Question

 ​Pybus, Inc. is considering issuing bonds that will mature in 25 years with an annual coupon rate of 11 percent. Their par value will be ​$1000​, and the interest will be paid semiannually. Pybus is hoping to get a AA rating on its bonds​ and, if it​ does, the yield to maturity on similar AA bonds is 10.5 percent. ​ However, Pybus is not sure whether the new bonds will receive a AA rating. If they receive an A​ rating, the yield to maturity on similar A bonds is 11.5 percent. What will be the price of these bonds if they receive either an A or a AA​ rating?

Answer 1

A rating

K = Nx2

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

k=1

K =25x2

Bond Price =∑ [(11*1000/200)/(1 + 11.5/200)^k]     +   1000/(1 + 11.5/200)^25x2

k=1

Bond Price = 959.18

AA rating

K = Nx2

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

k=1

K =25x2

Bond Price =∑ [(11*1000/200)/(1 + 10.5/200)^k]     +   1000/(1 + 10.5/200)^25x2

k=1

Bond Price = 1043.93