Just asking questions to the air, but if anyone knows the answer I’d love to know!
It sounds weird but it's not a bad idea, no. In essence an infinite set of future payments has a finite present value, due to inflation.
i.e., suppose inflation is 100%, this means prices will double every year, and the real value of a nominal amount will halven every year. So $100 today, will be worth $50 (in today's money) in a year from now. A year later (2 years), a $100 then will be worth $25 in today's money. Another year later (3 years) it'd be worth $12.5. And so on.
As you can see, a nominal future payment, say $100 in 300 years, will start to approach zero.
Of course interest rates aren't quite that high, but it's just to get the point across. The interest rate is essentially a discount rate, which lets you value a future amount of money, in today's prices. In the above example, $100 in 3 years would be worth 100 / 2^3 = 12.5
This means that an infinite series of payments (perpetuity) can be calculated as well by simply taking the payment divided by the interest rate to discount it with. So at an interest rate of say 5%, a $100 per year infinitely, would be worth $2000 today.
In other words, in a world with 5% interest rates, you'd be indifferent to receive $2000 today, or $100 ad infinitum. They have the same present value.
Is it really due to inflation?
Even without inflation, wouldn't there still be interest on loans to compensate the lender for not having the use of their money and for the risk that the loan will not be paid back. The present value of a future payment would thus still be discounted, and a stream of payments under a fixed interest rate would still lead to a convergent geometric series for the present value of the total stream.
In finance interest rates are typically used for the discount rate. But discount rates can be something else that's not directly related to interest rates, too.
For example, suppose I buy gold and it appreciates in value by 10% per year. You could in a way call that inflation (inflation of the price of gold, typically due to inflation of the money supply). And if you were to calculate the value of x amount of gold in one year, in this case you'd use the inflation rate of 10% to discount it to the present value.
I should've said discount rates, and in general discussions it's fine to speak of interest rates. Should not have mentioned inflation as it's confusing and often different from the discount rate.
Inflation counts, but this would still be true in the presence of strong deflation. A set of future payments has a finite present value due to the fact that the same amount of purchasing power is worth less in the future than it is right now, "time discounting".
Now I agree that as such money now is somewhat more valuable than money later in nominal terms simply due to the uncertainty of the future, and it's probably unwise to bet on everlasting strong deflation, but at least in the short or medium term I'd say strong deflation could certainly overcome even these built-in inflationary tendencies.
Yes, it does.
> Deflation means precisely that money will be worth more in the future than it is now
Deflation means that $X in the future will have more purchasing power in the future than $X has now.
It does not mean that the money will be worth more in the future than it is worth now; these are different concepts. You'll note that my comment says "the same amount of purchasing power is worth less in the future than it is right now". By the same token, more purchasing power in the future may still be worth less than less purchasing power right now.
People like to slam the intrinsic value of gold by saying "you can't eat gold". But even in the sense in which you can eat gold, you can't eat gold you don't have. The uncertainty of the future is one reason why money in the future is worth less than money in the present, but the bigger reason is option value. You can hold present money and spend it in the future. You cannot pre-realize future money and spend it in the present.
i'd conjecture that we could increase the number of economic friction knobs appropriately to easily get the real inflation rate under 1%, but we don't because that would lessen the advantage the already moneyed and their political appendages have with the current system.
Yeah about that..
Looks right, but do you have a proof?
S = sum from (i=1) to infinity of [a^i]
we can then multiply by a on each side:
aS = sum from (i=1) to infinity of [a^(i+1)]
Simplify/cancel out to:
aS = S - a
a = S(1 - a)
S = a / (1 - a)
where a = 1 / (1 + R)
so $100 perpetuity with R = 5%:
a = 1 / (1 + 0.05) = 1 / (1.05)
$100 x (1/1.05) / (1 - (1/1.05)) = $100 x 1 / (1.05 - 1) = $100 / 0.05
= $100 / 5%
= $2000
S = P (1+i)^n
P - Principal
S - Sum
i - interest rate p.a.
n - the number of years
A bond is a type of negotiable instrument, and laws regarding negotiable instruments--which also include checks, letters of credit, mortgages, etc--go back to at least the Medieval period in their literal terms, and in general terms to the Lex Mercatoria (i.e. merchant laws of the Mediterranean trading nations, including the Roman Empire, that were organically preserved through the Medieval period and even up to today). Other commercialized civilizations also had substantially similar laws. Bonds are a relatively safe investment for more than the reasons commonly recited today--e.g. hedging market volatility, etc.
There is a wiki on it which says “ Perpetual bond, which is also known as a perpetual or just a perp, is a bond with no maturity date. Therefore, it may be treated as equity, not as debt.”
However the wiki notes that they have no voting rights so aren’t as good as equity.
But in bankruptcy, they get paid after other creditors. The payments are dividends which may have tax advantages/disadvantages.
Replace water board with board of directors and interest payment with dividend and nobody would bat an eye at the perpetual aspect.
The big difference is that stock certificates usually don't have dividend entitlements outlined on them, while bonds do. However, historically, stock certificates could have either face values or distribution entitlements listed directly. Especially stocks in railways.
The disadvantage is that bonds do not just entitle you to periodic coupon payments, but also give you rights according to the face value of the bond in bankruptcy proceedings. Selling bonds far from the "par" you are theoretically owed in bankruptcy has big problems - either the bond is trading above par and you risk not being made "whole", or it is below par and the company is selling bankruptcy liabilities on their assets for pennies on the dollar. The movement of interest rates over time guarantees that one of these situations will eventually hold, so either issuers or buyers will want to adjust the nominal yield (and thus par value), resulting in the loss of interchangeability.
