# ROE DuPont HELP!!!

I was doing the end of chapter exercises last night and came across this ROE formula which was not mentioned in Schweser: ((EBIT/Revenue)*(Revenue/Assets)-(Interest/Assets))*(Assests/Equity)*(1-T) Does anyone know how they came up with this formula? I can’t get to this formula by using the 3-way or 5-way ROE decomposition. Thanks for your posts!

It took me a while to remember this…but this is how I did it- ROE = NI/Equity now multiple it by Revenue on both sides NI/Revenue * Revenue/Equity now multiply it by Assets NI/Revenue * Revenue/Assets * Assets/Equity now multiply it by EBIT and EBT NI/EBT * EBT/EBIT * EBIT/Revenue * Revenue/Assets * Assets/Equity

Priyanka, I know the formula you are talking about, it’s just the 5 way decomposition of ROE. I had a question about the specific formula I wrote in my previous post. I dont understand how they came up with that one… where they are subtracting stuff and multiplying something by the tax retention rate???

((EBIT/Revenue)*(Revenue/Assets)-(Interest/Assets))*(Assests/Equity)*(1-T) rewrite as: (EBIT/Revenue)*(Revenue/Assets) = EBIT/ASSETS EBIT/ASSETS - Interest/Assets = EBT/ASSETS (EBT/ASSETS)* (ASSETS/EQUITY) * (1-T) where (1-T) = Net income/EBT therefore rearrange: (Net income/EBT)*(EBT/ASSETS)*(ASSETS/EQUITY) = ROE you don’t really ‘come up’ with any formula, you can decompose ROE in any way, as long as you get that relationship NI/EQUITY in the end. that is really thee whole point of DuPont I think.

I got it! Thank you so much for your help and for such a great explanation!!! I appreciate it!

Let me take a shot at this: This is just a formula that gives you even more details… Asset turnover and financial leverage are constant. They breakdown operating margin, interest expense and the tax retention rate. (Operating Margin*TO-Interest Rate on total capital)—this gives you EBT. You still need to determine your risk (Assets/CE) and then obviously multiply that by your tax retention rate. http://www.stalla.com/solutions/archives.cfm# I did a quick search for this and I found the above link that offered a good explanation, obviously more eloquently than I could.

derive from first principles ROE = NI/CE = (EBIT-Int)(1-T) / CE = (EBIT-Int)/CE * (1-T) = (EBIT-Int)/TA * TA/CE * (1-T) — Multiplying and dividing by TA (Total Assets) = (EBIT/TA - Int/TA) * TA/CE * (1-T) = [(EBIT/NS * NS/TA) - Int/TA] * TA/CE * (1-T) = [Operating Margin * Total Asset Turnover - Int Turnover] * Financial Leverage * Tax Impact. **** 5 part ROE formula ****