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Present Value 2

104문장 100% 한국어 번역 68명 참여 출처 : 칸아카데미

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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. Today I will give you $100.

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 two is that not in 1 year, but in 2 years.

So let's say this is year 1.

And now this is year 2.

Actually I'm going to give you three choices.

That'll really hopefully hit things home.

So actually let me scoot this choice two over to the left.

Back to green. So now I'm back in business.

So choice two, I am willing to give you, let's say, oh I don't know, $110 in 2 years.

So not in 1 year. In 2 years I'm going to give you $110.

And so I'll circle in magenta when you actually get your payment.

And then choice 3. And choice 3 is going to be fascinating.

I've done it in a slightly different shade of green.

Choice 3, 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.

I'm going to pay you $50 in 1 year.

That's $70. Let me make this so it's close.

And then I'm going to pay you - I don't know - $35 in year 3.

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 risk-free as the federal government.

And I had a post on the previous present value, where someone talked about, well is the federal government really that safe?

And this is the point. The federal government, when it borrows from you, say, $100 - Let's say it borrows $100 and it promises to pay it in a year.

It'll give you that $100. The risk is, what is that $100 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 value problem.

And actually sometimes governments do default on debt.

But the U.S. government has never defaulted.

It has inflated its currency. So that's kind of a roundabout way of defaulting.

But it has 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 Choice 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 - WRITING: Risk-free rate is 5%.

And for the sake of simplicity - in the next video I will make that assumption less simple--

but for the sake 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 1 year?

We figured that out already. It's 100 times 1.05.

So that's $105. And then 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, which equals $110.25.

So that is the value in 2 years.

So immediately, without even doing any present value, we see that you'll actually be better off in 2 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 in 2 years, while I'm only willing to give you $110.

So 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 2 years, what is its 1-year value?

Well, you take $110 and you divide it by 1.05.

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 divided. If I were to divide by 1.05 again what do I get?

I divide by 1.05, and then I divide by 1.05 again.

I'm dividing by 1.05 squared. And what does 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 and our discounted cash flow, this type of dividing by 1 plus the discount rate to the power of however many years out, 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 2 years out.

So let's do that. 110 divided by 1.05 squared is equal to $99.77.

So once again we have verified, by taking the present value of $110 in 2 years to today, that its present value - if we assume a 5% discount rate.

And this discount rate, this is where all of the fudge factor occurs in finance.

You can tweak that discount rate and make a few assumptions in discount rate and pretty much assume anything.

But right now, for simplification, we're assuming a risk-free discount rate.

But when the present value is based on that, you get $99.77.

You say, wow, yeah, this really isn't as good as this.

I would rather have $100 today than $99.77 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 $20 today, well that's just $20.

What's the present value of $50 in 1 year?

Well the present value of that is going to be - so plus $50 divided by 1.05, right - that's the present value of the $50, because it's 1 year out.

And then I want the present value of the $35.

So that's plus $35 divided by what - it's 2 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.

Let's see, so the present value of the $20 payment is $20, plus the present value of the $50 payment.

Well that's just 50 divided by 1.05, plus the present value of our $35 payment.

35 divided by - and it's 2 years out, so we discount by our discount rate twice - so it's divided by 1.05 squared.

And then that is equal to - we'll round it - $99.37.

So now 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 for years a, b, and c, and I'll pay you that in years 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 it.

You present value all of the payments and you say well what is that worth to me today.

And here we did that. We said well actually choice number one is the best deal.

And it just depended on how the mathematics work out.

If I lowered 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.

