In an interest rate swap offered by a bank, Company A could pay 3.5% per annum and receive six-month LIBOR in return on a notional principal of $100 million with payments being exchanged every six months. The swap has a remaining life of 16 months. Six-month forward LIBOR for all maturities is currently 3.8% per annum. The six-month LIBOR rate two month ago was 3.2% per annum. OIS rates for all maturities are currently 3.0% with continuous compounding. All other rates are compounded semiannually.

1. Besides being able to choose a swap that pays a fixed rate of 3.5%, Company A could choose a swap that pays a floating rate of six-month Libor0.1% for business with the bank. The correspond choices for Company B are 4.6% and six-month Libor + 0.5%, respectively. Explain how could Company A get a more favorable interest rate swap than the one the bank offers.