Question

A 13 year maturity, 10% coupon bond paying coupons semiannually is callable in 8 years at a call price of $1,225. The bond currently sells at a yield to maturity of 9%. (Do not round answers)

A.) What is the yield to call?

B.) What is the yield to call if the call price is $1,175?

C.) What is the yield to call if the call price is $1,225, but can be called in 4 years instead of 8?

Answer 1

K = Nx2

Bond Price =∑ [(Semi Annual Coupon)/(1 + YTM/2)^k]     +   Par value/(1 + YTM/2)^Nx2

k=1

K =13x2

Bond Price =∑ [(10*1000/200)/(1 + 9/200)^k]     +   1000/(1 + 9/200)^13x2

k=1

Bond Price = 1075.73

a

K = Time to callx2

Bond Price =∑ [(Semi Annual Coupon)/(1 + YTC/2)^k]     +   Call Price/(1 + YTC/2)^Time to callx2

k=1

K =8x2

1075.73 =∑ [(10*1225/200)/(1 + YTC/200)^k]     +   1225/(1 + YTC/200)^8x2

k=1

YTC% = 12.45

b

K = Time to callx2

Bond Price =∑ [(Semi Annual Coupon)/(1 + YTC/2)^k]     +   Call Price/(1 + YTC/2)^Time to callx2

k=1

K =8x2

1075.73 =∑ [(10*1175/200)/(1 + YTC/200)^k]     +   1175/(1 + YTC/200)^8x2

k=1

YTC% = 11.65

c

K = Time to callx2

Bond Price =∑ [(Semi Annual Coupon)/(1 + YTC/2)^k]     +   Call Price/(1 + YTC/2)^Time to callx2

k=1

K =4x2

1075.73 =∑ [(10*1225/200)/(1 + YTC/200)^k]     +   1225/(1 + YTC/200)^4x2

k=1

YTC% = 14.09