Reinvestment coupon income question note, his, question, investor, income

johnnyBuz

Question #110 Schweser Exam 1  Afternoon Session
A 3year, 6% coupon, semiannualpay note has a yield to maturity of 5.5%. If an investor holds this note to maturity and earns a 4.5% return on reinvested coupon income, his realized yield on the note is closest to:
A. 5.46%
B. 5.57%
C. 5.68%
This questions is killing me, and Schweser gives a lame explanation. Can some please help me out with this.
Thank You
Simon

d2rockstar

YTM assumes that coupons are reinvested at YTM. This investor earns 4.5% on the coupon income which is less than YTM. So realized yield has to be less than 5.5.
By the process of elimination it should be A.

comp_sci_kid

is there a way to calculate the realized yield and not do it just by elimination??

KungFuPanda

What is the actual calculation to get to the answer?

chandsingh

Current market price of bond is $1,013 (N=6, I/Y=5.5/2=2.75, PMT=$30, FV=$1000, CPT PV)
If coupons are reinvested at 4.5%, FV of coupons at end of three years is $191. (N=6, I/Y=4.5/2=2.25, PMT=$30, PV=0, CPT FV)
YTM for investment in this bond is 5.46% (PV=$1,013, N=6, PMT=0, FV=$1,191 (191+1000), CPT I/Y = 2.73 X2 = 5.46%)