# Dictionary Definition

perpetuity n : the property of being perpetual
(seemingly ceaseless) [syn: sempiternity]

# User Contributed Dictionary

## English

### Noun

- The quality or state of being perpetual; endless duration; uninterrupted existence.
- Something that is perpetual.
- A limitation intended to be unalterable and of indefinite duration; a disposition of property which attempts to make it inalienable beyond certain limits fixed or conceived as being fixed by the general law.
- An annuity in which the periodic payments begin on a fixed date and continue indefinitely.

### References

# Extensive Definition

A perpetuity is an annuity
that has no definite end, or a stream of cash payments that
continues forever. There are few actual perpetuities in existence
(although the British government has issued them in the past, and
they are known and still trade as consols). A number of types of
investments are effectively perpetuities, such as real estate and
common stock, and techniques for valuing a perpetuity can be
applied to establish price. Perpetuities are but one of the
time value of money methods for valuing financial assets.

## Detailed description

A perpetuity is an annuity in which the periodic payments begin on a fixed date and continue indefinitely. It is sometimes referred to as a "perpetual annuity". Fixed coupon payments on permanently invested (irredeemable) sums of money are prime examples of perpetuities. Scholarships paid perpetually from an endowment fit the definition of perpetuity.The value of the perpetuity is finite because
receipts that are anticipated far in the future have extremely low
present value (present
value of the future cash flows). Unlike a typical bond, because
the principal
is never repaid, there is no present value for the principal. The
price of a perpetuity is simply the coupon amount over the
appropriate discount rate
or yield, that is

- PV \ = \

Where PV = Present Value of the Perpetuity, A =
the Amount of the periodic payment, and r = yield , discount
rate or interest
rate.

To give a numerical example, a 3% UK government
War Loan will trade at 50 pence per pound in a yield environment of
6%, while at 3% yield it is trading at par. That is, if the face
value of the Loan is £100 and the annual payment £3, the value of
the Loan is £50 when market interest rates are 6%, and £100 when
they are 3%.

## Real-life examples

For example, UK government bonds, called consols, that are undated and
irredeemable (e.g. War Loan) pay fixed coupons (interest payments)
and trade actively in the bond market. Very long dated bonds have
financial characteristics that can appeal to some investors and in
some circumstances, e.g. long-dated bonds have prices that change
rapidly (either up or down) when yields change (fall or rise) in
the financial markets.

A more current example is the convention used in
real estate finance for valuing real estate with a cap rate. Using
a cap rate, the value of a particular real estate asset is either
the net
income or the net cash
flow of the property, divided by the cap rate. Effectively, the
use of a cap rate to value a piece of real estate assumes that the
current income from the property continues in perpetuity.
Underlying this valuation is the assumption that rents will rise at
the same rate as inflation. Although the property may be sold in
future (or even the very near future), the assumption is that other
investors will apply the same valuation approach to the
property.

Another example is the constant growth Dividend
Discount Model for the valuation of the common stock of a
corporation, which assumes that the market price per share is equal
to the discounted stream of all future dividends, which is assumed
to be perpetual. If the discount rate for stocks (shares) with this
level of systematic
risk is 12.50%, then a constant perpetuity of per dollar of
dividend income is eight dollars. However if the future dividends
represent a perpetuity increasing at 5.00% per year, then the
Dividend Discount Model, in effect, subtracts 5.00% off the
discount rate of 12.50% for 7.50% implying that the price per
dollar of income is $13.33..

perpetuity in Dutch: Perpetuïteit

perpetuity in German: Ewige Rente

# Synonyms, Antonyms and Related Words

abidingness, age, all-comprehensiveness,
all-inclusiveness, antiquity, boundlessness, ceaselessness, chattering, constancy, constant flow,
continualness,
continuance,
continuity, countlessness, defeat of
time, defiance of time, distance, diuturnity, durability, durableness, duration, endlessness, endurance, eternity, exhaustlessness,
extension, extent, forever, illimitability, immeasurability,
immensity, incalculability,
incessancy, incomprehensibility,
inexhaustibility,
infiniteness,
infinitude, infinity, innumerability, interminability,
lastingness,
length, lengthiness, limitlessness, linear
measures, long standing, long time, long-lastingness,
long-livedness, longevity, longitude, longness, maintenance, measure, measurelessness,
mileage, noninterruption,
numberlessness,
oscillation, overall
length, perdurability, perennation, permanence, persistence, pulsation, quick fire, rapid
fire, rapid recurrence, rapid succession, rapidity, reach, regularity, repetition, span, stability, staccato, standing, steadfastness, steadiness, stretch, stuttering, survival, survivance, sustainment, tattoo, termlessness, timelessness, unintermission, uninterruption, universality, unmeasurability,
vibration, world
without end, yardage