Firm X has $100$ shares outstanding at $$20$ per share. Firm Y also has $100$ shares outstanding with a current price of $$5$ per share. Firm X offers Y$$s shareholders $$8$ per share in cash. Firm X$$s management expects the combined value of the firm to be $$3,000.$ The expected gain and the NPV of the merger to X are, respectively, closest to:

$$500$ and $$200$

Using this information, suppose Firm X makes a stock offer for Y$$s outstanding shares. The share price after the merger is closest to:

$($Here$,$ the acquisition price is $$800.$ Firm X$$s stock price is assumed to be $$20$ which is used for acquisition$)$

a$)$ $$17\mathrm{.}86$

b$)$ $$20\mathrm{.}00$

c$)$ $$21\mathrm{.}43$

d$)$ $$30\mathrm{.}00$