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This decision rule for IRR really becomes whether it has you are making more money

Â than the others. So, I'm going to spend a little bit of time on graphics. I think

Â the graphics can help a lot, especially by something so complicated. So, let me draw,

Â and I hope you follow with me, zero. And let me draw this NPV. And let me call this

Â R, okay? Why am I drawing this? For two reasons. I have value of zero here. Why am

Â I making it zero NPV? Because I know that if I'm going on the south side of this,

Â it's not good. Why? Because I'm actually destroying value, right? So, remember,

Â value creation means positive net, MPV. Why am I taking R to zero, up to zero?

Â Because we have assumed for the purposes of our whole course, that the R cannot be

Â negative, or will not be negative. I shouldn't say cannot, it can't. But, let's

Â stop there for a second. So now, I know what is my project. -100, time zero, +110,

Â time one, got it? Okay. Now, let me show you what the relationship is. Suppose I

Â don't know the IRR of this, right? I know, because I can calculate ten%. But suppose

Â I don't know, this is what a calculator will do. You'll start off with zero. So,

Â if the IRR is zero, if the discount rate is zero, what is the NPV of the project?

Â These are the best, easiest example I could ask. If in time value of money is

Â zero, what can you do? [laugh] You can add so the MPV will be ten, right? But if the

Â IRR, if the discount rate is ten%, what do we know about the NPV of this project?

Â It's zero, because that's the definition. If I use ten percent what is the NPV? Zero

Â because 110 / 1.1 - 100 so draw a line. And this is little bit, just pay attention

Â a little bit with this. How difficult in this example is it to calculate the IRR of

Â my project? Very easy. In the graph, ten percent is the IRR. Why? Because I know at

Â ten%, the NPV is zero. What's true now? What has this told me? One simple fact,

Â that my project is going to make ten percent rate of return. However, it

Â doesn't mean anything. Now, I know, that I have to compare it to whom? The cost of

Â capital R. What are other peo ple making? So, look what happens. If other people are

Â making less, is this project valuable? Answer is yes. This is positive NPV.

Â However, if other people are making more, which direction am I going, my idea?

Â Negative NPV. So, the rule of thumb is very obvious here. If IRR is greater than

Â R, yes. If IRR is less than R, no. But the tragedy of this rule is what? I'm choosing

Â this to be a yes only because NPV is positive. Why am I saying no? Because of

Â here, NPS is negative. So, the tragedy of IRR is IRR cannot work by itself. Ten

Â percent by itself doesn't mean anything. And I please encourage you to internalize

Â this, because this is so important. And Popular Press says, only reports returns,

Â they don't mean anything in isolation, you'll see. But in order to make

Â decisions, if you calculate your IRR, what do you have to compare it to? How much are

Â other people making? That's your benchmark, okay? So, if you use that

Â benchmark, you come up with the decision rule that you do things if you are doing

Â them better than other people. Another example. And this will show you why we use

Â formulas. Tell me what is the IRR of this idea? I'm going to pause for a second and

Â let you think about it. You see, this is going to make your mind go nuts. So, tell

Â me, let's draw the timeline. Let's draw the timeline of this, okay? So, what has

Â happened? Zero, one, two, does it look like the same problem we had before? Yes.

Â I've thrown one curve ball at you. I've said, you spend a hundred today, same as

Â last time, and let that be a million dollars again. But I said, you know, your

Â idea is such that in the first year you're more likely not to do anything, make any

Â money. Is that possible? Of course, it's possible. What do the best ideas of the

Â world do? Harboring money for a long period of time initially, and then boom,

Â alight? So, 110 in year two. Do the numbers, are the numbers the same? Yup.

Â But for I have one done, I have oranges time zero. Apples time one. And now, I've

Â thrown in bananas, time two. So, by shifting time by one, what have I done?

Â I've made life a little bit miserable. And that's why you have formulas. Okay. So,

Â what is the IRR over two years. So, if I want to say, suddenly, okay, I'll solve

Â this problem very easily, I'll just make my period two years. What is the IRR over

Â two years? So, you have -100, you have +110, ten%, right? Same answer, but is it

Â compatible to the previous one? No. Because two years is not the same as one

Â year. I mean, you have to remember time value and money. So, the question is, what

Â the do I do? What is the IRR of this per year? So, that's why things have to have

Â the same periodicity to be compared. So, what is the IRR per year? That's a tough

Â one right? Because what have I done, I've thrown an extra year were nothing is

Â happening. So, how will you solve this problem? Very easy to think about, very

Â tough to do. Make NPV zero. What would that do? -100 + zero, how much of

Â discounting do we do to the zero? In the year one, one + IRR. Plus in year two,

Â what do you have? 110 / (one + IRR)^2 square. Quick question. This is in r.

Â Quick question. How many unknowns in this equation? Zero = 100 negative + zero /

Â (one + IRR)^2 + 110 / (one + IRR)^2. How many unknowns? One. Which is IR. What's

Â the problem. It's not easy to calculate. Why? Because of, pause again, compounding.

