Question 1196651
To determine the weight of debt when calculating the cost of capital, we first need to calculate the market value of the bonds. Here's a step-by-step approach:

---

### **Step 1: Bond Valuation Formula**
The market value of a zero-coupon bond is calculated as:
\[
PV = \frac{FV}{(1 + r)^t}
\]
Where:
- \( PV \): Present value (market price of the bond)  
- \( FV \): Face value of the bond (\( \$1,000 \))  
- \( r \): Yield to maturity (per compounding period, semiannual)  
- \( t \): Total number of compounding periods remaining  

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### **Step 2: Identify the Given Information**
- Number of bonds: \( 225,000 \)  
- Face value per bond: \( \$1,000 \)  
- Total face value: \( 225,000 \times 1,000 = \$225,000,000 \)  
- Yield to maturity (current): \( 4.6\% \) annually, or \( 4.6\% / 2 = 2.3\% = 0.023 \) per semiannual period  
- Years to maturity remaining: \( 30 - 5 = 25 \) years  
- Total compounding periods remaining: \( 25 \times 2 = 50 \) periods  

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### **Step 3: Calculate the Market Price of One Bond**
\[
PV = \frac{1,000}{(1 + 0.023)^{50}}
\]

1. Calculate \( (1 + 0.023)^{50} \):
\[
(1 + 0.023)^{50} \approx 3.2094
\]

2. Calculate \( PV \) for one bond:
\[
PV = \frac{1,000}{3.2094} \approx 311.63
\]

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### **Step 4: Calculate the Total Market Value of Debt**
The total market value of the bonds is:
\[
\text{Total Market Value} = 225,000 \times 311.63 \approx 69,116,750
\]

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### **Step 5: Calculate the Weight of Debt**
The weight of debt is calculated as:
\[
\text{Weight of Debt} = \frac{\text{Market Value of Debt}}{\text{Market Value of Debt + Market Value of Equity}}
\]

Given:
- Market value of equity = \( \$120,000,000 \)  
- Market value of debt = \( 69,116,750 \)

\[
\text{Weight of Debt} = \frac{69,116,750}{69,116,750 + 120,000,000} \approx \frac{69,116,750}{189,116,750} \approx 0.3654
\]

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### **Final Answer**
The weight of debt to use when calculating the cost of capital is approximately:
\[
\boxed{36.54\%}
\]