Alpha Inc has earnings per share of $$2$ and $10$ million outstanding shares trading at $$20$ each. It is considering the acquisition of Gamma Plc$.$ Gamma Plc$,$ on the other hand, has earnings per share of $$1\mathrm{.}25$ with $4$ million shares outstanding, each traded at $$15.$ To acquire Gamma Plc$,$ Alpha Inc plans to issue new shares, all without anticipating any synergies resulting from the transaction.

a$.$ If Alpha acquires Gamma without paying any premium, what will be the earnings per share following the merger?

b$.$ If Alpha proposes an exchange ratio resulting in a $20\%$ premium based on the current pre$-$announcement share prices of both firms to acquire Gamma, calculate the per$-$share price of the combined company post$-$merger.

c$.$ If Alpha proposes an exchange ratio such that, at the current pre$-$announcement share prices of both firms, the offer indicates a $20\%$ premium to acquire Gamma, determine the exact premium that Alpha pays for the transaction.

d$.$ Discuss some of the uncertainties in merger analysis. How can real option analysis be employed in valuing a merger?