Question

A company has a weighted average cost of capital of 7.5%. it's cost of equity is 10% and the average yield to maturity on its bonds is 5%. if the tax rate is 35%, what is the company's market value debt-equity (d/e) ratio?

Answer 1

The company's market value debt-equity (D/E) ratio is approximately 0.56.

Step-by-step explanation:

To calculate the market value debt-equity (D/E) ratio, we can use the formula:
`\( D/E = \frac{\text{Market Value of Debt}}{\text{Market Value of Equity}} \)`. The weighted average cost of capital (WACC) is the weighted average of the cost of equity and the after-tax cost of debt. The formula for WACC is:
`\( WACC = \frac{\text{E}}{\text{V}} * \text{Re} + \frac{\text{D}}{\text{V}} * (\text{Rd} * (1 - \text{Tc})) \)`, where E is the market value of equity, D is the market value of debt,
`\( \text{V} \)` is the total market value (equity + debt),
`\( \text{Re} \)` is the cost of equity,
`\( \text{Rd} \)` is the cost of debt, and
`\( \text{Tc} \)` is the corporate tax rate.

Given that WACC is 7.5%, Re is 10%, Rd is 5%, and Tc is 35%, we can rearrange the WACC formula to find the market value debt-equity (D/E) ratio. Solving for
`\( \frac{\text{D}}{\text{E}} \)`, we get
`\( \frac{\text{D}}{\text{E}} = \frac{(WACC - \text{Re})}{(\text{Rd} * (1 - \text{Tc}))} \)`. Substituting in the values, we find
`\( \frac{\text{D}}{\text{E}} = ((0.075 - 0.10))/((0.05 * (1 - 0.35))) \)`, which results in approximately 0.56. Therefore, the company's market value debt-equity (D/E) ratio is approximately 0.56.