Net-Present-Value Calculation Question

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Farmer Brown's picture
Farmer Brown
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Net-Present-Value Calculation Question

I posted this within another thread and did not receive a reply.  I'm trying to convince a skeptic that the debt is closer to $50 trillion than it is to $10 trillion and it would help to know this.  I'd appreciate it if someone could help with this:

Quote:

I have a question regarding the approx. -$50 trillion net-present-value of social security, medicare and medicaid liabilities.

My queston is, over how many years was the NPV calculated?  If this
calculation goes out 50 years, then that would mean an annual shortfall
of about "only" $1 trillion (plus the interest not gained on the $50
trillion we currently don't have in the bank), whereas if it was
calculated going forward only 15 or 10 years, it would translate to a
shortfall of $3.3 to $5 trillion per year.  These are of course in
addition to the interest shortfall represented by not having the $50
trillion in the bank right now earning interest.  

Can somebody provide an answer to this, or show me where I may be
making a fundamental mistake in assumptions in arriving at this
question?   Of course I know that regardless of the time, these numbers
are disastrous.  

Thank you.

 

caroline_culbert's picture
caroline_culbert
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Re: Net-Present-Value Calculation Question

You're right that it's closer to 50 trillion since we DO NOT have the funds in our so-called Medicare and Social Security "funds".  Shouldn't "funds", by nature, contain money?  I mean, I could have a mutual fund portfolio but if there isn't any money in there, then can I still call it a mutual fund?

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Re: Net-Present-Value Calculation Question

 

Thanks Caroline. 

My actual question though is not wether we are behind $50 trillion - that I understand.

What I do not know is how the NPV calculation was made.  In the CC chapters 12 and 13, it is explained that the ss, medicare, and medicaid funds have an NPV of about negative $50 trillion.

It explains how NPV calculations are made, i.e.:  future cash inflows and outflows are added, and the result is brought back to present dollar values (using an assumed interest rate). 

My question is, for how many years going forward was the calculation made?  Probably Chris M is the only one that knows the answer on this one. 

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Re: Net-Present-Value Calculation Question

Yes, I've wondered that same thing. I don't have the dates and figures in front of me, but if I recall correctly the last (GAO?) estimate was that Medicare is dipping into the "trust fund" (which is already fictional) right now and will have to come completely out of general revenues in something like 2022, while the corresponding dates for Soc Sec are 2017 and 2041 or something like that. So as far as official government accounting goes, they don't become unfunded liablities until 2022 and 2041 respectively, although for our Crash Course purposes they really do so now and in 2017, since the trust fund doesn't really exist, it's just an IOU (I still remember that funny photo Chris put in the CC of Bush holding that binder).

So over how many years does this $50 trillion accrue? I guess that's simple accounting, with the Medicare starting now or last year, and SS in 2017 or so. I don't know about Medicaid.

  

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Re: Net-Present-Value Calculation Question

Hello Patrick,

Looking on Wikipedia, it would appear to be 75 years, so current NPV would be for the period 2009-2084 . See the unfunded Obligations section. As of September last year the total obligation was $53 trn.

http://en.wikipedia.org/wiki/United_States_public_debt#Calculating_and_projecting_the_debt

If anyone has a different figure I'm as keen as Patrick to know.

David

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Re: Net-Present-Value Calculation Question

Thanks, David! 

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Re: Net-Present-Value Calculation Question

Hi Bill.

Your friend has confused the issue a bit.  That's not really how NPV calculations work.

An NPV calculation already has all the future cash flows accounted for and the $50 trillion is a number that applies to today and today only.  Next year it will be a much larger number unless the principal balance is paid down with a kicker for the assumed rate of interest.

Perhaps this will help.  For the past 10 years the NPV value of the liability has expanded by more than $33 trillion.  This was during periods of both growth and recession - so it was probably a pretty good approximation of how the liability changes on a yearly basis without any paydown activity by the government.  

This means that the NPV liability was expanding by some $3.3 trillion a year.  

Using that as a crude baseline, we can roughly estimate that the underlying liability is expanding by some 6% or more per year currently.

