WEBVTT 00:00:01.858 --> 00:00:03.700 We'll now learn about what is arguably the most useful concept in finance 00:00:04.923 --> 00:00:06.800 and that is called the present value. 00:00:09.200 --> 00:00:10.681 And if you know the present value 00:00:10.681 --> 00:00:12.446 then it's very easy to understand 00:00:12.446 --> 00:00:15.418 the net present value and the discounted cash flow 00:00:15.418 --> 00:00:16.858 and the internal rate of return 00:00:16.858 --> 00:00:18.344 and we'll eventually learn all of those things. 00:00:18.344 --> 00:00:20.700 But the present value, what does that mean? 00:00:22.523 --> 00:00:25.031 Present value. 00:00:25.031 --> 00:00:29.443 So let's do a little exercise. 00:00:29.443 --> 00:00:32.508 I could pay you a hundred dollars today. 00:00:32.508 --> 00:00:37.216 So let's say today 00:00:37.216 --> 00:00:42.000 I could pay you one hundred dollars. 00:00:42.000 --> 00:00:50.480 Or (and it's up to you) in one year, I will pay you 00:00:50.480 --> 00:00:58.607 I don't know, let's say in a year I agree to pay you $110. 00:00:58.607 --> 00:01:00.800 And my question to you 00:01:00.800 --> 00:01:02.700 and this is a fundamental question of finance 00:01:02.700 --> 00:01:04.366 everything will build upon this 00:01:04.366 --> 00:01:06.800 is which one would you prefer? 00:01:06.800 --> 00:01:08.000 and this is guaranteed. 00:01:08.000 --> 00:01:10.200 I guarantee you, I'm either going to pay you $100 today 00:01:10.200 --> 00:01:14.211 and there's no risk, even if I get hit by a truck or whatever. 00:01:14.211 --> 00:01:16.500 This is going to happen, if the Earth exists, I will pay you $110 in one year. 00:01:21.100 --> 00:01:24.149 It is guaranteed, so there's no risk here. 00:01:24.149 --> 00:01:25.400 So it's just a notion of 00:01:25.400 --> 00:01:28.375 You're definitely gonna get $100 today, in your hand 00:01:28.375 --> 00:01:34.300 or you're definitely gonna get $110 one year from now. 00:01:34.300 --> 00:01:35.500 So how do you compare the two? 00:01:35.500 --> 00:01:38.200 And this is where present value comes in. 00:01:38.200 --> 00:01:39.900 What if there were a way 00:01:39.900 --> 00:01:41.982 to say, well what is $110 00:01:41.982 --> 00:01:45.047 a guaranteed $110 in the future? 00:01:45.047 --> 00:01:46.200 What if there were a way to say 00:01:46.200 --> 00:01:49.200 How much is that worth today? 00:01:49.200 --> 00:01:52.200 How much is that worth in today's terms? 00:01:52.200 --> 00:01:54.700 So let's do a little thought experiment. 00:01:54.700 --> 00:01:57.447 Let's say that you could put money 00:01:57.447 --> 00:02:00.558 in some, let's say you could money in the bank. 00:02:00.558 --> 00:02:02.600 And these days, banks are kind a risky. 00:02:02.600 --> 00:02:05.400 But let's say you could put it in the safest bank in the world. 00:02:05.400 --> 00:02:09.614 Let's say you could put it in government treasuries 00:02:09.614 --> 00:02:11.400 which are considered risk free 00:02:11.400 --> 00:02:15.047 because the US government, the treasury 00:02:15.047 --> 00:02:17.800 can always indirectly print more money. 00:02:17.800 --> 00:02:19.877 We'll one day do a whole thing on the money supply. 00:02:19.877 --> 00:02:21.270 But at the end of the day 00:02:21.270 --> 00:02:22.700 the US government has the rights on the printing press, etc. 00:02:25.500 --> 00:02:26.889 It's more complicated than that, but for these purposes, we assume 00:02:28.200 --> 00:02:29.815 that the US treasury, which essentially is 00:02:29.815 --> 00:02:31.905 you lending money to the US government 00:02:32.857 --> 00:02:33.809 that it's risk free. 00:02:33.809 --> 00:02:35.388 So let's say that 00:02:35.388 --> 00:02:36.400 you could lend money 00:02:36.400 --> 00:02:39.800 Let's say today, I could give you $100 00:02:39.800 --> 00:02:41.286 and that you could invest it 00:02:41.286 --> 00:02:45.400 at 5% risk free. 00:02:45.400 --> 00:02:49.366 So you could invest it 5% risk free. 00:02:49.366 --> 00:02:52.200 And then a year from now, how much would that be worth? 