 ### What are Perpetuities?

A perpetuity is a type of annuity that receives an infinite amount of periodic payments. The value of a perpetuity can change over time even though the payment remains the same. This occurs as the discount rate used may change. If the discount rate used lowers, the denominator of the formula lowers, and the value will increase.

An annuity is a stream of cash flows. A perpetuity is a type of annuity that lasts forever, into perpetuity. The stream of cash flows continues for an infinite amount of time. In finance, a person uses the perpetuity calculation in valuation methodologies to find the present value of a company's cash flows when discounted back at a certain rate.

### Perpetuity Variables

The future value of an investment is lower than the present value. This is due to the time value of money and because money has earning potential when it is invested. As such, the following variables are used in conjunction with the formula above to determine the present value of a perpetuity investment.

#### Cashflow (D)

The cashflow or dividend payment paid out by the perpetuity every period indefinitely, forever.

#### Discount Rate (r)

The discount rate is the rate in which future cashflows are discounted to adjust for financial factors such as inflation and interest. This variable can also be the rate of return required by investors when considering a project for investment.

#### Present Value of Perpetuity (PV)

The present value of the perpetuity in today’s dollars. This amount is calculated by the perpetuity formula and allows investors to compare it to actual market prices of the perpetuity in order to make informed investment decisions regarding the investment.

### How to Calculate Perpetuities

The fact that the fixed payments that you will receive have a constantly decreasing present value allows us to calculate a perpetuity’s value. The present value of a perpetuity is equal to the regular payment divided by the discount rate and can be expressed with the formula above. Using the following example, we can calculate the present value of a perpetuity with the provided variables and formula.

Assume you want to find the value of a perpetuity you have the opportunity of investing in. The perpetuity makes payments of \$5 a year and has a rate of return of 10%. Using the perpetuity formula, the value of the perpetuity can be worked out as follows:

PV = D / r

PV = 5 / 0.1

PV = \$50

The Present Value of the perpetuity you wish to invest in is \$50. If the selling price of the perpetuity is over \$50, it is overvalued and you should reconsider investing in it, however if it is under \$50 it is undervalued and may present an opportunity for investment. Actual perpetuities are hard to find in the real world. However, there are many investments based on selected features of perpetuities. In the case of real estate, the owner is entitled to recurring rental payments - so the real estate is valued as a perpetuity, but it is not guaranteed though.

### Perpetuities Summary

The general assumptions which are taken into account in case of Perpetuity are that the time frame is infinite. But in practice, there is a finite value for the perpetuity’s current value which is accrued in nature and is expected to deliver a return which has low value due to the inflation which is taken into account.

However, there might be a situation where the value of the perpetuity can change over a period of time including the same number of payment. This generally happens due to the change in discount or coupon rate. The value of perpetuity increases with a decrease of coupon rate and vice-versa. ### Perpetuities with On Equation Finance Calculator

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