JAMES WESTON: Hi, welcome back to finance for non-finance professionals.

In this video, I'd like to talk about a couple of wrinkles

with the internal rate of return.

In our last video, we introduced internal rate of return

as one of our capital budgeting tools for how to spend money within the firm.

There's a couple of things that we need to be

careful about with the internal rate of return.

We liked it-- we said it was a lot like net present value, which

was our gold standard capital budgeting tool.

And since IRR was a lot like NPV, we talked about a lot

of the benefits of using IRR.

But there's a couple of complications in practice

that I want to at least talk through with you.

The first is loan kinds of flows.

When the cash flows get reversed.

When they come in and go out, come in and go out,

IRR can get a little bit funky for some math reasons

that I'll talk about at a high level.

The other is the scale problems.

We can sometimes make bad capital budgeting decisions based only

on IRR because we got rid of the scale.

In other words, we'd rather have more money than less,

but IRR has gotten rid of how much money we're making overall.

Let's put it in percentage terms, we need to be careful about that.

The other is a timing problem.

And the other is some mathematical complications with IRR

that I'll talk about at sort of a high level.

OK, let's talk about loan flows.

When the cash flows are reversed, an IRR can sometimes

give me a misleading picture about whether or not

the project is adding value to the firm.

Money comes in and then money goes out, the sign can actually flip.

Any time the sign flips, I need to be careful about using IRR.

In other words, if I spend money on a machine,

then the machine generates revenue, and then

I have to retool the machine in year three, and I spend more cash,

and then money comes back in again, that's two sign changes.

Money out, money in.

Money out, money in.

Any time that flips a couple of times, you have to hesitate.

Say, whoa, hang on.

And be careful about using IRR.

So let's talk about that a little bit.

Consider these two projects, X and Y. In the first,

I'm going to spend $500-- so this is our normal capital

budgeting-- I'm going to spend $400 in order to generate $500 a year from now.

If work out the NPV, it comes out to 54.54.

If I compute the IRR, it comes out to 25%.

In the second project though, I've got $400 coming in.

And then I spend $500 in year one.

That's like a loan.

I'm getting money in, paying it back later.

What happens here?

The net present value is minus 54.54.

The whole thing flipped.

I'm not making $54, I'm losing $54.

I compute the IRR, it's the same, it's 25%.

What happened, did something get screwed up?

Not really.

The math is clean.

The solution to what rate sets that NPV equal to 0 is 25%.

It's just that the NPV flipped sign.

So we have to be careful any time there's

a flip in the sign of the cash flows.

If I think about it from the graph perspective

that we talked about when we talked about IRR, in the first project

the NPV kind of looks like this, and that's the IRR.

But in the second project, the returns, the NPV looks like that.

They have the same IRR, but for a low discount rate,

this one is going to give me a negative NPV, whereas the other one was

going to give me a positive NPV.

Something to be careful about, loan type flows.

Anytime the cash flows switch sign-- again, what's the solution?

Just put it next to an NPV.

If you compute an IRR, put it next to a net present value, that

always serves as a check on whether you're getting the right capital

budgeting decision.

OK, the other thing that we need to talk about is comparing scale with the IRR.

It's hard to compare two what we call mutually exclusive projects.

In other words, if I have an apple and an orange,

and I can only choose one piece of fruit,

I have to choose either the apple, or the orange.

I can't have both.

So in choosing those, we call those mutually exclusive choice.

In choosing the apple, I have to forego the orange.

In choosing the orange, I have to forego the apple.

OK, so let's think about how we would compare mutually exclusive projects

with the IRR.

The higher the IRR, it's hard to determine whether or not

that's going to imply a higher NPV.

Let's look through a simple example.

In project X, in my first project, I'm just going to spend $1.

Maybe I've got a rig and all I'm going to do

is leave the rig where it is to keep drilling the end of a well.

That's going to generate $2 in period 1.

Well, hey, that's a great project.

Because I'm only spending $1 in order to make $2, that's a 100% IRR.

Doesn't that look like a great project?

Here's the problem, I can move that same well to a new hole.

That would cost $100, but would generate $120.

Well, that's only a 20% IRR.

It looks like project X is bigger than project Y in terms of adding value,

because it's got such a bigger IRR.

But if I compute the net present value, this generates $0.82 per dollar.

This generates $9.10.

A much bigger net present value.

I should move the rig.

Project Y is much better from a net present value standpoint

because it's generating a lot more value for the firm.

It's just that project X is generating a relatively higher number.

That's what the IRR is telling me.

But in getting rid of the scale, we got rid of the scale.

Again, how do we solve the problem?

Or how do we make sure that we're making the right decision?

We take that IRR, put it next to a net present value,

and that checks whether or not the IRR is large enough,

or whether the scale is giving us the right decision with IRR.

Again, we could see this graphically as one project might have an IRR here,

but a similar project might have the same IRR,

but a much higher net present value.

Obviously, this project is preferable to this project,

because for all discount rates less than the IRR,

it's going to generate more NPV.

We just have to be careful of the scale.

Always put that IRR next to a net present value.

OK, it could be that there's no rate.

There's no solution to that polynomial.

You put it in Excel and it gives you that dreaded not applicable,

or it gives you dollar signs, or gives you some kind of weird symbol in Excel.

If you keep banging on it and it won't give you an answer,

it could be that there's multiple IRR's or no IRR's.

OK, if we consider this example on this slide, I've got two projects for you.

In both cases, we spend $100 in order to make $235 and $136.

Or in the next project, to make $120 and minus $50.

OK, in the first project there are actually two IRR's, not one.

In the second project, there's no IRR.

Well, how could that be?

If I put it in Excel and I hit Return, it

might be that there's actually no way to solve that problem.

And Excel kind of chokes on it.

Well, let's think about why that might be the case.

Remember, the IRR is just a solution to a math equation.

It could well be that the project looks something

like that-- the NPV gets bigger for a while, then starts to go down.

This project would have two IRR's like we had in that example.

It could be the project is such a total loser that it never

gets up to a positive NPV.

That also would have no IRR because it never crosses.

Again, how do we solve the problem?

It's easy.

Just put that IRR next to a net present value

and you can always check whether or not the IRR is giving you the right capital

budgeting decision.

OK, so IRR is a good capital budgeting tool.

But we need to be careful.

If there are changes in mutually exclusive projects, the scale

problem, timing, or whether or not there's an answer or solution,

always check next to a net present value.

As long as you put that IRR next to the NPV, it's a perfectly legitimate--

in fact, it's a nice way to get a scaled down or smushed down

version of what the return on the project

is relative to the discount rate.