# Perpetuity

## What does 'Perpetuity' mean

Perpetuity refers to an infinite amount of time. In finance, it is a constant stream of identical cash flows with no end, such as with the British-issued bonds known as consols. The concept of a perpetuity is also used in financial theory, such as in the dividend discount model (DDM).

## BREAKING DOWN 'Perpetuity'

By purchasing a consol from the British government, the bondholder is entitled to receive annual interest payments forever. Although it may seem a bit illogical, an infinite series of cash flows can have a finite present value. Because of the time value of money, each payment is only a fraction of the last.

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. Specifically, the perpetuity formula determines the amount of cash flows in the terminal year of operation. In valuation, a company is said to be a going concern, meaning that it goes on forever. For this reason, the terminal year is a perpetuity, and analysts use the perpetuity formula to find its value.

## Perpetuity Formula

The basic formula used to calculate a perpetuity is cash flows divided by some discount rate. The formula used to calculate the terminal year in stream of cash flows for valuation purposes is 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. Simplified, the terminal year is some amount of cash flows divided by some discount rate, which is the basic formula for a perpetuity.

## Perpetuity Example

For 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 \$100,000, multiplied by 1.03%, and then divided by or 5%. The answer is \$2.06 million. This is saying that \$100,000 paid into perpetuity, and 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.