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 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.)
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 |