# IRR Summary

Internal Rate of Return is derived from Net Present Value. IRR restates NPV as a percentage rate. It is a measure with intuitive appeal. It provides a way of grasping the rate of return a project, or income-producing asset, is yielding.

IRR takes into account the timing of cash flows, the opportunity costs, and the risk of an investment or project in a similar manner to NPV. IRR provides good information as a good capital budgeting tool, but it should not be relied upon as a standalone measure.

*Always compute it alongside the gold standard: NPV. Together IRR and NPV provide an informative set of metrics for capital budgeting and financial decision making.*

There is no fancy formula for IRR where you can just plug in the numbers and calculate the solution. It can only be calculated via an iterative process of trial and error, with each successive iteration getting closer and finally converging on the solution.

Excel does it for us by crunching through thousands of iterations in a fraction of a second. Before spreadsheets became ubiquitous on personal computers you could estimate IRR with cross-reference tables. Now with just a few mouse clicks, we get an accurate IRR solution.

# IRR Shortfalls and Caveats

IRR provides insight and an intuitive way to grasp the value of a stream of cash flows, but there are a couple of caveats. IRR is a summary type of number. And, as with all summaries, by compressing the solution, some of the information is squeezed out.

*By reducing the solution to a percentage IRR is easy to grasp, but there are issues surrounding the information that gets eliminated.*

NPV is our gold standard capital budgeting tool. IRR is similar to NPV and we have looked at the similarities and differences, and the benefits of including IRR in our analysis. IRR has a couple of complications in practice.

The first case is when cash flows in a stream get reversed or when they come in and go out, come in and go out, IRR can get confused for some math reasons that we will look at.

Another issue is that IRR provides no information about the scale of the project. We can end up making poor capital budgeting and allocation decisions based only on IRR because doesn’t take into account the size of a project: how big it is in terms of absolute dollars.

When analyzing and selecting between projects, one may have a better IRR but be an order of magnitude smaller and so the amounts of money generated are proportionately smaller. We would rather have more money than less. IRR has eliminated how much money a project is anticipated to make. IRR puts the solution in percentage terms and we need to be vigilant about the information that gets lost.

There is also a lack of information about the timing cash flows with IRR. And finally there are some mathematical complications with IRR that we need to be aware of.

Lets look at each of these scenarios in more detail.

# When Cash Flows are Reversed During a Project

IRR can sometimes give me a misleading picture about whether or not the project is adding value to the firm when cash flows reverse from positive to negative during a project. In a situation where money comes in and then money goes out, the sign, negative and positive, flips. Any time cash flows flip negative and positive in a stream of cash flows, we need to be careful using IRR.

For example, if we spend money on a machine, then the machine generates revenue, and then we have to retool the machine in year three, and we spend more cash, and then generate more revenue, that’s two sign changes: money out for the initial purchase, money in, money out for the retooling, and then more money in. Any time the cash flow direction flips a couple of times; IRR can give us confusing results.

# Borrower Type Loan Flow IRR Example

Consider these two projects, A and B. In the first, we are going to spend $400 in order to generate $500 a year from now. In this case the NPV comes out to $54.54 and the IRR comes out to 25%. In the second project we’ve got $400 coming in, and then I spend $500 a year from now. This stream looks like a loan from the borrower’s side. We are getting money in, and paying it back later. In the case of project B, the net present value is *negative* $54.54. It is the inverse scenario of Project A. In this case, we aren’t making $54; we are losing $54. But when we calculate IRR, it’s the same 25%.

Did something get messed up? No, the math is correct. Remember IRR is the interest rate that sets NPV to zero; where the Costs are equal to the present value of the future cash flows. The solution to what rate sets NPV equal to 0 is 25%. It’s just that the NPV flipped sign. We need be careful any time there’s a flip in the sign of the cash flows.

Let’s look at it from the graph perspective. For project A the NPV is downward sloping and above zero until it crosses at the IRR. But in project B the NPV is negative and upward sloping until it crosses zero at the IRR.

They have the same IRR, but for a low discount rate, project B is going to give us a negative NPV, whereas project A is going to give us a positive NPV. At a high discount rate, Project B is NPV positive. It really gets squirrely though when there are multiple changes in cash flow direction in a stream.

The solution is to always put IRR next to an NPV. If you compute an IRR, compare it with the net present value. NPV always serves as a check on whether you’re getting the right capital budgeting decision.

# Scale and IRR

Another issue is comparing the scale of different projects or investments using IRR. If we have mutually exclusive projects that we want to compare and decide between, it’s hard to meaningfully compare them with IRR alone. Mutually exclusive means we can’t pursue all proposed projects because of limited resources. We must choose one or the other. In choosing one, we must forgo the other. As financial officers our job is to make sure we decide to pursue the best opportunities that generate the most money.

It’s not clear whether a higher IRR indicates a higher NPV. Let’s go through an example of how we would compare mutually exclusive projects with the IRR.

In project 1 we are just going to spend $1. This would represent an incremental project such as a coffee shop and all we are going to do is leave the shop where it is to keep pumping out espressos. That’s going to generate $2 in period 1.

That looks like a great project from an IRR standpoint. We are spending $1 in order to make $2. That’s a 100% IRR.

Here’s the issue: we could move that same coffee shop to a new location in a popular neighborhood. That would cost $100, and would generate $120. That is only a 20% IRR. It looks like project 1 is better than project 2 in terms of adding value, because it’s got such a bigger IRR.

But if we compute the net present value, project 1 generates $0.82 per dollar. Project 2 generates $9.10. Project 2 has a much bigger NPV. We should move the shop.

Project 2 is much better from a net present value standpoint because it’s generating a lot more value in total dollars for the firm. It’s just that project 1 is generating a relatively higher number. IRR doesn’t take the scale of the project into account.

The best way to avoid being misled is, again, to put IRR next to NPV. That checks whether or not IRR is large enough to meet our hurdle rate *and* whether the scale is giving us the right decision with IRR.

We can analyze this graphically by looking at two projects. Projects A and B have the same IRR, but Project A has a much higher net present value. Project A is preferable to Project B, because for all discount rates less than the IRR, it’s going to generate more NPV.

Always put that IRR next to a net present value in order to check for scale issues.

# Multiple or No Solution to IRR

Situations exist where there is no solution to the IRR polynomial.

If you put the cash flows into the IRR formula in Excel and it won’t give you an answer, it could be that there’s multiple IRRs or no solution.

Consider the example above. We are analyzing two projects. In both projects we spend 100. In Project A we plan to make 235 in year 1 and 136 in year 2. Project B is forecast to make 120 and negative 50.

In Project A there are actually two IRR’s, not one. In Project B there is no IRR.

Remember, IRR is the solution to a math equation and there are scenarios where there is no solution to the math problem. Graphically, Project A and B look like this: for Project A the NPV gets bigger for a while, then starts to go down. This project has two IRR’s. NPV crosses zero twice as the discount rate increases.

It could be that a project is such a total loser that it never gets up to a positive NPV. That is the case with Project B. It has no IRR because it never crosses zero.

Again, how do we address this issue? Make sure to compare an IRR calculation to a net present value. This way you can always check whether or not the IRR is giving you the right capital budgeting decision.

# Shortfalls of IRR Summary

IRR is a good capital budgeting tool. But it is not a standalone measure.

*Because of the nature of mutually exclusive projects, the scale problem, cash flow timing issues, or whether or not there’s an answer or solution, always check IRR next to a net present value.*

As long as you aware of these caveats and compare IRR to the NPV, IRR is a legitimate analysis tool. IRR provides intuitive insight as way to get an idea of what the return on the project is relative to the discount rate.

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