Introduction to Present Value Video

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Introduction to Present Value

We’ll now learn about what is arguably the most useful concept in finance and that is 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? So, let’s do a little exercise. So today, I could pay you $100.00 or it’s up to you if, let’s say in a year, I agree to pay you a $110.00. 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 going to pay you a $100 today and there is no risk even if I get hit by a truck or whatever. This is going to happen; the U.S. government. If the earth exists, we will pay you a $110.00 in one year. It is guaranteed, so there is no risk here. So, it’s just a notion of you’re definitely going to get a $100.00 today in your hand or you’re definitely going to get a $110.00 one year from now. So, how do you compare the two? And this is where present value comes in. What if there was a way to say, “Well, what is a $110.00, a guaranteed $110.00 in the future.” What is there was a way to say, “How much is that worth today? How much is that worth in today’s terms?” So, let’s do a little thought experiment. Let’s say that you could put money in the bank and these days banks are kind or risky but let’s say you can put it in the safest bank in the world. Let’s say you put it in Government Treasuries which are considered risk-free because the U.S. Government, the treasury can always indirectly print more money. Well, one day, it will do a whole thing on the money supply but at the end of the day, the U.S. Government has the rights on the printing press, etc. It’s more complicated than that but for those purposes, we assume that a U. S. Treasury which essentially is your lending money to the U. S. Government, that it’s risk-free. So, let’s say that you could lend money. Let’s say today, I could give you a $100 and that you could invest it at 5% risk-free. So, you can invest it 5% risk-free. And then a year from now, how much would that be worth in a year? That would be worth $105 in one year. 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, you’re getting a $110.00. If I were to take the $100.00 and put it in something risk-free, in a year, I would have a $105.00.” So, assuming I don’t have to spend the money today, this is a better situation to be in. If I take the money today and risk-free, invest it at 5%, I am going to end up with a $105.00 in a year. Instead, if you just tell me, “Sal, just give me the money in a year. Give me a $110.00” You’re going to end up with more money in a year. You’re going to end up with a $110.00. And that is actually the right way to think about it. And remember and I keep saying it over and over again, everything I am talking about, it’s critical that we’re talking about risk-free. Once you introduce risk, then 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 $100.00 and you said, “Well, if I lend it to the government or if I lend it to a risk-free bank at 5%. In a year, they’ll give me a $105.00” This $105.00 is a way of saying, “What is the one year value of a $100.00 today?” What is one year out value of a $100.00 today? So, what if we wanted 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 a $100.00 and we multiplied by 1 + 5%, so that is 1.05. So, to go the other way, to say how much money if I were to grow it by 5% would end up being a $110.00, we’ll just divide by 1.05. And then, we will get the present value and the notation is PV. We’ll get the present value of $110.00 a year from now. So, the present value of $110.00 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 and assuming right now is 2008; a year from now is equal to $110 ÷ 1.05 which is equal to 104.76. So, it equals $104.76. 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 to get today, the present value is equal to $104.76. Another way to kind of just talk about this is to get the present value of $10 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, a 5% yield or 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 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 to get its present value. So, what does this tell us? This tells us if someone is willing to pay $110.00 assuming this 5% remember, this is a critical assumption. This tells us that if I tell you, I am willing to pay you $110.00 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 am willing to give you more than the present value. So, let’s say today, one year. So, we figured out that a $110 a year from now that its present value is equal to $104.76 because I used a 5% discount rate and that’s a key assumption. But what this tells you is that if you’re choice was between $110.00 a year from now and $100 today, you should take the $110.00 a year from now. Why is that? Because its present value is worth more than a $100.00. However, if I were to offer you $110.00 a year from now or a $105.00 today, the $105.00 today would be the better choice because its present value is itself. A $105.00 today is worth more than the present value of $110.00 which is $104.76. Another way to think about it is, I could take this $105.00 at the bank. Let’s assume I have a risk-free bank. I get 5% on it. What would I end up with? I would end up with 105 × 1.05 = $110.25. So, a year from now I’d be better off by a quarter and I have the joy of being able to touch by money for a year which is hard to quantify, so we leave it out off the equation. Anyway, I’ll see you in the next video.

