I have a list of investments with their expected IRR(Internal Rate of Return). I'm confused about which is the right metric to depict for my population: IRR of IRR or weighted average of IRR. It's tough to understand which is needed when. Can someone help? I'm not even sure what to term the IRR of all my individual IRRs?
You could add the cash flows (CF) by period and then compute the IRR for that accumulated cash flow (CCF). The resultant IRR will be like a weighted IRR. That will be different from IRR weighted by NPVs or Initial investment of each investment.
Let say you have two investments with this CFs:
       Inv1 -1560 200 1300 800 NA NA NA Inv2 -1560 200 1300 800 NA NA 1600
With a 25% discount rate you will have the NPVs and IRRs:
NPVs IRRs Inv1 -158.4000 0.1902671 Inv2 261.0304 0.3164824
The accumulated cash flow will be:
       CCF -3120 400 2600 1600 0 0 1600
You can verify that the total NPV is equal to the NPV of CCF at the same discount rate:
102.6304. Nothing new, this is one of the properties of NPV rule.
You could also compute the IRR of the CCF:
0.2652826, that will be the IRR of your investments.
That rate is different from the mean of IRRs (
0.2533748), and from the weighted IRR using as weights the NPVs (
0.5112835) or the initial investments (
Lets change the investment 1 to:
       Inv1 -2560 200 3300 1800 NA NA NA Inv2 -1560 200 1300 800 NA NA 1600
Then the NPVs and IRRs
NPVs IRRs Inv1 633.6000 0.3806551 Inv2 261.0304 0.316482
       CCF -4120 400 4600 2600 0 0 1600
Then the IRR of the CCF:
0.3528677. Again different from the mean of IRRs (
0.3485688), and from the weighted IRR using as weights the NPVs (
0.3619311) or the initial investments (
Each IRR is the [or rather a] solution of a polynomial equation, whose coefficients are the cash flows of the specific projects.
If all the projects are carried out at the same time, the cash flows from combining the projects form the coefficients of a new polynomial.
This overall polynomial equation must be solved from scratch to find the IRR of the overall project. There are AFAIK no "shortcuts" such as as adding or weighing the solutions (IRRs) of the subprojects. It is a whole new IRR problem that must be solved from scratch.