Internal Rate of Return explained in a clear and simple way.
NPV (Net Present Value) and IRR (Internal Rate of Return) are very closely related.
I strongly advise you to study Net Present Value before Internal Rate of Return!
So if you don’t know how NPV works, or only have a very basic grasp of the concept, then
watch my Net Present Value video first by clicking on the link in the top right corner
to become an NPV expert, and then come back to watch this Internal Rate of Return video.
See you in 5 minutes!
In a calculation of Net Present Value, we take future values and convert them one by
one to present values, using a discount rate or weighted average cost of capital, which
in this example is set at 20%.
The further out in the future the nominal amount, the lower the present value equivalent.
To get to NPV, you now simply sum the present value amounts.
The Net Present Value in this example is $35.
So how do NPV and IRR relate to each other?
With NPV, you start off quantifying the nominal cash flows over the years for your project.
You use the discount rate (also called WACC or hurdle rate) to calculate present values
of the estimated project cash flows.
The last step is to calculate the Net Present Value (or NPV)
by summing the discounted cash flows.
IRR basically swaps steps 2 and 3.
Just like in the NPV calculation, you start off quantifying the nominal cash flows over
the years for your project.
You then set the Net Present Value in the formula at zero.
You can now calculate IRR, which is the output variable or dependent variable.
Let’s illustrate that with numbers.
In NPV calculations, the main question is: what is the Net Present Value of the project?
Sum the present values of the future cash flows, and you have your NPV.
In IRR calculations, the main question is slightly different: what is the discount rate
that makes the NPV equal to zero?
So we start at the bottom of the page,
we want the outcome of the NPV calculation to be zero.
For the present values of the benefits we now have questionmark 1,
questionmark 2, questionmark 3, and questionmark 4.
We don’t know what numbers need to be in those four places, but will soon find out!
The future values of $400 nominally per year somehow lead to these questionmark numbers.
So we need to play around with the discount rate in the present value formula to get all
of that to add up to an NPV of zero.
In the earlier example, we saw that a 20% discount rate gives us an NPV of $35.
So that discount rate is too low, as the NPV is a positive number, higher than zero.
Let’s try with a discount rate of 25%.
Now our NPV is negative $55.
So that discount rate is too high, as the NPV is lower than zero.
Maybe a discount rate of 24%.
Our NPV is still negative at minus $38, but getting a bit closer to zero, which is our
ultimate goal in determining IRR.
A discount rate of 23% gets us to an NPV of minus $21.
A discount rate of (rounded up) 22% gets us to an NPV of $0.
We have found our Internal Rate of Return!!!
Here are the steps to use in the NPV formula.
Step 1: start with the nominal cash flows.
Step 2: apply the WACC or discount rate as an input variable.
Step 3: Calculate NPV as the dependent variable.
Here are the steps to use when you want to determine Internal Rate of Return.
Step 1: start with the nominal cash flows.
Step 2: set NPV to zero.
Step 3: Calculate IRR as the output variable.
In this video, I have shown you the “trial and error” step by step approach to determining
IRR, to show you how the concept works.
Now that you understand IRR, you can go to the next step of calculating IRR efficiently,
and that’s where Excel comes in.
Click on the link on the top right to see how IRR is easily calculated in Excel.
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