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Return on Equity is a ratio of Net Profit for some fiscal year let's say 2018 and Total equity at last date of the fiscal year.
But Total Equity is calculated by adding some amount from Net profit(after paying dividends). Isn't it wrong to calculate profit earned on every unit of equity invested this way?
e.g. Profit for fiscal year = x
Total Equity at the end of the fiscal year = Retained Earnings + Some part of x after dividends.
How can we say that ROE is a right way of calculation?
Return on Equity is a ratio of Net Profit for some fiscal year let's say 2018 and Total equity at last date of the fiscal year.
No - you use average equity (including retained earnings), so you'd take the starting equity plus the ending equity and divide by 2.
You are correct in your thinking that profits don't fully contribute to themselves, but they do help grow the company to some extent. A company will retain profits and use that to grow the company going forward, so it does play some part.
