i’ve read a couple places now that the IRR and NPV methods will conflict when the cost of capital is less than the crossover rate. can anyone explain the reasoning or math here?
Draw the NPV profile. It will be clear then
A project can have very small cash flows but a very high IRR because of the return on the small investment. You want to look at the value added, not just the return on the investment. A project that generates more profit but has a smaller IRR would be better from a shareholder’s point of view because it adds more value.
It’s got to do with timing of the cash flows as well if I’m not mistaken. There is a diagram and an explanation in the Schweser book, if you have it.
This type of problem typically involves something like the following scenario: Assume project A has an NPV at a zero discount rate of $600 and Project B’s NPV at the same zero discount rate is $800. These data give the points where their NPV profiles cross the Y axis on an NPV profile graph (remember - NPV is the Y axis, and the discount rate/cost of capital/reguired rate of return is the X axis). Project A’s IRR is 15% and B’s IRR is 12%. These are the points where their profiles cross the X axis. Just for grins, assume that the two profiles intersect at a discount rate of 9% (I made this point up - don’t try to solve for it, since it comes from my sleep-deprived and under-caffeinated brain). Project B’s NPV starts out greater than Project A’s, but falls faster as the discount rate increases. This is because (as Chad noted), it’s cash flows occurr further off in the future than does project A’s (it’s related to the concept of duration in fixed income). So, at discount rates less than 9%, project B has a higher NPV, but at rates > 9%, project A looks better. But B has a LOWER IRR. So, in this case, there are a number of critical regions: discount rate < 9%: both have positive NPV, but NPV(B) > NPV(A) discount rate =9%: NPV(A)=NPV(B), and both NPVs > 0 9% < discount rate <=12%: NPV(A)>NPV(B), and both NPVs > 0 12%< discount rate <15%: NPV(A) > 0; NPV(B) < 0 discount rate > 15%: NPV(A) > NPV(B), but both < 0 So, although A has a higher IRR, below the crossover rate, B has a higher NPV. If the projects were mutually exclusive, you’d chose B at any rate below 9%, A at rates between 9 and 15%, and neither at rates > 15%. Remember - for MUTUALLY EXCLUSIVE projects, you choose the “best” project among the “good” ones, so the rule is to “choose highest NPV among positive NPV projects”. If they were independent, you’d accept both at rates < 12%, A at rates between 12 and 15% and neither at rates > 15%. Remember - for INDPEPENDENT projects, you accept all “good” projects (i.e. those with positive NPVs) Draw the graph, and understand why the following relationships hold. It’s an easy question to test on the exam. Note: for conventional projects (those with all outflows followed by all inflows), if IRR > discount rate (or cost of capital or required rate of return), NPV>0, and vice-versa. So, if all you care about is whether or not it’s a “good” project (i.e. in the case of iondependent projects), wither rule works. But you can have cases where they rank incorrectly, which screws up the decision process for mutually exclusive projects.
this is great - thanks. makes sense now.