The venture capital fund, BBC Ventures, made a $5 million investment in Rearden Company 10 years ago and, in return, received 2 million shares of Series A convertible preferred shares. Each of these shares is convertible into 4 Rearden ordinary shares. Five years later, BBC Ventures participated in a second round of financing for Rearden and received 3 million shares of Series B convertible preferred shares in exchange for a $50 million investment. Each Series B share is convertible into 2 Rearden ordinary shares.

Rearden is now planning an IPO, but it must convert all its outstanding convertible preferred shares into ordinary shares before the offering. After conversion, Rearden will have 40 million ordinary shares outstanding and will create another 5 millionnewordinary shares for sale in the IPO. The underwriter handling Rearden's initial offering expects to sell these new shares for $20 each. BBC Ventures has chosen to exercise its demand registration rights and will sell its ordinary shares - alongside the newly created shares - in Rearden's IPO. The underwriter will keep 7% of the offer as an underwriting spread. Assume that the IPO is successful and that Rearden shares sell for $35 each immediately after the offering.

1. Calculate the compound annual return that BBC Ventures earned on its original and subsequent investments in Rearden shares.
2. What is the amount that Rearden raised during the IPO, net of underwriting fees? What is the firm's market value after IPO?
3. Assume that the post-IPO value of Rearden is its fair market value. Suppose Rearden could have issued shares directly to investors at their fair market value, in a perfect market with no underwriting spread and no underpricing. What would the share price have been in this case if Rearden raises the same amount as in part (b)?