Question

Baron buys a bond whose Par=$1,000, Coupon=6%, semiannually paid, Maturity=8 years, and Price= $1,000. He invests the coupons at a uniform rate of 3% per six months until he sells the bond at t=2years, shortly after receiving the fourth semiannual coupon. If Barons  realized return turns out to be 7% per year, what was the bond’s YTM at the time of its sale at t=2 years?

Answer 1

Accumulated value at maturity:

N=2

PMT=0

PV=-1000

I/Y=7%

CPT FV=1144.90000

Total coupon payments: =6%*1000/2*2*2=120.00000

Reinvestment income from coupons:

N=2*2

I/Y=6%/2

PMT=-6%*1000/2

PV=0

CPT FV=125.50881

Reinvestment income=125.50881-120.000=5.50881

Total value at 2 years: =x+120+5.50881

=>x+120+5.50881=1144.90000
=>x=1144.90000-120-5.50881
=>x=1019.39119

YTM after 2 years:

N=6*2

PMT=-6%*1000/2

FV=-1000

PV=1019.39119

CPT I/Y=2.8074%

YTM at the time of sale=2.8074%*2=5.6148%