Last year harrington inc. had sales of $325,000 and a net income of $19,000, and its year-end assets were $250,000. the firm’s total-debt-to-total-capital ratio was 45.0%. the firm finances using only debt and common equity and its total assets equal total invested capital. based on the dupont equation, what was the roe?

dupont equation: roe = profit margin * total asset turnover * equity multiplier
roe = (ni / sales) * (sales / total assets) * (total assets / total common equity)

Based on the DuPont equation and given information, ROE of Harrington Inc is 13.818%.

Explanation:

We have to find the total equity and total debt of Harrington Inc in order to apply the DuPont equation for finding ROE because net income, sales of Harrington Inc. are already given.

- To find Harrington Inc's total debt, apply the Debt-to-capital formula: The Harrington Inc's total debt/The Harrington Inc's total capital = 45% =>  Harrington Inc's total debt = The Harrington Inc's total capital * 45% = $250,000 x 45% = $112,500;

- To find Harrington Inc's total equity, apply the accounting equation Asset = Liabilities + Owner's Equity: The Harrington Inc's total equity = The Harrington Inc's total asset - The Harrington Inc's total debt = $250,000 - $112,500 = $137,500;

- Using the Dupont equation, calculate the ROE as followed:

(NI/Sales)* (Sales/ Total assets) * (Total assets/ Total common equity) = (19,000/325,000) * ( 325,000/ 250,000) * (250,000/137,500) = 13.818%.

- Thus, the ROE = 13.818%.