Final answer:
To compare projects with unequal lives, the Net Present Value (NPV) method is the most appropriate as it accounts for the time value of money and variations in project duration.
Step-by-step explanation:
When comparing projects with unequal lives, it is recommended to use the Net Present Value (NPV) method. The NPV allows for a comprehensive assessment of a project's profitability by discounting all future cash flows back to their present value, which takes into account the time value of money, differing project lifespans, and the cost of capital. Payback period, Internal Rate of Return (IRR), and Profitability Index can be useful in project evaluation, but for projects with different durations, using NPV is a more reliable comparison tool because it can adequately handle the variations in project life.