Synergistic Value and Acquirer's Gain

Synergistic value
V_AT = V_A + V_T + S - C

Also V_AT - V_A = S - C + V_T

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
Acquirer's gain = S - (P_T - V_T)
= S - C + V_T
= V_AT - V_A

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