Chapter 12 Questions and problems 6, 7, 10, 11, 12

6. Suppose you are long a 90-day LIBOR-based FRA (receive floating) with notional amount of $50,000,000. At expiration, LIBOR is 4 percent and the strike rate (the agreed-upon rate) is 3 percent. Assuming a 360-day year, what is the dollar profit or loss on this FRA? How would your answer change if you were short (receive fixed)?

7. Suppose you are long a 180-day LIBOR-based FRA (receive floating) with notional amount of $50,000,000. At expiration, LIBOR is 4 percent and the strike rate (the agreed-upon rate) is 3 percent. Assuming a 360-day year, what is the dollar profit or loss on this FRA? How would your answer change if you were short (receive fixed)? Is your answer to this question twice the amount of the previous question? Why or why not?

10. The following term structure of LIBOR is given.

Term Rate

90 days 6.00%

180 days 6.20%

270 days 6.30%

360 days 6.35%

a. Find the rate on a new 6 9 FRA.

b. Consider an FRA that was established previously at a rate of 5.2 percent with a notional amount of $30 million. The FRA expires in 180 days, and the underlying is 180-day LIBOR. Find the value of the FRA from the perspective of the party paying fixed and receiving floating as of the point in time at which this term structure applies.

11. You are the treasurer of a firm that will need to borrow $10 million at LIBOR plus 2.5 points in 45 days. The loan will have a maturity of 180 days, at which time all the interest and principal will be repaid. The interest will be determined by LIBOR on the day the loan is taken out. To hedge the uncertainty of this future rate, you purchase a call on LIBOR with a strike of 9 percent for a premium of $32,000. Determine the amount you will pay back and the annualized cost of borrowing for LIBORs of 6 percent and 12 percent. Assume the payoff is based on 180 days and a 360-day year. The current LIBOR is 9 percent.

12. A large, multinational bank has committed to lend a firm $25 million in 30 days at LIBOR plus 100 bps. The loan will have a maturity of 90 days, at which time the principal and all interest will be repaid. The bank is concerned about falling interest rates and decides to buy a put on LIBOR with a strike of 9.5 percent and a premium of $60,000. Determine the annualized loan rate for LIBORs of 6.5 percent and 12.5 percent. Assume the payoff is based on 90 days and a 360-day year. The current LIBOR is 9.5 percent.