The Joy of Internal Rate Of Return (IRR)

Episode 31 - 13 Apr 2016

The Risk Premium element of Discount Rate is tricky to determine.

If only there was a way to side-step the issue:

Internal Rate of Return (IRR) to the rescue!

Videos mentioned in this episode:

You have a project.

You've calculated its Net Present Value (NPV).

It's negative :(

But it's not very negative.


Should you proceed?


We've done Present Value (PV)

We've done Net Present Value (NPV)

We've dissected Discount Rate

If you've missed any of these, you'll find links on or around this video:

We've almost reached my level of incompetence....

... but there's one one more concept I want to share with you:

Internal Rate of Return - IRR for short.

Converting Annual Rates to Monthly Rates

Before we get to that, there's one bit of mathematically trickery

that glossed over in the last episode...

and which will be helpful for this one.

Remember last time that we spoke about splitting Discount Rate into the components:

  • Time Value of Money
  • Risk Premium

This help us, because at one of these - the Time Value of Money - can be looked up.

Let's continue our tradition of picking easy numbers and say that the interest rate that we could have got in a risk-free bank account is 7%.

Then we use our skill and judgement to choose a Risk Premium of 5%.

That gives us a Discount Rate of 12%.


With just one small problem. These is an annual rate.

Unless we're looking at a 10 year project, we've going to want the monthly rate.

Easy right?

12 months in a year: that's 12% divided by 12 months. Which gives us 1%.

Sounds right. But it's wrong.

Don't blame me. It's compound interest that's to blame.

The equation to convert from an annual rate (R) to a monthly rate is this little beauty:


Monthly Rate = (1 + R)^(1/12) - 1


(It looks a nightmare, but remember in practice a it will be a spreadsheet doing the heavy lifting.)

Plugging in 12% - 0.12 - gives us: 0.009488793

That's 0.95% per month

Evaluating Projects

Now that we can convert between annual and monthly discount rates,

we're ready for the main job of today: evaluating projects.

Let's start with this one: (Project A.)

Bad news, it has a negative Net Present Value.

However... it's not very negative.

It's close enough... to make us think twice.

After all, the Risk Premium part of Discount Value is... a bit of a guess.

We need something to reduce our reliance on the absolute value the Discount Rate.

One way is to have another project to compare it to.

The NPV of this project - Project B - is positive.

We have a winner.

Or do we?

What if we're wrong about this Discount Rate?

One quick check we can do it to vary the Discount Rate a few percentage points in either direction and see it changes the picture.

Drop the Discount Rate by 4%, and Project B is still a winner.

Increase the Discount Rate by 4%, and again Project B is the winner.

Looks like Project B is a good choice... and will still be a good choice if we've a little bit off with our Discount Rate.


This is all a bit fiddly. A bit messy.

Surely the finance and accounting types have come up with something more... elegant?

It would be great if we could have conversations like:

  • Project A will provide a return of X%
  • Project B will provide a return of Y%

The great news it that we can do exactly this.

Time to introduce Internal Rate of Return (IRR).

Internal Rate of Return (IRR)

The IRR is defined as the the Discount Rate that

reduces the Net Present Value of a project to zero.

This may sound counter-intuitive - it certainly did for me -

so let's try it on Project A and Project B

This is all set up in a spreadsheet. it's very easy to change the Discount Rate

to change the Net Present Value (NPV)

With a little bit of fiddling around, I can decrease the Net Present Value to zero.

The Discount Rate that achieves this - 0.0864 - 8.64% - is the Internal Rate of Return for this project.

If we do the same for Project B, we get - 0.263 - 26.3%

We now have our neat little statements:

  • Project A has a Internal Rate of Return of 8.64%
  • Project B has a Internal Rate of Return of 26.3%

All very tidy.

Next time

Thanks for watching.

In the next value we'll see if we apply what we've learned to a very specific question:

  • "Is Agile is more profitable than waterfall?"

Talk to you then.