>>Hello, we are back. Seems like a while since we've been together. If you are watching this, this is Lecture

#211. If you are watching this, you should have

taken your first test over Chapters 12, 13 and 15. If you folks at home online have not taken

that test yet, then you should not yet be watching this, okay? And we're not going to go over the test so

don't try to pull that one, okay? You should have taken the first test before

you watch this lecture, okay? I hope the test went well.

I'll reiterate a few of the things that, we've

already gone over the test before the cameras were rolling in this class, but I want to

reiterate a few of the things that I said about the test. First of all, as I said many times, the best

way to study for my tests is to get a blank piece of paper out and see if you can do the

homework, okay? Or for those handouts, you know, print them

off again, online folks, and see if you can do them, okay? Now if you didn't do as well on this test

as you would've liked, I bet you I could have just given you those same handouts that we've

done before and went over in class the answers and explained the answers.

I bet I could have just given you blank pages

of those handouts that you'd previously seen and it would've gone probably as badly, okay? Because a lot of times what I'll do is just

take those handouts and switch the numbers around, okay? So you're ready for the test when you can

do your homework with a blank piece of paper, okay? For you folks at home, if you had a blank

handout of all those handouts, would you be able to produce the answers? If you can't, then don't think you'll be able

to do that on the test, okay? I want you to do well and so. For you folks at home, I'm talking to you

guys, if you want to ever — if you want to schedule a time to come look through your

tests or talk to me about your tests, just shoot me an e-mail and we can do that, all

right? But I cannot e-mail you your tests, so just

e-mail me a time if you'd like to look through it otherwise just look for your grade on D2L,

all right? Okay.

I think that's the first order of business. Second order of business is, and I'm talking

to you folks and the online folks. I do something just a little differently. There's a lot of information in Chapters 12,

13 and 15, isn't there? There's a lot of information and it sometimes

doesn't even seem like it's related. You know, you issue stock, a new partner comes

in, treasury stock, investments. Okay, it seems like it jumps all over the

place which is kind of why I did the test the way I did with those problems, you know,

letting you choose. But I didn't want to add anything more to

your already full brains, so here's what I have done. If you go out to Connect, there is an assignment

and it says something like, read pages 529 to 531 in your book and then do this Connect

assignment, okay? And I have some specific instructions on that

Connect assignment that I want you to do.

Basically, that is over those three ratios

at the end of Chapter 13, do you remember those? They were on the end of your PowerPoint, so

you can take a look at your Chapter 13 PowerPoint if you want. But I did not want you, I did not want to

go over anything more for this test, you have enough information in your brains. So what I want you to do, the way that we're

going to do it is, I just want you to read pages 529 to 531 and you can take a look at

your Chapter 13 PowerPoint's, the last few pages if you'd like. And then do that Connect assignment, okay? You are never going to be tested over that

information, okay? Nor am I going to assign any other paper and

pencil homework.

All you're going to do is that Connect assignment. Now that Connect assignment is worth some

points, so you want to do it. But this is for you folks and for you online

students, okay? The Connect assignment should be called read

pages 529 to 531, okay? So any questions on that? Understand? All right. What we are going to talk about now — oh,

let me give you another true confession and I can tell you this now. I do not have an accounting degree. I'm kidding, I do have an accounting degree,

that was not my true confession.

The true confession is Chapters 12, 13 and

15 I think are a little bit dry. Did anybody else think that? I don't think they're the most exciting Chapters

in the world. I didn't want to tell you that before because

I didn't want to, you know, get you in the wrong frame of mind. But I enjoy and I think students enjoy, from

here on till the end of the class, a lot more than they enjoyed Chapter 12, 13 and 15. Twelve, 13 and 15 is just kind of, you know

like, how exciting is it to talk about par value of stock and, you know, the number of

shares authorized. You know, all these sort of things. It's just not really enthralling, okay? So if you've thought it's been a little bit

dry, students typically like from here on out a lot better, okay? And we're going to do a subject today and

the next period that students have a tendency to like. And it's kind of a nice break because we're

not going to even use our textbook — well, I take that back, we'll use it for one thing.

