Which of the following statements is CORRECT? Suppose a firm’s total assets turn

Question

Which of the following statements is CORRECT?

Suppose a firm’s total assets turnover ratio falls from 1.0 to 0.9, but at the same time its profit margin rises from 9% to 10% and its debt decreases from 60% of total assets to 40%. Under these conditions, the ROE will increase.

Suppose a firm’s total assets turnover ratio falls from 1.0 to 0.9, but at the same time its profit margin rises from 9% to 10% and its debt increases from 40% of total assets to 60%. Without additional information, we cannot tell what will happen to the ROE.

The Du Pont equation provides information about how operations affect the ROE, but the equation does not include the effects of debt on the ROE.

Other things held constant, an increase in the debt ratio will result in an increase in the profit margin on sales.

Suppose a firm’s total assets turnover ratio falls from 1.0 to 0.9, but at the same time its profit margin rises from 9% to 10%, and its debt decreases from 60% of total assets to 40%. Under these conditions, the ROE will decrease.

Explanation / Answer

TA/E=TA/(TA-D)=1/(1-D/TA)

RoE=Profit Margin * Asset Turnover * Equity Multiplier= Profit Margin * Asset Turnover * (TA/E) = Profit Margin * Asset Turnover *1/(1-D/TA)

1)   Incorrect. Because

So, 1st case RoE=9*1*1/(1-0.6)=22.5%

2nd case RoE=10*0.9*1/(1-0.4)=15%

Thus we see that RoE would decrease and not increase

2)   Incorrect. Because without any additional information ,we can tell the movement of RoE

3)   Incorrect. Because equation includes effects of debt on RoE in the form of equity multiplier

4)   Incorrect. Because profit margin would not be impacted by debt ratio

5)   Correct. Because

So, 1st case RoE=9*1*1/(1-0.6)=22.5%

2nd case RoE=10*0.9*1/(1-0.4)=15%

Thus we see that RoE would decrease

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