Question

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%

Answer 1

Answer:

c. 13.59%

Explanation:

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

$ROE = PM*AT*EM$

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

$PM = \frac{\ 315,000}{\ 17,832}=0.0566$

The assets turnovet (AT) is:

$AT=\frac{Sales}{Assets}=\frac{\ 315,000}{\ 210,000}=1.5$

The equity multiplier (EM) is given by:

$EM = \frac{Assets}{Equity}\\\frac{Equity}{Assets}+\frac{Debt}{Assets}=1\\\frac{Equity}{Assets}=1-0.375=0.625\\EM=\frac{1}{0.625}=1.6$

The ROE is:

$ROE= 0.0566*1.5*1.6\\ROE=0.1359 = 13.59\%$