All else constant, an increase in which of the following must increase the return on equity?

Question

BlackTom AI · Accepted Answer

To assess how return on equity (ROE) responds to changes, we recall the DuPont decomposition: ROE = Profit Margin × Asset Turnover × Equity Multiplier. The equity multiplier is a measure of financial leverage, and asset turnover captures how efficiently assets generate sales. With all else constant, increases in either asset turnover or leverage (as reflected by the equity multiplier or debt-to-equity ratio) can raise ROE, while changes that involve equity or cash flow without increasing net income or leverage may not.

Option 1: "Total assets and sales". Increasing total assets or sales by themselves does not guarantee a higher ROE if the profitability and leverage remain unchanged. If sales rise but profit margin remains the same and assets are funded evenly (no change in leverage), ROE may stay the same or move in ways not guaranteed to rise. This option mixes variables that do not directly map to a guaranteed ROE increase under the “all else constant” condition.

Option 2: "Debt-equity ratio and total debt". A higher debt-equity ratio implies more leverage, which can increase the equity multiplier and thus ROE, provided net income and asset utilization do not deteriorate. However, simply stating higher debt and leverage without confirming that net income or efficiency do not decline leaves some risk; in constrained scenarios, higher debt could depress ROE if returns do not cover the cost of debt. The implication is not as direct as the combination in Option 5.

Option 3: "Net income and total equity". Increasing net income would raise ROE directly, but increasing total equity (with net income held constant) could reduce ROE since ROE = NI / Equity. Unless net income rises proportionally with equity, ROE would not necessarily increase. This option includes a counteracting pair, making the net effect less certain.

Option 4: "Equity multiplier and total equity". Elevating the equity multiplier (more leverage) can raise ROE if returns on assets exceed the cost of debt and if profitability remains stable. However, increasing total equity tends to dilute ROE unless net income grows at a sufficient rate. The combination here is not guaranteed to increase ROE under all-else-constant assumptions, since the higher equity can offset the leverage benefit.

Option 5: "Total asset turnover and debt-equity ratio". This pair directly aligns with the DuPont framework: higher asset turnover increases the rate at which assets generate sales, boosting ROE through the Asset Turnover term, and a higher debt-equity ratio increases leverage, boosting the Equity Multiplier term. When both are increased while profitability and other factors remain constant, ROE is most consistently driven higher. The two components reinforce each other to lift ROE in a straightforward, predictable manner.

All else constant, an increase in which of the following must increase the return on equity?单项选择题

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