Question

Liberty Inc.'s semi-annual bonds currently sell for $1,175. The annual coupon rate is 12.5%. the bonds have a 15-year maturity, and a $1,000 par value, but they can be called in 6 years at $1,080. Assume that no costs other than the premium would be incurred to call and refund the bonds, also assume the yield curve is horizontal, with rates expected to remain at current levels on into the future. What is the difference between this bonds YTM and its YTC?

Answer 1

K = Nx2

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

k=1

K =15x2

1175 =∑ [(12.5*1000/200)/(1 + YTM/200)^k]     +   1000/(1 + YTM/200)^15x2

k=1

YTM% = 10.2

K = Time to callx2

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

k=1

K =6x2

1175 =∑ [(12.5*1060/200)/(1 + YTC/200)^k]     +   1060/(1 + YTC/200)^6x2

k=1

YTC% = 10.05

YTM-YTC = 10.20-10.05 = 0.15%