Question

A firm has an ROE of 9%, a debt/equity ratio of 0.3, a tax rate of 30%, and pays an interest rate of 6% on its debt. Firm’s asset turnover is 0.3

-What is firm’s operating ROA?

-What is the firm’ Margin

- What is the firms Tax burden?

- What is the firm’s Leverage factor?

- Given ROA that you found, what percentage of its total ROA firm has to pay as interest?

- What is the firm’s interest burden?

- Combine all given and found values that you have into the formula. Check that equation holds.

ROE = Tax burden × Interest burden × Margin × Turnover × Leverage

Answer 1

1... Calcualtion of ROA

ROE =  9%   debt/equity(D/E) ratio = 0.3, tax rate = 30%, interest rate = 6%, asset turnover= 0.3

ROA = {1/(1+D/E)}*{ROE/(1-t)} + {D/E / (1+ D/E)}*(interest rate)

ROA = {1/(1+0.3)}*{0.09/(0.7)} + {0.3 / (1+ 0.3)}*(0.06)

= {1/(1.3)}*{0.09/(0.7)} + {0.3 / (1.3)}*(0.06)

= 0.0989 + 0.0139 = 0.1128 or 11.28%

2. ROA = Profit Margin X Asset Turnover

0.1128 = Profit Margin * 0.3

Profit Margin = 0.1128/0.3 = 0.3759 OR 37.59%

3. Tax Burden = NI/ EBT which is effectively equal to = (1-tax rate) = (1-0.30) = 0.70 or 70%

4. Leverage Factor = Debt equity ratio / (1+Debt equity Ratio) = 0.3 / (1+0.3)

= 0.2308