Calculation of Exchange Ratio from the
perspective of the acquired and the acquiring firm
Whenever a firm ‘A’
acquires another firm ‘B’, the compensation to the shareholders
of the acquired firm is usually paid in the form of shares
of the acquiring firm. In other words, shares of firm A will
be given in exchange for shares of firm B. Thus, the exchange
ratio is a very important factor in any kind of merger. Firm
A will want to keep this ratio as low as possible, while firm
B will want it to be as high as possible. In any case, both
firms would ensure that post merger, their equivalent price
per share will at least equal their premerger price per share.
Given below is the model developed by Conn and Nielson
for determining the exchange ratio. The symbols used in this
model are: 
ER = Exchange ratio
P = Price per share
EPS = Earning per share
PE = Price earning multiple
E = Earnings
S = Number of outstanding equity shares
AER = Actual exchange ratio
In addition, the acquiring,
acquired and combined firms will be referred to by subscripts
A, B and AB respectively.
Firm A would ensure
that the wealth of its shareholders is preserved. This implies
that the price per share of the combined firm is at least
equal to the price per share of firm A before merger:
P_{AB} >=
P_{A }
For the sake of simplicity
consider that P_{ AB }=P_{ A}
Price earnings ratio
of the combined firm x Earnings per share of the combined
firm gives the Market Price per share.
P_{ AB }=PE_{
AB }x EPS_{ AB }= P_{ A
}
(1)_{ }
Earnings per share of
the combined firm can be expressed as:
EPS_{ AB }=
(E_{ A }+ E_{B }) / [S_{ A
}+ S_{ B }(ER_{ A })]
 (2)
ER_{ A
}= number of shares of firm A given in lieu of
one share of firm B.
Substituting formula
of EPS_{ AB }in equation 1 we get –
P_{ A
}= PE_{ AB} (E_{ A
}+E_{B})/[S_{ A} +S_{ B }(ER)]_{
}
From the above equation,
we may solve for the value of ER_{ A }as follows –
ER_{ A }= (S_{
A} /S_{ B })_{ }+ [(E_{ A }+E_{
B}) PE_{ AB}] / P_{ A} S_{ B }
After discussing the
maximum exchange ratio acceptable to the shareholders of firm
A above, we will now calculate the minimum exchange ratio
acceptable to the firm B(ER_{ B})
The basic condition
is –
P_{ AB} (ER_{
B}) >= P_{ B } 
(3)_{ }
Using the equality form
of above equation and substituting P_{ AB }from equation
1 in equation 3 we get
PE_{ AB} x EPS_{
AB } x ER_{ B} = P_{ B }
Substituting the value
of EPS_{ AB} from equation 2 in the above equation, and solving the equation
for ER_{ B}
we get –
ER_{ B} = P_{
B} S_{ A} / [(PE_{ AB})(E_{ A}
+ E_{ B}) – P_{ B} S_{ B}]
