Hi. Welcome back. We have had time and opportunity to do many different problems

and I have taken the time to go really deep in to them and I have spent a lot of

time today with you because I believe the value add in online is the explanation one

on one. And today is a lot of real world applications which will help you further

in the class so just bear with me for little time. We'll do one interesting

problem but before we go there, let's do my favorite financial concept. And my

favorite financial concept is called a perpetuity. A perpetuity is simply

something that pays you C dollars, roughly the same amount PMT which goes on forever,

right? It's pretty remarkable so what do you get? You get CCCCC forever and it

could be with or without growth. So when I saw this the first time, I said this is

nerdy dumb to the extreme. This is a textbook idea. When am I going to ever see

something like that, right? So let me just first of all give you, just think of some

examples of perpetuities, right? So there are bonds out there. There is something

that pays you say, one pound for a long period of time so that's one example. The

second example which is much more complicated but much more intuitive is

what is called a stock, a promise as opposed to a bond. I promise we'll spend

couple of weeks on stocks and bonds but I wanted to raise this, what's the basic

difference between the standard and bond? This is limited inn majority and this

hopefully goes on forever. So, for example when John Ford started the company, he

didn't say we will be there only for five years and I'll pay you some money and then

we are gone. That's not a company, that's not an idea. Great ideas last forever.

Great things last forever. What I want you to recognize in all of this is that

forever actually, doesn't mean forever. What do I mean by that? So take the

example and show you the power of perpetuities. Now let me ask you this,

suppose I gave you something, suppose I gave you something that paid $ten forever.

Guess what the power of perpetuity is. At time zero guess what the Pv is? We won't

derive this. I'm going to give you this one formula. When we have time towards the

end, I'll do stuff that is kind of nerdy and, you know interesting for derivations

if you have the time but I'll tell you that the terms are to be C/R. So the

simplest formula in the world is the formula for perpetuity. Which is the most

complex thing to comprehend. So what could this perpetuity be? It's a perpetuity that

lasts. It's like a stock that pays you $ten every year and is expected a company

that's expected to survive for the reasonable future. So turns out, what will

be the answer for this? Suppose the interest rate is ten%. This would be

$10/.1 is $100. Okay? So, what could be simpler, right? And would you like this

$ten to grow over time? Sure. If it's growing over time at the rate of G, is the

growth rate. So suppose the growth rate is ten%. So in the first year, how much is

this paying? $Ten. In the second year it's paying 1.1 and so on by the way, these

things in real life are called growth stocks. So something like what Microsoft

was in the beginning or Google, or technology firms that are successful. They

grow and pay out over time. Their growth rate is extremely high. What does the

formula become? C/r - G. Right? So because this growth rate is ten percent I can't

use this formula so lets make this growth rate five percent so what is R? Ten%. What

is G? Five percent and what is C? $Ten. Again, very simple to calculate. The

reason I'm introducing this now is not so much to start doing a lot of examples. I

just want to introduce it now because its a linear process. We went from annuity,

which ends after certain interval. You take loans and you pay them off. Then you

think of another concept that goes on forever and we'll come back to these

stocks. And as I showed you right now, if the growth rate is ten percent and your,

your interest rate is also ten%, you can't use this formula. That doesn't mean you

can't calculate the number. You have to the long route, long way. That emphasizes

one more important issue. Don't use form ulas blindly. Formulas are at your

disposal not the other way around, okay. So, we'll come back to perpetuities in the

future but for now I would say just keep it at the back of your mind that there is

something real world that looks like a perpetuity and it's very common it's what

called the share in the company or a stock of a company because it, we will last for

a very long period of time and in the real world, what happens is you don't know how

to value things beyond say ten years or 30 years, it's just too far because the world

is too uncertain. Such formula, C/R - G are really useful in approximating what

you think is going to happen. There's no point getting too refined after five or

six years because it's about the future. So actually these formulas, when I saw

first time, I said what are they talking about are the most useful ones in real

life because you want to get a sense of value. You don't want to get it so precise

when you know it's wrong, right? So approximate formulas like C/R - G are

actually so useful in grabbing the basics of what finance is trying to offer, okay.

