A firm raises capital by selling ​$30 comma 000

worth of debt with flotation costs equal to 3
​%
of its par value.  If the debt matures in 15

years and has an annual coupon interest rate of 9
​%,
what is the​ bond's YTM?
Question content area bottom
Part 1
The​ bond's YTM is enter your response here
​%.
​(Round to two decimal​ places.)

To calculate the bond's Yield to Maturity (YTM), we need to use the information provided. Here's how we break it down:

### Given Data:
- **Face Value (Par Value)**: \$30,000
- **Flotation Costs**: 3% of the face value
- **Annual Coupon Rate**: 9%
- **Maturity**: 15 years

### Step 1: Calculate the flotation costs
Flotation costs represent the fee incurred for issuing the debt. To find this:
\[
\text{Flotation Costs} = 30,000 \times 3\% = 30,000 \times 0.03 = 900
\]

### Step 2: Calculate the amount received by the firm
The firm doesn't receive the full \$30,000 due to flotation costs:
\[
\text{Amount Received} = 30,000 - 900 = 29,100
\]

### Step 3: Determine the annual coupon payment
The coupon payment is the interest the firm will pay each year:
\[
\text{Annual Coupon Payment} = 30,000 \times 9\% = 30,000 \times 0.09 = 2,700
\]

### Step 4: Use the YTM formula (approximate)
The formula to approximate the Yield to Maturity (YTM) for a bond is:
\[
YTM \approx \frac{\text{Coupon Payment} + \frac{\text{Face Value} - \text{Price}}{\text{Years to Maturity}}}{\frac{\text{Face Value} + \text{Price}}{2}}
\]

Where:
- **Coupon Payment** = \$2,700
- **Face Value** = \$30,000
- **Price** = \$29,100 (since this is the amount the firm receives)
- **Years to Maturity** = 15

Now, let's plug in the values:

\[
YTM \approx \frac{2,700 + \frac{30,000 - 29,100}{15}}{\frac{30,000 + 29,100}{2}} = \frac{2,700 + \frac{900}{15}}{\frac{59,100}{2}} = \frac{2,700 + 60}{29,550} = \frac{2,760}{29,550} \approx 0.0934 \text{ or } 9.34\%
\]

### Conclusion:
The bond's Yield to Maturity (YTM) is approximately **9.34%**.

Would you like a more detailed breakdown or any clarifications on the steps?

---

Here are some related questions to think about:
1. What would the YTM be if the flotation costs were higher?
2. How does the coupon rate affect the bond's YTM?
3. What if the bond's maturity was longer or shorter—how would that impact YTM?
4. How does a bond’s price affect its YTM calculation?
5. Why do flotation costs lower the effective amount received by the firm?

**Tip:** Flotation costs reduce the amount raised, which slightly increases the bond’s effective YTM.

A firm raises capital by selling $30,000 worth of debt with flotation costs equal to 3% of its par value. If the debt matures in 15 years and has an annual coupon interest rate of 9%, what is the bond's YTM? (Round to two decimal places.)

This finance problem involves calculating the Yield to Maturity (YTM) of a bond. A firm issues $30,000 in debt with flotation costs of 3%, a 9% annual coupon rate, and a 15-year maturity. Learn how to calculate the bond's YTM using key financial formulas.

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