respectively, decide their optimal bankruptcy triggers to maximize the equity value of each firm. Bring these optimal bankruptcy strategies back to the above pricing formulas, the optimal capital structures with respect to the acquiring firm, target firm and merger firm are completely obtained.

3.3 Financial Synergies

Similar to Leland (2005), the purely financial synergy of a cross-border M&A can be evaluated by the following measure.

( )

(

( )

( )

)

( )

( )

* * * * * m m d d f f d d f f v V v V Xv V FS v V Xv V − + = + (12) This measure demonstrates the percentage changes in the total firm values between the merger firm and the sum of the domestic acquiring firm and the foreign target firm. A positive financial synergy implies that merger increases the total firm value, while a negative one implies that the separation increases the value.

3.4 Optimal Stock Exchange Ratio

Based on our contingent claims model, the optimal stock exchange ratio can be expressed as:

( )

( )

* * , f f f d d d XE V S ER E V S = (13) where S and _f S respectively denote the total outstanding shares of the foreign _d and domestic firms’ equities at the time that the merger is determined.

The exchange ratio of Equation (13) only reveals the financial conditions of the acquiring and target firms, but does not take the financial synergy of the merger into

consideration. To address this problem, we provide the modified optimal exchange ratio in the following:

( )

(

( )

( )

)

( )

( )

* * * * * 1 m m d d f f . d d f f E V E V XE V OER ER E V XE V ⎛ _{− +} ⎞ ⎜ ⎟ = + ⎜ + ⎟ ⎝ ⎠ (14)

4 Numerical Examples

4.1 Two Symmetric Firms

Consider the two symmetric firms with the following parameters: P_d =100, 25P_f = , 10 d f T =T = , C_{d i,} =6,i=1,...,10 , C_{f i,} =1.5,i=1,...,10 , 150V_d = , 37.5V_f = , 0.3 d f δ =δ = , 0.5α_d =α_f = , 10S_d =S_f = , 0.2 d f V V σ =σ = , X = , 0.24 σ_X = , ,1 (0, ) 0.965, , i i B t = i d f= , B_i(0, ) 0.95,t_i,2 = i d f= , , B_i(0, ) 0.88,t_i,3 = i d f= , , ,4 (0, ) 0.835, , i i B t = i d f= , B_i(0, ) 0.79,t_i,5 = i d f= , , B_i(0, ) 0.745,t_i,6 = i d f= , , ,7 (0, ) 0.705, , i i B t = i d f= , B_i(0, ) 0.67,t_i,8 = i d f= , , B_i(0, ) 0.635,t_i,9 = i d f= , , ,10 (0, ) 0.6, , i i B t = i d f= , 0.2, ,ρ_ij = i j V V X B= _d, _f, , _d, andB_f and d B σ = 0.1 f B σ = .

In this case, the financial synergy is −0.141% and the optimal stock exchange ratio

is 0.8246. This shows that the merger of two symmetric firms under the same

environment may not be financially beneficial.

Table 1

Effects of all correlation coefficients on the financial synergy and optimal stock exchange ratio for a cross-border M&A of two symmetric firms

ρ value −0.75 −0.25 0.25 0.75

(%)

FS OER FS(%) OER FS(%) OER FS(%) OER

d f V V ρ _{-0.132 0.8241 -0.135 0.8243 -0.142 0.8247 -0.154 0.8254} d d V B ρ _{-0.148 0.8206 -0.145 0.8240 -0.140 0.8246 -0.137 0.8245} d V X ρ _{-0.150 0.8260 -0.142 0.8249 -0.141 0.8246 -0.141 0.8246} d f V B ρ _{-0.153 0.8256 -0.146 0.8250 -0.140 0.8246 -0.137 0.8244} f d V B ρ _{-0.152 0.8253 -0.145 0.8249 -0.140 0.8246 -0.137 0.8245} f V X ρ _{-0.150 0.8260 -0.142 0.8249 -0.141 0.8246 -0.141 0.8246} f f V B ρ _{-0.149 0.8273 -0.145 0.8253 -0.140 0.8246 -0.137 0.8244} d XB ρ _{-0.190 0.8282 -0.158 0.8258 -0.140 0.8246 -0.133 0.8242} f XB ρ _{-0.132 0.8241 -0.133 0.8242 -0.142 0.8247 -0.166 0.8269} d f B B ρ _{-0.153 0.8256 -0.146 0.8250 -0.140 0.8246 -0.137 0.8244}

Table 1 shows the effects of all the correlation coefficients on the financial synergy and optimal stock exchange ratio for a cross-border M&A of two symmetric firms. First of all, the effects on the financial synergy are all negative. Among correlation coefficients, only

d f

V V

ρ has a negative impact on the financial synergy, since the lower the

d f

V V

ρ , the greater the diversification effect of the M&A would be. The other correlation coefficients all have a positive effect on the financial synergy. Moreover, ρ_XBd is the most sensitive correlation coefficient, whereas ρ_{V Xd} and

f

V X

ρ are the least sensitive correlation coefficients when the sign is positive. In other words, the correlation between the foreign exchange rate and the domestic interest rate may play an important role for a cross-border M&A of two symmetric firms 4.2 Two Asymmetric Firms

