Question

A 30-year maturity, 8.9% coupon bond paying coupons semiannually is callable in five years at a call price of $1,145. The bond currently sells at a yield to maturity of 7.9% (3.95% per half-year).

a.	What is the yield to call? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

   

Yield to call

%

b.	What is the yield to call if the call price is only $1,095? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

   

Yield to call

%

   

c.	What is the yield to call if the call price is $1,145 but the bond can be called in two years instead of five years? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

    

Yield to call

%

Answer 1

K = Nx2

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

k=1

K =30x2

Bond Price =∑ [(8.9*1000/200)/(1 + 7.9/200)^k]     +   1000/(1 + 7.9/200)^30x2

k=1

Bond Price = 1114.2

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 =5x2

1114.2 =∑ [(8.9*1000/200)/(1 + YTC/200)^k]     +   1145/(1 + YTC/200)^5x2

k=1

YTC% = 8.44

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 =5x2

1114.2 =∑ [(8.9*1000/200)/(1 + YTC/200)^k]     +   1095/(1 + YTC/200)^5x2

k=1

YTC% = 7.7

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 =2x2

1114.2 =∑ [(8.9*1000/200)/(1 + YTC/200)^k]     +   1145/(1 + YTC/200)^2x2

k=1

YTC% = 9.28