Bond prices and maturity dates. Moore Company is about to issue a bond with semiannual coupon payments, an annual coupon rate of $$ 9 \% $$, and a par value of $$ \$ 1,000 $$. The yield to maturity for this bond is $$ 10 \% $$. a. What is the price of the bond if it matures in $$ 5,10,15 $$, or 20 years? b. What do you notice about the price of the bond in relationship to the maturity of the bond? $$ \$ 937.69 $$ (Round to the nearest cent.) What is the price of the bond if it matures in 15 years? $$ \$ \square $$ (Round to the nearest cent.)

Question

UpStudy AI · Accepted Answer

To determine the price of Moore Company's bond with a 15-year maturity, we'll follow these steps:

### **Given:**
- **Par Value (FV):** \$1,000
- **Annual Coupon Rate:** 9%
- **Semiannual Coupon Payment (PMT):** $$ \frac{9\% \times \$1,000}{2} = \$45 $$
- **Yield to Maturity (YTM):** 10% annually, or 5% per semiannual period
- **Number of Years to Maturity:** 15 years
- **Total Number of Semiannual Periods (N):** $$ 15 \times 2 = 30 $$ periods

### **Bond Pricing Formula:**
$$
\text{Price} = PMT \times \left(1 - (1 + r)^{-N}\right) / r + \frac{FV}{(1 + r)^N}
$$
Where:
- $$ PMT $$ = Semiannual coupon payment (\$45)
- $$ r $$ = Semiannual Yield (5% or 0.05)
- $$ N $$ = Total number of periods (30)
- $$ FV $$ = Par Value (\$1,000)

### **Calculations:**

1. **Calculate the Present Value of Coupon Payments:**
$$
PV_{\text{coupons}} = 45 \times \left( \frac{1 - (1 + 0.05)^{-30}}{0.05} \right)
$$
$$
(1 + 0.05)^{-30} \approx 0.231377
$$
$$
1 - 0.231377 = 0.768623
$$
$$
\frac{0.768623}{0.05} = 15.37246
$$
$$
PV_{\text{coupons}} = 45 \times 15.37246 \approx 691.76
$$

2. **Calculate the Present Value of the Par Value:**
$$
PV_{\text{par}} = \frac{1,000}{(1 + 0.05)^{30}} \approx \frac{1,000}{4.321942} \approx 231.38
$$

3. **Total Bond Price:**
$$
\text{Price} = PV_{\text{coupons}} + PV_{\text{par}} \approx 691.76 + 231.38 = 923.14
$$

### **Final Answer:**
**The price of the bond if it matures in 15 years is \$923.14.**
The price of the bond if it matures in 15 years is \$923.14.

Real Tutor Solution

Answer

Solution

Beyond the Answer

Related Questions

Latest Economics Questions