Question

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)

Answer 1

Using the DuPont equation, Harrington Inc.'s ROE is calculated to be approximately 13.7%, which is found by multiplying the company's profit margin (0.058), total asset turnover (1.3), and equity multiplier (1.8182).

Step-by-step explanation:

The DuPont equation is a formula that calculates a company's return on equity (ROE) by multiplying three financial ratios: profit margin, total asset turnover, and the equity multiplier. Given Harrington Inc.'s financial details, we can calculate each ratio:

Profit margin = Net Income / Sales = $19,000 / $325,000 = 0.058,

Total asset turnover = Sales / Total Assets = $325,000 / $250,000 = 1.3,

Total-debt-to-total-capital ratio = 45%, which implies an equity ratio of 55% because the firm uses only debt and equity to finance its assets. Therefore, Total equity / Total assets = 55%, or Total assets / Total equity = 1 / 0.55 = 1.8182.

Now, we apply these figures to the DuPont equation:

ROE = Profit Margin × Total Asset Turnover × Equity Multiplier

ROE = 0.058 × 1.3 × 1.8182 ≈ 0.137 or 13.7%

Therefore, based on the DuPont equation, Harrington Inc.'s ROE is approximately 13.7%.

Answer 2

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

Step-by-step 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%.