But I don't have PowerPoint's and there's

nothing that you read, okay? But students have a tendency to like this

area. This topic is in regards to time value of

money, the time value of money. Sometimes I abbreviate that TVM, okay? Time value of money. Has anybody gone over the time value of money

in any of the classes before? Does anybody know what I'm talking about? Okay, sometimes people will have done it before. Now most of you here are going to get a business

degree. You will, in your business degree, take a

class that's called finance or corporate finance. And in that class you will go over the time

value of money more than what we're going to go over here. This is just an introduction to the topic,

okay? It helps us understand a little bit of what

we'll do in Chapter 14. But I found that, through the years, that

it's nice and I think students appreciate to at least have an introduction to the time

value of money.

We're not going to go way, way deep into it,

okay? But it's going to be an introduction. And then when you take your corporate finance

class you'll be glad that I at least introduced it, okay? Cool? Okay, time value of money. What is the time value of money? Okay, let's do an example. Michael, let's say that I tried to make a

deal with you where you give me $1,000 today and in 4 years I will give you the thousand

dollars back, okay? You give me $1,000 today and in 4 years I

will give you $1,000 back, okay? Now, and you knew I was going to pay you back,

there wasn't any chance that I wouldn't show up in 4 years, okay? You would not want to make that deal, would

you? Okay. Because we intuitively know that $1,000 today

is worth more than $1,000 in 4 years. We intuitively know this, right? Okay. We know this because — now, you aren't all

as old as I am, but can you think of some things that when you were a little kids were

a lot cheaper? >>Gas. >>Gasoline.

Okay. What about movie tickets? >>Yeah. >>Okay. What's it cost to go to a movie now? >>Ten bucks. >>Ten, eleven bucks. >>10.50? I can remember when I was a kid and movies

went from $3.50 to $4. My dad was like, "That's it. No more movies, we're not paying $4," right? Well now $4 would be the matinee price, right? Okay. On an extreme example, let's say I could go

back in time and find my mother and I could go back — I went back in time to 1940 when

she was a little girl, okay? And let's say I found my mom in 1940 and I

gave her 25 cents.

I gave her a quarter. She would be pretty excited about that, would

she not? She could go do a lot of things with 25 cents. She could go to a movie. She could probably buy some candy and take

it to the movie. She could buy a couple of Superman comic books. She could go on a pony ride or whatever they

did in the 40's, okay? But she could do a lot with that 25 cents

and thus she would be pretty excited, right? Now, if I got one of my teenagers today in

2014 and I gave him a quarter, how excited do you think my teenager would be? >>He'd probably throw it back at you. >>Flip it back in my face, right? No, he'd probably take it but it's not that

big a deal, right? Because a quarter in 2014 is not worth what

it was way back in 1940, 1941, right? Okay, we intuitively know this, okay? Now let's go back to our example, Michael,

of the $1,000, okay? What if you said — what if I said, you give

me $1,000 today, Michael, and I will give you, in 4 years, I will give you $1,001.

There's a good deal. You're getting $1 more than what you did. Now you're still not excited about that, right? >>No. >>Because you intuitively know that still

is not a good deal for you, correct? Now there is an amount, there is an amount

out there and it depends on what you would require. But there is an amount that if you gave me

$1,000 today and I gave a higher amount to you in the future, there is a higher amount

that you might go for, okay? For example, I don't know what it is, but

maybe you'd give me $1,000 today and I give you $1,400 in 4 years. You might go for that, right? Because isn't that basically what you do when

you invest? Okay, so you know that there is some way to

deal with that, okay? But a dollar today is worth more than a dollar

in 4 years. That's the time value of money, does that

make sense? Now, going back to this thousand dollar example,

you intuitively know that money has a time value of money because if nothing else, I

could take that $1,000 and what could I do with it? >>Invest it.

>>I could put it into a savings account, right? Couldn't I put it into a savings account and

earn some interest on it? Even a really, really, like safe savings account,

okay? Let's think through this, okay? Again, I don't have any PowerPoint's on this

presentation so we're going to do some writing on the ELMO, okay? And as always, if I start to write and it's

not, if you can't see it, let me know, okay? This is also a good lecture to have your calculators

out. Okay, so get out your calculator. This is one of the few lectures that if you

don't have a calculator you can go ahead and have your phone, I don't care what calculator

you use, okay? Okay, let's say, let me draw a timeline here. Let's draw a timeline. This is timeline zero, that means that's today. This is one year from now. This is two years from now. This is three years from now and this is four

years from now, are you with me? Okay. Now, let's say, Michael, that you gave me

that $1,000 today, okay? So that is $1,000 today.

