Why don’t we actually call ROI ratio to ROCE because they are effectively using the same logic!
I watched your lecture where u said that “division doesn’t have capital employed” in their hands rather it is centrally managed by Head Office?
Since it is only one company & any capital employed will be injected by the Head Office but it is the manager’s job to invest the capital in the right way which would be profitable for the company as a whole.
Although the two are the same, the ROCE is calculated for the company as a whole whereas the ROI is calculated just for a division (or just for an individual investment).
Your last paragraph is correct (assuming that it is an investment division).