I hope you have taken a break and, you know got familiar with what we are doing.

As I said, today's going to be intense because I want you very early on in this

class to really get a feel for finance. I mean to me the beauty of finance as I keep

saying so is not the formula. It makes so much sense and once you get the hang of

why we are using an Excel and why we are doing the formula, you will get a sense of

that. It will be very, very easy for you to recognize the value of each. I have

nothing against Excel but here's a simple reason we use Excel, is because we don't

have time to calculate all these numbers. We know how to do it but we don't have the

time and it would be a pretty bizarre thing to calculate numbers for the heck of

it. The second reason is, these cash flows in this problem are fixed. They could

change. That's what life is and we'll do that later in the class but two aspects

about it. Most examples of loans or retirement funds are very realistic in

this respect too i.e. The C is fixed. People choose to operate like that whether

its convenience whatever and loans many times are fixed rate loans. So, what I

would encourage you to do is recognize that these are simplifications at some

level, the C being the fixed number but at the same time C, its not a simplification

of real life and we'll get to more complicated things. Why am I bringing this

up? Because if you didn't have compounding, we will need Excel. And if we

didn't have things changing over time, we wouldn't need Excel. So, Excel is awesome

but keep it where it is. It's, it's not controlling you. You control it. Okay,

let's move on to the second phase of an annuity which is present value. So again

I've, there's this chart. I would like you to look at it for a second. Same thing,

just to make life simple, what I'm going to do is I'm going to stick with the same

example of three years. And by the way as I'm doing this, I want to thank, instead

of just thanking oneself, I want to multiple times thanks to my colleagues. I

went to the University of Chicago for my PhD and before that I've started a lot. I

have, to say thanks to so many people for showing me the beauty of finance. I also

want to thank my colleagues at the University of Michigan, Ross School of

Business. Ronen Israel is one of them who with me taught. This introductory class

many, many years ago. And he has been a big influence in how I think and then a

lot of other colleagues like who's a great teacher. I want to thank all these guys

for letting me become who I am and if I'm worth anything, it's due to other people,

not due to me. Okay, so let's get started. The first cash flow at year 00 and not

because it's supposed to be, it's convention. And in this case remember,

because it's present value, I'm standing today, I'm doing the opposite of future

value. So I'm saying not years to the end, years to discount. And the word discount

is coming from a very simple reason and the R > zero. Because interest rates

are positive, future value grows but because interest rates are positive, the

future is discounted when you bring it back today, right? So how much? Zero years

of discounting because we are standing today and present value today is zero. But

the present value turns out to be zero. Why? That's simply because there's no cash

flow here. If there were, it would be exactly the same number, because of no

years to discounting. So in some sense, years to discounting is a key variable.

Now here, things are a little bit simpler. One, the first C is one year of A, two,

three. So because we have done this table before, I'm not going to spend too much

time on it. However, recognize that we are doing the exact opposite of what we did

last time and the reason we are doing present value after future value is in my

book, if you understand future value You understand compounding. And then when you

come backwards, you're not torn away by why you're dividing one + R, (one + R)^2.

So let's do it. This is C / (one + R) and the neat thing is we have done this last

time, only thing is we have to do it thre e times, C. Why am I putting one + R each

time in parentheses? Simply because it's the one + R is the factor, not one outside

or R outside anything like that. One + R is the factor and the reason it's getting

squared and cubed is because pause again, compounding, right? So, so once you

recognize this aspect of it, I want you to bear with me for a second and what I'm

going to do is I'm going to go to another page. Where I actually write out the

formula and again I'm not going to try to simplify it. Simplifications can be done

very easily by you and in some sense, it's useful to do it. So let me write out the

present value formula. Present value formula for a three year annuity and I use

this three just to remind me that it's just three years, is what? C / (one + R

),, + C / (one + R)^2 + C / (one + R)^3, right? So, I've just to do three PVs. Now

remember, these PVs are not easy to do, right? So that's why I'll, at some point

use a calculator and remember, I can replace this by PMT in my head. In

textbooks we don't use PMTs, we use C because C is a generic word for cash. The

other thing is Cs are fixed and that's because of the nature of the Bs that we

are dealing with right now, okay? Now let me show you that actually I can take C out

and have. Right? Pretty straightforward? So what is this? If you think about it a

little bit, this is a factor again. And it's a present value factor of an annuity

of what? What is the annuity? $One. So if you know the present, if you know this guy

for which what do you need to know? R and n. How many years and what's the interest

rate? If you know the value of $one payed three times, you can know the value of C

bucks whether it's half a buck or it's $100. That's the beauty of it. How does

this formula change if you go to Pv of n? Simple, one thing changes. This, there's a

bunch of dots + one / (one + R)^n. So you'll keep going until you arrive at the

end, right? I hope this clear. Again, why am I doing this? I first did the concept

then the formula but I'm really, really interested now in doing problems. And

again I repeat, if you need to pause now, it's good to do it because I do not want

you to get overwhelmed by formulas and so on, okay? So let's go on and I'm going to

even pause for a second to remind you, you can, you don't have to keep watching the

video. Take a break and let's do one problem at a time.