Tuttle Buildings Inc.has decided to go public by selling $5,000,000 of new common stock.The firm's investment bankers (underwriters) agreed to take a smaller fee now (6% of gross proceeds,versus their normal 10%) in exchange for a 1-year option to purchase an additional 200,000 shares at $5.00 per share.The investment bankers expect to exercise the option and purchase the 200,000 shares in exactly 1 year,when the stock price is forcasted to be $6.50 per share.However,there is a chance that the stock price will actually be $12.00 per share 1 year from now.If the $12 price occurs,what would the present value of the entire underwriting compensation be? Assume that the investment banker's required return on such arrangements is 15%,and ignore taxes.

Question

Quizplus · Accepted Answer

The present value of the entire underwriting compensation includes the initial fee and the value from exercising the option if the stock price is $12.00. The initial fee is 6% of $5,000,000, which is $300,000. The gain from exercising the option at $12.00 instead of $5.00 is $7.00 per share for 200,000 shares, totaling $1,400,000. The present value of this future gain, discounted at 15% for one year, is $1,217,391 ($1,400,000 / 1.15). Adding the initial fee of $300,000 to this discounted gain gives a total of $1,517,391.