discont margin frn

CFA Level I Fixed Income
#1

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:

(Index+QM)×FVm=(0.05+0.0125)×1004=1.5625" name=“DMT1” resolution=“300” src=“https://ondemand.questionmark.com/resources/399691/topicresources/25746546/DMT11706920-4a605c21-964881bc-c5a2c434.jpg” style=“width: 375px; height: 42px;” width=“391” />

The discount margin can be estimated by solving for DM in the equation:

96=1.5625(1+0.05+DM4)1+1.5625(1+0.05+DM4)2+⋯+1.5625(1+0.05+DM4)20" name=“DMT2” resolution=“300” src=“https://ondemand.questionmark.com/resources/399691/topicresources/25746546/DMT2e839e4b4-41fd44d4-62f8bfa2-c9605352.jpg” style=“width: 493px; height: 61px;” width=“573” />

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

#2

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.

#3

thanks a lot sir

#4

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