00:02:52.200 --> 00:02:53.780 In a year. 00:02:53.780 --> 00:02:57.531 That would be worth $105 in one year. 00:02:57.623 --> 00:03:03.271 Actually let me write $110 over here. 00:03:03.379 --> 00:03:05.654 So this is a good way of thinking about it. 00:03:05.654 --> 00:03:09.300 You're like, okay. Instead of taking the money 00:03:09.300 --> 00:03:11.300 from Sal a year from now 00:03:11.300 --> 00:03:13.097 and getting $110 dollars, 00:03:13.097 --> 00:03:16.348 If I were to take $100 today and put it in something risk free 00:03:16.348 --> 00:03:18.902 in a year I would have $105. 00:03:18.902 --> 00:03:22.900 So assuming I don't have to spend the money today 00:03:22.900 --> 00:03:26.900 This is a better situation to be in. Right? 00:03:26.900 --> 00:03:28.200 If I take the money today and risk-free 00:03:28.200 --> 00:03:29.908 invest it at 5%, I'm gonna end up at 00:03:29.908 --> 00:03:32.100 $105 in a year. 00:03:32.100 --> 00:03:33.800 Instead, if you just tell me 00:03:33.800 --> 00:03:36.271 Sal, just give me the money in a year and give me $110 00:03:36.271 --> 00:03:39.939 you're gonna end up with more money in a year. 00:03:39.939 --> 00:03:42.122 You're gonna end up with $110. 00:03:42.122 --> 00:03:44.300 And that is actually the right way to think about it. 00:03:44.300 --> 00:03:48.400 And remember, everything is risk-free. 00:03:48.400 --> 00:03:50.600 Once you introduce risk, 00:03:50.600 --> 00:03:53.593 And we have to start introducing different interest rates and 00:03:53.593 --> 00:03:56.008 probabilities, and we'll get to that eventually. 00:03:56.008 --> 00:04:00.744 But I want to just give the purest example right now. 00:04:00.744 --> 00:04:02.509 So already you've made the decision. 00:04:02.509 --> 00:04:05.249 We still don't know what present value is. 00:04:05.249 --> 00:04:06.503 So to some degree 00:04:06.503 --> 00:04:07.600 when you took this $100 and you 00:04:07.600 --> 00:04:09.600 said, well if I lend it to the government 00:04:09.600 --> 00:04:11.519 or if I lend it to some risk-free bank at 5% 00:04:11.519 --> 00:04:14.351 in a year they'll give me $105 00:04:14.351 --> 00:04:18.577 This $105 is a way of saying, what is the one-year value of $100 today? 00:04:24.847 --> 00:04:25.729 So what if we wanted to go in the other direction? 00:04:27.680 --> 00:04:29.119 If we have a certain amount of money 00:04:29.119 --> 00:04:31.100 and we want to figure out today's value 00:04:31.100 --> 00:04:33.020 what could we do? 00:04:33.020 --> 00:04:35.200 Well to go from here to here, what did we do? 00:04:35.200 --> 00:04:39.500 We essentially took $100 00:04:39.500 --> 00:04:44.300 and we multiplied by 1+5%. 00:04:44.300 --> 00:04:47.742 So that's 1,05 00:04:47.742 --> 00:04:49.367 So to go the other way, 00:04:49.367 --> 00:04:50.900 to say how much money 00:04:50.900 --> 00:04:53.200 if I were to grow it by 5% 00:04:53.200 --> 00:04:57.700 would end up being $110, we'll just divide by 1,05 00:05:01.900 --> 00:05:04.900 And then we will get the present value 00:05:04.900 --> 00:05:06.503 And the notation is PV 00:05:06.503 --> 00:05:12.308 We'll get the present value of $110 a year from now. 00:05:12.308 --> 00:05:20.600 So $110 year from now. 00:05:20.600 --> 00:05:22.900 So the present value of $110 in 2009 00:05:30.400 --> 00:05:31.906 It's currently 2008 00:05:31.906 --> 00:05:33.800 I don't know what year you're watching this video in. 00:05:33.800 --> 00:05:37.300 Hopefully people will be watching this in the next millenia. 00:05:37.300 --> 00:05:40.776 But the present value of $110 in 2009 00:05:40.776 --> 00:05:47.928 — assuming right now is 2008— a year from now, is equal to $110 00:05:47.928 --> 00:05:53.117 divided by 1,05. 00:05:53.132 --> 00:05:57.283 Which is equal to— let's take out this calculator 00:05:57.283 --> 00:06:02.859 which is probably overkill for this problem— let me clear everything. 00:06:02.859 --> 00:06:12.355 OK, so I want to do 110 divided by 1,05 00:06:12.355 --> 00:06:16.906 is equal to 104 (let's just round) ,76. 00:06:16.906 --> 00:06:24.894 So it equals $104,76. 