Question

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

19

years with an annual coupon rate of

11

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

Value of a Bond is the present value of all future cash flows. However, a discount rate (going interest rate) is not provided. So, we will use the formula for Yield to Maturity because the formula requires using coupon rate, price of bond, and umber of payments. Here, we have the values for yield to maturity, coupon rate and number of payments. So we can use it to solve for the price of the bond. [This will surely ignore time value of money - and that is the only way this is possible due to the question not giving the discount rate].

Fomula for Yield to Maturity,

;

C = Coupon Rate

F = Face value

N = Number of years

Note: In this case, as payments are semi-annual, we will take C as $55 [being 11% x $1000 x 1/2]; N as 38 [being 19 x 2], and P is to be solved.

In case of AA Rating:

• YTM = 8.5%. Therefore,
• 
• That is, 0.085(1000 + P]/2 = 55 + [1000 - p]/38
• That is, [42.5 + 0.0425p] x 38 = [55 x 38] + 1000 - p
• That is, 1615 + 1.615p = 3090 - p
• 2.615p = 1475
• p = 564.05

Therefore, price of the Bond in case of AA Rating is $564.05.

In case of A Rating:

• YTM = 9.5%. Therefore,
• 
• That is, 0.095(1000 + P]/2 = 55 + [1000 - p]/38
• That is, [47.5 + 0.0475p] x 38 = [55 x 38] + 1000 - p
• 1805 + 1.805p = 3090 - p
• 2.805p = 1285
• p = 458.11

Therefore, price of the Bond in case of AA Rating is $458.11.

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