Answer:
The range is between 40% and 60%.
Explanation:
To ascertain the equity for Primavera Holding, the financial leverage formula will be applied;
Financial Leverage = Asset / Equity
1.5 = $20 billion / Equity
Therefore, equity is calculated as $20/1.5 which equals $13.33 billion.
In order to determine net income, we first need to ascertain company sales using the asset turnover ratio;
Asset turnover = Sales / Assets
0.5 = Sales / $20 billion
This leads us to Sales = $10 billion.
Given that Primavera Holdings has a profit margin of 25%, the resulting net income is 25% of Sales resulting in $2.5 billion.
If the company maintains a payout ratio of 90%, shareholders would receive $9 billion in dividends, decreasing assets to ($20 - $9) $11 billion, and equity to ($13.33 - $9) $4.33 billion. Additionally, net income would drop by 3% of $9 billion, which is $0.27 billion.
Following the dividend payout, net income reduces to ($2.5 - $0.27) $2.23 billion
The Return On Equity (ROE) is determined using the formula = (Net Income / Equity) * 100
The calculation for ROE would be = ( $2.23 / $4.33 ) * 100
This results in an ROE of 51.50%
Given that the ROE falls within the range of 40% and 60%, this confirms the accuracy of the answer.