We might think of this as the implied discount rate for the NPV calculation, although I admit both that this is crude and that I do not know what the actual rate was that the government used to derive the $53 trillion liability (although I would guess that it is lower than 6%).

This is a long way of saying that one cannot simply take the time horizon of the NPV calculation and divide it into the current liability to find out how much the yearly payment would be....this isn't a mortgage, it's a moving target.

To make this point in a silly way, but not entirely, let me point out that most NPV calculations only go forward 7 to 10 years and then assign everything after that into a "terminal value" bucket that stretches into infinity.  This can be done because future dollars become so negligible after a while due to the accumulated impact of the discount rate that they can be effectively ignored. And so theyoften are.

But using your friends logic, we can divide the current liability by infinity and find out we owe almost nothing at all on a yearly basis.  Obviously, this is not quite the right way to think about this.

Hope that helps.

Best,
Chris

 

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Re: Net-Present-Value Calculation Question

Hi Patrick,

How are things in CR?

Just to follow-up more quantitatively in case anyone cares:

The NPV of a stream of payments "P" that goes out into infinity is:

NPV = P*S

Where S=r/(1-r) and r=1/(1+i), with "i" being your discount rate. That gives you a reference as the payments "P" aren't really equal...

On a side topic, this calculation is also related with the loss of capital experienced by productive companies in an environment of unstable and declining interest rates, as the present value of their debt and any stream of payments increases. Just look how sensitive this is with respect to "i".

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Re: Net-Present-Value Calculation Question
mred wrote:

Hi Patrick,

How are things in CR?

Just to follow-up more quantitatively in case anyone cares:

The NPV of a stream of payments "P" that goes out into infinity is:

NPV = P*S

Where S=r/(1-r) and r=1/(1+i), with "i" being your discount rate. That gives you a reference as the payments "P" aren't really equal...

On a side topic, this calculation is also related with the loss of capital experienced by productive companies in an environment of unstable and declining interest rates, as the present value of their debt and any stream of payments increases. Just look how sensitive this is with respect to "i".

sorry... what does 1 represent?  Just trying to figure out the math.  Does 1 represent "infinity"?

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Re: Net-Present-Value Calculation Question

 

Thanks very much, Chris.

What does this mean in terms of the NPV calculation made in Chapter 12 (or maybe it was 13):  i.e., was this taken out "to infinity", or was a 7-10 year horizon used, or was this provided by the government and so we really don't know?

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Re: Net-Present-Value Calculation Question

mred,

Thanks.  Now I have a headache.  One question:  if i = the discount rate, how would that rate be expressed in the formula?  That is if I'm using 6%, do I plug in "6" or "0.06"?

CR is great.  We got used to run away inflation and unpayable debts a long time ago.  The way we fixed them was by... borrowing money from you guys, or guaranteed by you guys!  So, guess that's out now.  Anyway, it is nice.  Don't think I'd want to be anywhere else when the SHTF. 

Cheers,

 

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Re: Net-Present-Value Calculation Question
Patrick Brown wrote:

mred,

Thanks.  Now I have a headache.  One question:  if i = the discount rate, how would that rate be expressed in the formula?  That is if I'm using 6%, do I plug in "6" or "0.06"?

CR is great.  We got used to run away inflation and unpayable debts a long time ago.  The way we fixed them was by... borrowing money from you guys, or guaranteed by you guys!  So, guess that's out now.  Anyway, it is nice.  Don't think I'd want to be anywhere else when the SHTF. 

Cheers,

 

your "rate" means percentage and thereby you would use .06 (which is the same as 6%).  You wouldn't use '6' since '6' is greater than 1.  Percentage always reflects 0-1.

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Re: Net-Present-Value Calculation Question

So mred and Caroline,

If my flow of payments is $1,000/yr and the discount rate is 6%/yr, would the NPV = $16,666.658?

Do I get a gold star? 

This is really cool!  Now I know what to say when people ask if they can "pay me tomorrow".

 

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Re: Net-Present-Value Calculation Question

I think your N-P-Value is 15.6933

That's not much current (right now) value.

