Question

Bond X is a premium bond making semiannual payments. The bond has a coupon rate of 7.5%, a YTM of 6%, and 13 years to maturity. Bond Y is a discounted bond making semiannual payments. This bond has a coupon rate of 6%, a YTM of 7.5%, and also 13 years to maturity. What are the prices of these bonds today assuming both bonds have a $1,000 par value? If interest rates remain unchanged, what do you expect the prices of these bonds to be in 1 year? In 3 years? In 8 years? In 12 years? In 13 years? What's going on here? Illustrate your answers by graphing bond prices versus time to maturity.

Answer 1

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

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

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

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

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

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