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

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%)

KungFuPanda

What is the actual calculation to get to the answer?

comp_sci_kid

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

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.