I'm going to move on to some, the third criteria, that criterion we are talking

about today, which to me, is extremely, extremely important for two reasons. One,

it's used even more now. I mean, almost as much now as it was 40 years ago. And it

competes with NPV in the proportion of people, even in the developed capital

markets we use it. It's called internal rate of return. I want to spent a lot of

time on it and emphasize it similarly as I did with NPV. I kind of went quickly over

paybag, but I'll recommend very strongly don't use it, okay? However, I think IRR

is used almost as much, or in fact, slightly more than NPV. And I want you to

understand it fully. So, that's why at the beginning of this class, I decided that

I'm not going to just teach you what is maybe the better thing to do. You need to

also recognize what's done in the real world. And recognize its strengths and

weaknesses. And IRR is very subtle. Irr is seductive, it's subtle, it's intuitive,

yet it has problems. It's not blatantly got issues like payback does, right? So,

let's start. And I want you to recognize that ironically, even though it's used a

lot and we all get a feeling like we know it, we don't. So, therefore I have to do a

lot of effort here on what the heck is it. So, let me ask you this, as always, what

is the IRR of this simple example? So, what is happening? At time zero, you're

spending 100 million dollars, and let's make it for convenience so that you're

not, let's make everything in millions. So, that we are not worried about all for

ten bucks, why should I even do this problem, right? You know [laugh], you want

some excitement in life, so let's make it exciting. You have an idea or somebody has

an idea which is involves 100 million dollars of outflow, setting up a factory,

getting the right thing and it'll last for one year. Again, for simplicity, we'll go

longer. How much does it get to you in one year? 110. Can you tell me the rate of

return on this? I'll pause for a second because I think if you have a little bit

of Math ability in your mind, you should tell me the answer. The return? Everybody

intuitively understands. It's how many did you make on the investment you put in. So,

look what you tell me, I think almost all of you will tell me the answer is ten%.

And the reason you're going to tell me that is how much of I made over one year?

Yes, I spent 100, subtracted out from the 110. But remember, the units, it's on how

much did I make ten bucks? 100. So, it's ten%, right? So, I give a very simple

example. So, what is the IRR of this problem? Ten%. Okay, let me see what you

have done. This is what you've calculated. I'm just reflecting what you did in your

mind. And I think this is an excellent way of teaching IRR that I've found over the

years rather than just throwing a formula at you. I think I really, I cannot say it

often enough how just a little bit of insight on how to teach or how to

understand something yourself, help goes a long way and I follow simple principle

which I hope I'm reflecting in everything I'm doing. I just try to think, what the

heck am I doing before I use a formula. So, think about R, it's very intuitive. Fv

is the future value. Pv is the present value. You subtract the present value from

the future value. And what's the present value? It's a negative number because I

made an investment of 100 and then you divide it by your investment, which was

the present value. And this is what you came up with. Two things to remember about

this One, its a percentage and it's per period, in this case, year. So, it's a

number that is calculated over time, alright? And, it's a percentage. Because

it's calculated over time, it applies to a period of time. So, if your time is one

year, the ten percent of the time is one month, probably a smaller number. How

would you say it in English? You'll say, what is my final sum and what is the

initial sum which is, what I put in. And the difference between the top and part

many times called, the money you made or the profit, divided by your investment,

which is ten bucks, divided by an investment of 100 bucks, right? Pretty

obvious, right? So, now I'm going to mess with you, meaning I'm going to try to

figure out whether you really know rate of return and what does it mean. Okay. What

is the intuition? What is the NPV of the idea if you use the IRR to calculate it?

What am I saying here? What is my cash flow, alright? What is the NPV of the idea

if I do, do it. So, let me just quickly before I go to the next bullet point, let

me just quickly write something here. The NPV of the idea would be -100 + 110 / one

+ R, alright. Why am I dividing by one + R? Because I want to bring the 110 back.

