Question

1. Briefly explain why one should NOT use the DuPont ratio (or ROE in general) in the rare circumstances where stockholders equity is negative?

2. Assuming stockholder’s equity is positive, indicate whether you want a high value or a low value for each ratio, independent of the other ratios, and give a brief explanation why.

There is a clear answer for the first two ratios (ROE and profit margin). However, the preference for a higher or lower asset turnover ratio and financial leverage ratio depends on the sign of the profit margin ratio. Therefore, for the asset turnover ratio and financial leverage ratio, identify if you want a high or low value when a) profit margin is positive, and b) when profit margin is negative.

Return on equity:

Profit margin ratio:

Asset turnover ratio when profit margin ratio is positive:

Asset turnover ratio when profit margin ratio is negative:

Financial leverage ratio when profit margin ratio is positive:

Financial leverage ratio when profit margin ratio is negative:   

Answer 1

1)ROE=(net income/equity)=(net income/sales)*(sales/assets)*(assets/equity)
=(profit margin)*(asset turnover)*(equity multiplier)
Here when the stockholder equity is negative we have negative ROE and it does not make sense so we should use other ratios like ROA

2)Asset turnover ratio when profit margin ratio is positive:The asset turnover ratio needs to high so that we have overall positive ratio
Asset turnover ratio when profit margin ratio is negative: here the profit margin negative, financial leverage positive so the asset turnover ratio lower so overall ROE is higher
Financial leverage ratio when profit margin ratio is positive: profit margin positive means positive net income means lower interest means lower financial leverage
Financial leverage ratio when profit margin ratio is negative : Here the profit margin negative means the net income is negative means we have higher interest and taxes cost . The higher interest is due to the high financial leverage