# 10. IRR Versus NPV

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# Next lesson: Investing with Loans Part 1

Overview

For a single project, IRR and NPV tend to give the same answer. However, with evaluating competing projects, they can disagree on the best course of action.

Lesson Notes

When IRR and NPV agree

- For individual projects with positive cashflows, IRR and NPV will recommend same decision
- This is due to the fact that both measures are derived from the same equation

When IRR and NPV disagree

- When choosing between projects, IRR and NPV often disagree
- NPV prioritises investments that deliver more absolute value in USD\$
- IRR prioritises investments that deliver a greater return on the initial investment

Investing with capital constraints

- Most companies operate under capital constraints and therefore prioritise return on initial investment
- NPV can be adapted for capital constraints, using a relative measure called the profitability index
Profitability index = NPV / Initial Investment

Transcript

Over the past few lessons we’ve discussed the pros and cons of using IRR and NPV.

For most individual projects, IRR and NPV will provide you with the same recommendation.

This is because IRR and NPV are based off the same equation shown on screen.

Let's take the example of the six year project which is discounted at 20%.

This discount rate provides an NPV of \$220,349 and an IRR of 25.7%.

If the IRR is greater than the discount rate, this means we should pursue the project.

If the NPV is positive, this also means we should pursue the project.

Now let's change the discount rate to 30%.

As you can see, the NPV is now negative, so we shouldn't pursue the project, and the discount rate is greater than the IRR, which implies the same decision.

If we continue to move around the discount rate for different values, you'll see that IRR and NPV continue to recommend the exact same decision.

The recommendations of IRR and NPV tend to divert, however, when we must pick one project from multiple options.

This can occur for two reasons.

First, the projects are mutually exclusive.

They both serve the same purpose, and so choosing one makes the other redundant.

And two, the firm has limited capital and cannot take advantage of every good investment opportunity.

In these cases, NVP and IRR can often provide different recommendations on which project to choose.

Let's now take a look at a new example of two mutually exclusive projects, only one of which we can fund.

Project A has a much lower initial investment amount than project B, and as a result, it has a much higher IRR.

However its cash flows are much lower than project B, and so its NPV is much lower.

So which project should we choose? Well, it depends.

If a company has a lot of surplus value projects in the pipeline, it will most likely be unwilling to spend all of its cash on project B, which has a lower IRR than project A.

If a company has limited access to capital, it is also more likely to choose project A.

On the other hand, if the business has substantial funds and limited surplus value projects available at the current time, it’s more likely to use NPV.

As a result, public companies and those in mature industries are more likely to use NPV when making investment decisions.

For almost all businesses, capital rationing is a fact of life.

NPV as a decision rule, is unsuited to capital rationing because its output is a dollar value, and it’s not affected by the original investment amount.

However, NPV can be converted to relative measure simply by dividing the NPV by the initial investment.

This is called the profitability index.

And so to calculate the profitability index, I simply divide the NPV by minus the initial investment, because it’s currently a negative number.

So I'll select the NPV and divide by minus cell C4.

And then I'll copy and paste this formula for project B.

Obviously, project A has a much higher profitability index than project B, and is likely the better investment option for a company with capital constraints.

If you're eager to avoid using IRR and stick with NPV as a decision rule, I would always recommend calculating the profitability index as well when choosing between projects.

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