Question

A floating-rate note has par value of $100, matures in 5 years, pays interest semi-annually based on 3-month LIBOR + 50 bps and has a discount margin of 200 bps (2%). Assume that today 3-month LIBOR is 8%. What is the price of the floating-rate note today?

Answer 1

Index rate = 8%; quoted margin = 0.5%; discount margin = 2%

Semi-annual coupon = (index rate + quoted margin)*par value/2 = (8%+0.5%)*100/2 = 4.25

Number of payments left = 5*2 = 10

Required semi-annual yield = (index + discount margin)/2 = (8%+2%)/2 = 5%

PV of coupons (using annuity formula) = 4.25*(1-(1+5%)^-10)/5% = 32.82

PV of par value at maturity = 100/(1+5%)^10 = 61.39

Current price = PV of coupons + PV of par value at maturity

= 32.82 + 61.39 = 94.21

answered by: anonymous