how to solve for weight of debt, weight of equity and WACC with debt-equity ratio, cost of equity, cost of debt and tax rate

To calculate the **Weight of Debt (Wd)**, **Weight of Equity (We)**, and the **Weighted Average Cost of Capital (WACC)** given the **Debt-Equity Ratio (D/E)**, **Cost of Equity (Re)**, **Cost of Debt (Rd)**, and the **Tax Rate (T)**, follow these steps:

### 1. **Calculate the Weights:**
   - The **Debt-Equity Ratio (D/E)** gives the proportion of debt to equity.
     - If \( D/E = x \), this means for every 1 unit of equity, there are \( x \) units of debt.
   - The weights of debt (\( W_d \)) and equity (\( W_e \)) are determined as follows:
     - \( W_e = \frac{1}{1 + D/E} = \frac{1}{1 + x} \)
     - \( W_d = \frac{D/E}{1 + D/E} = \frac{x}{1 + x} \)

### 2. **Calculate WACC:**
   The formula for **WACC** is:
   \[
   \text{WACC} = W_e \times R_e + W_d \times R_d \times (1 - T)
   \]
   Where:
   - \( W_e \) = Weight of Equity
   - \( R_e \) = Cost of Equity
   - \( W_d \) = Weight of Debt
   - \( R_d \) = Cost of Debt
   - \( T \) = Tax Rate (as a decimal)

### Example:
Let’s assume the following values:
- Debt-Equity Ratio (\( D/E \)) = 0.5
- Cost of Equity (\( R_e \)) = 12% or 0.12
- Cost of Debt (\( R_d \)) = 6% or 0.06
- Tax Rate (\( T \)) = 30% or 0.30

#### Step 1: Find the Weights
\[
W_e = \frac{1}{1 + 0.5} = \frac{1}{1.5} = 0.6667
\]
\[
W_d = \frac{0.5}{1 + 0.5} = \frac{0.5}{1.5} = 0.3333
\]

#### Step 2: Calculate WACC
\[
\text{WACC} = (0.6667 \times 0.12) + (0.3333 \times 0.06 \times (1 - 0.30))
\]
\[
\text{WACC} = 0.08 + 0.014 = 0.094 = 9.4\%
\]

### Summary:
- Weight of Debt (\( W_d \)) = 0.3333
- Weight of Equity (\( W_e \)) = 0.6667
- WACC = 9.4%

Let me know if you want further details or explanations!

### Related Questions:
1. How does an increase in the debt-equity ratio affect WACC?
2. Why is the tax rate applied only to the cost of debt in WACC calculations?
3. How can a firm lower its WACC?
4. What is the relationship between WACC and a firm’s risk profile?
5. How do changes in market conditions influence the cost of equity and cost of debt?

### Tip:
Using a higher proportion of debt (increasing the debt-equity ratio) generally lowers WACC, but it increases the firm's financial risk.

Learn how to calculate the weight of debt, weight of equity, and WACC using the debt-equity ratio, cost of equity, cost of debt, and tax rate. This guide covers key finance concepts, including weighted averages and the impact of taxes on cost of capital.

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