You” re obtaining cash. 1 year, but in 2 years. Allow” s say this is year 1.
Option two over to the. Now I” m back in business. And then selection three.
And option 3 is going to be interesting. I ‘ ve done it in a slightly various color of green. Choice 3, I am mosting likely 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 $70. Let me make’this It ‘ s close.
And after that I ‘ m mosting likely to pay you, I don ‘ t understand,$ 35 in year 3. All of these are payments.
And this is the factor. Let” s say it borrows $100. The threat is, what is.
that $100 well worth? Since they might inflate.
the money to death. Anyhow, I won” t go
into. that now. Allow ‘ s simply go back to this. present worth problem.
And in fact sometimes. federal governments do default on debt. However the U.S. federal government.
has actually never ever skipped. It has inflated its money. To ensure that” s type of a round.
concerning way of defaulting. Its never ever in fact claimed,.
I will not pay you. Our since if that took place.
entire monetary system would certainly blow up and we would certainly all be.
Anyhow, back to this problem. Enough discourse from Sal.
federal government at 5%. Risk-free rate is 5%. And for simplicity–.
in the following video clip I will make that presumption less.
straightforward– yet for the purpose simplicity, the government will.
pay you 5% whether you provide the cash for 1 year,.
whether you provide them the cash for 2 years, or.
Whether you give them the money for 3 years? So if I had $100, what would.
that deserve in 1 year? We figured that out already.It ‘ s 100 times 1.05’. To ensure that” s$ 105.
If you got, and after that. one more 5%? The government is giving.
It would be 105 times 1.05. I have 105 times 1.05,.
which equals $110.25. So that is the value.
in 2 years. So quickly, without even.
doing any existing value, we see that you” ll actually be. If you were to take the money now, far better off in 2 years.
and just provide it to the federal government. Because the government,.
That” s all good and reasonable. Let” s take every little thing.
in today” s money. And to take this $110 and say.
what is that worth today, we can simply discount it backwards.
by the very same approach, right? $110 in 2 years, what.
is its 1-year value? Well, you take $110 and.
you separate it by 1.05. You” re simply doing the opposite.
And then you get some. number right here.
Well that number you get. is 110 split by 1.05.
And after that to obtain its present. You obtain 110 split. I” m separating by 1.05 squared.
of separating by 1 plus the price cut price to the power of.
Several years out, this is what all of that” s. based on. We ‘ re just splitting by 1.05 twice because we ‘ re. Let ‘
s do that.
is equal to $99.77. So once again we have verified,.
by taking today value of $110 in 2. years to today, that its existing
worth– if we assume. a 5 % discount rate.
And this price cut price, this. is where every one of the fudge variable happens in finance. You can modify that discount.
price and make a few presumptions in price cut.
rate and practically think anything. Right now, for.
simplification, we” re assuming a risk-free price cut price. However when the present value is.
based upon that, you get $99.77. You state, wow, yeah, this truly.
isn” t as great
as this.I would certainly instead have $100 today.
than $99.77 today. Now this is intriguing. Option number three. Just how do we check out this? Well what we do is, we.
present worth each of the payments, right? The present value of $20.
today, well that” s simply $20.’What ‘ s the present worth. of $ 50 in 1 year? Well the present value of that. is mosting likely to be– so plus $50 separated by 1.05, right– that” s. the existing value of the $50, due to the fact that it” s. 1 year out. And after that I desire the here and now.
value of the $35. To ensure that” s plus $35 split by. what– it” s 2 years out, right, so you have to.
price cut it two times– split by 1.05 squared. Just like we did below. So allow” s identify what.
that present worth is. Notice I” m just building up the.
Let” s see, so the existing value.
of the $50 repayment. Well that” s simply 50 divided by.
1.05, plus the existing worth of our $35 payment. 35 separated by– and it” s 2 years.
we” ll round it– $99.37. Now we can make a very.
great contrast between the three choices. This might have been.
puzzling before. You understand, you have this.
individual coming up to you. And this man is usually in.
the type of some kind of retired life strategy or insurance.
company, where they claim, hey, you pay me this for years a,.
b, and c, and I” ll pay you that in years b, c, and d. And you” re like, boy, just how do I.
compare if that” s really a good value? Well this is how.
you compare it. You existing value every one of the.
repayments and you say well what is that worth to me today. And here we did that. We claimed well really selection.
primary is the most effective deal.And it simply depended upon how. the math job
out. If I reduced the price cut price,. if this discount price is lower, it could have changed. the outcomes.
And possibly I” ll really do that.
in the next video, simply to show you exactly how essential.
the discount rate is. Anyhow I” m out of time,.
and I” ll see you in the next video.
Let” s state this is year 1. I don ‘ t recognize,$ 35 in year 3. Let” s take whatever.
We ‘ re just dividing by 1.05 twice since we ‘ re. 35 separated by– and it” s 2 years.