Answer:
if YTM at 4% price : $2,902.1237
if YTM at 8% price : $1,788.0448
The bonds are above face value asthey offer a higher coupon payment than the market yield therefore the bond holders are willing to pay above theri face value
Explanation:
the market price of the bond will be the present value of coupo payment and maturity:
[tex]C \times \frac{1-(1+r)^{-time} }{rate} = PV\\[/tex]
C 150.000
time 30
rate 0.04
[tex]150 \times \frac{1-(1+0.04)^{-30} }{0.04} = PV\\[/tex]
PV $2,593.8050
[tex]\frac{Maturity}{(1 + rate)^{time} } = PV[/tex]
Maturity 1,000.00
time 30.00
rate 0.04
[tex]\frac{1000}{(1 + 0.04)^{30} } = PV[/tex]
PV 308.32
PV c $2,593.8050
PV m $308.3187
Total $2,902.1237
No we repeat the process with the yield at 8%
[tex]C \times \frac{1-(1+r)^{-time} }{rate} = PV\\[/tex]
C 150.000
time 30
rate 0.08
[tex]150 \times \frac{1-(1+0.08)^{-30} }{0.08} = PV\\[/tex]
PV $1,688.6675
[tex]\frac{Maturity}{(1 + rate)^{time} } = PV[/tex]
Maturity 1,000.00
time 30.00
rate 0.08
[tex]\frac{1000}{(1 + 0.08)^{30} } = PV[/tex]
PV 99.38
PV c $1,688.6675
PV m $99.3773
Total $1,788.0448
