Question $2(20$ Points$)$:

Suppose that Mars, a large private company, is planning to do an IPO. The company currently has $40$ million shares outstanding, and with the help of its lead underwriter, Morgan Stanley, Mars has decided to issue $5$ million shares priced at $$30$ each. In addition, the company has agreed to a typical overallotment provision of $15\%$ and an underwriting fee of $7\%.($Overallotment means that the underwriter has the option to sell more shares than initially planned if demand is higher than expected$)$

a$)$ Assuming Morgan Stanley decides to exercise the over$-$allotment provision, how much capital will be raised from investors during the IPO?

b$)$ How much will capital will Mars receive from the IPO?

c$)$ If the company's stock price rises to $$35$ after the IPO, how much value is lost by Mars' existing shareholders because of underpricing?

d$)$ What is the total cost of the IPO for Mars?