Which statement best describes the relationship between ROA and ROE when a firm has debt?

Which statement best describes the relationship between ROA and ROE when a firm has debt?

• A. ROE is always equal to ROA.
• B. ROE will be higher than ROA if there is positive debt financing.
• C. ROE will be lower than ROA if there is debt financing.
• D. ROE cannot be influenced by debt.

Answer: (B)

Using debt creates financial leverage, which changes how asset returns appear to shareholders. ROA measures how productive the entire asset base is, while ROE measures how productive the owners’ equity is. Since ROE equals net income divided by equity and ROA equals net income divided by total assets, you can relate them as ROE = ROA × (Assets / Equity). When debt is present, Assets / Equity = 1 + (Debt / Equity) > 1, so ROE becomes larger than ROA for a given level of net income. This amplification happens as long as there is positive debt financing and the firm is generating enough income to cover its financing costs. If profitability collapses or debt is excessive, the relationship can weaken, but with positive debt and solid earnings, ROE will be higher than ROA.

Using debt creates financial leverage, which changes how asset returns appear to shareholders. ROA measures how productive the entire asset base is, while ROE measures how productive the owners’ equity is. Since ROE equals net income divided by equity and ROA equals net income divided by total assets, you can relate them as ROE = ROA × (Assets / Equity). When debt is present, Assets / Equity = 1 + (Debt / Equity) > 1, so ROE becomes larger than ROA for a given level of net income. This amplification happens as long as there is positive debt financing and the firm is generating enough income to cover its financing costs. If profitability collapses or debt is excessive, the relationship can weaken, but with positive debt and solid earnings, ROE will be higher than ROA.