Ashes Divide Corporation has bonds on the market with 15 years to maturity, a YTM of 7.2 percent, and a current price of $856. The bonds make semiannual payments. What must the coupon rate be on these bonds?

To find the coupon rate on the bonds, we can use the bond price formula and solve for the coupon payment. The bond price is given by:

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

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)

Given:
- **Bond Price** = $856
- **YTM (annual)** = 7.2%
- **Number of periods per year** = 2 (since the bond pays semiannually)
- **Time to maturity** = 15 years
- **Face value (F)** = $1,000

### Step 1: Identify the values
- **Periodic yield (r)**: $ \frac{0.072}{2} = 0.036 $
- **Number of periods (n)**: $ 15 \times 2 = 30 $

### Step 2: Set up the equation to solve for $ C $
\[
856 = \left( C \times \frac{1 - (1 + 0.036)^{-30}}{0.036} \right) + \left( \frac{1000}{(1 + 0.036)^{30}} \right)
\]

### Step 3: Solve for the coupon payment $ C $

I'll calculate the coupon payment, and then the coupon rate can be found as:

\[
\text{Coupon Rate} = \frac{C \times 2}{F} \times 100\%
\]The coupon rate on these bonds must be approximately **6.06%**.

Do you have any questions or would you like a detailed explanation of the process?

Here are some related questions you might find interesting:
1. How would the coupon rate change if the bond price was higher?
2. What is the relationship between bond price and coupon rate?
3. How does YTM affect the coupon rate needed for a bond to sell at a given price?
4. What happens to the coupon rate if the bond has fewer years to maturity?
5. How does the frequency of coupon payments affect the bond's coupon rate?
6. Can you explain how the bond's price affects its yield?
7. What would happen to the coupon rate if the bond made annual payments instead of semiannual?
8. How does the coupon rate impact the total return on a bond?

**Tip:** The coupon rate is directly tied to the bond's price relative to its face value. If a bond is priced below face value (discount), its coupon rate is generally lower than the YTM, and vice versa.

Learn how to calculate the coupon rate on bonds with 15 years to maturity, a yield to maturity (YTM) of 7.2%, and a current price of $856. Understand the bond price formula and the steps involved in determining the coupon rate. Suitable for advanced learners in finance.

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