Evaluating a merger bid

Hi guys, i´m new here, but hopefully someone can help me with clarification of some basic stuff regarding evaluation of merger bid. In the study session 32 they state, that the post value of the company is defined as the sum of market cap of two companies (acquirer and the target) plus any synergy effect adjusted to the price paid for the target if it´s cash payment. The problem that i have with this is, it´s stated that the synergy value is the NPV of any cost reduction or whatever strategies. And from this NPV of synergy effects they subtract the cash paid to the target. I´m asking myself if the synergy value in the equation is the NPV, then its equals the PV of all the future benifits due to merger net of initial cost, but at the same time the initial cost of the investment is the price paid to target´s shareholder. It seems to me in this given equation that they doublecount some portion of initial investment. To make it more clear:

S= PV of future benefits (due to merger)- Price paid to target´s shareholders (initial investment, in this case ©)

Value of combined companies (post-merger) = V(A)+V(T)+S-C,

since C>V(T)= Gain to target´s shareholders, then the value of combined companies must equal = V(A)+S

I would be very thankful if somebody can help me with this.

Kind regards

The name NPV is confusing though. But my understanding is the value of synergies is independent whether it is cash, stock or mixed offer.

The acquirer pays a control premium C-V(T). You must deduct the control premium also from the combined company value. So your equation should be V(A) + S - control premium.

I think you are double counting. Haven’t looked at this material for a while but I can’t see why you would subtract the costs twice.

If you just think about it conceptually, the two companies post-merger must be worth their pre merger value, plus any extra value as a result of the merger (synergies), minus the merger costs.