The question I'm asking you is, you've calculated your IRR. And you put it in

here, ten%. What do you get? Zero. And don't, this is very important because I'm

going to use this formula later. So, see what, what IRR is doing. If I use my IRR

to calculate my NPV, the answer should always be zero. And the reason is very

simple. The internal rates of return is called internal rate of return because it

only needs one thing to calculate it. Remember, to calculate MPV you need two

things, you need 100, -110. But for IRR, to calculate it, look at this. All I

needed was the 110 and the 100 which is the cash flows. So, that's why its called

internal, its internal to the idea. So, when I calculate the ten percent rate of

return and use that same IRR which is based on the cash flows to then calculate

the NPV of the idea, what am I using? I am using the ideas own return to calculate

the NPV, is that right? Answer is obviously not. Why? Because if I use my

own rate of return to calculate my own value, I'll come up with what I've began.

Zero, right? So, remember, this equation is not what you should do to figure out

NPV. This equation just tells you what the textbook tells you. Suppose, you want to

calculate the IRR of the following problem. -100, 110. What is the rules

you'll use to calculate it? Well, you'll use the rule of figuring out that number

which makes your NPV, zero. And the intuition here is, to remember you're

using your c ash flows to figure out your rate of return. That's all you are doing.

And it's a mechanical process of calculating. So, let's use this use this a

little bit. What does this tell us? -100 =,, - 110 / one + R. So, both sides have

become negative. I have taken this to the other side which implies R = ten%. So,

this is the rule of thumb we use in, in, in, in calculating R. In this example,

it's very straightforward. So let, let me ask you, let's do a simple exercise. In

this example, suppose I don't know my IRR, the first number to start is what? Zero.

Try zero, what will you get? -100 + 110 / one + zero is ten bucks and it is not

equal to zero, right. Then try a higher number, its called trial and error which

the laptop or the computer will do to figure out your rate of return. But, its

such a simple problem, you don't need the Excel to do it, okay? So, I am going to

now, ask you, is this idea, a good idea? Sorry there's a little bit of overlap with

my writing but we'll manage. Is this idea, a good idea? Which idea? An idea where I

spent 100 bucks and get 110. What do you think? I hope you say you don't know,

because a lot of people will turn around and say, very cool idea, t10 percent rate

of return. But the tragedy of IRR is, that it has no benchmark built in. There's

nothing that tells me whether the ten percent is good or bad. So, let me bring

in that thing that I'll ask you to put away at the back of the head, risk. Right

now, we are ignoring risk so it is becoming difficult to internalize this.

But suppose, the risk of this business is such, that even twenty percent rate of

return is too low. Is this a good idea? Maybe not, right? On the other hand, if

the risk is so low, that you're a genius, you're able to create ten percent rate of

return, it's a good idea. So, here's the question. What if others in this type of

this business are making eight%? Tell me what is this eight percent now? What do I

mean by others in this type of business making eight%? This is called R, remember?

If I want to calculate the NPV of this idea, it is what others are doing who are

my com petitors in a similar business. That is to be used as my discount rate.

Now, tell me, what will you do? Will you do, is this idea good or bad? It's a great

idea. Why? Because I'm making ten percent and everyone else is making, less, what

should happen? Money should flow to me, not just mine, other people's. Is that

clear? Why, and please do this. What is the NPV of this at eight%? And you'll find

it's greater than zero. I'm not even going to do it. You can do it visually. -100 +

110 / 1.08 has to be a number greater than zero, because at 1.1, it is exactly equal

to zero. Now, let me throw in a little curve ball here. Suppose, instead, you

made a mistake, your analysis wasn't right, you go and try to figure out, did I

get other people in this business right, did I measure their return right and there

are ways doing that, we will get to it later in the class and you find out, oh

boy, no I was wrong. Other people are actually making twelve percent on ideas

like this. Should I do this or not? No, because, others are doing better than I

am. So R, in this case is greater than IRR. Don't do it. And you'll find that NPV

is less than zero. So, the important element in all of this is to remember,

that if you calculate an IRR of ten%, it doesn't mean anything in isolation. So,

the first thing to remember is doing an IRR calculation just requires you to know

your business well. It's internal to your business. All it needs is your business's,

business's initial investments and future profits. However, it's not telling you

anything, because there is no benchmark. So, if the benchmark is eight percent and

you'll be making it ten%, good news. But if your benchmark is twelve%. That's is

what other people are making, somebody would be really silly, including yourself,

to put your investment in your project rather than other people's project.