Question

A firm is 67.00% equity. It has a cost of equity of 18.00%, a pre-tax cost of debt of 8.00%, and a marginal tax rate of 21.00%. What is the firm's weighted average cost of capital?

Answer 1

To calculate the firm's weighted average cost of capital (WACC), we can use the following formula:

\[
\text{WACC} = \left( \frac{E}{V} \times r_e \right) + \left( \frac{D}{V} \times r_d \times (1 - T) \right)
\]

Where:
- \(E\) = market value of equity
- \(D\) = market value of debt
- \(V\) = \(E + D\) = total market value of the firm's financing (equity + debt)
- \(r_e\) = cost of equity
- \(r_d\) = pre-tax cost of debt
- \(T\) = marginal tax rate

From the information provided, we have:

- \(E/V = 67.00\% = 0.67\)
- Therefore, \(D/V = 1 - E/V = 1 - 0.67 = 0.33\)
- \(r_e = 18.00\% = 0.18\)
- \(r_d = 8.00\% = 0.08\)
- \(T = 21.00\% = 0.21\)

Now, substituting these values into the WACC formula:

1. Calculate the equity contribution:

\[
\frac{E}{V} \times r_e = 0.67 \times 0.18 = 0.1206
\]

2. Calculate the debt contribution (after tax):

\[
\frac{D}{V} \times r_d \times (1 - T) = 0.33 \times 0.08 \times (1 - 0.21)
\]
\[
= 0.33 \times 0.08 \times 0.79 = 0.020832
\]

3. Add the two components to get WACC:

\[
\text{WACC} = 0.1206 + 0.020832 = 0.141432
\]

Converting back to percentage:

\[
\text{WACC} = 14.14\%
\]

Thus, the firm's weighted average cost of capital (WACC) is approximately **14.14%**.