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.

For eg. If the questions mentioned that the bonus of divisional manager is linked to ROI, so it makes sense that the divisional manager will prefer to use ROI as selection criteria for investment projects. If the questions mentioned that the bonus of the divisional manager is linked to RI, so it makes sense that the divisional manager will prefer to use RI as selection criteria for investment projects. My question is if the bonus of divisional manager is linked to DIVISIONAL PROFIT <<, it refers the managers will use ROI or RI as selection criteria for investment projects? Thanks

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.

sorry sir, ya the company sets the bonus system like higher divisional profit, higher bonus something like tht.

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