Z&B Paints. future growth. IPO Question

Z&B Paints, Inc., is going public next month to raise the funds needed to finance the company's future growth. The company estimates that it needs $45 million to support its expected growth. The underwriting fees charged by the selected investment banking firm are based on the schedule provided in the following table: Bonds Straight Convertible Equity Seasoned Issues 13.30% Issue Size ($ million) Under 10.0 IPOS 8.80% 17.00% 4.40% 2.80% 10.0 -19.9 8.70% 8.70% 11.60% 20.0 - 39.9 2.40% 6.10% 6.90% 9.70% 40.0-59.9 1.30% 4.30% 5.90% 8.70% 8.20% 60.0 - 79.9 2.30% 3.20% 3.00% 5.20% 4.70% 80.0-99.9 2.20% 7.90% 100.0 - 199.9 2.30% 2.80% 4.20% 7.10% 200.0 - 499.9 2.20% 2.20% 6.50% 3.50% 3.20% 500 and larger 1.60% 2.10% 5.70% In addition, it is estimated that Z&B Paints, Inc. will incur $350,000 in other expenses related to the IPO. If Z&B Paints, Inc.'s stock can be sold for $30.40 per share, how many shares must be issued to net the company the $45 million needed? Show your work