Keller Cosmetics maintains an operating profit margin of 7% and asset turnover ratio of 4. a. What is its ROA? (Enter your answer as a whole percent.)
b. If its debt-equity ratio is 1, its interest payments are $9,300 and taxes are $10,600, and EBIT is $26,500, what is its ROE?

a. What is its ROA?

return on assets (ROA) = profit margin x asset turnover = 7% x 4 = 28%

mathematically it can be solved this way:

profit margin = net income / total sales

total sales = net income / 7%

asset turnover = total sales / total assets

total sales = 4 x total assets

net income / 7% = 4 x total assets

ROA = net income / total assets = 7% x 4 = 28%

b. If its debt-equity ratio is 1, its interest payments are $9,300 and taxes are $10,600, and EBIT is $26,500, what is its ROE?

ROE = profit margin x asset turnover x leverage

leverage = net income / earnings before taxes

net income = EBIT - interests - taxes

net income = $26,500 - $9,300 - $10,600 = $6,600

earnings before taxes = EBIT - interests = $26,500 - $9,300 = $17,200

leverage = $6,600 / $17,200 = 0.38372

ROE = 7% x 4 x 0.38372 = 10.74416% ≈ 10.74%

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