# Introduction to present value | Interest and debt | Finance & Capital Markets | Khan Academy

We will now learn what can be said to be the most beneficial in finance. This is called the current value. If you know the current value. Then it will be very easy to understand. Net present value and discounted cash flows And the internal rate of return And eventually we'll learn all of these things. But what is the present value and what does it mean? current value So let's do a little exercise. I could pay you hundreds of dollars today. So let's say today I can pay you a hundred dollars. Or (that's up to you) in a year, I'll pay you I don't know, let's say in a year I agree to pay you \$ 110.

My question is for you This is a fundamental question in finance Everything will be based on this Which is anything you prefer? This is guaranteed I'm sponsoring you, either I'm paying you \$ 100 today There is no danger here, even if you hit a cart or something else. This is what happens, if you're alive, I'm paying you \$ 110 in one year. It's guaranteed, so oh there's risk here. So it's just an idea You'd definitely have \$ 100 today in your hand Or definitely you'll get \$ 110 in one year from now. So how do you compare them? Hence the present value.

What if there was a way Let's say, well what's the \$ 110 \$ 110 guaranteed in the future? What if there was a argument to say How much is it worth today? How much is it worth and at the end of the day? So let's think about a little experiment. Let's say you can put the money in In other words, let's say you can put money in the bank.

These days, banks are somewhat of a risk. But let's say you can put it in the safest banks in the world. Let's say it can be put in government vaults. Which is considered risk free Because the United States government, the treasury You can print more money indirectly. One day we will do all the things we can do with providing cash. But at the end of the day The US government has rights to the printing press, etc. It's more complicated than that, but for these purposes, we assume That the US Treasury Department, which is at its core You are lending money to the US government This is risk free So let's say You can lend money Today, let's say, I can give you 100 dollars And you can invest in it 5% without risk So you are investing it at 5% without risk. Then, a year from now, how much will it be worth? in a year It'll be worth \$ 105 in one year. Actually let me write \$ 110 here. So here's a good way to think about it. You liked it, okay. Instead of taking the money Who asked after a year from now And get \$ 110, If I were to take 100 dollars today and put it in anything that risk-free In a year I'll get \$ 105.

Even assuming I can't afford to spend today This is the best condition I have been in. is not it? If you took the money today and the risk is zero Invest it at 5%, it will end up at \$ 105 a year. Instead, if you'd tell me Sal, just give me money in a year and give me \$ 110 You will end up with more money in a year You will eventually get \$ 110 And this is actually the right way to think about it. And remember, everything is free of risk. Once the risk is entered, We have to start by introducing the different interest levels and Chances are, we'll get to that eventually. But I want to give only the best example at the moment. So you really made the decision. We do not yet know what the present value is. So up to a point When you take the \$ 100 and you You say, well, if you loan it to the government Or if you lend it to some banks risk free at 5% At a year they will give me \$ 105 That's \$ 105 Way of saying, What's the value for a year at \$ 100 today? But what if we wanted to go the other way? If we had a certain amount of money And we want to know the value of today what can we do? We'll take it from here to there, what should we do? We basically took \$ 100 We doubled it by 1 + 5%. So it's 1.05 So another way, Let's say how many coins If I were to grow by 5% It'll end up at \$ 110, we'll just divide by 1.05 And then we'll get the current value The transcription is PV We'll get the present value of \$ 110 a year from now.

So \$ 110 a year from now. So the present value is \$ 110 in 2009 It's now 2008 I don’t know in which year you are watching this video. Hopefully, people will be watching this for the next millennium. But the current value is \$ 110 in 2009 – Assuming now it is 2008 – a year from now, it equals to \$ 110 Divided by 1.05. Which is equivalent to – let's get this calculator out Which is probably an exaggeration for this problem, let me explain everything. Okay, so I want to divide 110 by 1,05 Equals 104 (let's complete), 76. So it equals \$ 104.76. So the present value is \$ 110 a year from now Assuming we could invest the money at 5% risk-free – if we got it today, The current value of it is – let me do it in a different color, just to fight the monotony.

The present value equals \$ 104.76. Another way to just kind of talk about this is to get The present value is \$ 110 a year from now, and we've subtracted the value by the discount percentage. The discount rate is this And here we made money grow – arguably. Our yield, 5% yield, or our benefit. Here we deducted the money because we got back in time – We're going from a year until now. So this is our yield. To mix the amount of money we invested in it We multiplied the amount we invested by 1 plus the return. When we deducted the money in the future to the present, And we divide it by (1) with the discount rate – so that's it 5% discount rate. To get its current value. So what does this tell us? A tells us if someone is willing to pay \$ 110 – assuming that's 5%, remember This is a dangerous assumption – this tells us that if I told you I'm willing to pay you \$ 110 a year from now And you can get 5%, so you can say That 5% is your discount rate, risk free.

Then you must be ready to take the money today if Today I am willing to give you more than the current value. So, if this compares – let me explain all this, Let me just scroll down – so let's say That one year – today it was so, one year So we've counted \$ 110 a year from now, it is The present value equals – therefore the present value of \$ 110 – It's worth \$ 104.76. You – that's why I'm using a 5% discount rate (this is a key assumption) – What this tells you is – this is the dollar sign, and I know it's hard to read What this tells you is, if your choice is between \$ 110 a year from now, \$ 100 today. You should be taking the \$ 110 a year from now. why is that? Because the current value is worth more than \$ 110 However, if I give you 110 dollars a year from now or \$ 105 today, that's -105 dollars today, it would be the best choice, Because its present value is \$ 105 today I don't have to discount it, it is today – it's the present value It is by itself.

\$ 105 today equals more than the current value of \$ 110, which is She is \$ 104.76. Another way to think about it is, I can take this 105 bucks to the bank, Get 5% on that, and then it would be what would- I end up with? – I'd end up with 105 times 1.05, it's \$ 110.25. Even a year from now, I'd be better off by a quarter. I was happy that I was able to touch my money after a year That is hard to count, so we leave it out of the equation..