Question

1) Financial Ration:

a) Please prove the relationship between ROE and ROA by using Dupont Identity.

b) Based on relationship between ROE and ROA, please show the proof that ROE is greater than ROA when total debt is greater than 0.

c) We know ROE is 10%, capital structure ratio (TE/TD) is 0.45, please compute the ROA.

Answer 1

a) USingDuPont Identity

ROE= Net Profit Margin * Asset Turnover * Financial Leverage

= (Net Income / Sales) * (Sales / Total Assets) * (Total Assets / Total Equity)

ROA= Net Income/ Total Assets

= (Net Income / Sales) * (Sales / Total Assets)

Hence ROE= ROA*Financial Leverage

b) Assume a Total Asset value of $100 and a debt of $10. Hence Equity= 100-10 = $90

ROE= ROA*100/90

ROE= 1.11* ROA

Hence ROE will be more than ROA if there is a debt>0

c) ROE=10%, TE/TD= 0.45= 0.45/1

Total Assets= TE+TD= 0.45+1 = 1.45

Financial leverage= TA/TE = 1.45/0.45 = 3.2222

ROA= ROE/ Financial leverage

=10%/ 3.2222

ROA = 3.1%