Question

Bond Value as Maturity Approaches

An investor has two bonds in his portfolio. Each bond matures in 4 years, has a face value of $1,000, and has a yield to maturity equal to 8.4%. One bond, Bond C, pays an annual coupon of 11%; the other bond, Bond Z, is a zero coupon bond. Assuming that the yield to maturity of each bond remains at 8.4% over the next 4 years, what will be the price of each of the bonds at the following time periods? Assume time 0 is today. Fill in the following table. Round your answers to the nearest cent.

t	Price of Bond C	Price of Bond Z
0	$	$
1
2
3
4

Answer 1

Current Bond price

C Bond

K = N

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

k=1

K =4

Bond Price =∑ [(11*1000/100)/(1 + 8.4/100)^k]     +   1000/(1 + 8.4/100)^4

k=1

Bond Price = 1085.35

Z Bond

K = N

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

k=1

K =4

Bond Price =∑ [(0*1000/100)/(1 + 8.4/100)^k]     +   1000/(1 + 8.4/100)^4

k=1

Bond Price = 724.24

Price in 1 year

C Bond

K = N

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

k=1

K =3

Bond Price =∑ [(11*1000/100)/(1 + 8.4/100)^k]     +   1000/(1 + 8.4/100)^3

k=1

Bond Price = 1066.52

Z Bond

K = N

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

k=1

K =3

Bond Price =∑ [(0*1000/100)/(1 + 8.4/100)^k]     +   1000/(1 + 8.4/100)^3

k=1

Bond Price = 785.08

Price in 2 year

C Bond

K = N

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

k=1

K =2

Bond Price =∑ [(11*1000/100)/(1 + 8.4/100)^k]     +   1000/(1 + 8.4/100)^2

k=1

Bond Price = 1046.11

Z Bond

K = N

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

k=1

K =2

Bond Price =∑ [(0*1000/100)/(1 + 8.4/100)^k]     +   1000/(1 + 8.4/100)^2

k=1

Bond Price = 851.02

Price in 3 year

C Bond

K = N

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

k=1

K =1

Bond Price =∑ [(11*1000/100)/(1 + 8.4/100)^k]     +   1000/(1 + 8.4/100)^1

k=1

Bond Price = 1023.99

Z Bond

K = N

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

k=1

K =1

Bond Price =∑ [(0*1000/100)/(1 + 8.4/100)^k]     +   1000/(1 + 8.4/100)^1

k=1

Bond Price = 922.51

Price in 4 year

C Bond

K = N

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

k=1

K =0

Bond Price =∑ [(11*1000/100)/(1 + 8.4/100)^k]     +   1000/(1 + 8.4/100)^0

k=1

Bond Price = 1000

Z Bond

K = N

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

k=1

K =0

Bond Price =∑ [(0*1000/100)/(1 + 8.4/100)^k]     +   1000/(1 + 8.4/100)^0

k=1

Bond Price = 1000