Question

Omega Airline's capital structure consists of 3.1 million shares of common stock and zero coupon bonds with a face value of $18.6 million that mature in six months. The firm just announced that it will issue warrants with an exercise price of $85.30 and six months until expiration to raise the funds to pay off its maturing debt. Each warrant can be exercised only at expiration and gives its owner the right to buy a single newly issued share of common stock. The firm will place the proceeds from the warrant issue immediately into Treasury bills. The market value balance sheet shows that the firm will have assets worth $250.1 million after the announcement. The company does not pay dividends. The standard deviation of the returns on the firm's assets is 50 percent, and Treasury bills with a six-month maturity yield 6.6 percent. How many warrants must the company issue today to be able to use the proceeds from the sale to pay off the firm's debt obligation in six months? (Do not round intermediate calculations and round your answer to the nearest whole number, e.g., 32.)

Answer 1

Omega Airline must issue approximately 225,214 warrants to pay off its $18.6 million debt in six months, calculated by determining the future value of the debt and dividing it by the exercise price of the warrants.

Step-by-step explanation:

The student's question asks how many warrants Omega Airline must issue to be able to use the proceeds from the sale to pay off its maturing debt obligation of $18.6 million in six months. To calculate this, we need to determine the amount each warrant will raise, which involves knowing the exercise price and the future value of the money raised:

First, we calculate the future value of the debt using the formula FV = PV * (1 + r)^n, where FV is the future value, PV is the present value (debt amount), r is the interest rate per period, and n is the number of periods.

Since the Treasury bills have a six-month maturity with a yield of 6.6%, the semiannual rate (r) is 6.6% / 2 = 3.3%. The number of periods (n) is 1 because we have only one six-month period. So, FV = $18.6 million * (1 + 0.033) = $18.6 million * 1.033 ≈ $19.2138 million.

Now, divide $19.2138 million by the exercise price of the warrant, $85.30, to find the number of warrants needed:
$19.2138 million / $85.30 per warrant ≈ 225,214 warrants.

Therefore, Omega Airline must issue approximately 225,214 warrants to be able to pay off the $18.6 million debt in six months.