Answer:
Market value at 8% YTM $ 743.2156
at 10% YTM $ 619.6960
Explanation:
Assuming the face value is 1,000 as common outstanding American company's bonds:
Market value under the current scenario:
Present value of the coupon payment:
[tex]C \times \frac{1-(1+r)^{-time} }{rate} = PV\\[/tex]
Coupon: $1,000 x 5% = 50
time 15 years
rate 0.08
[tex]50 \times \frac{1-(1+0.08)^{-15} }{0.08} = PV\\[/tex]
PV $427.9739
Present Value of the Maturity
[tex]\frac{Maturity}{(1 + rate)^{time} } = PV[/tex]
Maturity 1,000.00
time 15.00
rate 0.08
[tex]\frac{1000}{(1 + 0.08)^{15} } = PV[/tex]
PV 315.24
PV c $427.9739
PV m $315.2417
Total $743.2156
If the interest rate in the market increaseby 2% then investor will only trade the bonds to get a yield 2% higher that is 10% so we recalculate the new price:
[tex]C \times \frac{1-(1+r)^{-time} }{rate} = PV\\[/tex]
C 50.000
time 15
rate 0.1
[tex]50 \times \frac{1-(1+0.1)^{-15} }{0.1} = PV\\[/tex]
PV $380.3040
[tex]\frac{Maturity}{(1 + rate)^{time} } = PV[/tex]
Maturity 1,000.00
time 15.00
rate 0.1
[tex]\frac{1000}{(1 + 0.1)^{15} } = PV[/tex]
PV 239.39
PV c $380.3040
PV m $239.3920
Total $619.6960
Giving a lower price than before
