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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Â