0:03

Hello, I'm Professor Brian Buchet.

Â Welcome back.

Â This will be the first of three videos in which we talk about time value of money.

Â Time value of money is a very important concept that we use in a lot of

Â applications, basically the concept is that the value of

Â a dollar today is not the same as the value of a dollar in the future or

Â the value of a dollar in the past.

Â In this video we'll do a general overview of the concept and

Â then we'll work on what are called future value calculations.

Â Let's get to it.

Â 1:15

I even fall into this trap myself and I should know better.

Â So I was reading an article a few months ago about the minimum wage which I

Â think is now $7.25.

Â Well when I first started working in 1984 the minimum wage was $3.35.

Â And so I thought wow, it's so much higher than when I was working.

Â But the fact of the matter is that a dollar in 1984 is not worth the same as

Â a dollar today.

Â And in fact, if you translate $3.35 of 1984 dollars into today's dollars,

Â it would be $7.53, which is basically what the minimum wage is.

Â So if you learn nothing else from these videos.

Â And by the way, I do hope you that you learn other stuff [LAUGH].

Â But if you learn nothing else, keep in mind that we can't make these comparisons

Â of dollars today and dollars in the past, because of this time value of money.

Â Also, I should note, everything in these videos will be dollars,

Â because I'm an American, and I'm used to talking about dollars, but

Â obviously it works the same whatever currency you're using.

Â Whether it's, Euros or Kroner or Yen, or whatever.

Â 2:23

[SOUND] So anyway, the reason why money has time value is because of

Â factors like inflation, interest and risk.

Â So inflation is that prices tend to rise over time.

Â Interest is that banks charge you money for having loans outstanding.

Â And so it costs more to pay something back in the future than it is to

Â borrow it today.

Â And risk, just having a dollar in your hand today is safer than getting a dollar

Â in the future, just because you don't know what's going to happen.

Â There's a lot of uncertainty, there could be another financial crisis.

Â So all these factors combine to determine what's called the discount rate or

Â the rate of return.

Â 2:59

Because of these factors, whenever we will receive or

Â pay cash in the future we have to adjust the cash flows to the same value,

Â usually today's value, if we want to compare them.

Â So, just like you'd have to adjust foreign currencies to the US dollar,

Â you would never directly compare Euros to dollars,

Â you would have to translate them either into dollars or into Euros.

Â Or you would never directly compare liters to gallons if you were looking at liquids.

Â You'd have to either convert everything to gallons, or everything to liters.

Â What we have to do is adjust future dollars or

Â past dollars to today's value, to make across-time comparisons.

Â So almost think of future dollars or

Â past dollars as a different currency than today's dollars.

Â And so we have to translate them into today's dollars to make some comparisons.

Â So let's do an example.

Â So, just proving that you can find any type of information on the internet.

Â I went and found some historical gas prices.

Â I want us to try to figure out who paid the highest price for gas.

Â Was it in May, 2011, when in Fort Worth, Texas, it cost $4.15 per gallon.

Â 4:09

Also in May 2011, in Saskatoon, Saskatchewan, in Canadian dollars it

Â was $1.04 per liter, and then if we go back to May of 1980,

Â in Fort Worth, Texas, gas was $1.53 per gallon.

Â Who do you think paid the highest price for gas?

Â 4:50

>> Not necessary.

Â I'll give you all the data you need to do the translations, but thank you for

Â giving us the exchange rate on liters to gallons.

Â 'Kay, so the way we're going to do this is translate everything back to May,

Â 2011, U.S. dollars per gallon and then we can compare these three data points.

Â So first, for May, 2011, in Saskatoon.

Â We have to do two translations.

Â We have to translate litres into gallon.

Â And then we have to translate Canadian dollars into U.S. dollars, then we

Â compare the price of gas in Saskatoon to the price of gas in Fort Worth, Texas.

Â 5:37

So if we've got a gas price of 1.04 Canadian dollars per liter,

Â if we take that times 3.79, so that's 3.79 liters per gallon.

Â The liters cancel out, and we get $3.94 Canadian per gallon.

Â Now we have to translate Canadian dollars into US dollars,

Â so if you go back to May of 2011 you can look this up on the internet.

Â At that time, C$1 was equal to1.05 in US dollars.

Â 6:29

Now we want to look at May 1980 for Fort Worth.

Â So here it's going to be in gallons, so we don't have to translate.

