During the lastest year Ruth Corp had sales of $300,000 and a net income of $20,000, an its year-end assets were $200,000. The firm's total debt to total assetts ratio is 40%. Based on the DuPont equation, what was the form's ROE?|||I'm not sure what your book uses as a Dupont equation, but the math to do this is relatively simple if you know what the terms mean.
Start at the beginning.
Equity = assets + liabilities.
Equity = 200,000 + liabilities
Equity = 200,000 + x the x = some number/200,000 that equals 40%, so X (or liabilities) must equal 500,000.
Equity = 200,000 + 500,000 = 700,000
Return on equity = net income divided by equity or 20,000/700,000 = 2.857%
Expressed as an equation, I would write the following:
ROE = Income/(Assets+(Assets/0.4)) or
ROE = 20,000/(200,000+(200000/.4)) = 2.857%
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