Consider a 10 year FRN trading at a price of 95 that pays a Libor + 200bps twice per year. Assume the forward curve is composed as follows:
Time Semi-annually compounded per annum rates (APR)
6mo spot rate 0.5%
6mo rate – 6 mos forward 0.5%
6mo rate – 1 yr forward 1.0%
6mo rate – 1.5 yrs forward 1.0%
6mo rate – 2 yrs forward 1.0%
6mo rate – 2.5 yrs forward 1.0%
6mo rate – 3 yrs forward 2.0%
6mo rate – 3.5 yrs forward 2.0%
6mo rate – 4 yrs forward 2.0%
6mo rate – 4.5 yrs forward 2.0%
6mo rate – 5 yrs forward 3.0%
6mo rate – 5.5 yrs forward 3.0%
6mo rate – 6 yrs forward 3.0%
6mo rate – 6.5 yrs forward 3.0%
6mo fate – 7 yrs forward 4.0%
6mo fate – 7.5 yrs forward 4.0%
6mo fate – 8 yrs forward 4.0%
6mo fate – 8.5 yrs forward 4.0%
6mo fate – 9 yrs forward 4.0%
6mo fate – 9.5 yrs forward 4.0%
a. Using this forward curve, what is the present value today of $1,000 received at the end of year 10? What is the semi-annually compounded spot rate to year 10?
b. Use this forward curve as the Libor reference rate to calculate the discount margin of this FRN.
c. What new price on this FRN would cause the discount margin to increase by 1bp (assume the forward curve remains constant)?