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 million new ordinary shares for sale in the IPO. The underwriter handling Reardens initial offering expects to sell these new shares for $20 each. BBC Ventures has chosen to sell its ordinary shares alongside the newly created shares in Reardens IPO. The underwriter will charge a 7% underwriting spread, so both Rearden and BBC Ventures will receive 93% of the $20-per-share offer price. 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? What is the firms 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)?