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

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

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

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

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

Â That is exactly what you have here.

Â And so, because, putting down smaller investments will help

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

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

Â You're putting down less capital in project C,

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

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

Â Option one gave you 100% return, but

Â you actually get an additional $1 in your pocket.

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

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

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

Â the IRR towards investing in projects with relatively small

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

Â So what's the bottom line?

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Â comparing different projects even, and that's important,

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

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

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

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

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

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

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

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

Â widely used, very useful and very, intuitive too.

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

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

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

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

Â So as you remember we calculated the in session four,

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

Â We had a couple one or more decimal but

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

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

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

Â That Starbucks can only get a five year lease so

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Â Obviously Starbucks problem in real life is much more complex,

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

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

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

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

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

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

Â that you keep in mind the initial investments of

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

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

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

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

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

Â So we discount the first.

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

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

Â And once we actually calculate that net present value,

Â that is going to give you $2.7 million.

Â Again, remember this is not very complex to do,

Â excel will do that in a second for you.

Â The real problem, with evaluating an investment is

Â foreseeing is those cash flows are going to be,

Â but calculate that is actually not a very complex calculation.

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

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

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

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

Â then you should invest in this project.

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

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

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

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

Â open this coffee shop.

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

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

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

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

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

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

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

Â it should give us the same recommendation as the NPV.

Â In other words once we calculate the IRR and

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

Â All right, so let's do that.

Â We, equate the initial investment and

Â the expected, they discounted expected cash flows to 0.

Â Now we need to solve for those denominators,

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

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

Â 15% looks like a good return,

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

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

Â then again we should invest in this project.

Â That is exactly what we expected.

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

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

Â therefore, whatever the IRR tells you,

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

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

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

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

Â in this case that is to invest in this project.

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

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

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

Â well they should actually go ahead with this project.

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