$$ 1 \leftarrow \quad \begin{array}{l} ext { Bond prices and maturity dates. Moore Company is about to issue a bond with semiannual coupon } \ ext { payments, an annual coupon rate of } 9 \% ext {, and a par value of } \$ 1,000 ext {. The yield to maturity for this bond is } \ 10 \% ext {. } \ ext { a. What is the price of the bond if it matures in } 5,10,15 ext {, or } 20 ext { years? } \ ext { b. What do you notice about the price of the bond in relationship to the maturity of the bond? } \ ext { a. What is the price of the bond if it matures in } 5 ext { years? } \ \$ \square ext { (Round to the nearest cent.) }\end{array} $$ (R)

Question

$$ 1 \leftarrow \quad \begin{array}{l}	ext { Bond prices and maturity dates. Moore Company is about to issue a bond with semiannual coupon } \ 	ext { payments, an annual coupon rate of } 9 \% 	ext {, and a par value of } \$ 1,000 	ext {. The yield to maturity for this bond is } \ 10 \% 	ext {. } \ 	ext { a. What is the price of the bond if it matures in } 5,10,15 	ext {, or } 20 	ext { years? } \ 	ext { b. What do you notice about the price of the bond in relationship to the maturity of the bond? } \ 	ext { a. What is the price of the bond if it matures in } 5 	ext { years? } \ \$ \square 	ext { (Round to the nearest cent.) }\end{array} $$ (R)

UpStudy AI · Accepted Answer

To determine the price of the bond maturing in **5 years**, we need to calculate the present value of its future cash flows, which include the semiannual coupon payments and the par value at maturity. Here's a step-by-step breakdown:

### **Given:**
- **Annual Coupon Rate:** 9%
- **Par Value (Face Value):** \$1,000
- **Yield to Maturity (YTM):** 10%
- **Maturity:** 5 years
- **Coupon Frequency:** Semiannual

### **Calculations:**

1. **Determine the Semiannual Coupon Payment:**
   $$
   \text{Semiannual Coupon Payment} = \left(\frac{9\%}{2}\right) \times \$1,000 = 4.5\% \times \$1,000 = \$45
   $$

2. **Calculate the Total Number of Periods:**
   $$
   \text{Total Periods} = 5 \text{ years} \times 2 = 10 \text{ periods}
   $$

3. **Find the Semiannual Yield:**
   $$
   \text{Semiannual Yield} = \frac{10\%}{2} = 5\%
   $$

4. **Calculate the Present Value of the Coupon Payments:**
   $$
   PV_{\text{coupons}} = C \times \left[\frac{1 - (1 + r)^{-n}}{r}\right]
   $$
   $$
   PV_{\text{coupons}} = \$45 \times \left[\frac{1 - (1 + 0.05)^{-10}}{0.05}\right] \approx \$45 \times 7.7217 \approx \$347.48
   $$

5. **Calculate the Present Value of the Par Value:**
   $$
   PV_{\text{par}} = \frac{\$1,000}{(1 + 0.05)^{10}} \approx \frac{\$1,000}{1.62889} \approx \$613.91
   $$

6. **Determine the Total Bond Price:**
   $$
   \text{Bond Price} = PV_{\text{coupons}} + PV_{\text{par}} \approx \$347.48 + \$613.91 \approx \$961.39
   $$

### **Answer:**
**a. The price of the bond maturing in 5 years is \$961.39.**

### **b. Observation on Bond Prices and Maturity:**
As bonds **increase in maturity**, their prices generally become more sensitive to changes in interest rates. In this case, longer maturities would result in lower bond prices when the yield to maturity is higher than the coupon rate, reflecting greater interest rate risk. Conversely, shorter maturities tend to have prices closer to their par value and are less sensitive to interest rate changes.
**a. The bond maturing in 5 years is priced at \$961.39.** **b. Generally, as the maturity of the bond increases, its price decreases when the yield to maturity is higher than the coupon rate.**

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