David Ortiz Motors has a target capital structure of 40% debt and 60% equity. The yield to maturity on the company's outstanding bonds is 8%, and the company's tax rate is 25%. Ortiz's CFO has calculated the company's WACC as 8.4%. What is the company's cost of equity capital? Round your answer to the nearest whole number.

To find the company's cost of equity capital, we can use the formula for the Weighted Average Cost of Capital (WACC):

\[
WACC = (E/V) \times r_E + (D/V) \times r_D \times (1 - T)
\]

Where:
- \( E/V \) is the proportion of equity in the capital structure (60% or 0.60),
- \( D/V \) is the proportion of debt in the capital structure (40% or 0.40),
- \( r_E \) is the cost of equity (which we are solving for),
- \( r_D \) is the cost of debt (yield to maturity on bonds, which is 8% or 0.08),
- \( T \) is the tax rate (25% or 0.25),
- WACC is given as 8.4% or 0.084.

Substituting the known values into the WACC formula:

\[
0.084 = 0.60 \times r_E + 0.40 \times 0.08 \times (1 - 0.25)
\]

Now, we will solve for \( r_E \) (cost of equity).

### Step-by-step:
1. Calculate the after-tax cost of debt:
   \[
   0.40 \times 0.08 \times (1 - 0.25) = 0.40 \times 0.08 \times 0.75 = 0.024
   \]

2. Substitute this back into the WACC equation:
   \[
   0.084 = 0.60 \times r_E + 0.024
   \]

3. Subtract 0.024 from both sides:
   \[
   0.084 - 0.024 = 0.60 \times r_E
   \]
   \[
   0.06 = 0.60 \times r_E
   \]

4. Solve for \( r_E \) (cost of equity):
   \[
   r_E = \frac{0.06}{0.60} = 0.10
   \]

Thus, the company's cost of equity capital is **10%**.

Let me know if you want further details or have any questions!

Here are 5 related questions you might explore:
1. How does a company's capital structure influence its WACC?
2. What role does the tax rate play in the cost of debt calculation?
3. Why is the cost of equity typically higher than the cost of debt?
4. What happens to WACC if the cost of equity increases?
5. How do market conditions impact the yield to maturity on bonds?

**Tip**: Always double-check the proportions in the capital structure, as they are key to calculating WACC accurately!

Learn how to calculate the cost of equity for David Ortiz Motors using the WACC formula, considering a capital structure of 40% debt and 60% equity, an 8% yield to maturity on bonds, and a 25% tax rate. This finance problem is ideal for students in undergraduate business courses.

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