If a company has a return on assets of 10% and a 50/50 debt-to-equity capital structure, what is the resulting return on equity?

If a company has a return on assets of 10% and a 50/50 debt-to-equity capital structure, what is the resulting return on equity?

• A. 15%
• B. 20%
• C. 25%
• D. 10%

Answer: (B)

The idea is that leverage from debt increases the return on equity relative to the return on assets. Return on equity is net income relative to shareholders’ equity, while return on assets is net income relative to total assets. If the company finances equally with debt and equity (D/E = 1), then total assets are twice the equity. With a 10% return on assets, net income is 10% of assets. If assets = 100, net income = 10. Debt would be 50 and equity 50. The return on equity is net income over equity: 10 / 50 = 0.20, or 20%. A quick way to see it: ROE = ROA × (Assets / Equity) = 0.10 × (1 + D/E) = 0.10 × 2 = 0.20, since D/E is 1. So the resulting ROE is 20%. This approach assumes no taxes or interest effects beyond this simplified leverage scenario.

The idea is that leverage from debt increases the return on equity relative to the return on assets. Return on equity is net income relative to shareholders’ equity, while return on assets is net income relative to total assets. If the company finances equally with debt and equity (D/E = 1), then total assets are twice the equity.

With a 10% return on assets, net income is 10% of assets. If assets = 100, net income = 10. Debt would be 50 and equity 50. The return on equity is net income over equity: 10 / 50 = 0.20, or 20%.

A quick way to see it: ROE = ROA × (Assets / Equity) = 0.10 × (1 + D/E) = 0.10 × 2 = 0.20, since D/E is 1.

So the resulting ROE is 20%. This approach assumes no taxes or interest effects beyond this simplified leverage scenario.