[chillpenguin]

The TLDR for how a bond that continues to pay interest forever can be valued at less than infinity dollars is due to the "time value of money", which states that $X in the future is worth less than $X today. This makes sense intuitively if you consider that if you had that money today, you could invest it and earn interest on it.

So since money in your hands is worth more than that same amount of money in the future, you can actually calculate how much a future cash flow is worth today by discounting it to its present value ("discounted cash flow" aka DCF).

To bring it back to perpetual bonds, if you DCF all of the future cash flows to their present value, you actually get a finite number (due to the diminishing nature of the cash flows that are further and further in the future).

For those who want to learn this in more detail, I recommend MIT's OCW course "Finance Theory I" with Andrew Lo.

[slavboj]

Default risk (either outright or de facto) is also extremely present. Most countries (including the US, cf Roosevelt's abrogation of gold-denominated debt) have defaulted at various times.

[JumpCrisscross]

> including the US, cf Roosevelt's abrogation of gold-denominated debt

How is Roosevelt abrogating America’s gold standard a counterfactual to default risk?

[milkshakes]

https://en.m.wikipedia.org/wiki/Cf.

[JumpCrisscross]

Whoops! Thanks!

[pdog]

You don't need the concept of "time value of money" to value a perpetual stream of payments.

Intuitively, only a sucker would pay $1,000,000,000,000 for the promise of $1 per year in perpetuity, even in the absence of discounted cash flows.

[ohyoutravel]

Thanks for the explanation, I saw the formula in the OP for pricing it and it seemed like using that simple formula, the price should be infinity. I came to ask about that and your comment answered the would-be question. Thanks!

[JumpCrisscross]

> seemed like using that simple formula, the price should be infinity

Deriving the value of a perpetuity is simple but revealing [1].

[1] http://fahmi.ba.free.fr/docs/Courses/2012%20HEC/FBA_FE_Chap1...