Sophia Co., is about to go public. Its pre-IPO equity accounts (Total of 150,000) are as follows:

• Common shares (1,500 shares outstanding) 100,000
• Retained earnings 50,000

Ikotun will issue 500 new common shares, each with a face value of $1 and an issuing price of

$150. Assume no issuance costs. On the first day of trading the price closed at $165.

1. Calculate the under-pricing of this IPO

2. Whats the book equity per share after the IPO?

3. The underwriters agree to provide their services and receive a gross spread of 100 basis points, calculated as a percentage of IPO price. How much cash did Sophia Co receive from their IPO?

4. The lead underwriter has a greenshoe option to issue an additional 10% of shares during the month following the IPO. The lead underwriter exercises the greenshoe option when the stock price climbs to $180 twenty days after the IPO. Whats the new ratio of price to book equity (per share)? (Assume no issuance costs.)

5. Back to settings in (A) where Sophia Co. issues 500 new shares only and there is no greenshoe option. Sophia Co. has a strong stock performance since IPO. Two years after its IPO, the stock price reaches $250. At that moment, the management is considering a rights offering to raise an additional $200,000 for a significant expansion. The subscription price for each new share is $100. Figure out the terms for the right offering:
   1. How many rights are needed for a share and

2. Whats the value for a right?

6. Firas, a shareholder of Sophia Co., has 100 shares and no desire (or money) to buy additional shares. Show that -in theory- Firas is not harmed by the rights offering (compare the value of Firas shareholdings with and with right exercising)