Question

​(Related to Checkpoint​ 9.3)  ​(Bond valuation)  ​Pybus, Inc. is considering issuing bonds that will mature in 21 years with an annual coupon rate of 12 percent. Their par value will be ​$1 comma 000​, and the interest will be paid semiannually. Pybus is hoping to get a AA rating on its bonds​ and, if it​ does, the yield to maturity on similar AA bonds is 8.5 percent. ​ However, Pybus is not sure whether the new bonds will receive a AA rating. If they receive an A​ rating, the yield to maturity on similar A bonds is 9.5 percent. What will be the price of these bonds if they receive either an A or a AA​ rating? a. The price of the Pybus bonds if they receive a AA rating will be ​$ nothing. ​ (Round to the nearest​ cent.) b.  The price of the Pybus bonds if they receive an A rating will be ​$ nothing. ​ (Round to the nearest​ cent)

Answer 1

a)

AA rating:

Coupon = (12% of 1000) / 2 = 60

Rate = 8.5% / 2 = 4.25%

Number of periods = 21 * 2 = 42

Price = Coupon * [1 - 1 / (1 + r)^n] / r + FV / (1 + r)^n

Price = 60 * [1 - 1 / (1 + 0.0425)^42] / 0.0425 + 1000 / (1 + 0.0425)^42

Price = 60 * [1 - 0.174103] / 0.0425 + 174.102628

Price = 60 * 19.432879 + 174.102628

Price = $1,340.08

b)

A rating:

Rate = 9.5% / 2 = 4.75%

Price = Coupon * [1 - 1 / (1 + r)^n] / r + FV / (1 + r)^n

Price = 60 * [1 - 1 / (1 + 0.0475)^42] / 0.0475 + 1000 / (1 + 0.0475)^42

Price = 60 * [1 - 0.142407] / 0.0475 + 142.406782

Price = 60 * 18.054594 + 142.406782

Price = $1,225.68