The leverage effect on ROA is represented by which expression?

The leverage effect on ROA is represented by which expression?

• A. ROA + rd
• B. ROA - rd
• C. (ROA - rd) × (D/E)
• D. ROA × (D/E)

Answer: (C)

The levered effect on ROE comes from the spread between what the firm earns on its assets (ROA) and the cost of debt financing (rd), scaled by how much debt relative to equity the firm uses (D/E). This spread represents how much extra return equity holders gain (or lose) from using debt to finance.assets: (ROA − rd) × (D/E). Intuitively, if ROA is higher than the cost of debt, borrowing to finance more assets increases the return earned on equity beyond the plain ROA. This extra boost is exactly proportional to both the debt-to-equity ratio and the difference between ROA and rd. If you compare with ROE, the relationship is ROE = ROA + (ROA − rd) × (D/E). When ROA > rd, leverage raises ROE; when ROA < rd, leverage lowers ROE. Examples help see the effect: with ROA = 10%, rd = 6%, and D/E = 1, the levered contribution is (0.10 − 0.06) × 1 = 0.04, so ROE would be 10% + 4% = 14%. The other forms—adding rd, subtracting rd, or multiplying ROA by D/E—do not capture how debt financing changes ROE relative to ROA.

The levered effect on ROE comes from the spread between what the firm earns on its assets (ROA) and the cost of debt financing (rd), scaled by how much debt relative to equity the firm uses (D/E). This spread represents how much extra return equity holders gain (or lose) from using debt to finance.assets: (ROA − rd) × (D/E).

Intuitively, if ROA is higher than the cost of debt, borrowing to finance more assets increases the return earned on equity beyond the plain ROA. This extra boost is exactly proportional to both the debt-to-equity ratio and the difference between ROA and rd. If you compare with ROE, the relationship is ROE = ROA + (ROA − rd) × (D/E). When ROA > rd, leverage raises ROE; when ROA < rd, leverage lowers ROE.

Examples help see the effect: with ROA = 10%, rd = 6%, and D/E = 1, the levered contribution is (0.10 − 0.06) × 1 = 0.04, so ROE would be 10% + 4% = 14%. The other forms—adding rd, subtracting rd, or multiplying ROA by D/E—do not capture how debt financing changes ROE relative to ROA.