Â But the problem is,

Â a dollar in 1980 is not worth the same thing as a dollar in 2011.

Â Again, think of it like a different currency and

Â we need an exchange rate to get from 1980 to 2011.

Â I went on to the web and if you just Google consumer price index,

Â you can find these calculators which translate the value of a dollar over time.

Â And basically $1 in 1980 is equivalent to $2.72 in 2011 so

Â because of inflation a dollar in 1980 would buy $2.72 in 2011 terms.

Â So, now we can take the $1.53 per gallon in 1980 dollars

Â 7:22

times 2.72 which is 2011 dollars to 1980 dollars.

Â And we end up with $4.16 per gallon in 2011 terms.

Â So even though gas seemed so much cheaper in 1980,

Â if you think about what a 1980 dollar is worth compared to today's dollars, and

Â you translate it all into today's terms.

Â Basically it's the same price of gas.

Â So whether you're in Canada or whether you were looking back in 1980

Â in Fort Worth Texas, gas prices have been the same in today's dollars.

Â The key to see this though was to do the translations of both liters to gallons,

Â Canadian dollars to U.S. dollars, and then of course, 1980 dollars to 2011 dollars.

Â 8:13

Next we're going to talk about compound interest,

Â which is one of the big factors that creates this time value of money.

Â There is an urban legend that Albert Einstein was asked,

Â he's the famous physicist, Theory of Relativity.

Â He was asked what is the most powerful force in the universe, and

Â he reportedly said, compound interest because it makes the money grow so fast.

Â So this slide will show you what Einstein was reportedly talking about.

Â 8:59

>> Dude, where do you do your banking?

Â I can't even get 1% interest rate at my bank.

Â So the interest rates that we're going to use throughout these videos are not

Â necessarily going to bear any resemblance to current interest rates.

Â I tend to use fairly large numbers so that we can look at big effects.

Â And, you know, maybe if these videos are around long enough, interest rates will

Â eventually climb up to 8% or later, we're even going to look at 15%.

Â So don't try to think about the rates as matching today's rates.

Â Just think of this as just, in general, these are examples of interest rates and

Â what the effects would be.

Â 9:52

Another way to write this is it's a $100 times 1 plus .08.

Â So basically that $100 is going to grow at a rate of 1 plus the interest rate,

Â gives you $108.

Â Now, I switched that notation because it's going to help us down the road.

Â But it's just saying that at the end of each year you have your

Â original principle.

Â That's the 100 times 1 plus it grows by the interest rate of 8%,

Â so that's the 100 times 0.08.

Â At the end of the second year.

Â We're going to have $108 times 1.08 equals $116.24.

Â Here's the compound interest,

Â where in the second year you get interest not only on your original $100.

Â But you earn interest on the interest.

Â So as long as you leave the interest in there from the first year,

Â you get interest on that interest in the second year.

Â So that's the compound interest,

Â that interest starts applying to interest and things grow much faster.

Â Because, what we don't have now, be careful here,

Â we don't have a $100 plus two years of $8 interest equals $116.

Â That's not compound interest because that would be only applying interest to

Â your original principle each year.

Â But compound interest, which is what we always have,

Â applies to whatever interest and principle stays in the CD.

Â And notice we get an extra $0.64 in the first year by

Â getting the compound interest.

Â [NOISE] Another way to write this is the original investment in

Â a CD of a $100 grows at 1.08 in the first year, and

Â then 1.08 in the second year, giving us a $116.64,

Â which is the same as a $100 times 1.08 squared equals 116.64.

Â So that little 2 which is called an exponent, what it means is that you take

Â 100 times 1.08 twice, you multiply it twice when you see that exponent over two.

Â And at the end of the third year, you have 116.64.

Â So what you have at the end of the second year grows by 1.08 in

Â the third year getting you up to $125.97.

Â Or another way to write that would be it's your

Â original investment of 100, grows by 1.08 three times so

Â there's an exponent of three for a total of $125.97 at the end of the third year.

Â 12:36

>> Yeah sorry. I am going to use formulas which look like

Â highfalutin math in some of these slides.

Â But even if you're not comfortable with that highfalutin math you can

Â still solve these problems.

Â So I'll give you the formulas and

Â if you're comfortable with exponents you can punch those into your calculator.

Â But I'll also give you other ways to solve these problems that will involve looking

Â up numbers in present value tables or using Excel where you don't have to

Â know anything about exponents or complex formulas.

