What Is the Meaning of Perpetual-Annuity?
An Annuity is a regular payment made at fixed intervals over a set period of time on a cash investment. A Perpetual Annuity is an annuity with no assigned end, a stream of cash payments that will continue indefinitely regardless of the recipients' or of their beneficiaries' life-spans. A Perpetual Annuity can also be referred to as a Perpetuity.
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Function
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The value of a perpetual annuity or perpetuity is calculated using a simple mathematical formula. "PV" stands for Perpetual Value of the annuity, "A" is the amount of the periodic payment and "R" is the yield or discount rate. The formula is PV = A/R. Although the payments on a perpetual annuity are assumed to continue indefinitely, there is a finite value on the perpetuity. This is because anticipated returns in the distant future have a low present-day value.
Types
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Examples of perpetuities include consols (see History section). More recent examples include the use of a cap rate to value real estate and the dividend stream on shares. A cap rate in real estate effectively assumes that the current income from the property will continue indefinitely, while a dividend stream model assumes that the discounted future dividends on the shares will be perpetual.
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History
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One example of a perpetual annuity are the British government bonds that were issued during the eighteenth century. These bonds were called "consols," short for either consolidated annuities or consolidated stock. They came into existence in 1752 when all existing government stock was converted into one stock: Consolidated 3.5 percent Annuities. This was part of a bid to reduce the coupon rate on government debt. (coupon rate is the amount of interest paid annually on a bond and, in this example, the coupon rate is 3.5 percent of its value yearly.) The 3.5 percent coupon rate on these bonds dropped to 3 percent and then to 2.25 percent before settling on its current rate of 2.5 percent in 1903.
Considerations
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True perpetual annuities are very rare. Consols, as mentioned above, are among the few perpetual annuities that are still in existence. However, some investments, such as real estate, can be considered to be effectively perpetuities, and the value of the investment can be established by using the same equations applied to a perpetuity.
Significance
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Despite their relative scarcity, perpetual annuities, particularly consols, have appeared in various works of literature, such as "David Copperfield" by Charles Dickens, "Vanity Fair" by Wiliam Thackery and "The Forsyte Saga" by John Galsworthy.
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