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What Is Perpetuity?

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James Kent Profile
James Kent answered
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. Assuming that payments begin at the end of the current period, the price of a perpetuity is simply the coupon amount over the appropriate discount rate or yield, that is PV = A over V

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 three per cent UK government War Loan will trade at 50 pence per pound in a yield environment of six per cent, while at three per cent 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 six per cent, and £100 when they are three per cent.

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.
Anonymous Profile
Anonymous answered

Perpetuity is basically a concept of Finance in business Management. It can be considered as one of the methods of time value of money through which financial assets are valuated. Perpetuity is a form of annuity through which a person can get a continuous stream of cash forever. It does not have a definite end. Since it is difficult to maintain such an annuity, it normally does not exist in the current world except for some offered by the British Government.

There is no present value for the principal amount, this is because the principal is never repaid. The receipts anticipated in the future have a low present value. The total price of Perpetuity can be mathematically written as

PV = A/r

Here

PV= Present Value
A = Amount of Periodic Payments
r= Interest rate or the discount rate.

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