The NPV of a MergerNPV of merger to acquirer = Synergy Premium Synergy = VAB (VA + VB)Premium = Price paid for B VBNPV of merger to acquirer = VAB VA Price paid for B

NPV of a Merger An ExampleFirm A value= $ 500 Firm B value= $ 100 Both firms all equityFirm A acquires Firm B for $150 in cash Firm AB has a value = $700 due to synergies of $100.Firm A uses its RE for the acquisition

Example Cash AcquisitionNPV of a merger to acquirer = Synergy PremiumNPV of merger to firm A = $700 - $150 - $500 = $50Value of Firm A after cash acquisitionV(A) =V(AB) - Cash V(A) =$700 - $150V(A) =$550

Example Cash AcquisitionBefore acquisition After acquisitionFirm AFirm BFirm AMarket Values$500 $100 $550 Shares25 10 25Price $20 $10 $22

NPV of a Merger: Common StockValue of Target firm post merger =a x New Firm value

a = New Shares IssuedOld Shares + New Shares Issued

Example : Stock SwapValue of firm a after common stock acquisitionVA = VAB$700 = $700Determining the Exchange Ratio for an offer of $150 $ 150 =aX700a=21.43%a= New shares 25 + New sharesNew shares=6.819 sharesExchange Ratio = 0.6819:1

Common Stock Swap before acquisitionafter acquisitionFirm AFirm AFirm B0.6819:1Market Values$500$100 $700Shares251031.819Price2010 $22

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