Question

A company is planning to borrow $120 million after three months for a period of six months. The quote for the loan is LIBOR. The loan rate, LIBOR, will be determined at the start of loan and stay the same for its duration. Currently LIBOR is 3%. The company is willing to pay 3.25% fixed interest on the loan to avoid variable interest.

Part a. Construct a Forward Rate Agreement (FRA) for the company.

Part b. Should the company buy or sell the FRA?

Part c. Show the cash flows at the beginning of the loan for cases if LIBOR equals 2.5%, 3.25%, and 3.75%.

Answer 1

a. The company will enter into 3*9 FRA where the company will borrow 120 million for period of six months @ 3.25%.

If the LIBOR int rate goes above 3.25% the company shall receive teh difference and if the interest rate is below the fixed rate the company shall pay the difference amount.

b. The company is a borrower and afraid of interest rate rising hence company will buy the FRA.

c. The cashflows will be present value of the difference at the starting of the loan. The discounting rate shall be the libor rate after 3 months.

If LIBOR = 2.5%

THE Company shall lose . Loss to the company = ( 3.5 - 2.5)% * 120 * 6/12 = 0.6 million

cash outflow at the start of loan = 600000 / ( 1 + 0.025/2) = 592593

If LIBOR = 3.25%

The Company shall lose . Loss to the company = ( 3.5 - 3.25)% * 120 * 6/12 = 0.18 million

cash outflow at the start of loan = 180000 / ( 1 + 0.0325/2) = 177122

If LIBOR = 3.75%

The comoany shall gain . Gain to the company =( 3.75-3.5)%*120 *6/12 = 0.18 million

cash inflow at the start of the loan = 180000 / ( 1 + 0.0375/2) = 176687