Okay? Now we need to think of what an annual interest

rate might be. Let's say I decide to put it into a savings

account, okay? Now I know savings accounts do not pay the

following rate but I want to, I want to have easier math, okay? So let's say that I have a savings account

that will pay me 3% annually, okay? That'd be sweet. Okay. But let's say the interest rate is 3%, okay? Now I put $1,000 into that savings account

today, it pays 3% annually, how much will that $1,000 would've grown to one year from

now? >>1,030? >>1,030, that is correct. Now how did you get that? Well, it's pretty easy but let me go ahead

and say it.

You could do this. You could take $1,000 times .03 and that equals

$30 interest earned and then add it to your principal and get 1,030, right? You could do that. Or what I usually do is just shortcut it and

take 1,000 times 1.03 to see what the amount would have grown to for 3%. And that equals 1030; is that correct? You with me? Okay. Now this $1,000 grew to 1,030 in one year,

what do you think it will have grown to in two years? Now, we are now earning interest on the interest

previously earned, aren't we? So what are we going to do? We're going to take that 1,030 once again

times 1.03, aren't we? And let me bang that out on my calculator,

you do that too to maybe catch if I make a mistake. Did you get 1,060.90? Okay, so that is worth 1,060.90 right here

when we took that 1,030 times 1.03 to get that, correct? I'm going to take that off now. Okay, well what will that have grown to at

this point? What'd you get? >>1,092.73. >>What'd you get again, Henry? >>1,092.73. >>Okay. You had to round a little bit, that's fine,

round to the penny.

1,092.73; is that right, Henry? Okay. And let's take that one more time to see what

it'd equal in 4 years. Okay, 1,125.51, are you with me? Everybody know what we just did there? Okay. Now the other way that you could've got this

number and just hopped over there is taking 1,000 times 1.03 to the fourth, right? Isn't that what we did? Okay. But anyways, let's just concentrate on this

right here. One thousand in four years grew to 1,125.51

at an annual interest rate of 3%, cool? Let's come off that. Let's say that a few different ways. If Michael gives me $1,000 today and in 4

years I give him $1,125.51 he has earned what percent annually on his money? 3%, agree? Okay. Here's another way to say it, if I want to

be able to withdraw $1,125.51 from my savings account in 4 years and it pays 3% annually,

how much do I need to deposit today? What's the answer to that question? >>$1,000.

>>$1,000, okay? Here's another way to say it, if I put $1,000

in my savings account today and it earns 3% annually, how much can I withdraw in 4 years? $1,125.51, correct? Okay. Here's another way of saying it, a certain

set of tires, a certain set of 4 tires costs $1,000 today. If the rate of inflation on those tires is

3% annually, how much will they cost in 4 years? $1,125.51, are you with me? Cool? Okay. All right, now we figured out how to do that

and it wasn't too difficult, right? Now I want to show you a different way, okay? And before I do that, I want to let you know

that, yes, I do understand that there are financial calculators out there and computer

programs and stuff where you can just literally enter 3 variables and push the variable that

you don't know and it will spit it out at you.

Yeah, I know that. But I'm going to teach you a little bit how

to do it the old school way because — and you won't always use the old school way but

it's kind of like when — remember when they taught you how to do multiplication on paper? You know, carry this — you know you're not

going to do that your whole life but there's something about doing it that basic way that

kind of reinforces it, okay? So I'm going to kind of have you do that,

okay? So don't just think 'I have a financial calculator

I don't need to know any of this', okay? All right, here's the way I'm going to do

this, I'm going to just define some variables in this example, okay? Let's say — and I don't even care about these

numbers right now so I'm just going to cover them up. Okay? I don't care about those right now so let's

just cover those up. The way we're going to solve this is, let

me write this down and then I'm going to explain it.

