Chen Corporation issued 15-year bonds two years ago at a coupon rate of 7.3 percent. The bonds make semiannual payments. If these bonds currently sell for 103 percent of par value, what is the YTM?

Note: Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16

To calculate the yield to maturity (YTM) of the bonds, we can use the following information:

- **Coupon rate**: 7.3% per year (or 0.073 as a decimal)
- **Coupon payments**: Semiannual, so the semiannual coupon payment is \( \frac{7.3\%}{2} = 3.65\% \) of the par value
- **Current price**: 103% of par value
- **Time to maturity**: 13 years (since the bonds were issued two years ago, and the original maturity was 15 years)
- **Semiannual payments**: Therefore, the number of periods left is \( 13 \times 2 = 26 \) semiannual periods

We will use the following formula for YTM calculation, which involves solving for \( r \):

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

Where:
- \( P \) = Current bond price (103% of par value, or 1.03 \times 1000 = 1030)
- \( C \) = Coupon payment per period (semiannual) = \( 1000 \times 3.65\% = 36.50 \)
- \( F \) = Face value of the bond = 1000
- \( n \) = Total number of periods = 26
- \( r \) = Semiannual yield to maturity (the unknown we are solving for)

We will now solve for \( r \) (the semiannual YTM) and then multiply by 2 to annualize it. Let me calculate that.It seems there was an issue with the calculation. I’ll retry solving for the YTM using a more efficient method.

Let’s rework the formula to find the YTM using an approximation based on financial calculations. I’ll manually derive the YTM from the semiannual bond pricing equation.The yield to maturity (YTM) for the bonds is approximately **6.95%**.

Would you like any further details or clarifications? Here are some related questions that might expand your understanding:

1. How is the YTM affected by changes in the bond's price?
2. What factors contribute to the difference between coupon rate and YTM?
3. How does semiannual compounding influence the YTM calculation?
4. What happens to the YTM if the bond is called early?
5. How would the YTM change if interest rates fluctuate?

**Tip**: The YTM calculation assumes the bond is held to maturity and that all coupon payments are reinvested at the same rate.

Chen Corporation issued 15-year bonds two years ago at a coupon rate of 7.3 percent. The bonds make semiannual payments. If these bonds currently sell for 103 percent of par value, what is the YTM?

Learn how to calculate the Yield to Maturity (YTM) for Chen Corporation's 15-year bonds issued at a 7.3% coupon rate. This bond valuation problem covers key financial concepts like YTM, semiannual payments, and the time value of money, suitable for finance students.

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