Question

eBook Problem Walk-Through An investor has two bonds in her portfolio, Bond C and Bond Z. Each bond matures in 4 years, has a face value of $1,000, and has a yield to maturity of 9.4%. Bond C pays a 12.5% annual coupon, while Bond Z is a zero coupon bond. a. Assuming that the yield to maturity of each bond remains at 9.4% over the next 4 years, calculate the price of the bonds at each of the following years to maturity. Round your answers to the nearest cent. Years to Maturity Price of Bond C Price of Bond Z 49

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 =∑ [(12.5*1000/100)/(1 + 9.4/100)^k]     +   1000/(1 + 9.4/100)^4

k=1

Bond Price = 1099.56

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 + 9.4/100)^k]     +   1000/(1 + 9.4/100)^4

k=1

Bond Price = 698.12

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 =∑ [(12.5*1000/100)/(1 + 9.4/100)^k]     +   1000/(1 + 9.4/100)^3

k=1

Bond Price = 1077.91

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 + 9.4/100)^k]     +   1000/(1 + 9.4/100)^3

k=1

Bond Price = 763.74

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 =∑ [(12.5*1000/100)/(1 + 9.4/100)^k]     +   1000/(1 + 9.4/100)^2

k=1

Bond Price = 1054.24

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 + 9.4/100)^k]     +   1000/(1 + 9.4/100)^2

k=1

Bond Price = 835.54

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 =∑ [(12.5*1000/100)/(1 + 9.4/100)^k]     +   1000/(1 + 9.4/100)^1

k=1

Bond Price = 1028.34

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 + 9.4/100)^k]     +   1000/(1 + 9.4/100)^1

k=1

Bond Price = 914.08

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 =∑ [(12.5*1000/100)/(1 + 9.4/100)^k]     +   1000/(1 + 9.4/100)^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 + 9.4/100)^k]     +   1000/(1 + 9.4/100)^0

k=1

Bond Price = 1000