I understand well separately the ROI/ROIC and the IRR. I know how to use and calculate them. However, I am still confused. Is there a relation between the ROI/ROIC and the IRR? Can I get the ROI knowing all the calculation of the IRR?
ROI is the same as a single term of the IRR. E.g.
NPV = C/(1 + r) 100 = 105/(1 + 0.05)
while in ROI, with future value
FV & invested capital
ROI = FV/IC - 1 = 105/100 - 1 = 0.05
Can I get the ROI knowing all the calculation of the IRR?
No - you need the actual cash flows to calculate either of them; you cannot get one from just the other. There are cases where they may be equal, such as when there is only one outflow at the beginning and one inflow at the end, but in general there is no way to get one from the other.
There is no definitive answer to whether or not there is a relationship between ROI/ROIC and IRR. Each metric is used to evaluate different aspects of an investment, so it is difficult to make a direct comparison between the two. However, it is possible to use both ROI/ROIC and IRR in order to get a more complete picture of an investment's performance.