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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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