Return on equity can be decomposed into:

Question

BlackTom AI · Accepted Answer

Begin by recalling the fundamental decomposition of return on equity (ROE). ROE can be expressed as the product of two components: return on assets (ROA) and the leverage multiplier. This reflects how profitability relative to assets interacts with how effectively leverage amplifies equity returns.

Option a: 'the sum of the profit margin, leverage multiplier, and the interest ratio.' This statement wrongly combines elements that do not algebraically generate ROE. ROE is not simply additive across profit margin, leverage, and interest ratio; the standard model uses multiplication, not addition, and does not include an 'interest ratio' term in this basic decomposition.

Option b: 'the sum of return on assets and the leverage multiplier.' Here the idea of adding ROA and leverage multiplier is incorrect. ROE is not derived by adding these two components; multiplication captures how leverage amplifies asset-based profitability.

Option c: 'the sum of the profit margin and the leverage multiplier.' This misses ROA entirely and treats ROE as a combination of profit margin and leverage in an additive form, which does not align with the canonical multiplicative decomposition.

Option d: 'the product of the profit margin and the leverage multiplier.' While this looks closer to a multiplicative structure, it still omits ROA as a distinct component. The standard decomposition includes ROA (which itself equals profit margin times asset turnover) multiplied by the leverage multiplier; focusing only on profit margin ignores asset efficiency and the full ROA concept.

Option e: 'the product of return on assets and the leverage multiplier.' This aligns with the widely taught formula ROE = ROA × Leverage Multiplier. It correctly captures that ROA (return on assets) scaled by how much leverage amplifies equity produces ROE.

In summary, the incorrect options either use addition where multiplication is required or omit key components (like ROA or asset turnover embedded in ROA), while the correct option matches the established multiplicative relationship between ROA and leverage multiplier to yield ROE.

Return on equity can be decomposed into:Single choice

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