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%

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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.