A bond's credit rating provides a guide to its price. In December 2020, Aaa bonds yielded 1.29%, and Baa bonds yielded 3.11%. Some bad news causes a 10% five-year bond to be unexpectedly downrated from Aaa to Baa. Assume face value is $1,000.

Note: Do not round intermediate calculations. Round your answers to 2 decimal places.

What is the bond's price if it is rated as Aaa?
What is the bond's price if it is rated as Baa?

We can calculate the bond's price using the present value (PV) formula for bond pricing. The formula for bond price is based on the present value of future coupon payments and the face value of the bond discounted by the yield. The formula is:

\[
P = C \times \left(1 - (1 + r)^{-n}\right) \div r + \frac{F}{(1 + r)^n}
\]

Where:
- $P$ is the price of the bond.
- $C$ is the annual coupon payment.
- $r$ is the yield or interest rate (in decimal form).
- $n$ is the number of years until maturity.
- $F$ is the face value of the bond.

### Step 1: Coupon Payment
The bond has a 10% annual coupon rate, meaning the coupon payment is:

\[
C = 10\% \times 1000 = 100
\]

### Step 2: Price if Rated as Aaa
For an Aaa-rated bond, the yield is 1.29%. Convert the yield to decimal form:

\[
r = 1.29\% = 0.0129
\]

Now, using the bond pricing formula:

\[
P_{\text{Aaa}} = 100 \times \left(1 - (1 + 0.0129)^{-5}\right) \div 0.0129 + \frac{1000}{(1 + 0.0129)^5}
\]

Let's compute this.

### Step 3: Price if Rated as Baa
For a Baa-rated bond, the yield is 3.11%. Convert the yield to decimal form:

\[
r = 3.11\% = 0.0311
\]

Using the same formula:

\[
P_{\text{Baa}} = 100 \times \left(1 - (1 + 0.0311)^{-5}\right) \div 0.0311 + \frac{1000}{(1 + 0.0311)^5}
\]

Now, I'll calculate both prices.The bond prices are as follows:

1. If the bond is rated as **Aaa**, its price is **$1419.14**.
2. If the bond is rated as **Baa**, its price is **$1314.55**.

Would you like more details or have any questions?

Here are 5 related questions to expand on this topic:
1. How would changes in interest rates impact the bond prices further?
2. What is the relationship between bond price and yield?
3. How does bond duration affect sensitivity to yield changes?
4. What would the bond's price be if it was downgraded further to a lower rating?
5. How does credit risk affect bond yields?

**Tip:** A bond's price moves inversely to its yield—higher yields lead to lower bond prices and vice versa.

A bond's credit rating provides a guide to its price. In December 2020, Aaa bonds yielded 1.29%, and Baa bonds yielded 3.11%. Some bad news causes a 10% five-year bond to be unexpectedly downrated from Aaa to Baa. Assume face value is $1,000.

What is the bond's price if it is rated as Aaa?
What is the bond's price if it is rated as Baa?

Learn how to calculate the price of a 10% five-year bond with a face value of $1,000, under Aaa and Baa credit ratings. Understand the bond pricing formula and apply the present value theorem. Suitable for finance and economics students.

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