Perpetuity

Present Value of a perpetuity is used to determine the present value of a stream of equal payments that do not end. The present value of a perpetuity formula can also be used to determine the interest rate charged, and the size of the regular payment. Use the perpetuity calculator below to solve the formula.

Perpetuity Definition

Perpetuity is a stream of equal payments that does not end.

Variables

PV=Present value of the perpetuity
Pmt=Payment amount
R=Annual interest rate

Perpetuity

A Perpetuity is simply a stream of equal payments that carries on indefinitely.  Sometimes a Perpetuity is known as a perpetual annuity.  An investor purchases a Perpetuity and in return receives a stream of equal payments that never ends.  The initial principal is never returned to the investor. 

Since the Perpetuity returns a fixed payment, payments in the future have a lower present value the farther away they occur.  This means that the present value of future payments will eventually approach zero.  This actually simplifies the calculation of the present value of a Perpetuity, since the present value is simply equal to the regular payment divided by the discount rate.  This means that the only factor that will affect the market price of a Perpetuity once it has been issued is the discount rate required by the market. 

In the real investing world, there are few actual perpetuities.  Preferred shares are similar, in that they promise a fixed dividend payment, and that the price of these preferred shares is determined by the same formula as a Perpetuity.  The difference is that a preferred share can have its payment halted in some cases, or could lose value if the company fails.

Although the thought of a perpetual stream of income payments might seem attractive to a low risk investor, one must remember that inflation will have a large effect on the value of this type of investment over a long time.  Since a Perpetuity by definition pays out for ever, inflation will erode the purchasing power of this interest payment and the purchase price will not grow with other assets that appreciate over time.

This is why investors need to include some element of capital growth into their long term investing strategy.  Without some appreciation in the principal, an investors purchasing power will dwindle over time, as the fixed income payments do not have the purchasing power that they once had.  Even preferred shares are often repurchased by the company at some time, rarely are they left in the market perpetually.

Other investments will include some capital appreciation as part of their attraction.  Typically these will include common shares of public companies, and real estate assets.  Both of these assets are expected to generate some income, that will grow with inflation.  As well, the value of these assets will grow as their income streams grow.  Real estate investment models and stock valuation formulas will allow for this growth rate to affect the present value of the asset.