번역 0% 대기중

Present Value 2발음듣기

다른 번역문 등록

Now I'll give you a slightly more complicated choice between two payment options.발음듣기

다른 번역문 등록

Both of them are good, because in either case you're getting money.발음듣기

다른 번역문 등록

So choice one. Today I will give you $100.발음듣기

다른 번역문 등록

I'll circle the payment when you get it in magenta.발음듣기

다른 번역문 등록

So today you get $100. Choice two.발음듣기

다른 번역문 등록

And I'll try to write this choice a little bit neater.발음듣기

다른 번역문 등록

Choice two is that not in 1 year, but in 2 years.발음듣기

다른 번역문 등록

So let's say this is year 1.발음듣기

다른 번역문 등록

And now this is year 2.발음듣기

다른 번역문 등록

Actually I'm going to give you three choices.발음듣기

다른 번역문 등록

That'll really hopefully hit things home.발음듣기

다른 번역문 등록

So actually let me scoot this choice two over to the left.발음듣기

다른 번역문 등록

Back to green. So now I'm back in business.발음듣기

다른 번역문 등록

So choice two, I am willing to give you, let's say, oh I don't know, $110 in 2 years.발음듣기

다른 번역문 등록

So not in 1 year. In 2 years I'm going to give you $110.발음듣기

다른 번역문 등록

And so I'll circle in magenta when you actually get your payment.발음듣기

다른 번역문 등록

And then choice 3. And choice 3 is going to be fascinating.발음듣기

다른 번역문 등록

I've done it in a slightly different shade of green.발음듣기

다른 번역문 등록

Choice 3, 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.발음듣기

다른 번역문 등록

I'm going to pay you $50 in 1 year.발음듣기

다른 번역문 등록

That's $70. Let me make this so it's close.발음듣기

다른 번역문 등록

And then I'm going to pay you - I don't know - $35 in year 3.발음듣기

다른 번역문 등록

So all of these are payments.발음듣기

다른 번역문 등록

I want to differentiate between the actual dollar payments and the present values.발음듣기

다른 번역문 등록

And just for the sake of simplicity, let's assume that I am guaranteed.발음듣기

다른 번역문 등록

I am the safest person available.발음듣기

다른 번역문 등록

If the world exists, if the sun does not supernova, I will be paying you this amount of money.발음듣기

다른 번역문 등록

So I'm as risk-free as the federal government.발음듣기

다른 번역문 등록

And I had a post on the previous present value, where someone talked about, well is the federal government really that safe?발음듣기

다른 번역문 등록

And this is the point. The federal government, when it borrows from you, say, $100 - Let's say it borrows $100 and it promises to pay it in a year.발음듣기

다른 번역문 등록

It'll give you that $100. The risk is, what is that $100 worth?발음듣기

다른 번역문 등록

Because they might inflate the currency to death.발음듣기

다른 번역문 등록

Anyway, I won't go into that right now.발음듣기

다른 번역문 등록

Let's just go back to this present value problem.발음듣기

다른 번역문 등록

And actually sometimes governments do default on debt.발음듣기

다른 번역문 등록

But the U.S. government has never defaulted.발음듣기

다른 번역문 등록

It has inflated its currency. So that's kind of a roundabout way of defaulting.발음듣기

다른 번역문 등록

But it has 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.발음듣기

다른 번역문 등록

Anyway, back to this problem. Enough commentary from Sal.발음듣기

다른 번역문 등록

So let's just compare Choice 1 and Choice 2 again.발음듣기

다른 번역문 등록

And once, again let's say that - risk-free - I could put money - I could lend it to the federal government at 5%.발음듣기

다른 번역문 등록

And it doesn't matter over what - WRITING: Risk-free rate is 5%.발음듣기

다른 번역문 등록

And for the sake of simplicity - in the next video I will make that assumption less simple--발음듣기

다른 번역문 등록

So if I had $100, what would that be worth in 1 year?발음듣기

다른 번역문 등록

We figured that out already. It's 100 times 1.05.발음듣기

다른 번역문 등록

So that's $105. And then if you got another 5%?발음듣기

다른 번역문 등록

So the government is giving you 5% per year.발음듣기

다른 번역문 등록

It would be 105 times 1.05.발음듣기

다른 번역문 등록

And what is that? So I have 105 times 1.05, which equals $110.25.발음듣기

다른 번역문 등록

So that is the value in 2 years.발음듣기

다른 번역문 등록

So immediately, without even doing any present value, we see that you'll actually be better off in 2 years if you were to take the money now and just lend it to the government.발음듣기