Notably, the US government has zero risk of being able to pay its nominal obligations, so is a prime candidate for issuing perpetuals in a way that corporations cannot. Currently, if you buy a new 20-year treasury bond and wait 2 years, you end up with an off-the-run bond that is difficult to efficiently trade. It'd be much better if these instruments did not "expire" as such, and the increased usefulness to investors would wind up reflected in lower financing costs for the government. Theoretically, the entire US treasury bond structure could be replaced with a zero-duration overnight interest account, a perpetual that pays a $1 coupon per day, and an inflation-linked perpetual that pays the CPI as coupon.
This is often forgotten when people say 'but the state can get 0.01% interest loans!'. Sure, true, but if the rate goes to 5%, that 3xGNP loan becomes quite cumbersome to service.
At 2.5% fixed forever perhaps it's interesting to keep. Also, I suppose that there are not many bonds that survive 367 year. So a lot of the debt 'disappears' as time goes on.
Some context: I could only go 5% down but wanted to avoid PMI, so the other 15% for 20% down on the first mortgage was taken from a 2nd mortgage, which had the perpetual terms. It's more commonly known as an interest-only payment loan. The interest rate is adjustable and I only pay the monthly accumulated interest.
I give you money to be a part of something, and collect a royalty into perpetuity.
Or, it's even more like buying land under a building.
I sell the land under my building to get some quick cash. And in turn agree to lease the land back from the new owner permanently.
Depending on how badly I need the money, it may be my best and only choice...
As long as the perpetual interest are lower than the inflation, then it make sense.
I'd imagine all debt so marked in German marks before the German hyperinflation in 1920s gets essentially wiped this way.
Let's say I need $1000 now. I'd like to borrow it, and I'm willing to pay some amount of money back over time to obtain it. Money now is more valuable than money later, so I know the payments will sum to more than $1000. You have some cash on hand right now, and you'd like it to be larger; you're willing to lose access to it for a while in order to get more money later. Let's say I'm a SUPER trustworthy borrower, and that SUPER trustworthy borrowers generally borrow at 2% per year right now.
Here are some options that we would expect I (as the borrower) and you (as the lender) would find fairly equivalent:
1. You give me $1000 now, I give you $1,040.78 in 2 years.
2. You give me $1000 now, I give you $20 every month, and $551.46 in 2 years.
3. You give me $1000 now, I give you $17.53 every month for 5 years.
4. You give me $1000 now, I give you $9.20 every month for 10 years.
5. You give me $1000 now, I give you $1.67 every month for 10 years, and $1000 in 10 years.
6. You give me $1000 now, I give you $5.06 every month for 20 years.
7. You give me $1000 now, I give you $1.93 every month for 100 years.
Excel has all these functions build in; provide all but one of the rate, the number of periods, the present value (aka PV, here, $1000), the future value (aka FV, the final payment at the end), and the periodic payment size, and it's simple math to calculate the missing value.
Note that these all have, at least in theory, an equivalent value. Less money sooner, versus more money later, with the tradeoff defined by the rate (here 2%). If you, as a borrower, look that that and go "I'd really prefer a shorter term" that means the correct rate (for you) should be higher, but if 2% is the right rate, all 7 options will seem about the same.
Modern bonds often have the same value for PV and FV (that is, you pay the face value back at the end), but every combination you can imagine exists in the real world, and much financial activity involves people with a payment stream structured one way getting it transformed into one structured another way.
One thing you might have noticed: As the period gets longer, the amount you'd need to pay each period gets smaller and smaller, but it's asymptotic to a value. If $1000 now is "worth" $1.93 a month for 100 years, it'd be "worth" $1.67 a month over 500 years. Or indeed, over 1000 years.
Turns out, the payment per period works out to the PV times the interest rate. 12% APR is ~0.1667% per month, and $1000 * 0.1667% = ~$1.67 per month.
That's the finance 101 calculation, at any rate. In the real world, there's always risk in various forms.
One other point: Did you notice that the interest payment on the perpetuity was $1.67, same as for the "standard" 10 year bond? (And note, bond term doesn't matter here; it's the same for 1 year, 5 years, or 20 years.) That's not a coincidence, because they're economically equivalent (ignoring risk, liquidity, etc.). In fact, consider that as practical matter, most bonds issued by national governments will never, ever really be paid off. Instead, as they come due, they are "rolled". The principle for one lot of bonds is paid off by the issuing a new lot. But consider the math: Today I get $1000 by selling you a 5 year bond. Then every month for 5 years I pay $1.67 in interest. Then at the end of 5 years I issue a new bond for $1000 (which, let's say, you ALSO buy), and I use the proceeds to pay off the first bond. Then for 5 years I pay $1.67 in monthly interest, before we do it again. Ignoring the $1000 payments every 5 years, since they cancel out to $0, this borrowing deal is "I get $1000 now, then I pay $1.67 forever", which is...a perpetuity.
Conversely, if I did sell you a perpetuity, you could just sell it in 5 years. You'd expect to get $1000 when you sell a perpetuity on those terms, if interest rates haven't changed, so the cash flows for you buying and later selling a perpetuity is identical to buying a bond and holding it to maturity.
So in short: Not a bad idea, still happens ALL THE TIME, we just package it differently for various practical reasons.