Perpetuity

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Perpetuity

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 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

:$PV = \left\{A over r\right\}$

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..

ee also

*Time value of money
*Present value
*Geometric progression
*Consols
*Perpetual bond

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• perpetuity — per·pe·tu·i·ty /ˌpər pə tü ə tē, tyü / n pl ties 1: the quality, state, or duration of being perpetual devised to them in perpetuity 2 a: the condition of a future estate limited in such a way as not to vest within the period fixed by law for the …   Law dictionary

• Perpetuity — Per pe*tu i*ty, n. [L. perpetuitas: cf. F. perp[ e]tuit[ e].] 1. The quality or state of being perpetual; as, the perpetuity of laws. Bacon. [1913 Webster] A path to perpetuity of fame. Byron. [1913 Webster] The perpetuity of single emotion is… …   The Collaborative International Dictionary of English

• perpetuity — ► NOUN (pl. perpetuities) 1) the state or quality of lasting forever. 2) a bond or other security with no fixed maturity date. ● in (or for) perpetuity Cf. ↑in perpetuity …   English terms dictionary

• perpetuity — [pʉr΄pə to͞o′ə tē, pʉr΄pətyo͞o′ə tē] n. pl. perpetuities [ME perpetuite < OFr perpetuité < L perpetuitas] 1. the state or quality of being perpetual 2. something perpetual, as an annuity or pension to be paid indefinitely or, often specif …   English World dictionary

• Perpetuity — A constant stream of identical cash flows without end, such as a British consol. The New York Times Financial Glossary * * * perpetuity per‧pe‧tu‧i‧ty [ˌpɜːpˈtjuːti ǁ ˌpɜːrpˈtuː ] noun in perpetuity LAW for all future time: • The contract… …   Financial and business terms

• perpetuity — A constant stream of identical cash flows without end, such as a British consol. Bloomberg Financial Dictionary * * * perpetuity per‧pe‧tu‧i‧ty [ˌpɜːpˈtjuːti ǁ ˌpɜːrpˈtuː ] noun in perpetuity LAW for all future time: • The contract allows them …   Financial and business terms

• Perpetuity — (Roget s Thesaurus) >Endless duration. < N PARAG:Perpetuity >N GRP: N 1 Sgm: N 1 perpetuity perpetuity eternity everness aye sempiternity immortality athanasia Sgm: N 1 interminability interminability agelessness everlastingness …   English dictionary for students

• Perpetuity — A constant stream of identical cash flows with no end. The formula for determining the present value of a perpetuity is as follows: This is not as abstract a concept as you may think; the British issued bonds, called consols, which are a great… …   Investment dictionary

• perpetuity — n. in perpetuity ( forever ) * * * [ˌpɜːpɪ tjuːɪtɪ] in perpetuity ( forever ) …   Combinatory dictionary

• perpetuity — I (New American Roget s College Thesaurus) Endless duration Nouns perpetuity; everlastingness, unceasingness, etc.; eternity, infinity, aye, timewithout end, sempiternity; deathlessness, immortality, athanasia; incessance, continuity, durability …   English dictionary for students