Broke Benjamin Company has a bond outstanding that makes semiannual payments with a coupon rate of 6.3 percent. The bond sells for $981.73 and matures in 23 years. The par value is $1,000. What is the YTM of the bond?

Multiple Choice

3.23%

4.84%

5.81%

6.13%

6.45%

To find the Yield to Maturity (YTM) of the bond, we’ll use the following known information:

1. **Coupon Rate:** 6.3% annually, which translates to 3.15% per semiannual period.
2. **Bond Price:** $981.73.
3. **Par Value (Face Value):** $1,000.
4. **Time to Maturity:** 23 years (or 46 semiannual periods).
5. **Coupon Payment per Period:** $ 1000 \times 0.0315 = 31.5 $.

The YTM is the interest rate that equates the bond's price to the present value of its future cash flows. This calculation requires solving iteratively or using a financial calculator. However, we can approximate the answer with these inputs.

Let's denote:

- **P** = Price of the bond = $981.73
- **C** = Semiannual coupon payment = $31.5
- **F** = Par value = $1,000
- **n** = Total number of periods = 46

The present value equation for a bond is as follows:

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

where $ r $ is the semiannual YTM. Since this equation requires solving iteratively for $ r $, we can proceed by trial and error or using a financial calculator. In this case, solving gives:

The **closest answer** is approximately **3.23% semiannually**, which corresponds to an annual YTM of:

\[
3.23\% \times 2 = 6.46\%
\]

This is closest to the option **6.45%**, making it the correct answer.

### Answer: 6.45%

Would you like a deeper breakdown of the calculations or have any questions?

---

1. How does the YTM compare to the coupon rate in this example?
2. Why does the bond's price differ from its par value?
3. What happens to the bond’s price if interest rates decrease?
4. How would changing the frequency of payments impact YTM?
5. How is YTM different from current yield?

**Tip:** YTM can be solved using financial calculators or iterative software methods since it involves a complex equation for large periods and non-integer rates.

Broke Benjamin Company has a bond outstanding that makes semiannual payments with a coupon rate of 6.3 percent. The bond sells for $981.73 and matures in 23 years. The par value is $1,000. What is the YTM of the bond?

Determine the Yield to Maturity (YTM) of Broke Benjamin Company's bond with a 6.3% coupon rate and a selling price of $981.73. This detailed solution explains YTM calculation for a bond making semiannual payments over 23 years. Ideal for finance students and those interested in bond valuation.

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