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so far we've been assuming that the discount rate isn't is it it it's the same thing no matter how long of a period we're talking about but we know if you go to the bank and you say hey Bank I want to essentially invest in a one-year CD they'll say okay one year CD will give you two percent and you're like well what if we give you the money for two years so you can keep our money or locked it in for even longer let's say oh then we'll give you a little bit more interest because you know what we can do we have more flexibility for two years we don't have to worry about paying you so instead of giving you two percent I don't know we'll give you seven percent because we get to keep your money for two years and maybe if you say well you know I actually don't even need my money for ten years so let me give you the money for ten years and say oh ten years if we get to keep your money we'll give you twelve percent so in general and this tends to be the case although it's not always the case that the longer that you you defer your money or the the longer you lock up the money the higher and interest rate you get so the same thing is true when you're when you're doing a discount rate oftentimes you want to discount a a payment two years out by a higher value than something that's only one year out so how do you do that so let's say the risk-free rate so if you were to go out and get a government bond if you were to get a government bond the one year rate the one year rate let's say that they're only giving you one percent but let's say that the two year rate the two year rate they'll give you I don't know they'll give you five percent so what does that mean let's take the example so that means you could take that hundred dollars you could take that hundred dollars and essentially lend it to the federal government and in a year it will give you one percent on it so that these are annual rates so one percent 1.0 one times one hundred that's just one hundred and one dollars right fair enough now your other option is you could lock it in you could lend it to the federal government for two years not see your money and they say oh then we're going to give you five percent a year so then you're going to go five percent a year so how much do you end up with in two years well remember this is an annual rate these are always quoted in annual rates so if you're getting five percent a year that's going to be equal to let's do it on the calculator that's going to be a hundred you're after one year you're going to get 1.05 and then after two years you're going to get 1.05 or you could view that as 100 times 1.05 squared so you'd have one hundred ten dollars and twenty five cents you'd have one hundred and ten and twenty five cents so you already see not even doing any present value this is actually you can almost view this as a future value calculation if you take a future value you already know that this option is better than this option when you have a when you have a kind of these varying interest rates but anyway the whole topic of this is to talk about present values so let's do that so in this circumstance what is the present value of one hundred and ten dollars the present will actually what is the present value of the hundred dollars well we always know that that's easy that is a hundred dollars a present value of a hundred dollars today is 100 dollars what is the present value of 110 so we take 110 and we're going to use the two-year rate and discount twice right and that makes sense because essentially you're deferring your money for two years you're not going to get anything even a year from now so you're deferring your money for two years so you divide it by one so it's a 5% rate 1.05 squared and then that is equal to I think that was our first problem right so I'll just do it again 110 divided by 1.05 squared is equal to 99 dollar 77 cents right that was our first problem and now this one is interesting right the $20 you get today and this is just as a sign that's very important when you're doing this you know when they talk about year one or year zero just make sure is that today is that a year from now because if it's a year from now you would have to discount it right by the one year interest rate if it's today you don't discount it so anyway I I clarified that now it's a little ambiguous about that in the last few videos but I clarified the $20 is now so the present value of something giving you today is the value of it so it's $20 plus $50 now $50 what do we use do we use the one year rate or the two year rate well of course we use the one year rate right because you are you're not deferring the pleasure of that $50 for two years you're actually getting it in one year so plus $50 / one point the one-year rate / 1.0 1 plus $35 / the 2-year rate but this is an annual rate so you have to discount it twice divided by 1.05 squared let's get the ti-85 out see you get 20 plus 50 divided by 1.0 1 + 35 divided by 1.05 squared is equal to 100 $1.25 100 and $1.25 so notice these the actual payment streams I did not change in any of the three scenarios and let me just draw a line between them because I got a little bit messy so that was scenario 1 this is scenario 2 and this is scenario 3 but in scenario 1 because of the we use a 5% discount rate for all you could say I don't want to get used fancy words but for all durations out we use a 5% discount rate we saw that choice number one was the best but then if the discount rate were to change if we were to change our assumption if we had a 2% rate if for whatever reason we could lend money to the federal government in in the form of buying bonds from them we could lend the federal government two years over any time period at 2% or any time period at 2% then all of a sudden choice 2 became the best option and then finally if we had this kind of this is the most realistic scenario and even though the math is fairly simple we're actually doing fairly something fairly sophisticated here when I had a different when I had a different discount rate for my one year out cash flows and my two year out cash flows the end and it was these exact numbers I had to play with the numbers to get the right result then all of a sudden choice 3 choice 3 was the was the best option and so and and I'll leave it to you I want you to think about why this was better for choice three than it was for choice two and and if you really understand that then you I think are starting to have a lot of intuition about present values and frankly what we're learning here is a discounted cash flow right what is it discounted cash flow I'm giving you I'm telling you I'm giving a stream of cash flows twenty dollars now fifty dollars a year from now thirty-five dollars in two years and you are essentially discounting them back to get today's present value so when someone says oh you know I can use Excel to do a discounted cash flow that's all they're doing they're making some assumption about the discount rate and they're just using this fairly you know straightforward mathematics to get the present value of those future cash flows but it's it's a very powerful technique because if you were to take if you're going to Excel and you were to say oh I have a business and based on my assumptions and year one right now this business gives me twenty dollars the next year is going to give 50 dollars the year after that's thirty five dollars and you know this risk-free is a big assumption but if it was risk for you could discount it like that you say oh this business is worth you know if these are the interest rates this business is worth a hundred and $1.25 you know that's what I'm willing to pay for or I'm neutral if I could get it for $90 that's a good deal for me that's all that this kind of cash flow is but the the big learning from this is how dependent the present value of a a future of future payments are on that your discount rate assumption the discount rate assumption is everything in finance and and this is this is where finance really diverges from a lot of other fields especially in the sciences there really is no correct answer it's all assumption driven all of these discounted cash flows and all these models they're really just to help you understand the dynamics of things and frankly and this happens a lot in the real world of finance if you ever become a an analyst in the investment at an investment bank you'll probably do this yourself but you can almost justify any present value by picking the right discount rate and actually the whole topic of how do you decide on the right discount rate because we assumed risk-free right everything is risk for you're guaranteed these payments but we know in the real world if you're investing in if you're investing in pets.com and they tell you that they're going to pay these cash flows to you that's risk free there's some risk implicit in that so actually most of finance and most of well yeah and portfolio theory and modern finance is based on figuring out that discount rate and it's it and that is the crux of everything because if we see that that completely changes which of these options is the best but anyway I don't want to confuse you too much what you have already is a very powerful tool that if you can think of a discount rate you can make a very rational comparison between three or you know or 10 or whatever different types of payments and this is actually really useful you don't realize how many how many things in the world are like this right you could you know these these college these you know college payment schemes where you pay some company you know twenty five dollars a year for twenty years and then in in year twenty one they're willing to pay for your college tuition or your kids college tuition that's a you could figure out what that really is worth how much money are they making off of you by taking a discounted cash flow and of course if you're paying out these become negative numbers and when they pay you it becomes a positive number anyway maybe I'll do that in a couple of videos because I think that's a fairly useful thing to be able to analyze see you in the next video