4

Both an annuity and a perpetuity pay a stream of income on a periodic basis. What is the difference from the beneficiary's point of view? Possible differences might be:

  • an annuity isn't payable until retirement
  • annuities can be inflation indexed; perpetuities can't
  • tax treatment of an annuity might be more favorable
  • annuities cease upon death, but perpetuities are transferable

Do perpetuity instruments even exist in the USA? I've heard of consol bonds in the UK only.

8

In the academic sense, an annuity is payable annually for a term of years and a perpetuity is payable annually forever. An annuity has an end date and a perpetuity does not.

Many commonly seen annuities are structured to pay until death of the recipient, which for the issuer can be averaged and anticipated using actuarial tables (i.e. the anticipated average number of years for the aggregate is known, even though individual payees may live longer or shorter lives). This is still analyzed as an annuity for a term of years.

An annuity may be payable upon retirement, but there's no financial reason you couldn't delay a perpetuity by a term of years. You'd value it as a perpetuity, but discount it for the future value based on the retirement date. I don't believe anybody does this currently. You could also index a perpetuity, but of course that would raise its cost to purchase at the front end.

Tax treatment of annuities can be favorable to the extent that insurance rules are more favorable than one might expect. But the payment of interest is generally ordinary income under IRC §61, whether it is payable every year or for a term of years.

The last difference you list is the actual rule. Perpetuities are payable forever, so do not cease with death. An annuity that ceases with death is payable only for a term of years (even though the term may not be known ahead of time for any individual annuitant). A perpetuity continues paying, so it's just a stream of income. Of course, perpetuities could be called back by the issuer in exchange for some value (possibly a cash settlement sum or determined by a formula), which terminates the perpetuity obligation. But the mathematical valuation is still based on the idea of endless payment.

Annuity valuation: annuity formula

Perpetuity valuation: perpetuity formula

  • Thank you, that's a good answer. Do any perpetuity instruments exist in the USA? – Ellie Kesselman May 8 '14 at 23:03
  • 1
    I don't know of any generally offered perpetuities. Theoretically, you could pay a counterparty to package a bond ladder and pay you part of that (waste of your money) or try for a constant-dividend stock. A perpetuity-like investment would have a premium for the rate risk; it would make more sense to get other investments. It would also produce a stream of interest taxable currently at ordinary rates rather than appreciation of value with deferred taxation at capital rates. There are also testamentary tax planning concerns that advantage capital assets versus income-producing assets. – NL7 May 9 '14 at 13:43
  • 1
    Note that the common law "Rule Against Perpetuities" does not directly implicate financial perpetuities. The RAP (where it still exists) forbids testamentary future interests that will not vest (or fail) within a stated timeframe (classically, all lives in being plus 21 years). It's the same word but a different technical concept. – NL7 May 9 '14 at 13:48
  • 1
    @EllieKesselman Also note that assuming the interest rate used to calculate a perpetuity is around 7%, 75% of the value of a perpetuity is received within 20 years (and about 95% of the value is received within 40 years). Therefore within the span of a lifetime, an annuity that ceases on death may be theoretically worth nearly the same amount as a perpetuity. – Grade 'Eh' Bacon Jun 28 '16 at 13:55
1

The British government issued perpetual redeemable bonds called Consols to fund the government and various wars in the 18th Century. The first Consols were issued in 1751 and technically could still be kicking around if the government hadn't redeemed them all!

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.