Consider the two asymmetric firms with the following parameters: P_d =80, P_f = , 5 10 d T = , 5T_f = , C_{d i,} =4.8,i=1,...,10 , C_{f i,} =0.4,i=1,...,5 , 120V_d = , 8V_f = , 4 X = , 0.3δ_d =δ_f = , 0.4α_d = , 0.6α_f = , 8S_d = , 2S_f = , 0.4 f V σ = , 0.2 d V σ = , 4 X = , 0.2σ_X = , B_i(0, ) 0.965,t_i,1 = i d f= , , B_i(0, ) 0.95,t_i,2 = i d f= , , ,3 (0, ) 0.88, , i i B t = i d f= , B_i(0, ) 0.835,t_i,4 = i d f= , , B_i(0, ) 0.79,t_i,5 = i d f= , , ,6 (0, ) 0.745 d d B t = , B_d(0,t_d,7) 0.705= , B_d(0,t_d,8) 0.67= , B_d(0,t_d,9) 0.635= , ,10 (0, ) 0.6 d d

B t = , 0.2, ,ρ_ij = i j V V X B= _d, _f, , _d, andB_f and σ_Bd =σ_Bf = 0.1 . The domestic acquiring firm is supposed to acquire a foreign firm with smaller size (P , _f

f

V and S ), higher risky (_f

f

V

σ , C P and_{f f} α_f ) and shorter maturity (T ) , while _f the foreign exchange rate, the term structure of short rates and all the correlation coefficients are remaining the same. For the cross-border M&A of these two asymmetric firms, the financial synergy is 0.012% and the optimal stock exchange ratio is OER=0.9895. This result demonstrates that a cross-border M&A may result in a positive financial synergy when the characteristics of the two firms are different to some extent.

Table 2 shows the effects of all the correlation coefficients on the financial synergy and optimal stock exchange ratio for a cross-border M&A of two asymmetric firms. First of all, the effects on the financial synergy are all beneficial. This is because the debt-coinsurance effect of these two asymmetric firms is notable. ρ_{V Bf f} has a significant negative effect on the financial synergy in this case. Because the unlevered asset’s return volatility of the foreign acquired firm is much higher than that of the domestic acquiring firm, the diversification effect is very sensitive to the correlation coefficient between the foreign acquired firm and the foreign interest rate. In our example,

d f

V V

ρ with positive sign and

d d

V B

ρ with negative sign are negatively and positively correlated to the financial synergy, respectively, while other correlation coefficients play a minor role.

5

Concluding Remarks

This research first utilizes a contingent claims approach to pricing debts and total firm values with consideration of tax benefits and bankruptcy costs, and then derives the optimal capital structures of the acquiring firm, target firm and merger firm. The

interest rate risks of the acquiring and acquired firm and foreign exchange risk are taken into consideration, while optimality is driven by equityholders choosing their bankruptcy strategies to maximize equity values. Moreover, based on the model, the closed-form formulas of the purely financial synergy and the optimal stock for stock exchange ratio are provided. The numerical examples show that the cross-border M&A of two symmetric firms would result in a negative financial synergy, whereas that of two asymmetric firms may lead to a positive financial synergy. The model is capable to analyze a cross-border M&A in practice; however, a lot of parameters which need to be estimated might be a defect.

Table 2

Effects of all correlation coefficients on the financial synergy and optimal stock exchange ratio for a cross-border M&A of two asymmetric firms*

ρ value −0.75 −0.25 0.25 0.75

(%)

FS OER FS(%) OER FS(%) OER FS(%) OER d f V V ρ _{0.013 0.9894 0.013 0.9894 0.012 0.9895 0.007 0.9900} d d V B ρ 0.003 0.9850 0.009 0.9888 0.012 0.9895 0.013 0.9894 d V X ρ 0.013 0.9894 0.012 0.9894 0.012 0.9895 0.011 0.9895 d f V B ρ _{0.011 0.9896 0.012 0.9895 0.012 0.9895 0.012 0.9894} f d V B ρ _{0.007 0.9900 0.010 0.9897 0.012 0.9895 0.013 0.9894} f V X ρ _{0.012 0.9894 0.012 0.9895 0.012 0.9895 0.012 0.9895} f f V B ρ _{0.043 1.0086 0.024 0.9973 0.011 0.9887 0.002 0.9835} d XB ρ 0.009 0.9899 0.011 0.9896 0.012 0.9895 0.012 0.9894 f XB ρ _{0.013 0.9894 0.012 0.9894 0.012 0.9895 0.011 0.9896} d f B B ρ _{0.011 0.9895 0.012 0.9895 0.012 0.9895 0.012 0.9895}

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