When selecting between mutually exclusive projects where NPV and IRR rankings conflict, the NPV criterion is the theoretically sound and preferred method. This is because NPV directly measures the increase in shareholder wealth. While IRR and other metrics like ROIC can be calculated, NPV provides the most reliable basis for decision-making. Options B and C are incorrect as they either prioritize IRR (B) or suggest indifference (C), neither of which aligns with the NPV rule.