What is the cost of equity for a company with an ROA of 10%, financed with 50% debt and 50% equity, if the cost of debt is 5%?

What is the cost of equity for a company with an ROA of 10%, financed with 50% debt and 50% equity, if the cost of debt is 5%?

• A. 10%
• B. 15%
• C. 5%
• D. 20%

Answer: (B)

To determine the cost of equity for a company, we can use the Modigliani-Miller theorem in a scenario where we have a mix of debt and equity financing. In this case, the company has an ROA (Return on Assets) of 10%, which indicates the company's profitability relative to its total assets. Since the company is financed with 50% debt and 50% equity, we can derive the cost of equity using the overall return and the cost of debt. Given the cost of debt is 5% and the ROA is 10%, we can use the following formula to calculate the cost of equity: Cost of equity = ROA + (ROA - Cost of debt) * (Debt/Equity) Substituting the known values into the formula: - ROA = 10% - Cost of debt = 5% - Debt/Equity = 0.5/0.5 = 1 Plugging these values into the formula results in: Cost of equity = 10% + (10% - 5%) * 1 Cost of equity = 10% + 5% Cost of equity = 15% This calculation illustrates how the cost of equity reflects both

To determine the cost of equity for a company, we can use the Modigliani-Miller theorem in a scenario where we have a mix of debt and equity financing.

In this case, the company has an ROA (Return on Assets) of 10%, which indicates the company's profitability relative to its total assets. Since the company is financed with 50% debt and 50% equity, we can derive the cost of equity using the overall return and the cost of debt.

Given the cost of debt is 5% and the ROA is 10%, we can use the following formula to calculate the cost of equity:

Cost of equity = ROA + (ROA - Cost of debt) * (Debt/Equity)

Substituting the known values into the formula:

• ROA = 10%

• Cost of debt = 5%

• Debt/Equity = 0.5/0.5 = 1

Plugging these values into the formula results in:

Cost of equity = 10% + (10% - 5%) * 1

Cost of equity = 10% + 5%

Cost of equity = 15%

This calculation illustrates how the cost of equity reflects both