Â And you can still do these calculations.

Â So you're going to see this done a number of different way,

Â a number of different ways as we go through the examples.

Â 13:13

So now we're going to make this idea more general.

Â So, we've gone out through three years what if you wanted to go

Â out through n years.

Â So n being whatever number you want it to specify.

Â Well then the Future Value in n years which we're going to call FV so

Â anytime you see FV that stands for Future Value n years from now,

Â that's going to equal to a 100 times 1.08 raised to the nth power.

Â So a way to think about that is if you wanted to do this for 10 years.

Â It would be 100 times 1.08 ten times.

Â You'd multiply it time, ten times over.

Â If n was 20, it'll be 100 times 1.08, 20 times.

Â So you can put in whatever period you want in the exponent.

Â [SOUND] If the CD paid r% interest instead of 8% interest,

Â then the future value is going to be 100 times 1 plus r raised to the n.

Â So now we caould try this with 3% or 10% or 1%.

Â If it was 1%, then it would be 1.01.

Â And then if it was five years it would be raised to the fifth power.

Â So you can specify whatever interest rate you want, whatever peerage you want.

Â And then if your initial investment was $PV instead of a $100,

Â here PV is going to stand for Present Value or today's value.

Â Then we have future value equals present value, times 1 plus r to the n,

Â and that gets us to the general formula that we can use for

Â any level of in, initial investment, any interest rate, or any number of years or

Â number of periods that we're going to have the money invested.

Â So again, [NOISE] the terminology, Present Value, PV,

Â of what you invest today is going to grow at an interest rate r,

Â to earn a Future Value, FV, n years from now,

Â using this formula FV equals PV times 1 plus r raised to the n power.

Â >> Okay, this makes sense.

Â Will there also be a formula to compute past values?

Â Or does this formula just work going into the future?

Â >> No we won't have a separate formula for past values, because

Â as it turns out you can use the same formula to calculate values in the past.

Â So I'll talk about on the next slide the terminology, but what you'll see is.

Â Present value doesn't necessarily need to mean today, it could mean 20 years ago,

Â and future value could be today.

Â So just think of it as, present value and future value as before and

Â after we have things grow or compound, as I'll shown on the next slide.

Â 15:52

So just to summarize this terminology in, in one handy slide.

Â Whenever we do these Time Value of Money Calculations there's going to be

Â four elements that we need to have in our formula.

Â There's going to be PV or

Â present value which is the value before effects of interest or discounting.

Â FV is the future value.

Â The value after the effects of interest or discounting.

Â Again as we just talked about, present value doesn't have to

Â mean today with the future value being some time in the future.

Â It could be the future value was today and

Â the present value is the value in say, 1980.

Â So, even though we use the terms present value and future value.

Â It really doesn't have to be today and then in the future.

Â It just has to be the present value is the value before you do

Â any interest or discounting.

Â And the future value is the value afterwards.

Â Present value could be 1980.

Â It could be 1681.

Â All it says is that it's going to be the value before you apply the interest rate,

Â 17:34

Or you can calculate this using formulas in Excel.

Â So you could put in the formula FV and

Â then fill in the interest rate, the number of periods.

Â Zero for payment which we'll talk about later in present value, and

Â Excel will calculate the answer for you.

Â The only thing to watch out for

Â here is that if the interest rate is 10% you need to enter it as .10.

Â Now, and I'll show you examples of doing the calculations with the tables, and

Â with Excel in a little bit.

Â So here's the first question.

Â If you invested $10,000 in the stock market today,

Â how much money would you have at retirement?

Â Now to do this we need to assume that it's 20 years to retirement, and

Â that the expected rate of return in the stock market is going to be 15% which

Â is compounded annually.

Â 18:40

Okay, let's so, let's try to solve this problem using the different methods.

Â So the first would be, if you wanted to use the formula method, so

Â we're trying to figure out the future value,

Â the value 20 years from now, the present value is going to be $10,000.

Â That's the amount you're putting in the stock market today,

Â which is the amount before you start growing it by the interest rate.

Â 19:02

The r, the rate of return, is 15% and n is 20, for the number of periods.

Â So you could fill those all in the formula,

Â future value equals 10,000 times 1.15 raised to the 20th power.

Â And it grows to 163,665.

Â Now if you're not comfortable using the formula or

Â punching this in your calculator, then you can also use this table approach.

