NPV and IRR

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the show NY

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If 2 projects have the same NPV will they have the same IRR and vice versa?
 
I don't think so? IRR is dependent on timing, scale and reinvestment rates of the projects I believe. If those change from one to the next the IRR's could be totally different but the discounted CF's could coincidently come out to the same NPV.

Don't take this to the bank though, just my rationalization
 
haha now that I reread the question, I'm not saying that can't, they can for sure, but I imagine the timing of CF and scale of the projects should be similar or the changes in both offset each other
 
what is the difference between npv and irr when it comes to timing>
 
Delay in CF will make a projects NPV more sensitive to changes in the discount rate (which makes sense) increased sensitivity is illistrated by a steeper slope in the NPV profile
 
i know that but im saying how do irr and npv differ on this matter.


for example:

reinvestment: irr assumes reinvestment at irr, npv assumes reinvestment at the weighted average cost of capital (correct me i im wrong)

scale: npv doesnt take scale into account (100 npv for a 100M proejct and a 1M project), while irr takes it into consideration, as a 100 npv on a 1M project would be a higher rate

timing: how do the assumptions differ?
 
the show NY Wrote:
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> If 2 projects have the same NPV will they have the
> same IRR and vice versa?


If they have the same NPV, they could have the same IRR, but most likely not. If a $1M project has a NPV of $100K and a $200K project has a NPV of $100K, clearly those are not two investments that have the same bang-for-your-buck.

Alternatively, an IRR of 10% off a project size of $1M would provide a much higher NPV than a project size of $100K with the same IRR.
 
Two projects will only have the same IRR and NPV if the discount rate is the same as their IRR. THis is because at that rate, both will have an NPV of zero.
 
Usually, two projects having the same NPV assumes that the two being discounted at the same rate (there is a small chance that you would use a different discount rate if one project were substantially more risky than the other).

If you suddenly change the discount rate by a little (but still use the same rate for each), and the cash flows come in at different times, you will suddenly have a different NPVs. However, if each NPV is positive, the projects are (if non-exclusive) still worth doing.

It is very possible that one project will still be profitable (i.e. NPV>0) at a higher discount rate than the other, and that NPV=0 at different discount rates. Therefore they do not have the same IRR, necessarily.

So, the answer is that it is possible that two projects with the same NPV could have the same IRR, but there is no reason that two projects with the same NPV *must* have the same IRR.
 
After reading bchadwick's answer, I'm adding to mine. Two projects can hjave the same discount rate and IRR in only two cases:

1) the NPV profiles are different, but they have the same IRR -- and you calculate the NPVs of both projects at the common IRR (in this case, NPV will be zero). However, for these two projects, the NPV will differ for all other discoutn rates

2) The two projects have identical cash flows in all years. In this case, the two projects are (by definition) identical.

In any other case, either the two NPV profiles never cross (so that the projects never have identical NPVs, or they do cross. But in the lst case, they will have identical NPVs only at this crossover rates. At all other rates, the NPVS would differ (including the rate that forces one or the other to a zero NPV). So, in this case, since they have different NPVs, the rate that results in a zero NPV for project (A) will not result in a zero NPV for project (B). Therefore, it's not (B)'s IRR.
 
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