If the return on assets (ROA) is 6.7% and the equity multiplier is 2.5, what will be the return on equity (ROE)?

In Finance MCQs, calculating Return on Equity (ROE) using the DuPont formula is a core concept in corporate finance. ROE measures the profitability of a company relative to the equity invested by shareholders, providing insight into how efficiently management uses shareholders’ funds to generate profits. Understanding ROE is critical for investors, analysts, and finance students because it connects operational efficiency, asset management, and financial leverage.

The DuPont identity breaks ROE into two key components:

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  Return on Assets (ROA): ROA measures the profitability of the company relative to total assets. It reflects how efficiently the company generates profit from its asset base. In this question, the ROA is 6.7%, or 0.067 as a decimal.

  
  


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  Equity Multiplier (Financial Leverage): The equity multiplier shows the extent to which a company uses debt to finance its assets. It is calculated as:
  Equity Multiplier = Total Assets ÷ Total Equity
  A higher equity multiplier indicates greater leverage, which amplifies ROE but also increases financial risk. Here, the equity multiplier is 2.5.

  
  

The DuPont formula then links these elements:

ROE = ROA × Equity Multiplier

Substituting the given values:

ROE = 0.067 × 2.5 = 0.1675

Converting to a percentage:

ROE = 16.75%

This calculation shows that the company generates a 16.75% return on shareholders’ equity, demonstrating strong profitability relative to the equity invested. It also highlights how leverage magnifies returns: although the ROA is only 6.7%, using financial leverage increases ROE to 16.75%.

Why the other options are incorrect:

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  2.68% underestimates the effect of leverage. Some students mistakenly divide ROA by the equity multiplier instead of multiplying.

  
  


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  0.37% is likely a calculation error, possibly from misinterpreting decimals or percentage conversions.

  
  


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  9.20% does not correctly include the leverage effect. Without applying the equity multiplier properly, the resulting ROE underrepresents the impact of financial leverage.

  
  

Understanding the DuPont formula and ROE calculation is important in Finance MCQs because it:

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  Demonstrates the impact of financial leverage on shareholder returns. Higher leverage increases ROE but also increases the company’s risk exposure.

  
  


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  Connects asset efficiency and capital structure to shareholder profitability. ROA reflects operational efficiency, while the equity multiplier shows financing strategy.

  
  


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  Helps investors and analysts compare companies with different capital structures and operational efficiency.

  
  

From an exam perspective, this question tests both numerical accuracy and conceptual understanding. It ensures students know how operational performance (ROA) and financial leverage (equity multiplier) combine to determine shareholder returns (ROE). This is a common topic in corporate finance, accounting, and business management exams, including NTS, FPSC, CSS, and PMS exams.

In practice, ROE is used by investors to assess how effectively management is generating returns from shareholders’ equity. Companies with high ROE are generally considered efficient in using equity capital, but excessively high ROE may also indicate high financial risk due to leverage.

Conclusion:

If the return on assets (ROA) is 6.7% and the equity multiplier is 2.5, the return on equity (ROE) is 16.75%. This calculation shows the combined effect of operational efficiency and financial leverage on shareholder returns. Therefore, in Finance MCQs, the correct answer is 16.75%, making option A the right choice.