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caroline_culbert
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Re: Net-Present-Value Calculation Question

mred wrote: 

NPV = P*S

Where S=r/(1-r) and r=1/(1+i), with "i" being your discount rate. That gives you a reference as the payments "P" aren't really equal... [end quote]

 

r = 1 / 1+i

r = 1 / 1+.06

r = 1 / 1.06

r =  .9433

S = .9433 / 1-.9433

S = .9433 / .0567

S = 16.6366

NPV = P x 16.6366

NPV = 1000 x 16.6366

NPV = 16,636

 

Sorry... did the math again and got the same as you did.

 

 

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Re: Net-Present-Value Calculation Question

You both get A+   ;-)

You can check yourselves that that amount in the example, $16,636 and change is exactly what is needed to generate a $1,000 interest at 6%, so the stream of $1k payments could be maintained forever, at least in principle. Caroline, are you still philosophizing about the meaning of the symbols? There is no black magic there, the "1" stands for one, as you showed in your calculation. The only trick is that one can express some infinite sums in one number because, as CM said, the contributions of the terms get smaller and smaller. Just like you can add 1/2 + 1/4 + 1/8 + 1/16 + ... (forever) and get: 1

CR has the strength that it can be self-sufficient in food relatively easily and that it has quite a bit of hydro power. With foresight, the transportation fleet could be converted to electric when oil makes its run. It is in the "foresight" part where I have my doubts...How long have you lived there? 

 

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Re: Net-Present-Value Calculation Question

Given the argument I gave in my last post, I noticed one can get the same result by simply doing

NPV=P/i

embarrassing... so I get the F...

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Re: Net-Present-Value Calculation Question

... and the difference in the result is only due to roundoff error in the long form of the calculation. Embarassed

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Re: Net-Present-Value Calculation Question

This also agrees perfectly with what Chris noted above.  If you solve for P and use a NPV of $50 trillion, you get a P value of about $3 trillion, which is what Chris estimated.

Back to CR:  Yes, the hydroelectric power  (96%) is near the top of my list.  It also has a very moderate climate.  Most parts of the country do not need air conditioning or heating.  Also very fertile (in case the name Rich Coast didn't give it away).  As for powering cars, you got that one right.  We are totally dependent on foreign oil for our vehicles, but as you pointed out, solutions for that are already here, it's just a matter of getting the price down.  I was born and raised here, but I have a very "American" upbringing: my Dad is from Missouri, my mom is CR.  I went to and American school in CR and attended college at WPI in Worcester, MA, and stayed in the US another 11 yrs after college working in this that and the other.  I've been back in CR going on 5 years.

Nice to meet you, mred.

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Re: Net-Present-Value Calculation Question

Oh man, you had me fooled... you're a tico for real!

So you are the perfect person to ask this: have you been able to get physical gold in CR? If so, where?

Nice to meet you too, Patrick.

 

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Re: Net-Present-Value Calculation Question

haha.  I wish I knew where to buy gold here.  If you happen to find out, let me know.  Sounds like you've been here or are here or have some familiarity.  You can always buy it elsewhere and bring it in, as long as it's less than $10k worth per person.  Better hurry up before $10k can only buy a couple of ounces.

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Re: Net-Present-Value Calculation Question

Hello --

 I have a slightly different question on the net present value.  I can't tell if the NPV of future entitlement liabilities takes account of the NPV of future income.

Let me use a a simpler example to explain my question.

 I pay a certain amount of rent every month,  and assuming that I am going to stay in the same place and keep renting, you could do a (for instance) 30 year NPV of my future rents and determine that I am bankrupt!

But I'm not bankrupt, because for that entire 30 years I will be earning enough income to pay the rent.  So you have to compare the NPV of future rents to the NPV of future earnings.

So my question is: shouldn't that $50 trillion NPV of future liabilities be compared to the NPV of future national income, or tax revenue, or something like that?  Or is it already accounting for that somehow?

 Thanks!

Rich

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Farmer Brown
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Re: Net-Present-Value Calculation Question

Rich,

The NPV calculations that result in -$50 trillion do already take into account future cashflows - both positive and negative.  See Chapter 11-13 in the CC.   I had the same queston though at one point.

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drhilarius
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Re: Net-Present-Value Calculation Question

Thanks Patrick.  Sorry if that went over my head; I will review those chapters again to make sure i get it...

 Thanks again,

Rich

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