In Finance MCQs, Return on Equity (ROE) measures how effectively a company generates profit from shareholders’ equity. ROE is one of the most important profitability ratios for investors and analysts because it shows the efficiency with which management uses equity... Read More
In Finance MCQs, Return on Equity (ROE) measures how effectively a company generates profit from shareholders’ equity. ROE is one of the most important profitability ratios for investors and analysts because it shows the efficiency with which management uses equity capital to produce earnings. The formula to calculate ROE using Return on Assets (ROA) is derived from the DuPont equation:
ROE = ROA × (Total Assets ÷ Common Equity)
This formula demonstrates the relationship between a company’s overall profitability (ROA) and financial leverage, represented by the ratio of Total Assets to Common Equity, also known as the equity multiplier. By multiplying ROA by the equity multiplier, we can see how asset returns are amplified through the company’s capital structure to create returns for shareholders.
In this question, the company’s ROA is 5.5%, which we convert into decimal form for calculation:
ROA = 5.5% = 0.055
The Total Assets are given as $3,000, and the Common Equity is $1,050. The equity multiplier is calculated as:
Equity Multiplier = Total Assets ÷ Common Equity = 3,000 ÷ 1,050 ≈ 2.8571
Now, applying the DuPont formula:
ROE = ROA × Equity Multiplier = 0.055 × 2.8571 ≈ 0.1571
This means the company has a Return on Equity of approximately 15.71%, indicating that for every dollar of equity invested, the company generates 15.71 cents of net income. This ROE reflects both the company’s operational efficiency (ROA) and its use of leverage through equity financing.
Understanding this concept is essential for Finance MCQs, Accounting MCQs, corporate finance exams, and banking job tests. Many exam questions provide ROA, total assets, and equity and require candidates to apply the DuPont formula to calculate ROE correctly.
The other options are incorrect. Option 22275 is unrealistic and results from miscalculating units. Option 0.01925 underestimates ROE, likely due to dividing incorrectly or not applying the equity multiplier. Option 1.925 times misrepresents ROE as a multiplier rather than a ratio or percentage.
It is important for candidates to remember the key keywords in such MCQs: ROE, ROA, Total Assets, Common Equity, Equity Multiplier, DuPont Formula. Recognizing these terms ensures quick identification of the correct method to solve the problem in exams.
From a practical perspective, ROE is an essential measure for investors because it shows how efficiently the company uses shareholders’ funds to generate profit. Companies with higher ROE are generally considered more efficient and profitable, though extremely high ROE may indicate higher financial risk due to leverage.
In conclusion, using the DuPont equation, a company with a 5.5% ROA, $3,000 in total assets, and $1,050 in equity will have a Return on Equity of 0.1571, making this the correct answer for this Finance MCQ.
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