Even though most corporate bonds in the United States make coupon payments semiannually, bonds issued elsewhere often have annual coupon payments. Suppose a German company issues a bond with a par value of €1,000, 7 years to maturity, and a coupon rate of 7.8 percent paid annually. If the YTM is 9.8 percent, what is the current bond price in euros?

To calculate the current bond price, we can use the present value formula for bonds. The bond price is the sum of the present value of the annual coupon payments and the present value of the par value at maturity.

Here's the breakdown of the bond pricing formula:

\[
\text{Bond Price} = \left( \sum_{t=1}^{T} \frac{C}{(1 + r)^t} \right) + \frac{F}{(1 + r)^T}
\]

Where:
- \(C\) is the annual coupon payment.
- \(F\) is the face value (par value) of the bond.
- \(r\) is the yield to maturity (YTM) per period.
- \(T\) is the number of periods (years in this case).

### Given:
- Par value (\(F\)) = €1,000
- Coupon rate = 7.8% (hence annual coupon payment \(C = 0.078 \times 1000 = €78\))
- YTM (\(r\)) = 9.8% = 0.098
- Time to maturity (\(T\)) = 7 years

### Step 1: Calculate the present value of the coupon payments
The coupon payment is made annually, so we calculate the present value of each coupon payment over the 7 years.

\[
\text{PV of coupons} = \sum_{t=1}^{7} \frac{78}{(1 + 0.098)^t}
\]

### Step 2: Calculate the present value of the face value
The present value of the face value (€1,000) paid at maturity in 7 years is:

\[
\text{PV of par value} = \frac{1000}{(1 + 0.098)^7}
\]

### Step 3: Add the two components together to get the bond price

Let me now compute the result for you.The current price of the bond is approximately €901.99.

Would you like further details or have any questions about the calculations? 

Here are 5 related questions to expand on this topic:
1. How does increasing the YTM affect the bond price?
2. What would the bond price be if the coupon payments were made semiannually?
3. How does the bond's price change if the coupon rate equals the YTM?
4. What is the relationship between bond prices and interest rate risk?
5. How does time to maturity influence the sensitivity of a bond's price?

**Tip:** A bond's price decreases when the yield to maturity (YTM) exceeds the coupon rate because investors demand a higher return for the bond's risk level.

Learn how to calculate the current price of a 7-year German corporate bond with an annual coupon rate of 7.8% and a YTM of 9.8%. This detailed solution involves the present value of coupon payments and par value, following core bond pricing principles.

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