Final answer:
The method that should be used when ranking competing projects with different initial investments is Net Present Value (NPV) or Profitability Index (PI).
Step-by-step explanation:
When ranking competing projects with different initial investments, the method that should be used is Net Present Value (NPV). NPV takes into account the time value of money and calculates the present value of future cash flows for each project. The project with the highest NPV is considered the most favorable.
Additionally, Profitability Index (PI) can also be used to rank projects. PI is calculated by dividing the present value of future cash flows by the initial investment. The project with the highest PI is considered the most favorable.
Both NPV and PI consider the initial investment and the time value of money, making them suitable methods for ranking projects with different initial investments.