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Answer (A) is correct.
The ROE using the DuPont analysis is calculated as follows:
Net profit margin × Total asset turnover × Equity multiplier (Total assets ÷ Total equity)
The best way to solve this problem is to use actual numbers for the return on equity comparison of this year to last year. Assuming that last year the corporation had a net profit margin of .025, total asset turnover of 1.05, total assets of $500,000, and total equity of $200,000, last year's ROE is equal to 6.56% [.025 × 1.05 × ($500,000 ÷ $200,000)].
By using the information given in the problem, the current-year amounts can be calculated, resulting in a net profit margin of .03125 (increased by 25%), total asset turnover of 1.47 (increased by 40%), total assets of $450,000 (decreased by 10%), and total equity of $280,000 (increased by 40%). Therefore, this year's ROE is equal to 7.38% [.03125 × 1.47 × (450,000 ÷ 280,000)].
The increase in ROE from last year to this year can now be calculated as 12.5% [(7.38 – 6.56) ÷ 6.56].
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