Answer:
A) ROA = 28%
B) ROE = 20%
Explanation:
Requirement A
We know,
Return on Asset = [tex]\frac{Net Income}{Average Total Assets}[/tex]
If we break the ROA formula, we can get,
ROA = [tex]\frac{Net Income}{Net Sales}[/tex] × [tex]\frac{Net Sales}{Average total assets}[/tex]
We know, Profit margin = Net Income ÷ Net Sales; and
Asset Turnover ratio = Net sales ÷ Average total assets
Therefore, ROA = Profit margin × Asset Turnover
Given,
Profit Margin = 7% = 0.07
Asset Turnover = 4.0
Hence, Return on Asset = 0.07 × 4 = 0.28 = 28%
It shows how assets generate income over a period.
Requirement B
We know,
Return on Equity = [tex]\frac{Net Income}{Stockholders' Equity}[/tex]
If we break the formula, ROE = (Asset ÷ Equity) × (Debt Burden) × ROA
Given,
Debt-Equity ratio = 1
We know, Debt-equity ratio = [tex]\frac{Total Debt}{Total Stockholders' Equity}[/tex]
As debt-equity ratio is 1, debt = equity
Therefore, assets = Â 2 times of debt or equity
Debt Burden = Net Income ÷ (EBIT - Interest)
Debt Burden = (EBIT - Interest - Tax) ÷ (EBIT - Interest)
Debt Burden = $(21,000 - 8,200 - 8,200) ÷ $(21,000 - 8,200)
Debt Burden = $4,600 ÷ $12,800
Debt Burden = 0.359375
We have already got ROA from requirement A, ROA = 28% = 0.28
Hence, ROE = (2 ÷ 1) × 0.359375 × 0.28
ROE = 0.20125
ROE = 20%
