It should be net income/shareholders equity. Let’s say net income is 10 in 2014. Beginning 2014 equity 90 and ending 2014 at 100. I thought we should divide 100 by the beginning equity of 2014, hence 10/90. But it seems to me the formula says we should ending equity? It seems more logical to me to use beginning equity, because that is the equity we used to generate the net income in 2014. Maybe I am wrong here?
You are wrong.
BS predictor in denomintor is ending balance date and P/L predictor in nominator (NI) is derived from P/L.
If you analyse a company from volatile sector, to use more relevant predictor in denominator you may simply take an average equity balance, thus (ending PY or beginning in CY + ending in CY)/2. NI predictor in nominator is derived from P/L thus is already shown in FS on average basis by booking entries in company ledger during year.