Stock offer vs. cash offer


So today, I came across a problem regarding cas vs. stock offer on a merger of two companies.

Pre merger value of the acquier: 132 million

cash paid for the target: 90 million

post merger value of the combined entity via cash buyout: 135 million

pot merger value of the combined entity via stock buyout (shares issued to target shareholders): 132 + 90 + 3 (synergy value)

Not exactly sure why the value of the combined entity would be different under the stock buyout (225 million) vs. the cash buyout?

Is it because we are issuing shares under the stock buyout (therefore, “expanding” the size of the firm) whereas under a cash buyout, we are simply exchanging the assets of the target entity for cash from the target shareholder (thus no “expansion” of the firm occurs)?


Something like this, which has obviously results in different numbers for post merger value.

Cash buyout: (Value of Acquirer+ Value of Target + Value Synergies - Cash of Acquirer) / # of shares of Acquirer

Stock Buyout: (Value of Acquirer + Value of Target + Value of Synergies) / (# of shares of Acquirer + #of new shares)