Question

  ​(Bond valuation) ​Pybus, Inc. is considering issuing bonds that will mature in 22 years with an annual coupon rate of 12 percent. Their par value will be ​$1,000​, and the interest will be paid semiannually. Pybus is hoping to get a AA rating on its bonds​ and, if it​ does, the yield to maturity on similar AA bonds is 11.5 percent. ​ However, Pybus is not sure whether the new bonds will receive a AA rating. If they receive an A​ rating, the yield to maturity on similar A bonds is 12.5 percent. What will be the price of these bonds if they receive either an A or a AA​ rating? a. The price of the Pybus bonds if they receive a AA rating will be ​$

Answer 1

For AA rating

K = Nx2

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

k=1

K =22x2

Bond Price =∑ [(12*1000/200)/(1 + 11.5/200)^k]     +   1000/(1 + 11.5/200)^22x2

k=1

Bond Price = 1039.76

For A rating

K = Nx2

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

k=1

K =22x2

Bond Price =∑ [(12*1000/200)/(1 + 12.5/200)^k]     +   1000/(1 + 12.5/200)^22x2

k=1

Bond Price = 962.78