What is a roadshow? What is book-building? What are some of the costs of going p

What is a roadshow? What is book-building?
What are some of the costs of going public? What is leaving money on the table?
A privately held company has an estimated value of equity equal to $100 million. The founders own 10 million shares. If the company goes public and sells 1 million shares with no underwriting costs, how much should the per share offer price be? If instead the underwriting spread is 7%, what should the offer price be?
A company is planning an IPO. Its underwriters have said the stock will sell at $50 per share. The underwriters will charge a 7% spread. How many shares must the company sell to net $93 million, ignoring any other expenses?