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Now here's another example.

Â Project B and Project B again you put $100 million today,

Â you expect to get a negative cash flow of 300 million.

Â Excuse me, you get $100 million today, you expect to put down $300 million

Â a year from now, and you expect to get $250 million a year from now.

Â And we're still dealing,

Â let's say with the same company that has the same discount rate of 12%.

Â Now, let's look at the picture first and, and remember.

Â The, by definition, the internal rate of return is the rate,

Â the discount rate for which the NPV is equal to zero.

Â But take a look at that picture there.

Â That blue line never crosses the horizontal line and

Â that basically means that there's no solution for that.

Â In fact, if you throw these three cash flows into Excel and

Â you apply the IRR command, that then you're going to get no solution.

Â And that's basically Excel's way of saying, I cannot solve for this.

Â And the reason why you cannot solve for this, you have it in front of your eyes.

Â That blue line never crosses the horizontal axis.

Â There's no discount rate for which this NPV is equal to zero and obviously,

Â while in this case we cannot use the IRR, if we cannot compute a number, we have

Â nothing to compare to, to the discount rate, and therefore we cannot use the IRR.

Â Now, again, we fall back to our rule that we said before,

Â we calculate the NPV, we got over $31 million of positive NPV and

Â therefore we should go ahead with this project.

Â But, the problem to highlight here is that it may well be the case

Â that you're trying to find the IRR of your project and this project doesn't have.

Â You cannot calculate an IRR.

Â So we have two opposite problems.

Â We can have no IRR or we can have more than one IRR.

Â Both cases are problematic.

Â In both cases you need to fall back on whatever the NPV happens to recommend.

Â Now there's, there's many other problems that we could actually discuss, and

Â in fact the complementary reading that goes with this session it'll explore more

Â than the problems that we're discussing here in our limited time.

Â But there's one more that I want to highlight because it's important and

Â actually it's a problem that you may encounter in practice more than once.

Â Before we get to that problem, let me ask you that simple question.

Â Suppose that I give you this option.

Â Option number one, you give me $1 today and I give you back $2 next week.

Â Now let's suppose you believe me.

Â I am going to give you those two dollars next week so let's, let's

Â consider two propositions that I will put before you as risk free propositions.

Â Whatever I tell you, I'm going to deliver.

Â You believe I'm going to deliver.

Â So proposition number one, give me $1 today, I give you back $2 a week from now.

Â Proposition number two, you give me a million dollars today and

Â I give you back $1.9 million next week.

Â And I know that you may think that I may not give you

Â back $1.9 million next week but again bear with me.

Â Trust me.

Â I'm going to give you those $1.9 million.

Â This is a risk free proposition for you and I the only thing I say is look

Â either you have to go for option one or you have to go for option two.

Â Which one would you choose?

Â Well here's the thing with that.

Â If you think exclusively in terms of return.

Â Option number one.

Â Gives you 100% return.

Â You give me one hu, $1 today, I'll give you $2 next week.

Â Your return between one week and the next is exactly 100%.

Â Now if you give me $1 million today, and

Â I give you back $1.9 million next week, your return is not 100%.

Â It's only 90%.

Â That's a pretty good return for one week.

Â Now but still, you know,

Â what really counts there is that in one week you're going to be $900,000 richer.

Â So would you prefer to be $1 richer in a week or $900,000 richer in one week?

Â Well although the return on the second project is lower.

Â You know, every time that I ask this question to my students,

Â everybody chooses option two.

Â You obviously prefer to go from.

Â One million dollars to $1.9 million rather then from $1 to $2 although the return

Â on the first proposition is higher then the return on the second proposition.

Â Why is this example important?

Â Well, we're going to see a,

Â another example now in just a minute to compliment this, but notice that what this

Â example is telling you is that return only is not the only thing that matters.

Â That is, in the first case you get 100%,

Â in the second case, you get 90%, but you're also thinking in terms of

Â the amount of money that you put in your pocket.

Â And that is important, why?

Â Well, let's look at these two possibilities.

Â We have two very simple projects.

Â Project C, we put $100 million today.

Â We expect to get $150 million a year from now.

Â Project D, and we have to go either/or.

Â Either we go for one, or we'll go for the other.

Â Project D, I need to put $200 million today, and

Â I get $280 million a year from now.

Â We're still dealing with a company that has discount rate of 12% and

Â the question is you know what we call before competitive projects.

Â Should we go for Project C or should we go for Project D?

Â Well there's more than one way of looking at that.

Â But first let's look at the internal rates of return.

Â The IRR of Project C is 50%.

Â The IRR of Project D is 40%.

Â So if we go by the, I wouldn't call it informal, but

Â the rule we suggested before, that the higher the IRR the better the project,

Â then we should go for Project C.

Â But, remember, we also said, but

Â be careful with this rule, because it is not universally true.

Â There are some loopholes, and we'll talk about it.

Â Well, we're talking about it right now.

Â It looks like if we go by IRR, the first project, C has 50% IRR.

Â The second project, D has 40% IRR.

Â We should go for Project C.

Â However, look at the NPVs.

Â The NPVs tell you exactly the opposite thing.

Â That it is the Project C has an NPV of almost 34 million, but

Â Project D has an NPV of 50 million, and so this is one situation in

Â which the NPV rule and the IRR rule actually pulling in different directions.

Â And as we said before,

Â whenever you have one rule suggesting that you should do one thing, and another rule,

Â the NPV rule, suggesting the opposite, you should always fall back on the NPV rule.

Â So in this particular case, although the IRR of Project D

Â is lower than the IRR of Project C, because the NPV of Project D

Â is higher than that of Project C you should actually choose Project D.

Â Now there's another way of seeing why we need to go to Project D.

Â And let me just put that, those cash flows.

Â And notice that we're calling that Project E.

Â And we're calling project in quotation, because it's not really a project.

Â If, if you actually pay attention to those numbers,

Â that actually is the differential cash flow between Project D and Project C.

Â In other words, if I invest in Project D as opposed to Project C, I need

Â to put an additional $100 million, which is a number that you have right there, and

Â if I invest in Project D as opposed to Project C, I expect to get an additional

Â $130 million, so instead of getting 150 million, I'm going to get 280.

Â And instead of putting down a hundred million, we're going to get 200.

Â So as you see if you subtract the two cash flows in,

Â in the column Project D to the two cash flows in the column Project D,

Â then you're going to get the cash flows in the project E.

Â And now the question becomes, does it pay to put an additional $100

Â million in Project D in order to expect an additional $130 million, in, in Project E.

Â And if you actually calculate the IRR of that.

Â It's clearly positive at 30% which is higher than our discount rate of 12%.

Â It's got a clearly positive net present value and

Â that basically says yes it does pay to put an additional $100 million in Project D

Â in order to expect an additional $130 million in Project D.

Â So one way or the other what we're coming up to the same solution we,

Â we come up that we should invest in Project D by comparing the NPVs or

Â by looking at the differential cash flows and

Â the internal rate of return on the NPV of those differential cash flows.

Â This is what is called the scale problem.

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