Â So, I have a lot of stuff to do mentally because of compounding when the number of

Â periods increase. If it's one period, it's relatively easy. And that's why who do we

Â go to? To the computer, and I'm going to do so in a second. Before I do it, I have

Â two things to do. One, I'll show you the formula generically which shouldn't

Â surprise you. It's how do you make NPV zero in a second. But number two, I'll go

Â to the calculator, but before I do that, the second thing I wanted to say is can

Â you guess what it is? So, over two years, if I asked you, suddenly the world is two

Â years is one year. You know? One period of time. You know what the answer is. The

Â answer is ten%. What will it be per year? I think many of you will be tempted to

Â choose five%, but then again you are kind of stabbing me. You know you are

Â forgetting what, your forgetting compounding. So, if money earns no

Â interest on the money, you are on the right track but then life is very easy we

Â don't need to do most of this class. Chances are the IRR will be less than

Â five%. I Can guess that, simply because I know there's compounding. And the actual

Â answer is probably 4.9 or something like that. It'll be slightly less than ten%.

Â So, I want to do this in a calculator. But before I do that, let's just stare at the

Â generic formula. Irr is the rate to solve the following equation, where I note = c1

Â + c2, I would rewrite it if I may in a slightly different way, where NPV which is

Â equal to -I note plus all these junk is equal to zero. So, equating I note to the

Â right-hand side, if I take I note to the right-hand side, it becomes NPV formula

Â and then you force it to be equal to zero. So, let me ask you this, in our period how

Â many cash flows were there? Nothing here, 110 here. Now, you could have many more

Â cash flows. The problem is from being a quadratic problem, it becomes a problem

Â like which E = mc^2 was cool for Einstein, because he stopped at squared. But when he

Â saw N, he said, man this is too cool. This is just too much mind boggling. And it is

Â the power of compounding now is in reverse, it's in the denominator. We did

Â future value and are trying to figure out present value. It's a tough thing to do.

Â So, what I want to do now is take that problem, simple problem, and do some

Â calculations on the calculator. So, let's go on a tab and let's keep those numbers

Â there. And, actually no. Why, why don't we just delete that number, and what was our

Â problem? I am spending -100, right? This was what? Zero. This was what, 110.

Â Alright. Everybody, okay? I think you're okay. Let's do it. So, what is the

Â function IRR? Open up the brackets, parenthesis, what do you know? You want to

Â just throw in values. Now, remember, in IRR, you have to throw in all the values

Â because if you don't throw in A1, IRR, they'll laugh at you. In fact, Excel would

Â say, come on get re al. You're getting 110 for not bringing anything. So, IRR has to

Â have A1, C1. And you don't want to look stupid even to Excel, you know, because

Â there is no point, Now, you can't throw in a guess, I'm not going to and the reason

Â is the answer is pretty straight forward and the reason I'm getting five percent is

Â because the number of decimals in this is not big enough. So, the answer here should

Â be, actually, if you increase the number of decimals, it should be four, 4.88%,

Â okay? And the way to double-check this is what? If I use 4.88 to discount 110, what

Â answer will I get? I'll get exactly 100 bucks. So, let's do that. Let's take, PV

Â of, a rate of 0.0488, right/ Am I okay here, yup. Number of periods, two, PMT,

Â zero, future value 110, future value, I'm sorry, 110, exactly 100. So, by this, I

Â know that 4.88 is the answer and that the decimals are not showing up in the five

Â percent and the way its set up right now. So, what you want to do is you want to

Â make sure is that the decimals are showing. So, let me just go here and do

Â that for you. One, two. So, now I am showing not just zero decimals, I'm

Â showing all. So, you see it, my answer was right because of this simple problem that

Â number was in my head. Now, when you come back, let's take a break. When you come

Â back, we'll do more complicated examples, we'll talk about IRR as a principle and

Â we'll take it to the last piece of today's session. But I think you need to

Â understand right now how to calculate IRR. And what does it mean? Two things.

Â Calculations requires making NPV of your project zero simply because it's the

Â easiest way to figure out IRR in the [unknown] context. Quadratic, higher

Â ordered numbers throwing in because of compounding. The second getting 4.88 by

Â itself doesn't mean anything. It doesn't mean anything. 4.88 is better than zero,

Â yup. But how do you judge whether this is a value creating idea? You cannot judge

Â something just by your own cash flows. You have to go figure out what other people

Â are making. In the banana business, this is awesome. Why am I saying that? Because

Â if you earn five%, 4.88%t per year in banana business, you're doing great. But

Â if you are talking about iPads or technology, probably not such a good idea.

Â Because others may be making more and money won't come to you to create a new

Â project. So, take a break. We'll come back. We'll keep flying through this

Â stuff. This is actually both intuitive and practical. Take care. See you soon.

Â