00:06:24.894 --> 00:06:28.656 So the present value of $110 a year from now 00:06:28.656 --> 00:06:33.400 if we assume that we could invest money risk-free at 5%— if we would get it today— 00:06:33.400 --> 00:06:39.500 the present value of that is— let me do it in a different color, just to fight the monotony— 00:06:39.500 --> 00:06:47.092 the present value is equal to $104,76. 00:06:47.092 --> 00:06:50.300 Another way to kind of just talk about this is to get 00:06:50.300 --> 00:06:56.845 the present value of $110 a year from now, we discount the value by a discount rate. 00:06:56.845 --> 00:07:00.400 And the discount rate is this. 00:07:00.400 --> 00:07:02.800 Here we grew the money by— you could say— 00:07:02.800 --> 00:07:07.993 our yield, a 5% yield, or our interest. 00:07:07.993 --> 00:07:10.916 Here we're discounting the money 'cause we're backwards in time— 00:07:10.916 --> 00:07:13.099 we're going from a year out to the present. 00:07:13.099 --> 00:07:18.021 And so this is our yield. To compound the amount of money we invest 00:07:18.021 --> 00:07:22.400 we multiply the amount we invest times 1 plus the yield. 00:07:22.400 --> 00:07:24.801 Then to discount money in the future to the present, 00:07:24.801 --> 00:07:30.276 we divide it by 1 plus the discount rate— so this is 00:07:30.276 --> 00:07:37.300 a 5% discount rate. 00:07:37.300 --> 00:07:39.337 To get its present value. 00:07:39.337 --> 00:07:41.300 So what does this tell us? 00:07:41.300 --> 00:07:46.860 This tells us if someone is willing to pay $110— assuming this 5%, remember 00:07:46.860 --> 00:07:52.108 this is a critical assumption— this tells us that if I tell you 00:07:52.108 --> 00:07:56.427 I'm willing to pay you $110 a year from now 00:07:56.427 --> 00:07:58.703 and you can get 5%, so you can kind of say 00:07:58.703 --> 00:08:02.000 that 5% is your discount rate, risk-free. 00:08:02.000 --> 00:08:06.179 Then you should be willing to take today's money if 00:08:06.179 --> 00:08:09.616 today I'm willing to give you more than the present value. 00:08:09.616 --> 00:08:14.910 So, if this compares in— let me clear all of this, 00:08:14.910 --> 00:08:17.100 let me just scroll down— so let's say 00:08:17.100 --> 00:08:24.400 that one year— so today, one year— 00:08:24.400 --> 00:08:31.164 so we figured out that $110 a year from now, its 00:08:31.164 --> 00:08:40.127 present value is equal to— so the present value of $110— 00:08:40.127 --> 00:08:45.607 is equal to $104,76. 00:08:45.607 --> 00:08:50.855 So— and that's 'cause I used a 5% discount rate (and that's the key assumption)— 00:08:50.855 --> 00:08:53.700 what this tells you is— this is a dollar sign, I know it's hard to read— 00:08:53.700 --> 00:08:58.517 what this tells you is, is that if your choice was between 00:08:58.517 --> 00:09:03.765 $110 a year from now and $100 today, 00:09:03.765 --> 00:09:08.800 you should take the $110 a year from now. 00:09:08.800 --> 00:09:09.756 Why is that? 00:09:09.756 --> 00:09:13.749 Because its present value is worth more than $100. 00:09:13.749 --> 00:09:17.372 However, if I were to offer you $110 a year from now or 00:09:17.372 --> 00:09:26.000 $105 today, this— the $105 today— would be the better choice, 00:09:26.000 --> 00:09:29.214 because its present value— right, $105 today 00:09:29.214 --> 00:09:31.954 you don't have to discount it, it's today— its present value 00:09:31.954 --> 00:09:33.022 is itself. 00:09:33.022 --> 00:09:38.700 $105 today is worth more than the present value of $110, which 00:09:40.340 --> 00:09:41.981 is $104.76. 00:09:41.981 --> 00:09:49.545 Another way to think about it is, I could take this $105 to the bank, 00:09:49.545 --> 00:09:53.781 get 5% on it, and then I would have— what would 00:09:53.781 --> 00:10:04.601 I end up with?— I would end up with 105 times 1,05, it's equal to $110,25. 00:10:04.601 --> 00:10:08.753 So a year from now, I'd be better off by a quarter. 00:10:08.753 --> 00:10:11.614 And I'd have the joy of being able to touch my money for a year, 00:10:11.614 --> 00:10:16.585 which is hard to quantify, so we leave it out of the equation.