Question

Bond X is a premium bond making semiannual payments. The bond pays a coupon rate of 8 percent, has a YTM of 6 percent, and has 14 years to maturity. Bond Y is a discount bond making semiannual payments. This bond pays a coupon rate of 6 percent, has a YTM of 8 percent, and also has 14 years to maturity. The bonds have a $1,000 par value. What is the price of each bond today? If interest rates remain unchanged, what do you expect the price of these bonds to be one year from now? In five years? In 10 years? In 12 years? In 14 years?

Answer 1

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:

$C \times \frac{1-(1+r)^{-time} }{rate} = PV$

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

$40 \times \frac{1-(1+0.03)^{-28} }{0.03} = PV$

PV $750.5643

The maturity the present value of a lump sum:

$\frac{Maturity}{(1 + rate)^{time} } = PV$  

Maturity   1,000.00

time   28.00

rate  0.03

$\frac{1000}{(1 + 0.03)^{28} } = PV$  

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:

$C \times \frac{1-(1+r)^{-time} }{rate} = PV$

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

$30 \times \frac{1-(1+0.04)^{-28} }{0.04} = PV$

PV $499.8919

$\frac{Maturity}{(1 + rate)^{time} } = PV$  

Maturity   1,000.00

time   28.00

rate  0.04

$\frac{1000}{(1 + 0.04)^{28} } = PV$  

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