Random thought for the day...
Why are people so dogmatic and scared when IRR has multiple solution points or when the derivative of IRR is disussed (i.e. it has both magnitude and direction)? "Bah. IRR is no good, since it has multiple solutions." Why not interpret anyway?
I believe IRR has both magnitude and direction. In addition, my experience is that one of the IRR's is often pretty unstable and might go away with small tweaks in input variables.
NPV profiles are underutilized and can answer a lot of questions. Note the NPV at 0% and also whether the deriviative of each IRR solution (of NPV with respect to IRR) is positive or negative.
One personal argument from the past is when an investment ran with a 6% IRR, so colleague said it fell below the investment hurdle rate of 10%. However, the derivative was actually positive at this point, indicating that value was created at any discount rate greater than 6%. Why? Because it was a project to accelerate revenues that therefore lost value on an undiscounted basis but actually created value on any time value of money of at least 6%. He is a very smart guy but refused to listen to this argument due to a dogma of 6% being "the IRR", even though NPV was clearly positve at 10%.
So, even if you let a computer solve for IRR, check the derivative and interpret accordingly. Try seeding a solver close to zero. Better yet, use an NPV profile. And next time you find multiple IRR solutions, see if one goes away with mild sensitizing on key input variables. Edited to add:
I just remembered a case where the second IRR is more meaningful than the first. You might have a cash flow stream with a huge liability out in the future, enough to make the undiscounted cash flow negative overall. However, the liability is so far out in the future that the negative NPV impact of it is small at any reasonable discount rate. What you will see on an NPV profile is two IRR's - both meaningful.
The first IRR is a fairly small discount rate where the NPV crosses over to positive - this represents the discount rate above which your future liability no longer drags the NPV negative overall. The second IRR is the traditional solution where NPV crosses over to negative. This is what I would consider the most representative IRR for this investment, with the caveat that your discount rate is at least as high as the first IRR.
Again, just another example where both IRR's are meaningful and can be correctly interpreted with the derivative of NPV with respect to discount rate. But many NPV purists would scoff that this is just another example of IRR being invalid due to multiple solutions. Plus, both IRR's in this example are fairly mathematically stable with respect to input variable fluctuations.
This post was edited on 5/24 at 6:29 am