Could use some help with this finance hw!! :)?

Question

Which of the following statements is correct?

Suppose a firm's total assets turnover ratio falls from 10% to 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%. Under these conditions, the ROE will decrease.

Suppose a firm's total assets turnover ratio falls from 10% to 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%. Under these conditions, the ROE will increase.

Suppose a firm's total assets turnover ratio falls from 10% to 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 modified Du Pont equation provides information about how operations affect the ROE, but the equation does include the effects of debt on the ROE.

Other things held constant, an increase in the debt

Answer 1

Under these conditions, the ROE will decrease.

Since return on equity ROE=Profit ratio*Asset turnover*Assets/Equity

And you have following residual changes:

Profit ratio change=0.10/0.09= +11.1%=1.111

Asset turnover=0.09/0.10= -10%=0.9

Assets/Debt=0.60/0.40=+50%=1.5

So ROE will change=(1.11*0.9/1.5)=

=0.66(6)= -33.3%

Right answer is: "Under these conditions, the ROE will decrease"

And to be more precise it will decrease for -33.3% (in ceteris paribus conditions).

Changes in "Asset turnover" and "Profit ratio" actually offset each other in this case due to size and directions of changes.

Though it's not so clear what "debt" means in this case, for most calculations it means non-equity liabilities, so it reduces equity returns.

Answer 2

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