Present value 2

now I'll give you a slightly more complicated choice between two payment options both of them are good because in either case you're getting money so choice one so choice one choice choice choice one today I will give you let's say I will give you $100 choice oh then I'll Circle the payment when you get it in magenta so today you get $100 choice two and I'll try to write this choice a little bit neater choice - is that not in one year but in two years so let's say this is year one year one and now this is year two actually I want to give you three choices that that'll that'll really hopefully hit things home it's actually let me scoot this choice - over to the left if I scoot it over to the left look back at the green so now I'm back in business a choice - choice - I am willing to give you let's say oh I don't know one hundred and ten dollars in two years so not in one year in two years I'm going to give you one hundred and ten dollars and so I'll circle in magenta when you actually get your payment and then choice 3 and choice three is going to be fascinating choice three I've been in a slightly different shade of green choice three I am going to pay you I'm making this up on the fly as I go I'm going to pay you $20 today $20 today I'm going to pay you $50 in one year so let's see it's 70 let me make this so it's close and then I'm going to pay you I don't know 35 dollars in year three thirty-five dollars in year three so all of these are payments I want to differentiate between the actual dollar payments and the present values and just for the sake of simplicity let's assume that I am guaranteed I am the safest person available if the world exists if the Sun does not supernova I will be paying you this amount of money so I'm as I am as risk free as the federal government and I had a a post on the on the previous present value where someone talked about well is the federal government really that safe and and this is the point the federal government when it borrows from you $100 let's say it borrows $100 and it promises to pay it in a year it'll give you that hundred dollars the risk is what is that hundred dollars worth because they might inflate the currency to death anyway I won't go into that right now let's just go back to this present this present value problem and actually sometimes governments do default on debt but you know that the US government has never defaulted its inflated its currency so that's that's kind of a roundabout way of defaulting but it's never actually said I will not pay you because if that happened our entire financial system would blow up and we would all be living off the land again anyway back to this problem enough commentary from Sal so let's just compare twice 1 and choice 2 again and once again let's say that risk-free I could put money I could lend it to the federal government at 5% and it doesn't matter over what risk free rate risk-free rate is 5 percent and for the sake of simplicity in the next video I'll I will make that assumption less simple but for the sake of simplicity the government will pay you 5% whether you give them the money for 1 year whether you give them the money for 2 years or whether you give them the money for 3 years right so if I had $100 what would that be worth in one year we figured that out already it's 100 times 1.05 so that's 105 dollars and then what if you got another 5% so the government is giving you 5% per year it would be 105 times 1.05 and what is that so I have 105 times 1.05 so is equal one hundred and ten dollars and twenty five cents one hundred and ten dollars and twenty five cents so that is a value in two years so immediately without even doing any present value we see that you'll actually be better off in two years if you were to take the money now and just lend it to the government because the government risk-free will give you $110 25 cents in two years while I'm only willing to give you 110 dollars so let's that's all fair and good but the whole topic what we're trying to solve is present value so let's take everything in today's money and to take this $110 and say what is that worth today we can just discount it backwards by the same method right so $110 in two years what is its one-year value well you take one hundred and ten dollars and you divide it by 1.05 right you're just doing the reverse and then you get some number here well that number you get is 110 divided by 1.05 and then to get its present value its value today you divide that by 1.05 again so you get 110 divide it if I were to divide by 1.05 again what do I get I divided by 1.05 and then I divided by 1.05 again I'm dividing by 1.05 squared and what is that equal and I'm writing this on purpose because I want to get you used to this notation because this is what all of our present values in our discounted cash flow this this type of dividing by plus the discount rate ^ however many years out this is this is what all of that's based on and that's all we're doing though we're just dividing by 1.05 twice because we're two years out so let's do that okay just well let's just do that 110 divided by 1.05 squared is equal to ninety-nine point seven seven dollars so it equals let me do that in a different color it equals ninety-nine point seven seven so once again we have verified by taking the present value of $110 in two years two today that today it's present value if we assume a five percent discount rate and this discount rate this is this is where all of the all of the the fudge factor occurs in finance you can you can tweak that discount rate and make a few assumptions in discount rate and pretty much assume anything but right now first for simplification we're assuming a risk-free discount rate but when you present value it based on that you get ninety nine dollar seventy seven cents you say wow yeah this really isn't as good as this 99 I would rather have $100 today than ninety nine dollars and seventy seven cents today now this is interesting choice number three how do we look at this well what we do is we present value each of the payments right so the present value of twenty dollars a day well that's just twenty dollars what's the present value of fifty dollars in one year well the present value of that is going to be so plus fifty dollars divided by 1.05 right that's the present value of the fifty dollars because one year out and then I want the present value of the thirty-five dollars so that's plus thirty five dollars divided by what it's two years out right so you have to discount it twice divided by 1.05 squared just like we did here so let's figure out what that present value is notice I'm just adding up the present values of each of those payments get out my virtual ti-85 and see so the present value of the twenty dollar payment is twenty dollars plus the present value of the $50 payment well that's just fifty divided by 1.05 plus the present value of our $35 payment 35 divided by and it's two years out so we discount by our discount rate twice so it's divided by 1.05 squared and then that is equal to ninety nine dollars and thirty will rounded ninety-nine dollars and thirty seven cents ninety nine dollars and thirty seven cents so now we've we can make a very good comparison between the three options this might have been confusing before you know you have this guy coming up to you and this guy is usually in the form of some type of retirement plan or insurance company where they say hey you pay me this four years a B and C and I'll pay you that here's B C and D and you're like boy how do I compare if that's really a good value well this is how you compare you present value all of the payments and you say well what is that worth to me today and here we did that and we said well actually choice number one is the best deal and just depending on how the mathematics work out if I lower the discount rate if this discount rate is lower it might have changed the outcomes and maybe I'll actually do that in the next video just to show you how important the discount rate is anyway I'm out of time and I'll see you in the next video