I'm struggling with being able to solve this question:
A company wants to raise money in the capital markets. The firm intends to sell $18 million of common stock; the expected return is 15%. In addition, the company plans to issue $5 million of debt, the cost of this debt is 12%, and the tax rate is 35%. What is the WACC?
To calculate the Weighted Average Cost of Capital (WACC), you need to find the weighted average of the cost of equity and the cost of debt. Here's how you can calculate it:
1. Start by calculating the cost of equity:
The cost of equity represents the return expected by the shareholders. In this case, it is given as 15%. So, the cost of equity is 15%.
2. Calculate the cost of debt:
The cost of debt represents the interest paid on the debt. In this case, the debt amount is $5 million, and the cost of debt is 12%. However, since the interest on debt is tax-deductible, you need to consider the tax benefit. Multiply the cost of debt by (1 - tax rate). In this case, the tax rate is 35%, so the tax benefit is (1 - 0.35) = 0.65. Multiply this tax benefit by the cost of debt (12%) to get the after-tax cost of debt: 0.65 * 12% = 7.8%.
3. Determine the weights:
The weights represent the proportion of equity and debt in the company's capital structure. In this case, the company intends to sell $18 million of common stock and issue $5 million of debt. The total value of the company's capital is $18 million + $5 million = $23 million. Calculate the percentage of equity by dividing the value of equity by the total capital: ($18 million / $23 million) = 78.26% and the percentage of debt is 21.74%.
4. Calculate the WACC:
Multiply the cost of equity by the weight of equity (0.7826) and the after-tax cost of debt by the weight of debt (0.2174). Then, sum these two values to get the WACC:
WACC = (Cost of equity * Weight of equity) + (After-tax cost of debt * Weight of debt)
WACC = (15% * 0.7826) + (7.8% * 0.2174)
WACC ≈ 11.73%
Therefore, the WACC for the company is approximately 11.73%.
To calculate the weighted average cost of capital (WACC), we need to consider the cost of equity and the cost of debt, weighted by their respective proportions in the company's capital structure.
Step 1: Calculate the cost of equity:
The cost of equity can be calculated using the dividend growth model or the capital asset pricing model (CAPM). Since the question does not provide any information regarding dividends or risk-free rate, we will use the CAPM.
The CAPM formula is:
Cost of equity = Risk-free rate + Beta * Equity risk premium
Assuming the risk-free rate is 5% and the equity risk premium is 8%, we can calculate the cost of equity as follows:
Cost of equity = 5% + 1.5 Beta * 8%
= 5% + 12%
= 17%
Step 2: Calculate the after-tax cost of debt:
The after-tax cost of debt takes into account the tax shield provided by deducting interest expenses. We need to calculate the interest expense first.
Interest expense = Debt * Cost of debt
= $5,000,000 * 12%
= $600,000
Tax shield = Interest expense * Tax rate
= $600,000 * 35%
= $210,000
After-tax cost of debt = Cost of debt * (1 - Tax rate)
= 12% * (1 - 35%)
= 12% * 65%
= 7.8%
Step 3: Calculate the WACC:
WACC = (Equity proportion * Cost of equity) + (Debt proportion * After-tax cost of debt)
To calculate the equity and debt proportions, divide the respective amounts by the total capitalization:
Equity proportion = $18,000,000 / ($18,000,000 + $5,000,000)
= $18,000,000 / $23,000,000
≈ 0.7826
Debt proportion = $5,000,000 / ($18,000,000 + $5,000,000)
= $5,000,000 / $23,000,000
≈ 0.2174
Now we can calculate the WACC:
WACC = (0.7826 * 17%) + (0.2174 * 7.8%)
≈ 13.289%