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And scale problem is just a fancy name for saying that if your investment is

very small, then it's very easy to get a very high rate of return.

If you put down one dollar, it's not too difficult to actually find ways in

which you can get $1, but if you put down a $ billion,

it's not that easy to find ways in which you can get $2 billion.

That is exactly what you have here.

And so, because, putting down smaller investments will help

you get a higher return, the IRR has these buyer stores investing little capital,

and that is when you compare project C and project D that is exactly what happens.

You're putting down less capital in project C,

therefore, it's easier to get a higher return, but as we've seen in the other

options that I put before you before, well that's not the only thing that matters.

Option one gave you 100% return, but

you actually get an additional $1 in your pocket.

Option two gave you only quote unquote, only 90% in one week,

but you put $900,000 in your pocket, that's the scale that actually matters.

And so again, the what we call the scale problem is the bias of

the IRR towards investing in projects with relatively small

investments because it's easier to get a higher rate of return.

So what's the bottom line?

Well, I go full circle into the beginning of this discussion where I

told you well remember, we're not going to say that you shouldn't use the IRR, or

that's it's useless or it's not intuitive, it's actually very useful number.

So the bottom line is, the IRR is very intuitive,it's very useful,

it's very widely used, but it's also tricky.

It is mathematically complex and therefore you need to be aware of this

particular complexities,it is not as straight forward as the NPV calculation.

So, as long as you're aware of the limitations, as long as you

know the structures of your cash flows, then you can use it with some confidence.

So, the bottom line of this is that when you're discussing a projects IRR you

need to make sure, first, that you know the structure of your cashflows,

because if you have negative and then positive and that's it,

then you're not going to have any problem, you can use the IRR with confidence.

Or if you have positive and then negative, then you use the IRR with confidence.

Now if you have negative cashflows, positive cashflows, negative cashflows,

positive cashflows, then you have to be really careful about using the IRR.

You really have to know what you're doing otherwise you may run into trouble, and

in all those cases, whenever in doubt, fall back on the Net Present Value.

Second thing for you to take into account is, remember that when you're

comparing different projects even, and that's important,

even if you don't have any of the problems that we talked about before.

Multiple solutions or no solutions, and so forth, it's important that you

keep in mind that the IRR is always going to push you a little, going to push you

a little bit towards investing in things that require small initial investment.

It's easier to get a return out of those investments.

And therefore again, it's very important that you keep in mind we're not trying to

be be negative about the IRR, we're just trying to be realistic,

it's a complex number but as long as you know how to use it properly it's a very

widely used, very useful and very, intuitive too.

All right, all this said, now we're going to go back and apply these two.

So far we've been discussing the intuition and the reservations you

need to have particular with respect to the Internal Rate of Return, now we're

going to run a specific calculation and we're going to go back to Starbucks.

So as you remember we calculated the in session four,

we calculated a cost of capital for Starbuck at 7.2%.

We had a couple one or more decimal but

it doesn't really matter so we're going to round it up to 7.2%, and we're going to

assume the Starbucks now it's evaluating opening a coffee shop in a mall and just

to make this project a little short, that is not too many cashflows in the future.

That Starbucks can only get a five year lease so

basically the question here will be look they need to start this coffee shop and

in order to do that they need to put down $10 million today and

they can get a five year lease and run the coffee shop for five years.

And whatever other cash flows that they're, expect to get over these

five years they need to compare to the $10 million that they need to put down.

And everything has to be related, or tied to the cost of capital of 7.2%.

So, first let's look at that little table, that little table actually summarizes

the cash flows, you need to put down $10 million today, and what you expect 1, 2,

3, 4, and 5 years down the road, are 1.6 million, 2.1, 3.2, 4.1 and 5.2 million.

So, we have the initial investment that we know for sure, and we have the expected,

and I underline again the expected cashflows of this particular coffee shop.

Those expected cashflows, remember, now that I gave you this, and

that you also have the discount rate which is 7.2%,

well, you know, now is throwing basically numbers into a formula.

Obviously Starbucks problem in real life is much more complex,

which is coming up with what kind of money they're going to

make if they invest in this particular coffee shop over the years.

Well, you know, once I give you the expected cash flows, I give you 99%

of the problem solved, now you actually need to run a simple calculation,

which is the NPV, and the IRR, and that is exactly what we are going to calculate.

Back to the numbers, we're going to keep that table there just so

that you keep in mind the initial investments of

the cash flows that you expect to make, that is the NPV calculation.

I put in all the numbers at once, here so remember we have an initial cash flow that

we don't discount because that is money that we need to put down today.

And we have five expected cashflows,1, 2, 4, 3, 4, 5 years down the road, which we

need to discount at 7.2% cost of capital adjusting by when we get those cashflows.

So we discount the first.

At the rate of 1%, we raise the second of the race of,

the rate of 2%, only way that raising 1 plus 7.2% at 5.

And once we actually calculate that net present value,

that is going to give you $2.7 million.

Again, remember this is not very complex to do,

excel will do that in a second for you.

The real problem, with evaluating an investment is

foreseeing is those cash flows are going to be,

but calculate that is actually not a very complex calculation.

And in one of the exercises that I'm going to ask you to do,

you're going to have to calculate one of those NPVs.

That, NPV of $2.7 million, it's obviously positive, and

our rule was very simple, if you actually get a positive net present value,

then you should invest in this project.

So, as you see, the calculation is not very different.

And, again, you don't have to do this by hand, you basically throw the numbers into

Excel, and Excel will give you what that net present value is going to be.

So, as far as the Net Present Value is concerned, then we should go ahead and

open this coffee shop.

Now, take a look at that Net Present Value equation, or

take a look at the cash flows in the table, same thing.

Notice that, we have a first negative cash flow, and

then we have all positive cash flows, which means that we have only one change

of sign from negative to positive in the cashflows, and that means that

the IRR that we're going to calculate, is not going to be a problematic IRR.

That is, this is going to be straightforward IRR, and

it should give us the same recommendation as the NPV.

In other words once we calculate the IRR and

we compare it to the cost of capital, it should tell us go ahead with this project.

All right, so let's do that.

We, equate the initial investment and

the expected, they discounted expected cash flows to 0.

Now we need to solve for those denominators,

those Internal Rate of Returns, and once we do that, I, if you do that, I mean,

if you throw these numbers in Excel, Excel is going to give you a number of 15%.

15% looks like a good return,

particularly if you compare with the cost of capital of 7.2%.

And because the IRR is higher than the discount rate of 7.2%,

then again we should invest in this project.

That is exactly what we expected.

We didn't know the number, but we knew that the IRR was going to suggest to

invest in the project, simply because these cash flows are not problematic, and

therefore, whatever the IRR tells you,

should point in the same direction, as the NPV that we discussed before.

Now, we're not comparing projects, so we, we're not

going to have this scale problem here, and so everything was guaranteeing the NPV and

the IRR were going to give you exactly the same recommendation, and

in this case that is to invest in this project.

So the bottom line of this is if we, Starbucks is more or less certain, or

more, we're never certain but, you know, if they're confident about

getting those expected cash flows that we're getting the table then,

well they should actually go ahead with this project.

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