Question

Keller Cosmetics maintains an operating profit margin of 7% and asset turnover ratio of 4.

Answer 1

Answer:

A) ROA = 28%

B) ROE = 20%

Explanation:

Requirement A

We know,

Return on Asset = $\frac{Net Income}{Average Total Assets}$

If we break the ROA formula, we can get,

ROA = $\frac{Net Income}{Net Sales}$ × $\frac{Net Sales}{Average total assets}$

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 = $\frac{Net Income}{Stockholders' Equity}$

If we break the formula, ROE = (Asset ÷ Equity) × (Debt Burden) × ROA

Given,

Debt-Equity ratio = 1

We know, Debt-equity ratio = $\frac{Total Debt}{Total Stockholders' Equity}$

As debt-equity ratio is 1, debt = equity

Therefore, assets =  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%