(12 of 20) Ch.9 - The IRR approach: explanation & example - YouTube

The IRR rule, the internal rate of return rule or approach.

This is the fourth investment valuation approach that we are learning in Chapter 9.

This is another important alternative to the net present value, the NPV approach.

It's very often used in practice actually in the business world and it can also be intuitively

explained very easily.

Let's look at the following example.

You're considering an investment with the following cash flows.

In year zero, you would be investing $10.

Maybe it's all in millions, right?

Then in year one, your profit would be $6, in year two, $5, in year three, $8 and in

year four, another $8.

So, these are our cash flows for this four-year investment project.

What do we want to do with them?

Well, let's calculate the net present value.

OK.

Let's start with the net present value.

And then, you're going to see the link between the net present value and the internal rate

of return approaches.

To calculate the net present value, normally, we would need to also know some discount rate,

right?

Well, it's not given here.

So, let's calculate the NPV for several-- more or less randomly paid discount rates.

Let's try 30%, 50%, and 70% for our discount rate.

And then one question we're going to answer is at which discount rate do we break even?

So, let's not worry about the second question yet.

So, we want to calculate three net present values, right, separately at a different,

you know, discount rate r.

If you want to do it by hand, then the NPV would equal negative 10 plus 6 divided by

1 plus r where r can be either 30%, or 50%, or 70%, plus 5 divided by 1 plus r squared,

plus 8 divided by 1 plus r cubed, plus another 8 divided by 1 plus r to the fourth power.

Or, of course, you can do it in the financial calculator.

Cash flow keys, one step.

You enter cash flow zero as negative 10, cash flow 01, 6, cash flow 02, 5, cash flow 03,

8, and cash flow 04 also 8.

And then when it asks you for the I, that's your rate.

So that rate you will first try 30, right?

And then compute NPV.

And when you try the 30% discount rate, your NPV will be $4.2.

Then when you redo the whole thing and instead try the 50% discount rate, your net present

value will be 17 cents.

And then when you try the highest discount rate of 70%, your net present value is negative

$2.15.

So, let's illustrate it in a more visual way what is going on and what the results mean.

If you put the discount rate on the horizontal axis, right, so as we move to the right the

discount rate is increasing.

And then for each discount rate, we calculate the net present value and that's what we have

along the vertical axis.

So above the horizontal axis, the net present value is above zero dollars.

That's a good thing.

That's when we say the project should be accepted.

But if we are below the horizontal axis, that's where the net present value is below zero

dollars and that's when we say reject the project.

So, when we try the 30% discount rate, the net present value was $4.2.

That's above zero and we plug this point above the horizontal axis.

Then when we instead picked a higher discount rate, 50%, the net present value dropped and

it's now only 17 cents.

So, close to zero, right?

And then when we tried, you know, randomly did even higher discount rate, 70%, that's

when we saw an even smaller net present value.

And, in fact, it was a negative number, negative $2.15.

So, if we tried, you know, a few more discount rates, then we would keep adding more and

more points and all of them could be connected with this downward sloping curve.

We call it the NPV profile, the net present value profile.

So, this downwards sloping line shows that the higher the discount rate, the lower the

net present value.

And this is something we actually had already in Chapters 5 and 6 a long time ago where

we saw how the higher the interest rate, the lower the present value, right?

And present value of all future cash flows is a big part of the net present value calculation.

So, the net present value profile is a graphical representation of the relationship between

the net present value and various discount rates and it's a negative relationship because

the line slopes down into the right.

Now, see this blinking point here.

That's where this net present value profile crosses the horizontal axis.

What does this point mean?

It means that at this specific discount rate, and we don't know yet what it is yet, the

net present value is how much?

It's exactly zero dollars.

And that's the meaning of breaking even.

We break even.

We neither make money nor loss money.

The net present value is neither positive nor negative.

It's exactly zero.

And we can actually figure out what this specific discount rate should be in order for us to

break even.

There is a way to calculate it and if you know that trick, you will find that it's 51.2%.

So, if the previous calculations of the net present value, if you use 51.2% for the discount

rate, the cash flow keys will give you the NPV of exactly zero.

So, 51.2% is the internal rate of return, the IRR.

The meaning of the word "internal" means that it-- this is a-- it's-- this rate of return

on our money every year is only based on the so-called internal information about this

investment project.

And that internal information is the cash flows that are given.

So, if we invest $10 now, we get 6 back in a year, another 5 back in two years then 8

and then another 8, right?

So, we only used the cash flows, right?

The money invested and the money that would be received to figure out what it all implies

about the annual return on our money, an annual return on the $10 that would be spent now.

So that's why it's called internal rate of return.

So, you can think of a much simpler example.

Let's say you invest 10, you get 11 back in a year, and that's it.

There are no more years in the future.

So, if you invest 10 and get 11 back in one year, that's always a 10% return.

That's also the IRR.

The IRR is 10%.

So here, it's more complicated.

It's a four-year project, right?

And so, it's more tricky to calculate that sort of implied, you know, fixed annual rate

of return of all money, the same return every single year for four years.