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We’ll now learn about what is arguably the most useful concept in finance and that is 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? So, let’s do a little exercise. So today, I could pay you $100.00 or it’s up to you if, let’s say in a year, I agree to pay you a $110.00. 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 going to pay you a $100 today and there is no risk even if I get hit by a truck or whatever. This is going to happen; the U.S. government. If the earth exists, we will pay you a $110.00 in one year. It is guaranteed, so there is no risk here.

So, it’s just a notion of you’re definitely going to get a $100.00 today in your hand or you’re definitely going to get a $110.00 one year from now. So, how do you compare the two? And this is where present value comes in. What if there was a way to say, “Well, what is a $110.00, a guaranteed $110.00 in the future.” What is there was a way to say, “How much is that worth today? How much is that worth in today’s terms?”

So, let’s do a little thought experiment. Let’s say that you could put money in the bank and these days banks are kind or risky but let’s say you can put it in the safest bank in the world. Let’s say you put it in Government Treasuries which are considered risk-free because the U.S. Government, the treasury can always indirectly print more money. Well, one day, it will do a whole thing on the money supply but at the end of the day, the U.S. Government has the rights on the printing press, etc. It’s more complicated than that but for those purposes, we assume that a U. S. Treasury which essentially is your lending money to the U. S. Government, that it’s risk-free.

So, let’s say that you could lend money. Let’s say today, I could give you a $100 and that you could invest it at 5% risk-free. So, you can invest it 5% risk-free. And then a year from now, how much would that be worth in a year? That would be worth $105 in one year. 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, you’re getting a $110.00. If I were to take the $100.00 and put it in something risk-free, in a year, I would have a $105.00.”

So, assuming I don’t have to spend the money today, this is a better situation to be in. If I take the money today and risk-free, invest it at 5%, I am going to end up with a $105.00 in a year. Instead, if you just tell me, “Sal, just give me the money in a year. Give me a $110.00” You’re going to end up with more money in a year. You’re going to end up with a $110.00. And that is actually the right way to think about it. And remember and I keep saying it over and over again, everything I am talking about, it’s critical that we’re talking about risk-free. Once you introduce risk, then 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 $100.00 and you said, “Well, if I lend it to the government or if I lend it to a risk-free bank at 5%. In a year, they’ll give me a $105.00” This $105.00 is a way of saying, “What is the one year value of a $100.00 today?” What is one year out value of a $100.00 today?

So, what if we wanted 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 a $100.00 and we multiplied by 1 + 5%, so that is 1.05. So, to go the other way, to say how much money if I were to grow it by 5% would end up being a $110.00, we’ll just divide by 1.05. And then, we will get the present value and the notation is PV. We’ll get the present value of $110.00 a year from now.

So, the present value of $110.00 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 and assuming right now is 2008; a year from now is equal to $110 ÷ 1.05 which is equal to 104.76. So, it equals $104.76. 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 to get today, the present value is equal to $104.76.

Another way to kind of just talk about this is to get the present value of $10 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, a 5% yield or 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 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 to get its present value.

So, what does this tell us? This tells us if someone is willing to pay $110.00 assuming this 5% remember, this is a critical assumption. This tells us that if I tell you, I am willing to pay you $110.00 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 am willing to give you more than the present value. So, let’s say today, one year. So, we figured out that a $110 a year from now that its present value is equal to $104.76 because I used a 5% discount rate and that’s a key assumption. But what this tells you is that if you’re choice was between $110.00 a year from now and $100 today, you should take the $110.00 a year from now. Why is that? Because its present value is worth more than a $100.00. However, if I were to offer you $110.00 a year from now or a $105.00 today, the $105.00 today would be the better choice because its present value is itself. A $105.00 today is worth more than the present value of $110.00 which is $104.76.

Another way to think about it is, I could take this $105.00 at the bank. Let’s assume I have a risk-free bank. I get 5% on it. What would I end up with? I would end up with 105 × 1.05 = $110.25. So, a year from now I’d be better off by a quarter and I have the joy of being able to touch by money for a year which is hard to quantify, so we leave it out off the equation. Anyway, I’ll see you in the next video.

Transcription by: Scribe4you Transcription Services