divisional performance

The manager will prefer whichever of the two methods results in the higher bonus, and neither of them will always give a higher bonus than the other – sometimes ROI would give a higher bonus, and sometimes RI would give a higher bonus.

It depends on the figures in the question (for example, what rate of notional interest is used by the company in the RI calculation, and how the bonus is calculated on the ROI or on the RI).

It is the company who decides on the method used. If a question asks you which method the manager would have preferred then you would be expected to calculate the bonus on both methods and state that the manager would have preferred whichever of the two resulted in the higher bonus on the actual figures given in the question.

But again, it is not the managers choice as to which measure is used.

The company decides on the bonus system in order to motivate the managers to do what is best for the company as a whole, and it is the company that decides as to how the performance is measured. It is not a question as to which method the managers themselves would prefer.

Yes. It is the company who decides how to measure the managers performance and how any bonus is to be calculated.