Answer:
Market value of the bonds with the current change: 1,150.4630
Explanation:
if the inflation premium decrease to 3 from 5
then the YTM will decrese as well.
4 + 5 inflation + 5 maturity = 14 bonds rate
4 + 3 inflation + 5 maturity = 12 YTM
We will calcualte the present value of the bond at 12% discount rate:
The coupon payment will be done using the ordinary annuity formula
[tex]C \times \frac{1-(1+r)^{-time} }{rate} = PV\\[/tex]
Coupon payment: 1,000 x 14%/2 = 70
time 40 (20 years x 2 payment per year)
rate 0.06 (12% divide into 2 paymetn per year)
[tex]70 \times \frac{1-(1+0.06)^{-40} }{0.06} = PV\\[/tex]
PV $1,053.2408
[tex]\frac{Maturity}{(1 + rate)^{time} } = PV[/tex]
Maturity 1,000.00 (face value)
time 40.00
rate 0.06
[tex]\frac{1000}{(1 + 0.06)^{40} } = PV[/tex]
PV 97.22
now we add-up both values:
PV c 1,053.2408
PV m 97.2222
Total 1,150.4630