https://file.aiquickdraw.com/mathbot/file/17294417507037hrwop3v.jpg

To help you with this problem, I will use the table and the tax rate of 50% to calculate the Weighted Average Cost of Capital (WACC) for each debt-equity mix percentage.

### The formula for WACC is:
\[
WACC = \left( E/V \times Re \right) + \left( D/V \times Rd \times (1 - Tc) \right)
\]
Where:
- \(E/V\) is the proportion of equity in the total capital.
- \(D/V\) is the proportion of debt in the total capital.
- \(Re\) is the cost of equity.
- \(Rd\) is the cost of debt before tax.
- \(Tc\) is the tax rate.

I'll compute the WACC for each mix and suggest the best debt-equity mix based on the lowest WACC.

1. **0% Debt (100% Equity)**:
   - \(D/V = 0\), \(E/V = 1\)
   - \(Re = 16\%\), \(Rd = 12\%\), \(Tc = 50\%\)
   - \(WACC = 1 \times 16\% + 0 = 16\%\)

2. **20% Debt, 80% Equity**:
   - \(D/V = 0.2\), \(E/V = 0.8\)
   - \(Re = 16\%\), \(Rd = 12\%\)
   - \(WACC = (0.8 \times 16\%) + (0.2 \times 12\% \times (1 - 0.5))\)
   - \(WACC = 12.8\% + 1.2\% = 14\%\)

3. **40% Debt, 60% Equity**:
   - \(D/V = 0.4\), \(E/V = 0.6\)
   - \(Re = 20\%\), \(Rd = 16\%\)
   - \(WACC = (0.6 \times 20\%) + (0.4 \times 16\% \times (1 - 0.5))\)
   - \(WACC = 12\% + 3.2\% = 15.2\%\)

4. **50% Debt, 50% Equity**:
   - \(D/V = 0.5\), \(E/V = 0.5\)
   - \(Re = 22\%\), \(Rd = 20\%\)
   - \(WACC = (0.5 \times 22\%) + (0.5 \times 20\% \times (1 - 0.5))\)
   - \(WACC = 11\% + 5\% = 16\%\)

5. **60% Debt, 40% Equity**:
   - \(D/V = 0.6\), \(E/V = 0.4\)
   - \(Re = 24\%\), \(Rd = 22\%\)
   - \(WACC = (0.4 \times 24\%) + (0.6 \times 22\% \times (1 - 0.5))\)
   - \(WACC = 9.6\% + 6.6\% = 16.2\%\)

6. **75% Debt, 25% Equity**:
   - \(D/V = 0.75\), \(E/V = 0.25\)
   - \(Re = 28\%\), \(Rd = 24\%\)
   - \(WACC = (0.25 \times 28\%) + (0.75 \times 24\% \times (1 - 0.5))\)
   - \(WACC = 7\% + 9\% = 16\%\)

### Conclusion:
- The lowest WACC occurs with **20% debt and 80% equity**, resulting in a **14% WACC**. Thus, this is the best debt-equity mix for the company.

Would you like more details on the calculations or any other clarification?

Here are 5 questions you might explore next:
1. How would changes in the tax rate affect the WACC for different debt-equity mixes?
2. Why does increasing debt initially decrease the WACC but then increase it?
3. How do real-world companies decide on their optimal debt-equity mix?
4. What are the risks associated with a higher debt-equity ratio despite lower initial WACC?
5. How does the cost of capital affect a company's valuation?

**Tip:** Companies with high debt must be cautious of rising interest rates, as they can significantly increase the cost of debt over time.

PQ Ltd estimates the cost of equity and debt components of its capital for different levels of debt equity mix as follows: Debt as % to total capital and cost of equity and cost of debt are given. Suggest the best Debt-equity mix for the company. Tax rate 50%.

Learn how to calculate the optimal debt-equity mix for PQ Ltd by using the WACC formula. The problem involves estimating the cost of equity and debt components with varying capital structures and a tax rate of 50%. The solution identifies the best mix to minimize WACC, using core finance concepts such as cost of capital and weighted average.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation