NPV vs. IRR on independent projects

CFA Level I
#1

I do not get how for independent project,s the NPV and IRR would produce the same rankings. Couldn’t they still produce conflicting rankings even if two projects are indepedendent of eachother?

Also, what are the main reasons to choose NPV over the IRR method between two projects that are mutually exclusive (or ones I should know for the test)?

#2

They don’t necessarily produce the same rankings for independent projects; what makes you think that they do?

Choose NPV over IRR because:

  • NPV tells you the value that you’re adding to the company by undertaking the project, while IRR does not.
  • IRR assumes that cash inflows are reinvested at the IRR, while NPV assumes that they are reinvested at the cost of capital (which is lower, so likely more reasonable)
  • For projects with nonstandard cash flows, you might get multiple IRRs, or no IRR; you’ll get only one NPV.
#3

NPV and IRR can rank two mutually exclusive projects the same or differently, because they measure different things.

  • IRR is a “return” metric - in some sense it’s the annualized return PER DOLLAR INVESTED
  • NPV is a “wealth” metric. I meausres TOTAL VALUE created.

It’s possible that the project with the highest percentage return per dollar creates less total wealth. In this case, one project could have the higher IRR and the other one have the higher NPV. One obvious case where this could happen is if the higher IRR project is smaller in scale.

In other cases, the “higher return” project also creates more total value, in which case, they’ll rank tow projects the same.

The big probelms with IRR are:

  1. that it measures “return”, not “Value created”
  2. It makes a possibly unrealistic assumption on reinvestment of intermediate cash flows (i.e. if you have a high IRR project and can;t reinvest subsequent cash flows at the same IRR, your realized return won’t be the IRR), and
  3. If the project’s cash flows change signs more than once (and zeros don’t count), the project could potentially have multiple IRRs.

edited: OOPS - looks like Magician beat me to the punch.

#4

https://www.youtube.com/watch?v=fmNxlBg47UY&list=PLcmt2ZfkV0M0yk93DqX4Y9alMdZP2lq5X&index=1

go to 13:23 in the video, he says “if the NPV is positive, the IRR will be greater than the cost of capital”

#5

I don’t need to watch the video: the statement is correct.

What are you concluding from that statement?

#6

Well in the video he is saying that the NPV and IRR will always produce the same decision/ranking between two indepedent projects.

What I am wondering is that there is a possibility that the ranking could be different between NPV and IRR even if the projects are independent.

#7

NPV and IRR will always produce the same do / don’t do decision:

  • If NPV says do the project, IRR will say do the project.
  • If NPV says don’t do the project, IRR will say don’t do the project.

They will not necessarily produce the same ranking.

Suppose that you have 5 projects: A, B, C, D, and E.

NPV might rank them (best to worst, with “|” being the dividing line between “do” and “don’t do”): A C E | D B.

IRR might rank them (best to worst): E A C | B D.

Same do / don’t do for each project (A, C, and E are dos, B and D are don’t dos), but different rankings.

#8

There’s a condition that must be met in order for this relationship to hold (i.e. Positive NPV <==> IRR>Cost of capital) - it must be a normal" project. In other words, the initial cash flow (At time zero) is negative, followed by all positive cash flows. In that case the NPV function is monotonically decreasing.

If it’s a non-normal project (kind of an unusual case), you could have an NPV function that slopes upward (i.e. initial cash inflow followed by all cash outflows) or is positive over some ranges and negative over others. This last case occurs when the sign of the cash flows changes more than once. In this case, it’s possible to have multiple IRRs.

#9

Which of the following is least accurate?

  1. The IRR can be positive even if the NPV is negative.

  2. When the IRR is equal to the cost of capital, the NPV will be zero.

  3. The NPV will be positive if the IRR is less than the cost of capital.

I get why the answer would be #3 (if we assumed conventional cash flows), but I do not get why it could not be number 1. How can you understand the fact that a project may produce a return when it has a negative NPV value?

#10

Try some numbers:

  • CF0 = -100
  • CF1 = 110
  • WACC = 11%
#11

Maybe I am just confused behind the intuition. It does make any sense how a project that hinders the value of a firm would still generate a positive return.

#12

Did you try the numbers?

#13

Yeah, the NPV is negative.

#14

But I guess you have to compare the WACC against the IRR, which make more sense why this would still have a negative NPV (since cost of capital here is greater than the IRR).

#15

Exactly.