You are considering investing in Lenny's Lube, Inc. You have been able to locate the following information on the firm: total assets = $20 million, accounts receivable = $6 million, ACP = 20 days, net income = $5 million, and debt-to-equity ratio = 2.5 times. What is the ROE for the firm?
A) 2.5000 percent
B) 13.9882 percent
C) 35.0000 percent
D) 87.50 percent

Question

Quizplus · Accepted Answer

ROE (Return on Equity) is calculated as Net Income / Shareholder's Equity. Given the debt-to-equity ratio is 2.5, we can find the equity as a fraction of total assets. The debt-to-equity ratio formula is Total Debt / Total Equity. Rearranging this to solve for equity gives us Total Equity = Total Debt / 2.5. Since the firm's total assets are $20 million and assuming the firm is financed only through debt and equity, Total Assets = Total Debt + Total Equity. We can express Total Debt as Total Assets - Total Equity. Substituting this into the rearranged debt-to-equity formula and solving for Total Equity gives us Total Equity = $20 million / 3.5 (since Total Debt / Total Equity = 2.5 implies Total Debt is 2.5 parts and Total Equity is 1 part, for a total of 3.5 parts). This results in Total Equity of $5.714 million approximately. Therefore, ROE = $5 million / $5.714 million = 87.5%.

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