Tuttle Buildings Inc. has decided to go public by selling $5,000,000 of new common stock. Its investment bankers 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 one year, when the stock price is forecasted to be $6.50 per share. However, there is a chance that the stock price will actually be $12.00 per share one 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.
$1,517,391
To calculate the present value of the entire underwriting compensation, we need to consider the cash flows from the initial offering and the potential cash flows from exercising the option.
Let's break down the calculation into two parts:
1. Initial Offering:
The gross proceeds from the initial offering are $5,000,000. The investment bankers' fee is 6% of the gross proceeds, which amounts to 0.06 * $5,000,000 = $300,000.
To calculate the present value of the fee, we need to discount it at the investment banker's required return of 15%. The present value can be calculated using the formula:
PV = FV / (1 + r)^n
Where:
PV = Present Value
FV = Future Value
r = Required return
n = Number of periods
Using the above formula, we can calculate the present value of the fee:
PV of the fee = $300,000 / (1 + 0.15)^1 = $260,869.57
2. Option Exercise:
The investment bankers have the option to purchase an additional 200,000 shares at $5.00 per share in one year. If the stock price is $12.00 per share, exercising the option would be beneficial. In this case, the investment bankers will purchase the shares for $5.00 per share and immediately sell them at the market price of $12.00 per share, resulting in a profit of $7.00 per share.
The total profit from exercising the option will be 200,000 * $7.00 = $1,400,000.
To calculate the present value of this profit, we also need to discount it at the investment banker's required return of 15%. Using the same formula as above:
PV of the option exercise profit = $1,400,000 / (1 + 0.15)^1 = $1,217,391.30
Finally, to calculate the present value of the entire underwriting compensation, we add the present values of the fee and the option exercise profit:
Present value of the entire underwriting compensation = PV of the fee + PV of the option exercise profit
= $260,869.57 + $1,217,391.30
= $1,478,260.87
Therefore, the present value of the entire underwriting compensation would be $1,478,260.87.