Question

Bond X is a premium bond making semiannual payments. The bond has a coupon rate of 8.4 percent, a YTM of 6.4 percent, and has 17 years to maturity. Bond Y is a discount bond making semiannual payments. This bond has a coupon rate of 6.4 percent, a YTM of 8.4 percent, and also has 17 years to maturity. Assume the interest rates remain unchanged and both bonds have a par value of $1,000.

1. What are the prices of these bonds today?
2. What do you expect the prices of these bonds to be in one year?
3. What do you expect the prices of these bonds to be in three years?
4. What do you expect the prices of these bonds to be in eight years?
5. What do you expect the prices of these bonds to be in 12 years?
6. What do you expect the prices of these bonds to be in 17 years?

Answer 1

Bond X $1,205.41

as it was issued at premium I expect the bond price to decrease as time passes to match the maturity value

Bond Y $820.69

As it is below face value and at maturity the company with the coupon will receive 1,000 this value of 820.59 will increase over time to match it.

Step-by-step explanation:

The market value of the bond will the present value of the coupon payment and maturity considering the yield to maturity rate

Bond X

`C * (1-(1+r)^(-time) )/(rate) = PV\\`

C 42.000 (1,000 x 0.084 / 2 )

time 34 (17 years x 2 payment per year)

rate 0.032 (0.064 annual / 2 semiannual )

`42 * (1-(1+0.032)^(-34) )/(0.032) = PV\\`

PV $862.7309

`(Maturity)/((1 + rate)^(time) ) = PV`

Maturity 1,000.00

time 34.00

rate 0.032

`(1000)/((1 + 0.032)^(34) ) = PV`

PV 342.68

PV c $862.7309

PV m $342.6812

Total $1,205.4121

Bond Y

`32 * (1-(1+0.042)^(-34) )/(0.042) = PV\\`

PV $573.8007

`(1000)/((1 + 0.042)^(34) ) = PV`

PV 246.89

Total $820.6873