Question

(Bond valuation)  ​Pybus, Inc. is considering issuing bonds that will mature in 19 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 8.5 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?

Answer 1

Solution :

Price of the bond when it receives AA Rating = $ 859.82

Price of the bond when it receives A Rating = $ 781.96

Please find the detailed calculations for the solution as follows :

Statement showing calculation of Price of the bond if it receives AA Rating

Sl.No.	Particulars	Period	Cash Flow (1)	Annuity Factor @ 4.25 % (2)	Discounted Cash Flow (3) = (1) * (2)
1	Half yearly Interest ( $ 1,000 * 7 % * (6/12))	1 – 38	$ 35	18.690801	$ 654.178035
2	Maturity Amount	38	$ 1,000	0.205641	$ 205.641000
3	Price of the bond	$ 859.819035
4	Price of the bond ( when rounded off to two decimal places)	$ 859.82

Note :

1.Since Interest is payable half yearly and the no. of years to maturity is 19 years, the price per bond is calculated by converting 19 years into (19 *2) = 38 half yearly periods

2.Thus, the Interest earned per period = $ 1000 * 7 % * (6/12) = $ 35

3. Since the Interest is paid semi annually the discount rate used is = 8.5 % * (6/12) = 4.25 %

4. Interest earned during the 38 periods is discounted using PVIFA ( 4.25 % , 38 ) = 18.690801

5.The Present value of $ 1,000 recoverable at maturity is to be calculated using the half yearly discount rate of (8.5 * (6 /12) ) = 4.25 %

Thus PVF ( 4.25 % , 38 ) = 0.205641

Statement showing calculation of Price of the bond if it receives A Rating

Sl.No.	Particulars	Period	Cash Flow (1)	Annuity Factor @ 4.75 % (2)	Discounted Cash Flow (3) = (1) * (2)
1	Half yearly Interest ( $ 1,000 * 7 % * (6/12))	1 – 38	$ 35	17.443081	$ 610.507835
2	Maturity Amount	38	$ 1,000	0.171454	$ 171.454000
3	Price of the bond	$ 781.961835
4	Price of the bond ( when rounded off to two decimal places)	$ 781.96

Note :

1.Since Interest is payable half yearly and the no. of years to maturity is 19 years, the price per bond is calculated by converting 19 years into (19 *2) = 38 half yearly periods

2.Thus, the Interest earned per period = $ 1000 * 7 % * (6/12) = $ 35

3. Since the Interest is paid semi annually the discount rate used is = 9.5 % * (6/12) = 4.75 %

4. Interest earned during the 38 periods is discounted using PVIFA ( 4.75 %, 38 ) = 17.443081

5.The Present value of $ 1,000 recoverable at maturity is to be calculated using the half yearly discount rate of (8.5 * (6 /12) ) = 4.75 %

Thus PVF ( 4.75 % , 38 ) = 0.171454