### What is the fraction of ownership does the firm need to sell

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Question - Through IPO, an investment bank is helping a manufacturing firm to issue new equity to finance the firm's \$120 million investment project that has a present value of \$165 million. The firm has a debt of \$45.1 million in place. The firm's average annual earnings has been \$12.8 million, and EBITDA \$17 million. P/E and V/EBITDA ratios of similar firms without debt are 14 and 11.3, respectively.

a) If the issuing firm wants to increase its old shareholders wealth by a minimum of 20% with the issuance and investment, what is the maximum issuance costs (IC) the investment bank can charge?

b) Given the IC calculated above, what is the fraction of ownership does the firm need to sell to the new investors?

c) If the target share price after the issuance is \$22.60, how many shares need to be sold to the new investors?

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