Question

In: Finance

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 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.) 

Solutions

Expert Solution

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

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