Merger: Acquirer's Gain and Share Price of the combined company

Table

Company	A (acquirer)	T (target)	AT (merged company)
Number of shares	117.6 (millions)	213.1 (millions)
Stock price per share	$68	$35

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(Question 1)
Cash is paid to acquire the target company's shares.

Assuming that the estimate of the value of the merged companies is correct, calculate the acquirer's gain from the merger. Cash paid to the target company is $45 (given) * 213.1 (million) = 9,589.5 (million).


V_AT = $17,500 (millions) (given)

V_AT = V_A + V_T + S - C

where:
V_AT = the combined value of the firm
V_A = the value of the acquirer before the merger
V_T = the value of the target before the merger
S = the synergistic value from the merger
C = the cash paid to the target

Acquirer's gain = S - (P_T - V_T)

where:
S = the synergistic value from the merger
P_T = the price paid for the target; P_T = C, if only cash is paid to acquire the company.
V_T = the value of the target before the merger

S = V_AT - V_A - V_T + C = $17,500 - 117.6 * $68 - 213.1 * $35 + $9,589.5 = 11,634.2

Acquirer's gain
= S - (P_T - V_T)
= V_AT - V_A - V_T + C - (C - V_T)
= V_AT - V_A
= $17,500 - 117.6 * $68 = $9,503.2 million

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(Question 2)
The acquirer's stock is offered to acquire the target company's shares.
Assume that the acquirer A offers 63 million shares of its stock, rather than cash, to acquire the target company T. The price of the combined company is:

Total AT shares = 117.6 + 63 = 180.6 million

S = 11,634.2 (given; derived in Question 1)

V_AT = V_A + V_T + S - C = 117.6 * $68 + 213.1 * $35 + $11,634.2 - 0 = $27,089.5 million
Share price_AT  = V_AT / Total AT shares = 27,089.5/180.6 = $149.9972