Question

 ​(Bond valuation)  ​Pybus, Inc. is considering issuing bonds that will mature in 18years with an annual coupon rate of 8percent. Their par value will be ​$1 comma 000

​,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 7.5

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 8.5

percent. What will be the price of these bonds if they receive either an A or a AA​ rating?

Answer 1

A rating price

K = Nx2

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

k=1

K =18x2

Bond Price =∑ [(8*1000/200)/(1 + 8.5/200)^k]     +   1000/(1 + 8.5/200)^18x2

k=1

Bond Price = 954.32

AA rating price

K = Nx2

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

k=1

K =18x2

Bond Price =∑ [(8*1000/200)/(1 + 7.5/200)^k]     +   1000/(1 + 7.5/200)^18x2

k=1

Bond Price = 1048.95