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Current time:0:00Total duration:10:19

we'll now learn about what is arguably the most useful concept in finance and that's called the present value and if you know the present value then it's very easy to understand the net present value and the discounted cash flow and the internal rate of return and we'll eventually learn all of those things but the present value what does that mean present value so let's let's do a a little exercise I could pay you a hundred dollars today so let's say today today I could pay you 100 dollars or it's up to you or in one year in one year I will pay you I don't know let's say in a year I agree to pay you a hundred and ten dollars and my question to you and this is a fundamental question of Finance everything will build upon this is which one would you prefer and this is guaranteed I guarantee you I'm either gonna pay you a hundred dollars today and there's no risk even if I get hit by a truck or whatever this is going to happen the US government if the earth exists we will pay you 110 dollars in one year it is guaranteed so there's no risk here so it's just a notion of you're definitely going to get a hundred dollars today in your hand or you're definitely going to get $100 110 dollars one year from now so how do you compare the two and this is where present value comes in what if there were a way to say well what is $110 a guaranteed $110 in the future what if there were a way to say how much is that worth today how much is that worth in today's terms so let's let let's do a little thought experiment let's say that you could put money in some let's say you could put money in the bank and you know these days banks are kind of risky but let's say you could put it in the safest bank in the world let's say you although someone would debate you put it in government Treasuries which are considered risk safe because a risk free because the US government the Treasury can always indirectly print more money well will one day do a whole thing on the money supply but at the end of the day the US government has the rights on on the printing press etc it's more complicated than that but for those purposes we assume that a US Treasury which essentially is you're lending money to the US government that it's risk-free so let's say that you you could lend money let's say today I could give you $100 and that you could invest it at 5% risk-free so you could invest it five percent risk-free and then in a year from now how much would that be worth in a year that would be worth 100 five dollars in one year actually let me write the 110 dollars over here right so this was a good way of thinking about it you're like okay instead of taking the money from Sal a year from now I'm getting $110 if I were to take the hundred dollars today and put it in something risk-free in a year I would have a hundred and five dollars so assuming I don't have to spend the money today this is a better situation to be in right if I take the money today and risk-free invested it five percent I'm going to end up with 105 dollars a year instead if you just tell me Sal just give me the money in a year give me $110 you're going to end up with more money in a year right you're going to end up with $110 and that is actually the right way to think about it and remember everything and I keep saying it over and over again everything I'm talking about it's it's critical that we're talking about risk-free once you introduce risk and we have to start introducing different interest rates and probabilities and we'll get to that eventually but I want to just give the purest example right now so already you've made the decision but we still don't know what present value was so to some degree when you took this hundred dollars and you said well if I lend it to the government or five lend it to a risk-free bank at five percent in the year they'll give me $105 this $105 is a way of say what is the one-year value of $100 today right what is a one-year out value of $100 today so what if we want it to go in the other direction if we have a certain amount of money and we want to figure out today's value what could we do well to go from here to here what did we do we essentially took $100 we took $100 and we multiplied by one we multiplied by one plus five percent so that's 1.05 so to go the other way to say how much money if I were to grow it by five percent would end up being $110 we'll just divided by 1.05 and then we will get the present value and the notation is PV we'll get the present value of one hundred and ten dollars a year from now so one hundred ten year from now year from now so the present value the present value of $110 in let's say in 2009 it's currently 2008 I don't know what year you're watching this video in hopefully people will be watching this in the next millennia but the present value of $110 in 2009 assuming right now is 2008 a year from now is equal to $110 $110 divided by 1.05 which is equal to and let's take out this calculator which is probably overkill for this problem let me clear everything okay so I want to do 110 divided by 1.05 is equal to 100 for pointless round 0.76 so it equals 100 four point seven six dollars so the present value of $110 a year from now if we assume that we could invest money risk-free at 5% if we were get today the present value of that is let me do it in a different color just to fight the monotony the present value is equal to one hundred and four dollars and seventy six cents another way to kind of just talk about this is to get the present value of $100 ten dollars a year from now we discounted the value by a discount rate and the discount rate is this right here we grew the money by you could say I don't are yielding our interest here we're discounting the money because we're going backwards in time we're going from year out to the present and so this is our yield to to compound the amount of money we invest we multiply the amount we invest times one plus the yield then to discount money in the future to the present we divide it by one plus the discount rate so this is a 5% discount rate 5% discount rate to get its present value so what does this tell us this tells us if if someone's willing to pay $110 assuming this 5% from this is a critical assumption this tells us that if I tell you I'm willing to pay you $110 a year from now and you could get 5% so you could kind of say that 5% is your discount rate risk-free that you should be willing to take today's money if today I'm willing to give you more than the present value so if this comparison were let me let me clear all of this or let me just scroll down so let's say that one year so today one year so we figured out that $110 $110 a year from now its present value its present value is equal to so the present value of that 110 is equal to 104 dollars and 76 cents so and that's because I used a 5% discount and that's a key assumption but what this tells you is this is a dollar sign and it's hard to read what this tells you is is that if if your choice was between $110 a year from now and $100 today $100 today you should take $110 a year from now why is that because it's present value is worth more than 100 however if I were to offer you a hunt the $110 a year from now or a hundred and five dollars today this the $105 today would be the better choice because its present value right $105 today you don't have to discount it it's it's today it's present value is itself $105 today is worth more than the present value of 110 which is 104 dollars and 76 cents another way to think about it is I can take this 105 dollars in the bank get let's see I let's assume I have a risk for you rank get 5% on it and then I would have what would I end up with I would end up with 105 times 1.05 is equal to $110 and a quarter so a year from now I'd be better off by a quarter and I have the joy of being able to touch my money for a year which is hard to hard to quantify so we leave it out of the equation anyway I'll see you in the next video