A firm has a ROE of 14 percent and a debt-to-equity ratio of 40 percent. If the total asset turnover is 3.4, what is the firm's profit margin?

The firm's profit margin is 2.94%

Explanation:

The formula to find profit margin is

ROE=Net profit margin * Assets/Equity*Total asset turnover

We know the Roe is 14% and asset turnover is 40 %.

We need to find the assets/Equity through debt to equity ratio. In the question we are told that debt to equity ratio is 40%, which means that debt is only 40% of equity. So if we assume equity to be 1 then debt is 0.40 (0.4*1). Assets will be the sum of debt and equity so assets are (1+0.4) = 1.40. Now in order to find the asset/equity we will divide assets by equity.

1.4/1=1.4. Assets/Equity = 1.4

Now we input these values in the formula.

0.14=3.4*1.4*Profit Margin

0.14/4.76 = Profit Margin

Profit Margin = 0.0294=2.94%