Question

Pybus, Inc. is considering issuing bonds that will mature in 21 years with an annual coupon rate of 7 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 8 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 percent. What will be the price of these bonds if they receive either an A or a AA​ rating?

The price of the Pybus bonds if they receive a AA rating will be ​$

Answer 1

The price of the bonds if they receive an A rating is $1,062.77, and if they receive a AA rating is $1,110.84.

Step-by-step explanation:

To determine the price of the bonds if they receive either an A or AA rating, we can use the bond pricing formula:

Price = (C / r) * (1 - (1 + r)^-n) + (F / (1 + r)^n)

where C is the annual coupon payment, r is the yield to maturity, n is the number of periods to maturity, and F is the face value.

First, let's calculate the annual coupon payment:

C = 7% * $1,000 = $70

Next, we'll calculate the number of periods to maturity:

n = 21 years * 2 (because interest is paid semi-annually) = 42

Now, if the bonds receive a AA rating, the yield to maturity is 8%. We can use this yield to maturity to find the price of the bonds:

Price = ($70 / 0.08) * (1 - (1 + 0.08)^-42) + ($1,000 / (1 + 0.08)^42) = $1,110.84

Alternatively, if the bonds receive an A rating, the yield to maturity is 9%. We can use this yield to maturity to find the price of the bonds:

Price = ($70 / 0.09) * (1 - (1 + 0.09)^-42) + ($1,000 / (1 + 0.09)^42) = $1,062.77

In conclusion, the price of the bonds if they receive an A rating is $1,062.77, and if they receive a AA rating is $1,110.84.