Grohl Co. issued 11-year bonds a year ago at a coupon rate of 6.5 percent. The bonds make semiannual payments. If the YTM on these bonds is 8.2 percent, what is the current bond price?

To find the current bond price, we can use the formula for the present value of a bond, which is the sum of the present value of the bond's coupon payments and the present value of the bond's face value (par value) at maturity.

The formula is:

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

Where:
- $ C $ is the coupon payment
- $ r $ is the periodic yield (YTM divided by the number of periods per year)
- $ n $ is the total number of periods
- $ F $ is the face value of the bond (typically $1,000)

### Step 1: Identify the values
- **Coupon rate (annual)**: 6.5%
- **YTM (annual)**: 8.2%
- **Number of periods per year**: 2 (since the bond pays semiannually)
- **Time to maturity**: 11 years (but one year has passed, so 10 years remain)
- **Face value (F)**: $1,000

### Step 2: Calculate the values
- **Coupon payment (C)**: $ 0.065 \times 1000 = 65 $ per year, but since the bond pays semiannually, each payment is $ \frac{65}{2} = 32.5 $
- **Periodic yield (r)**: $ \frac{0.082}{2} = 0.041 $
- **Number of periods (n)**: $ 10 \times 2 = 20 $ periods remaining

### Step 3: Apply the formula
\[
\text{Bond Price} = \left( 32.5 \times \frac{1 - (1 + 0.041)^{-20}}{0.041} \right) + \left( \frac{1000}{(1 + 0.041)^{20}} \right)
\]

Now, I'll calculate the bond price.The current bond price is approximately **$885.50**.

Do you have any questions or would you like a detailed breakdown of the steps? 

Here are some related questions you might find useful:
1. How does the bond's coupon rate affect its price?
2. What happens to the bond price if the YTM increases?
3. How would the bond price change if it had annual payments instead of semiannual?
4. What is the relationship between YTM and bond price?
5. How do changes in interest rates impact bond prices?
6. Can you explain how the time to maturity affects the bond price?
7. What is the difference between coupon rate and YTM?
8. How would the bond price change if it was a zero-coupon bond?

**Tip:** When interest rates rise, bond prices typically fall, and vice versa. This is because the present value of the bond's future cash flows decreases as interest rates increase.

Learn how to calculate the current bond price for Grohl Co.'s 11-year bonds issued with a 6.5% coupon rate and an 8.2% YTM. Follow a detailed step-by-step solution using the present value of a bond formula. Suitable for finance students and professionals.

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