As promised I am going to spend a little more time today and this time is not on

the next three slides. The next three slides that you see here, don't worry

about them. I'm just emphasizing them to remind myself, and to remind you, that if

you are oriented towards formulas which I would encourage you to be because formulas

reflect in the end of your understanding of what's going on, not the other way

around. I would encourage you to walk through these formulas and as I said I'm

not going to spend the time for you to read them. This is one part of this

overhead slides that are used or visuals that I will provide you as a resource. As

I said, I want the main resource to be the videos but I am providing you resources

like the course syllabus with chapters from various books, written by wonderful

people. I also want you to learn from them not just from me. I don't have the control

on learning. Your learning is, you are in charge but I'll give you some formulas so

that we can go back and confirm your knowledge. So I just wanted to remind you

and me, we'll do that. That will put everything together but I want to end

today's class by doing a problem with you and I would say I am going to read this

problem first. Could you try to understand the context and then I encourage you to

take a break. And hopefully you have taken several breaks over different days during

this content, because I am committed in week two to make you understand why we do

things the way we do, and the reason is we can learn a lot in ten weeks and I have

taken a lot of time today, simply to make you understand how real things are even

though they are problems written on a little spreadsheets or in a little

Powerpoint so lets go through it. You are 30 years old. You believe you'll be able

to save for the next twenty years until you're 50 and why am I saying that?

Typically, that's when a lot of people earn money and save but after that, for

ten years. You'll, until your retirement at 60 you will have a spike in your, I

shouldn't even call it a spike in your expenses, many spikes in your expenses so

that you will not be in a position to save for the next ten years. So remember what's

going on, starting at 30, 50, and then under a break at 60. These are artificial

but believe me, very useful points in your life. After 60 what are you going to do?

You want to retire but you want to be able to live, right? And you want to be able to

live at the standard of living which in this problem is pretty high. Because most

people in the world cannot afford even one-tenth of this or 1/20 but that's, I

want big round numbers so that I don't have to deal with decimals and I'm not

trying to make a statement about what my expectations or yours are. So you'll

retire at 60 and then you expect to live until 80 and you want to take care of the

next twenty years at the rate of $100,000, right? You want to but now, now what is

happening now? You were saving between 30 and 50 so that you could do this between

60 and 80. And the fact that both are twenty years is just an artifact of the

example. Who controls all of this? You do. Who controls now, the next decision? What

interest rate will you earn on your savings will depend on you. It'll depend

on what type of risks you're willing to take and for convenience or for just fun,

I'm assuming that you are a person inclined to invest in risky stuff. And

therefore you will be rewarded on average in the long run at eight%. So, this is the

nature of the beast. This is the problem. I'm encouraging you now to do two things.

Think about it for about five to ten minutes and do the most important thing in

life which is more important than even finance, I can't believe I just said that

but draw a timeline and put your problem on that timeline. If you can do that, we

can do this problem in five minutes. If you can't do that, remember it's not the

problem of finance. Finance is going to help you not hurt you. It's because common

sense is not that common. [laugh] Is, finance is full of common sense but the

word common sense is a, is a wrong expression. I've found whenever I look at

common sense, it's pretty complicated. That's why after a while it becomes common

to you but finance is only going to help you. So do that, I'll come back in about

five minutes and we'll do this problem together and that will be the end of today

and I promise you this will enable you to do the assignment and crank up the heat in

the assignment. I want this week to be intense for you and the purpose fully

served. And the reason is we can go very far, we can go very far not in the

mechanics but in the understanding of the world, okay. So break for five to ten

minutes and I'll come back and do the problem.

2.8 Valuing Perpetuities

Principles of Valuation: Time Value of Money

Meet the Instructors