Question

A 20-year maturity $1,000 par value 9% coupon bond paying coupons annually is callable in five years at a call price of $1,050. The bond currently sells at a yield to maturity of 8%. What is the yield to call?

please show full steps of the work. thank you!!!

Answer 1

K = N

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

k=1

K =20

Bond Price =∑ [(9*1000/100)/(1 + 8/100)^k]     +   1000/(1 + 8/100)^20

k=1

Bond Price = 1098.18

K = Time to call

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

k=1

K =5

1098.18 =∑ [(9*1000/100)/(1 + YTC/100)^k]     +   1050/(1 + YTC/100)^5

k=1

YTC% = 7.44