what does perpetuity mean in finance 
a perpetuity is an investment asset that pays a stated return for an infinite amount of time an annuity with no termination date is an example of a perpetuity sadly perpetuities are extremely rare in modern times however the abstract concept of perpetuity lives on in the financial world and the field of economics in finance perpetuity is defined as a continuous stream of identical cash flows with no end the concept of perpetuity is used in several financial theories such as in the dividend discount model ddm investopedia jiaqi zhouunderstanding perpetuityan annuity is a stream of cash flows a retiree for example might invest a sum of cash in an annuity in return for a monthly stream of income for a set number of years or for an indefinite lifespan a perpetuity is a type of annuity that lasts forever the stream of cash flows does not have an end date in finance a perpetuity calculation is used to determine the present value of a company s cash flows when discounted back at a certain rate the british issued bonds known as consols were an example of a financial instrument with perpetual cash flows the bank of england phased these out in 2015 by purchasing a consol from the british government the bondholder was entitled to receive annual interest payments forever 1beginning in 1751 the british consol was a means of passing wealth down through the generations although it may seem illogical an infinite series of cash flows can have a finite present value because of the cumulative time value of money each payment is worth only a fraction of the previous payment specifically the perpetuity formula determines the amount of cash flows in the terminal year of operation when companies are valued they are valued as going concerns meaning they are assumed to continue forever for this reason the terminal year is a perpetuity and analysts use the perpetuity formula to find its value perpetuity present value formulathe formula to calculate the present value of a perpetuity or security with perpetual cash flows is as follows pv c 1 r 1 c 1 r 2 c 1 r 3 c r where pv present value c cash flow r discount rate begin aligned text pv frac c 1 r 1 frac c 1 r 2 frac c 1 r 3 cdots frac c r textbf where text pv text present value c text cash flow r text discount rate end aligned pv 1 r 1c 1 r 2c 1 r 3c rc where pv present valuec cash flowr discount rate the basic method used to calculate a perpetuity is to divide cash flows by some discount rate the formula used to calculate the terminal value in a stream of cash flows for valuation purposes is a bit more complicated it is the estimate of cash flows in year 10 of the company multiplied by one plus the company s long term growth rate and then divided by the difference between the cost of capital and the growth rate simply put the terminal value is some amount of cash flows divided by some discount rate which is the basic formula for a perpetuity example of perpetuity in valuationfor example if a company is projected to make 100 000 in year 10 and the company s cost of capital is 8 with a long term growth rate of 3 the value of the perpetuity is as follows cash flow year 10 1 g r g 100 000 1 03 0 08 0 03 103 000 0 05 2 06 million begin aligned frac text cash flow text year 10 times 1 g r g frac 100 000 times 1 03 0 08 0 03 frac 103 000 0 05 2 06 text million end aligned r gcash flowyear 10 1 g 0 08 0 03 100 000 1 03 0 05 103 000 2 06 million this means that 100 000 paid into a perpetuity assuming a 3 rate of growth with an 8 cost of capital is worth 2 06 million in 10 years now a person must find the value of that 2 06 million today to do this analysts use another formula referred to as the present value of a perpetuity growing perpetuitiesthe net present value of a perpetuity is not as large as it might seem because the time value of money erodes the value of dollars far into the future due to inflation therefore the cash flows received by a fixed perpetuity many years from now can become negligible in terms of future buying power a growing perpetuity adjusts the amount of perpetual payments each period by a given rate helping to maintain buying power over time the present value of a growing perpetuity will therefore be greater than a fixed or non growing perpetuity the higher the growth rate of future payments per period the greater the present value the formula for a growing perpetuity is nearly identical to the standard formula but subtracts the growth rate g from the discount rate r in the denominator note that the rate of growth in a growing perpetuity remains fixed over its infinite life meaning it may or may not cover inflation since the growth rate remains fixed in this formula if we use it to value future cash flows it is also only a rough estimate businesses do not grow at the same rate each year 