Question

Pybus, Inc. is considering issuing bonds that will mature in 21 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 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

Price of the bond if Pybus gets a AA rating:

Information provided:

Par value= future value= $1,000

Time= 21 years*2= 42 semi-annual periods

Coupon rate= 11%/2= 5.50%

Coupon payment= 0.055*1,000= $55

Yield to maturity= 7.5%/2= 3.75% per semi-annual period

The price of the bond is calculated by computing the present value.

Enter the below in a financial calculator to compute the present value:

FV= 1,000

N= 42

PMT= 55

I/Y= 3.75

Press the CPT key and PV to compute the present value.

The value obtained is 1,367.24.

Therefore, the price of the bond if it receives a AA rating is $1,367.24.

Price of the bond if Pybus gets a A rating:

Information provided:

Par value= future value= $1,000

Time= 21 years*2= 42 semi-annual periods

Coupon rate= 11%/2= 5.50%

Coupon payment= 0.055*1,000= $55

Yield to maturity= 8.5%/2= 4.25% per semi-annual period

The price of the bond is calculated by computing the present value.

Enter the below in a financial calculator to compute the present value:

FV= 1,000

N= 42

PMT= 55

I/Y= 4.25

Press the CPT key and PV to compute the present value.

The value obtained is 1,242.91

Therefore, the price of the bond if it receives a A rating is $1,242.91.