참여번역 : 어학사전

Present Value 2발음듣기

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

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

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

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

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So today you get $100. Choice two.발음듣기

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

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

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So let's say this is year 1.발음듣기

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And now this is year 2.발음듣기

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

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That'll really hopefully hit things home.발음듣기

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

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

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

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

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

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

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

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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

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

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

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

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So all of these are payments.발음듣기

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

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

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I am the safest person available.발음듣기

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

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

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

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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

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

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Because they might inflate the currency to death.발음듣기

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

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

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And actually sometimes governments do default on debt.발음듣기

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

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

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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

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

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

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

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

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

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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?발음듣기

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

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

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

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

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It would be 105 times 1.05.발음듣기

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

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So that is the value in 2 years.발음듣기

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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

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

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So that's all fair and good.발음듣기

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

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

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

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

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

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

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

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

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

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

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

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

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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.발음듣기

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

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

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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

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

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

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

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

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

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

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Now this is interesting. Choice number three.발음듣기

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How do we look at this?발음듣기

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

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

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

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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

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

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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

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

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

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Get out my virtual TI-85.발음듣기

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

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

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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

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

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

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This might have been confusing before.발음듣기

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

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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

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And you're like, boy, how do I compare if that's really a good value?발음듣기

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Well this is how you compare it.발음듣기

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

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

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And it just depended on how the mathematics work out.발음듣기

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If I lowered the discount rate, if this discount rate is lower, it might have changed the outcomes.발음듣기

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And maybe I'll actually do that in the next video, just to show you how important the discount rate is.발음듣기

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Anyway I'm out of time, and I'll see you in the next video.발음듣기

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참여번역

Present Value 2

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