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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
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is 12.50%, then a constant perpetuity of dividend income per dollar 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
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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
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for the valuation of the common stock of a corporation is another example. This model 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
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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
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This of course follows the fact that for bigger changes the new price must be calculated with the present-value formula given that for changes greater than a few basis-points the calculated duration is not reflective of the true-change in price.
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that affect the results of a perpetuity, and prices can be established using techniques for valuing a perpetuity. Perpetuities are but one of the
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that has no end, or a stream of cash payments that continues forever. There are few actual perpetuities in existence. For example, the
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long-dated bonds have prices that change rapidly (either up or down) when yields change (fall or rise) in the financial markets.
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The value of the perpetuity is finite because receipts that are anticipated far in the future have extremely low present value (
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is never repaid, there is no present value for the principal. Assuming that payments begin at the
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of the current period, the price of a perpetuity is simply the coupon amount over the appropriate
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and are a form of ordinary annuities. The concept is closely linked to
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of the future cash flows). Unlike a typical bond, because the
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496:"fixed income – Duration of perpetual bond"
288:= the amount of the periodic payment, and
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159:and were all finally redeemed in 2015.
27:Payments made at equal intervals forever
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405:except by act of Parliament. As with
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373:or cap rate (the convention used in
184:Perpetuities can be structured as a
58:adding citations to reliable sources
500:Quantitative Finance Stack Exchange
393:UK government perpetuities (called
284:= present value of the perpetuity,
270:{\displaystyle PV\ =\ {A \over r}}
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503:. Retrieved
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444:"Perpetuity"
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110:August 2016
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548:Annuities
407:war bonds
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292:= yield,
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517:See also
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