We're going to use the variable P and that

stands for present value. P stands for present value, okay? P stands for present value and in this example

what does our present value equal? >>$1,000. >>$1,000, okay? Now, let's say that we don't know that number. I mean, we do know that number, but let's

say we don't know it, okay? Well, I'm going to use that variable — I'm

going to use the variable F to stand for future value.

Are you with me? And let's act like we don't know what it is,

cool? Okay, I equals our annual percentage rate. And in this case, what does I equal? 3%, okay. And we're going to use a variable called N

and that's going to equal the number of periods. Now, notice I did not say the number of years

because it's not always years, sometimes it'll be months or quarters or whatever. But N equals the number of periods. But in this example, what does N equal? Four. One, two, three, four. Four. So in this example, P equals 1,000. We're acting like we don't know F. I equals

3%, N equals 4. Here's the way that you could solve for this

example, okay? Let me write this down. Well, once again, you start off with P equals

F and then we're going to — let me just write this down and then I'll explain it. That looks very confusing mathematically. This looks very confusing mathematically:

P=F(P/F,i,n).

It's not that complicated. Here's what this is saying. Our present value equals $1,000, we know that,

right? We're acting like we don't know what F is

so we're just going to have that be called F. Now, what is this (P/F,i,n)? Well what that goes to is this, look in the

back of your book, the very back of your book, and look for page B-10, okay? B-10. If you have your book, get that out, okay? Now if you — did anybody here not bring their

book? Okay, all right. Here's a few of these tables if you didn't

bring your book. You guys can distribute those as needed.

But get your book out and look at this table. You folks at home, always be doing what we're

doing. You look in the back of your book and look

for table B.1 on page B-10, are you with me? Yeah, I got a couple more. Okay. Okay. Yeah, if you get a Xeroxed one you probably

got, it looks different, it's the same thing. Okay, go ahead and write in your book, I know

you're not supposed to write in your book. But on table B.1, present value of 1, go ahead

and write P/F right there. Are you with me? This is the P — present value of future amount

table. And these are different interest rates, okay? And these are different numbers of periods,

okay? Are you with me? So we're going to come back to that table

in just a second.

But what this notation is telling us, folks,

is that we are going to go — and I can't find my red pen so I'm switching colors here,

okay? We are going to go to the P of F table. What is the I in our example? Yeah, but what's the number? Three percent. And what is the N in our example? Four. All this is saying, between my fingers is,

go to the P of F table and look in column 3% and row 4 and put that value in the parenthesis. That's all that's saying, okay? So let's go ahead and do that. What is that value? Did anybody find it? Okay, let me do a big time zoom on that, okay? This is the P of F table, table B.1. And this is P of F table, table B 1. And this is P of F 3%, 4. So I go to the column 3% and I go to row 4

and I got what? .8885; is that correct? >>Yup. >>Okay. So all I'm going to do, and going back to

this, let me zoom back out. $1,000 equals F times, what is it? .8885? >>Yup.

>>Is that correct? So how do I solve for F? I don't take that times that, I take $1,000

and divide it by it, right? >>What we got earlier. >>So what's the answer? I got F equal to 1,125.49? Okay? Now what did we figured out —

>>51. >>I don't care about that 2 cent difference,

okay? I don't care about that, that's fine. But do you see how we did that using the table? You see how we did it? Okay. Now, one important thing — you can come off

the camera. You can come off the ELMO. One important thing you always want to do

after you solve for these, folks, is you want to ask yourself, does this — is this a reasonable

answer? Is it a reasonable answer that I would put

$1,000 — you can go back to the thing.

Is it a reasonable answer that I could put

$1,000 in my savings account, it earns 3% and it's grown to 1,125.49? That's somewhat reasonable. Here are some unreasonable answers. For example, sometimes people will make a

mistake and they'll multiply 1,000 times .885. Well does it make any sense that you'd put

$1,000 in the bank and in four years it's grown to $888.50? That doesn't make sense, does it? Or every now and then I'll get somebody that

says, the future value of this is .88. So I put $1,000 in the bank and it grew to

.88? You see what I'm saying? Or they'll go the other way.