Â So I told you that future value equals present value,

Â which again is $10,000 times the factor from table one for 20 years, and 15%.

Â So let me show you the table one.

Â 19:45

So here is the table one that I'm talking about.

Â And this will be part of the PDF file with the slides that you

Â can download along with the video.

Â So if you want to print it out for handy reference you can do so.

Â So we're looking for 20 years, and so

Â the rows are the period, so you can look down the rows until you get to 20.

Â 15%, so we've got interest rates in the columns, so

Â you look across the columns until you get to 15%.

Â You look at the intersection of the 20 row, the 15% column, and you see 16.3665.

Â So we can take this number times 10,000 to calculate the future value.

Â 20:42

The future value's going to be a $163,665, so

Â this shows you the power of compounding.

Â That basically 10,000 grows into a 163,000 over 20

Â years as long as it grows 15% per year.

Â And of course, that 15% is not only based on the original investment, but

Â whatever return has compounded up until that point.

Â >> Before you go on, can you show me how to do this in Excel?

Â 21:32

Then we enter the rate so that was 15% which we enter in as 0.15.

Â Number of periods is 20 periods.

Â Payment is zero.

Â We'll come back to what that means in a later video.

Â The present value is 10,000.

Â So remember we have $10,000 today that we're investing for 20 years at 15%.

Â For type, you can always leave it blank.

Â This is, has to do with whether the payment comes at the beginning or

Â ending of the period.

Â You could, for almost everything I could think of, you could leave this blank and

Â you'll get the right answer.

Â So then we hit OK, and you get negative $163,665.

Â The reason why it shows up as a negative is Excel says if you

Â put a positive number in, you get a negative number back, so it's almost like

Â you're receiving $10,000 today, you have to pay 163,665 in the future.

Â What I always do is I amend the formula by putting a little negative sign in

Â front if it, and then I get a positive number.

Â And the positive number is the same as what we got using the other two methods.

Â 22:35

Now let's play around with this a little bit and try varying these assumptions.

Â So what if the expected return was only 5% instead of 15%.

Â So, now for our $10,000 present value we still have 20 years to retirement but

Â we have to change r to 5%, I'm going to go ahead and bring up the pause sign and

Â ask you to stop the video and try to do it, but

Â before that, let me bring up the Table 1, in case you want to use this method.

Â 23:10

Okay, before we leave this slide, I just want to point out the factor that you

Â should have grabbed if you're using the table is 20 years, so

Â the 20 row, 5% column, those intersect at 2.6533.

Â So now if we go back to the problem, you could have done it using

Â the formula, 10,000 times 1.05 raised to the 20th punched in your calculator.

Â Or take that 10,000 times the 2.6533 that we just saw in the table.

Â And you end up with a future value of 26,533, much lower present

Â value when we, or much lower future value when we have only the 5% rate of return.

Â 24:34

we can either do the formula, 10,000 times 1.15 raised to the 10th power.

Â Or 10,000 times that factor we just saw in table 1.

Â Which is 4.0456 and we get a future value of 40,456

Â which again is much lower than the 163,000 we saw originally.

Â So if you are going to have fewer years to retirement,

Â you're going to have less money when you retire.

Â 25:27

Yeah, so we can generalize this then go you know how about 30 years, so

Â go more years than 20.

Â How about 25%, go higher than 15%.

Â So this is something I did in Excel, where I, I tried different.

Â Interest rates are,

Â or rate of returns are, I tried different number of periods to retirement and, and

Â what you can see is if you look at the 25% rate of return

Â as the number of periods to retirement grows then the future value grows.

Â Or if you look at the same number of periods, if you look at all the 30's.

Â That as we go from 5% to 15% to 25% the future value grows.

Â So the general rule is, that future value is positively related to the rate of

Â return and the number of periods.

Â So as the rate of return gets bigger,

Â as the number of periods gets bigger the future value grows, and if you see this,

Â and it, as we see in this example if you put $10,000 in stock market today and

Â happen to get 25% return over the next 30 years, it would grow to over $8 million.

Â 26:32

Now that we've seen how to run the time machine forward,

Â to take a present value and figure out what it would be worth in the future,

Â the future value, in the next video, we're going to run the time machine backward.

Â We're going to start with the future value, and

Â see if we can calculate a present value, or in other words,

Â the amount before applying the interest rate or the discount rate.

Â I'll see you then.

Â