  ​Pybus, Inc. is considering issuing bonds that will mature in 15 years with an annual coupon rate of 9 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 9.5 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 10.5 percent.  What will be the price of these bonds if they receive either an A or a AA​ rating?


To determine the price of the bonds, we need to calculate the present value of the bond's future cash flows, which include the semiannual interest payments and the par value at maturity. The bond's price can be calculated using the following formula:

\[
\text{Bond Price} = \sum \left( \frac{C}{(1 + r/2)^{2t}} \right) + \frac{\text{Par Value}}{(1 + r/2)^{2N}}
\]

Where:
- $ C $ is the semiannual coupon payment
- $ r $ is the annual yield to maturity (YTM)
- $ t $ is the period number (from 1 to $ N $)
- $ N $ is the number of years to maturity

### Given Data:
- Par value $ = \$1,000 $
- Annual coupon rate $ = 9\% $
- Coupon payment $ = 9\% \times 1,000 / 2 = \$45 $ per semiannual period
- Number of years to maturity $ = 15 $
- Number of semiannual periods $ = 15 \times 2 = 30 $

We'll calculate the bond price for both the AA and A ratings.

### 1. If the bonds receive a **AA rating** (YTM = 9.5%):
- $ r = 9.5\% $
- Semiannual YTM = $ \frac{9.5\%}{2} = 4.75\% $

### 2. If the bonds receive an **A rating** (YTM = 10.5%):
- $ r = 10.5\% $
- Semiannual YTM = $ \frac{10.5\%}{2} = 5.25\% $

Let's calculate the bond prices for both scenarios.The price of the bonds under each rating scenario is as follows:

1. **If the bonds receive a AA rating:** The bond price would be approximately **$960.45**.
2. **If the bonds receive an A rating:** The bond price would be approximately **$887.92**.

Would you like more details or have any questions about this calculation?

Here are some related questions you might consider:
1. How does a change in interest rates affect the bond prices?
2. What would be the impact on the bond price if the bonds had a different maturity period?
3. How does the frequency of coupon payments influence the bond's price?
4. What are the implications for the company's financing strategy if the bonds receive an A rating instead of AA?
5. How would the bond prices change if the coupon rate were higher or lower?

**Tip:** When assessing bond investments, remember that bond prices and yields are inversely related. As interest rates increase, bond prices decrease and vice versa.

Learn how to calculate the price of bonds issued by Pybus, Inc., considering different credit ratings (AA and A). Includes formulas for bond valuation and detailed calculations. Suitable for advanced college-level students and professionals.

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