Question

Bond X is a premium bond making semiannual payments. The bond has a coupon rate of 7.5 percent, a YTM of 6 percent, and 13 years to maturity. Bond Y is a discount bond making semiannual payments. This bond has a coupon rate of 6 percent, a YTM of 7.5 percent, and also 13 years to maturity. Assume the interest rates remain unchanged and a $1,000 par value. 

a. What are the prices of these bonds today? (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.) 

b. What do you expect the prices of these bonds to be in one year? (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.) 

c. What do you expect the prices of these bonds to be in three years? (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.) 

d. What do you expect the prices of these bonds to be in eight years? (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.) 

e. What do you expect the prices of these bonds to be in 12 years? (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.) 

f. What do you expect the prices of these bonds to be in 13 years? (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.) 

Answer 1

a

Current Bond price

X Bond

K = Nx2

Bond Price =∑ [( Coupon)/(1 + YTM/2)^k]     +   Par value/(1 + YTM/2)^Nx2

k=1

K =13x2

Bond Price =∑ [(7.5*1000/200)/(1 + 6/200)^k]     +   1000/(1 + 6/200)^13x2

k=1

Bond Price = 1134.08

Y Bond

K = Nx2

Bond Price =∑ [( Coupon)/(1 + YTM/2)^k]     +   Par value/(1 + YTM/2)^Nx2

k=1

K =13x2

Bond Price =∑ [(6*1000/200)/(1 + 7.5/200)^k]     +   1000/(1 + 7.5/200)^13x2

k=1

Bond Price = 876.8

b

Price in 1 year

X Bond

K = Nx2

Bond Price =∑ [( Coupon)/(1 + YTM/2)^k]     +   Par value/(1 + YTM/2)^Nx2

k=1

K =12x2

Bond Price =∑ [(7.5*1000/200)/(1 + 6/200)^k]     +   1000/(1 + 6/200)^12x2

k=1

Bond Price = 1127.02

Y Bond

K = Nx2

Bond Price =∑ [( Coupon)/(1 + YTM/2)^k]     +   Par value/(1 + YTM/2)^Nx2

k=1

K =12x2

Bond Price =∑ [(6*1000/200)/(1 + 7.5/200)^k]     +   1000/(1 + 7.5/200)^12x2

k=1

Bond Price = 882.66

c

Price in 3 year

X Bond

K = Nx2

Bond Price =∑ [( Coupon)/(1 + YTM/2)^k]     +   Par value/(1 + YTM/2)^Nx2

k=1

K =10x2

Bond Price =∑ [(7.5*1000/200)/(1 + 6/200)^k]     +   1000/(1 + 6/200)^10x2

k=1

Bond Price = 1111.58

Y Bond

K = Nx2

Bond Price =∑ [( Coupon)/(1 + YTM/2)^k]     +   Par value/(1 + YTM/2)^Nx2

k=1

K =10x2

Bond Price =∑ [(6*1000/200)/(1 + 7.5/200)^k]     +   1000/(1 + 7.5/200)^10x2

k=1

Bond Price = 895.78

d

Price in 8 year

X Bond

K = Nx2

Bond Price =∑ [( Coupon)/(1 + YTM/2)^k]     +   Par value/(1 + YTM/2)^Nx2

k=1

K =5x2

Bond Price =∑ [(7.5*1000/200)/(1 + 6/200)^k]     +   1000/(1 + 6/200)^5x2

k=1

Bond Price = 1063.98

Y Bond

K = Nx2

Bond Price =∑ [( Coupon)/(1 + YTM/2)^k]     +   Par value/(1 + YTM/2)^Nx2

k=1

K =5x2

Bond Price =∑ [(6*1000/200)/(1 + 7.5/200)^k]     +   1000/(1 + 7.5/200)^5x2

k=1

Bond Price = 938.4

e

Price in 12 year

X Bond

K = Nx2

Bond Price =∑ [( Coupon)/(1 + YTM/2)^k]     +   Par value/(1 + YTM/2)^Nx2

k=1

K =1x2

Bond Price =∑ [(7.5*1000/200)/(1 + 6/200)^k]     +   1000/(1 + 6/200)^1x2

k=1

Bond Price = 1014.35

Y Bond

K = Nx2

Bond Price =∑ [( Coupon)/(1 + YTM/2)^k]     +   Par value/(1 + YTM/2)^Nx2

k=1

K =1x2

Bond Price =∑ [(6*1000/200)/(1 + 7.5/200)^k]     +   1000/(1 + 7.5/200)^1x2

k=1

Bond Price = 985.8

f

Price in 13 year

X Bond

K = Nx2

Bond Price =∑ [( Coupon)/(1 + YTM/2)^k]     +   Par value/(1 + YTM/2)^Nx2

k=1

K =0x2

Bond Price =∑ [(7.5*1000/200)/(1 + 6/200)^k]     +   1000/(1 + 6/200)^0x2

k=1

Bond Price = 1000

Y Bond

K = Nx2

Bond Price =∑ [( Coupon)/(1 + YTM/2)^k]     +   Par value/(1 + YTM/2)^Nx2

k=1

K =0x2

Bond Price =∑ [(6*1000/200)/(1 + 7.5/200)^k]     +   1000/(1 + 7.5/200)^0x2

k=1

Bond Price = 1000