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Last year Vaughn Corp. had sales of $315,000 and a net income of $17,832, and its year-end assets were $210,000. The firm's total-debt-to-total-assets ratio was 37.5%. Based on the DuPont equation, what was Vaughn's ROE? Select the correct answer. a. 12.55% b. 13.07% c. 13.59% d. 12.03% e. 11.51%

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Answer:

c. 13.59%

Explanation:

According to the DuPont equation, the ROE is determined by:

[tex]ROE = PM*AT*EM[/tex]

The company's profit margin (PM) is given by:

[tex]PM = \frac{\$315,000}{\$17,832}=0.0566[/tex]

The assets turnovet (AT) is:

[tex]AT=\frac{Sales}{Assets}=\frac{\$315,000}{\$210,000}=1.5[/tex]

The equity multiplier (EM) is given by:

[tex]EM = \frac{Assets}{Equity}\\\frac{Equity}{Assets}+\frac{Debt}{Assets}=1\\\frac{Equity}{Assets}=1-0.375=0.625\\EM=\frac{1}{0.625}=1.6[/tex]

The ROE is:

[tex]ROE= 0.0566*1.5*1.6\\ROE=0.1359 = 13.59\%[/tex]

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