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IRR is an indicator that does not evaluate the length of the project, hence the amount of time needed to get any returns on your investment, unlike NPV, which proves to be one of the the best ways to tell you the value of your investment on the long term, I would use ROI and payback period mainly to evaluate projects primarily, taking into consideration the other ratios as well.
I use NPV, and payback period, becuase payback period give me an estimate when I return my investement but it is not enoght, NPV use desired rate of return which say to me the monetry value of the future.
Each of them has an indication from a point of view:
1- IRR is preferable when the project is self-financed.
2- NVP is preferale when the project is externally financed.
3- PBP is perferable when the period of returning the your cash back is more important to you
IRR & Payback period
I would go with IRR and pay back method and pay back method. It will give me idea that what will be rate of return to my invetment and expected period of return. It would help to keep satisfy my project stakeholders. it would help to derived project profitablity. However, it need to be ensure that cash flows should be changed frequently.
I' d like to add that: NPV IRR are functions that report to a planning horizon and could result in complex polynomies of order10,20,30 etc.
Sometimes when using a set of KPI the resulting scenarios have confliting interests; this normally happens if one also includes social responsability or internal learning or other intangible KPI. In these situations I use Data Envelopment Analisys to determine the most efficient scenario and determine where others sould move to the efficiency frontier.
Situations like these are normally related to public investment.
Each organisation has its own way of looking at financial benefits, it is not about preference or one fits all.
the most common are; Payback, ROI (return on Investment) and NPV (net present value