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 22.5%. Based on the DuPont equation, what was Vaughn's ROE?

Select the correct answer. a.9.19%
b.10.37%
c.10.96%
d.8.60%
e.9.78%

Answer 1

Using the DuPont equation, Vaughn Corp.'s ROE is calculated by multiplying the net profit margin (5.66%), asset turnover (1.5), and equity multiplier (1.2903) together, which results in an ROE of 10.96%. The correct answer is (c) 10.96%.

Step-by-step explanation:

The student is asking about calculating the Return on Equity (ROE) using the DuPont equation for Vaughn Corp. The DuPont equation breaks ROE into three parts: the net profit margin, asset turnover, and equity multiplier.

First, we calculate the Net Profit Margin by dividing Net Income by Sales:

Net Profit Margin = $17,832 / $315,000 = 0.0566 or 5.66%

Next, we calculate the Asset Turnover by dividing Sales by Average Assets:

Asset Turnover = $315,000 / $210,000 = 1.5

Then, the Equity Multiplier is calculated using the total debt-to-total assets ratio. The Equity Multiplier is Total Assets / Total Equity. Since Total Debt is 22.5% of Total Assets, Equity is 77.5% of Total Assets:

Equity Multiplier = 1 / 0.775 = 1.2903

To find ROE, we multiply these three components:

ROE = Net Profit Margin * Asset Turnover * Equity Multiplier

ROE = 0.0566 * 1.5 * 1.2903 = 0.1096 or 10.96%

Therefore, the correct answer is: c.10.96%.