다른 번역문 등록

Because the government, risk-free, will give you $110.25 in 2 years, while I'm only willing to give you $110.발음듣기

다른 번역문 등록

So that's all fair and good.발음듣기

다른 번역문 등록

But the whole topic, what we're trying to solve, is present value.발음듣기

다른 번역문 등록

So let's take everything in today's money.발음듣기

다른 번역문 등록

And to take this $110 and say what is that worth today, we can just discount it backwards by the same method, right?발음듣기

다른 번역문 등록

So $110 in 2 years, what is its 1-year value?발음듣기

다른 번역문 등록

Well, you take $110 and you divide it by 1.05.발음듣기

다른 번역문 등록

You're just doing the reverse. And then you get some number here.발음듣기

다른 번역문 등록

Well that number you get is 110 divided by 1.05.발음듣기

다른 번역문 등록

And then to get its present value, its value today, you divide that by 1.05 again.발음듣기

다른 번역문 등록

So you get 110 divided. If I were to divide by 1.05 again what do I get?발음듣기

다른 번역문 등록

I divide by 1.05, and then I divide by 1.05 again.발음듣기

다른 번역문 등록

I'm dividing by 1.05 squared. And what does that equal?발음듣기

다른 번역문 등록

And I'm writing this on purpose, because I want to get you used to this notation.발음듣기

다른 번역문 등록

And that's all we're doing though, we're just dividing by 1.05 twice because we're 2 years out.발음듣기

다른 번역문 등록

So let's do that. 110 divided by 1.05 squared is equal to $99.77.발음듣기

다른 번역문 등록

So once again we have verified, by taking the present value of $110 in 2 years to today, that its present value - if we assume a 5% discount rate.발음듣기

다른 번역문 등록

And this discount rate, this is where all of the fudge factor occurs in finance.발음듣기

다른 번역문 등록

You can tweak that discount rate and make a few assumptions in discount rate and pretty much assume anything.발음듣기

다른 번역문 등록

But right now, for simplification, we're assuming a risk-free discount rate.발음듣기

다른 번역문 등록

But when the present value is based on that, you get $99.77.발음듣기

다른 번역문 등록

You say, wow, yeah, this really isn't as good as this.발음듣기

다른 번역문 등록

I would rather have $100 today than $99.77 today.발음듣기

다른 번역문 등록

Now this is interesting. Choice number three.발음듣기

다른 번역문 등록

How do we look at this?발음듣기

다른 번역문 등록

Well what we do is, we present value each of the payments, right?발음듣기

다른 번역문 등록

So the present value of $20 today, well that's just $20.발음듣기

다른 번역문 등록

What's the present value of $50 in 1 year?발음듣기

다른 번역문 등록

Well the present value of that is going to be - so plus $50 divided by 1.05, right - that's the present value of the $50, because it's 1 year out.발음듣기

다른 번역문 등록

And then I want the present value of the $35.발음듣기

다른 번역문 등록

So that's plus $35 divided by what - it's 2 years out, right, so you have to discount it twice - divided by 1.05 squared.발음듣기

다른 번역문 등록

Just like we did here. So let's figure out what that present value is.발음듣기

다른 번역문 등록

Notice I'm just adding up the present values of each of those payments.발음듣기

다른 번역문 등록

Get out my virtual TI-85.발음듣기

다른 번역문 등록

Let's see, so the present value of the $20 payment is $20, plus the present value of the $50 payment.발음듣기

다른 번역문 등록

Well that's just 50 divided by 1.05, plus the present value of our $35 payment.발음듣기

다른 번역문 등록

35 divided by - and it's 2 years out, so we discount by our discount rate twice - so it's divided by 1.05 squared.발음듣기

다른 번역문 등록

And then that is equal to - we'll round it - $99.37.발음듣기

다른 번역문 등록

So now we can make a very good comparison between the three options.발음듣기

다른 번역문 등록

This might have been confusing before.발음듣기

다른 번역문 등록

You know, you have this guy coming up to you.발음듣기

다른 번역문 등록

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 for years a, b, and c, and I'll pay you that in years b, c, and d.발음듣기