Answer:
Bonds X
Today: $1,187.64
a year from today:$1,178.77
5-years: $1,137.54
10-years: $1,070.20
at maturity: 1,000
Bond Y
Today: $833.37
a year from today:$840.17
5-years: $873.41
10-years: $932.67
at maturity: 1,000
Explanation:
The current value of the bonds will be the future coupon payment and maturity discounted at yield to maturity. Thus we must calcualte the present value for each bond at the given times:
Bond X
The coupon payment will be an ordinary annuity:
[tex]C \times \frac{1-(1+r)^{-time} }{rate} = PV\\[/tex]
C = 1,000 x 8% / 2 payment per year = 40.00
time = 14 years x 2 payment per year= 28
YTM = 6% annual/ 2 = 3% semiannual = 0.03
[tex]40 \times \frac{1-(1+0.03)^{-28} }{0.03} = PV\\[/tex]
PV $750.5643
The maturity the present value of a lump sum:
[tex]\frac{Maturity}{(1 + rate)^{time} } = PV[/tex]
Maturity 1,000.00
time 28.00
rate 0.03
[tex]\frac{1000}{(1 + 0.03)^{28} } = PV[/tex]
PV 437.08
PV coupon $750.5643 + PV maturity $437.0768 = $1,187.6411
for the subsequent year we have to decrease the time value.
one year from now then t = 26 (13 years to maturity x 2 payment)
five years:t = 18
ten years = 8
At maturity it will have a same makret price as the market value.
Bond Y
Present value of the coupon:
[tex]C \times \frac{1-(1+r)^{-time} }{rate} = PV\\[/tex]
C = 1,000 x 6% / 2 payment per year = 30.00
time = 14 years x 2 payment per year= 28
YTM = 8% annual/ 2 = 4% semiannual = 0.04
[tex]30 \times \frac{1-(1+0.04)^{-28} }{0.04} = PV\\[/tex]
PV $499.8919
[tex]\frac{Maturity}{(1 + rate)^{time} } = PV[/tex]
Maturity 1,000.00
time 28.00
rate 0.04
[tex]\frac{1000}{(1 + 0.04)^{28} } = PV[/tex]
PV 333.48
PV coupon $499.8919 +PV maturity $333.48 = $833.3694
Same as Bond X the only difference will be change time according to the years left to maturity.
Again, at maturity the market price equals the face value of the bond of $1,000