And it turns out to be 51.2%, right?

So, if you invest 10 you get, you know, 6 and 5, and 8 and 8 back.

And the IRR sort of connects what you spent with what you receive.

So, what you spent kind of equals in today's dollars what do you receive across all future

years.

That's why the difference between the present value of all future cash inflows and the cash

outflow today is zero.

The NPV equals zero, right?

So, you cannot break even.

OK.

So, IRR is nothing but a discount rate but it's a special discount rate.

It's that discount rate it reached.

When you calculate the net present value, you get exactly zero dollars.

So, at this rate, we break even.

We make neither profit nor loss with our investment project.

So, the internal rate of return definition is it's the discount rate at which the NPV

equals zero.

And it's called internal because it's based entirely on the estimated cash flows for future

years and the estimated required initial investment today.

And it's completely independent of other sort of external thing such as the typical rate

of return on this kind of projects that was, you know, observed by other companies somewhere

else.

Now-- OK.

How do we calculate the IRR?

Well, there is always the trial and error approach.

It might take a while and the idea is you try, you know, plugging in different discount

rates and you stop when the NPV is zero.

But, of course, our lifesaver will be the financial calculator.

Let's learn something new.

If you look at the second row of our calculator, Texas Instruments, BA II Plus, you'll see

the button IRR.

It's right next to the NPV button.

So, IRR is the internal rate of return.

And let's learn how we use it.

What we do is let's take out our financial calculator.

Let's turn it on.

Let's start by clearing everything, second, plus, minus, enter, off and on again.

Imagine you're calculating the NPV.

The first several steps are identical.

You start by pressing the cash flow key in the second row.

Cash flow zero is the initial investment which is negative 10.

So, you press 10 plus, minus, enter, it saved.

Then you press the down arrow key, cash flow 01, the first cash flow in the future, that's

6, 6 enter, down.

What's the frequency of it?

F01.

The default is 1 and that's also the case in our example because $6 is not repeated

in the second year.

It's only once in a row.

So, if you leave the frequency as 1 and you can either save it by pressing enter and then

you press the down arrow key or you can immediately press the down arrow key because 1 is the

default number.

So, I'm pressing the down arrow key.

And then the same way I'm entering cash flow 02, $5, cash flow 03, $8, and cash flow 04,

$8.

So, the second cash flow in the future is 5.

I press 5, enter, down and the frequency is again left at the default value of 1.

I press the down arrow key.

Cash flow 03, that's $8, 8 enter down.

Here, I can speed things up a little bit and change my frequency to 2.

I press 2, enter down.

And if I do this trick then there will no longer be cash flow 04 because that was that

second $8.

Then normally if you're calculating the net present value, you would press the NPV button,

the display will ask you what's the value for the I which is the rate, you would enter

that and press compute, right?

To find the internal rate of return, you do something different.

You press the IRR button and then you press compute.

So, after entering all cash flows where you would be pressing the NPV button now, instead

you press the IRR button and compute, 51.20, right?

So, 51.2% per year, that's the annual return on our money on the $10 that we would be investing

in this project if we decide to accept.

OK.

Let's go back to this graphical illustration of what's going on.

How are we going to use this IRR approach to make our investment decision?

And we are talking about, in which case, would we say accept the project or reject the project?

Well, we have just calculated the internal rate of return.

So, we would be making a 51.2% return on our invested money every single year, right?

If the required return, and that's the so-called external number, right, something that is

given in addition to the cash flows, right?

Let's say the required return is 40%.

So, the required return is 40 but we are going to make a better return, 51.2% every year.

So, does that make our project a good one or a bad one?

A good one.

And so, in this case, when the required return is less than the IRR that we have calculated

then we say that the project should be accepted.

Otherwise, if the required return which is a number that's given, right, is more than

the IRR that we have found then the project should be rejected.

There's another way to intuitively explain this conclusion.

Whenever the required return is to the left from the IRR, that's where on our graph the

net present value line is above the horizontal axis, which means the net present value is

above zero dollars, which is a good thing.

And instead, when the required return that's given to us is greater than the IRR that we

calculate first, then that corresponds to the part of our graph where the NPV line lies

below the horizontal axis, which means the net present value is negative.

And that's when we say reject the project.

So, the internal rate of return rule, to summarize, says that the project should be accepted if

the required return is less than the IRR, otherwise, it should be rejected.

And, you know, there is this very strong link between the IRR approach and the net present

value approach because whenever a project is accepted using the IRR rule, that's when

the net present value of the project is positive.

So that's when we also say accept when using the net present value approach.

And when a project is rejected using the IRR rule, that's when it's also rejected using

the NPV rule because the NPV is below zero dollars.

So, the only calculation we do to use the IRR approach is in one step the cash flow

keys in our financial calculator.

So, we use the cash flow keys to find the IRR, nothing else.

And the second step is we compare the IRR that we found with the required return, so-called

required return which is a number that's always given to us.

So, we just check whether our IRR is above or below the required return.

If it's above, that's a good thing, accept the project, otherwise, reject it.