Facebook $($Acquirer$)$ has current value of $$1000$ and seeks to acquire Messenger $($Target$)$ with a current market value of $$500.$ The financial manager at Facebook believes that the two firms combined would be valued at $$1,800.$

a$.$ Calculate the gain $($synergy$)$ to the merger.

b$.$ Calculate the NPV of the merger if Facebook offers $$550$ for Messenger.

c$.$ Discuss the distribution of gains if Messenger will only accept an offer of $$850.$