discont margin frn

[erwar]

Hello Guys, this is a problem and the answer for the discount margin of a FRN. How do they get the the answer of 221? please your help
$DMT Corp. issued a five-year floating-rate note (FRN) that pays a quarterly coupon of three-month LIBOR plus 125 bps. The FRN is priced at 96 per 100 of par value. Assuming a 30/360 day-count convention, evenly spaced periods, and constant three-month LIBOR of 5%, the discount margin for the FRN is closest to:
221 bps.
400 bps.
180 bps.

Question not answered
The interest payment each period per 100 of par value is:
The discount margin can be estimated by solving for DM in the equation:
The solution for the discount rate, r = (0.05+DM)/4 is 1.8025%. Therefore DM = 2.21%, or 221 bps.
2014 CFA Level I

 

[freecfa]

Hi there,
First calculate the quarterly coupon payment as above which will give you 1.5625.
Then you can use your calculator to find the YTM for the FRN
N=20
PV=-96
PMT=1.5625
FV=100
This will give you a YTM of 1.8025. As this is based on quarterly periods multiply by 4 to give 7.21%. The discount margin is the yield over and above LIBOR that is being given so
7.21%-5% = 2.21% or 221bps which is the answer you are looking for.