The future value is $125,697, really? I put $1,000 in the bank, it pays 3% annually

and in 4 years it's grown to 125 and thousand dollars or some odd dollars, right? That's not reasonable, is it? So this is reasonable, is that correct? Now what I want you to do is let's just, you

don't even have to play the music. But let me ask you this — well first of all,

let me ask you, is there any questions here? Any questions? Okay. Let me ask you this, how much will this $1,000

have grown to in 20 years if the interest rate is 3%, okay? You don't need to roll the music but just

go ahead and, you folks at home, you do this as well with that table.

How much will that $1,000 have grown to in

20 years? Don't feel like you need to shout out the

answer, let everybody solve for it. Okay. How much would that $1,000 would've grown

to in 20 years at an annual interest rate of 3%? Cool? Well, anybody get it? Check with your neighbor to see if you got

it right, talk amongst yourselves. Okay. Well, let's go back to — let's go back to

this. P equals F times P/F,i,n. Present value is $1,000, correct? We're trying to figure out our future value. But now we're going to go to the P of F table,

what's I? Still 3%. What's N? >>Twenty. >>Twenty. Now we're going to go to our P of F table,

look in the 3% column, look on the row 20 and we're going to put that value in there,

okay? So if I go to my table, my P of F table. Don't worry about any of those other tables

except table B.1, P of F, present value of 1.

Three percent, 20, did you get .5537? Did anybody find that value? So that's .5537 times F equals 1,000. So F equals —

did you get 1,806.03 cents? Okay. If you're off by a penny or two, I don't care. First of all, is that a reasonable answer? >>Yeah. >>I think it's reasonable. Okay? I think it's a reasonable answer, cool? Any questions on that? So I want you to learn how to use these tables. You with me? Okay. Let me give you a different problem now, okay? Question: How much do I need to deposit today

if I want to withdraw $10,000 in 7 years? Interest rate, let's say the interest rate

is 2%. How much do I need to deposit today if I want

to withdraw $10,000 in 7 years? The interest rate is 2%, okay? You don't need to roll the music but go ahead

and solve that if you can.

All right. How much do I need to deposit today if I want

to withdraw $10,000 in 7 years, the interest rate is 2%. Confer with your neighbor to see if you got

the same answer. Okay. All right, P=F(P/F,i,n). This time we don't know the present value,

do we? So that's the unknown. Do we know the future value? What is it? Now we're going to go to our P of F table.

What's our interest rate? >>15%. >>And what's N, our number of periods? >>7. >>We're going to go to the P of F table, column

of 2%, row 7 and we're going to find that value. P of F, 2% row 7, did you get .8706? Did anybody else get that? Okay. So that is .8706 times 10,000 equals P. So

I can do that one without a calculator. That equals 8,706. Is that a reasonable answer? Is that a reasonable answer? I think it's reasonable, don't you? What if this was $43,000,892.12 cents, was

that reasonable? Okay. What if this were 67 cents? Is that reasonable? What if this were $190, is that reasonable? Okay, I think you get the idea. Always ask yourself, is this a reasonable

number, cool? Does that make sense? Okay, any questions on that, folks? Okay. What I want you to do is — and let me give

you this handout, okay.

So you folks at home know which one I am talking

about. It looks like this. Handout #1, okay? Okay. That's the first part of it, I don't want

to show you the answer. But let's go ahead and start working on this. I'm not going to give you time to do the whole

thing. But let's at least do a few of them and I'll

show you the answers and then I'll let you go and you can do, the remainder of it is

homework.

But let's go ahead and play that music and

let's go ahead and work on Handout #1, time value of money problems, okay? So let's go ahead and do that, all right? Let's play the music. (Music)

Okay, let's go over the first couple of answers just to see if you're on the right track. I just did this myself so check my answers. Did anybody else get this number? >>Yup. >>Okay, is that a reasonable answer? I think it is, okay. So that's how we did number 1. Let's take a look at number 2. Did anybody get that answer? >>Yeah. >>Anybody? >>Yup. >>Okay. Is that reasonable? Okay. All right, any questions on those first two? Okay. We are done. All I want you to do for your homework is

— my writing is a little sloppy today, sorry. Do the entire handout of TVM #1, time value

of money Handout # 1. There's two pages, there's 7 total questions,

okay? So do all 7 of those on time value of money

Handout#1 and we will see you next time. Bring your calculators if you didn't have

them today, bye-bye.