What is Perpetuity ? - Definition and Concept

Perpetuity is a very important concept in corporate finance. The concept of perpetuity makes it possible to value stocks, real estate and many other investment opportunities. The valuation of perpetuities is theoretically very simple. The concept of perpetuity as well as the formula required for its calculation has been explained in this article:

Stream of Cash Flows that Never Terminates

In corporate finance, we try to compare the value of different streams of cash flows. Sometimes, we exchange a lump sum value for a finite stream of future payments. However, in case of perpetuity, the payments will never cease. A perpetuity is basically a stream of cash flows that never terminates. This means that if we purchase a perpetuity right now after paying a certain lump sum, we should expect repayments that last till the end of time.

Examples of Perpetuities

Although, valuing a perpetuity may not seem intuitive in the first place, it is required. There are many forms of investments that mimic the features of a perpetuity.

Consider the example of common stocks. Common stocks are basically an investment in the operations of a company. Theoretically the company has an infinite life. Therefore the shareholder is entitled to an infinite stream of future dividends for paying the stock price now. It is for this reason that common stocks are valued as a perpetuity.

Similarly consider the example of real estate. Once the purchase price of real estate has been paid, the owner is entitled to receive an infinite stream of rental payments. Thus real estate is also valued as a perpetuity.

Many universities have endowment funds that pay scholarships to students. They have been doing so for centuries and plan to continue to do so forever. These funds were invested in a perpetuity by a philanthropist many years ago. Now it continues to make payments till the end of time!

Why Perpetuities Have a Finite Value ?

The most counter-intuitive part of perpetuity is the fact that it has a finite value. The question that comes to everybody’s mind is that how can a series of infinite cash flows have a finite valuation. The answer is because the real value of future cash flows keeps on falling. The present values are high in the early years. However, the payment amount is fixed under a perpetuity. Therefore in the later years as and when inflation keeps on increasing, the real value of the payments are continuously decreasing. It is because of this that the cash flows in the very distant future will have a near zero valuation although it will never exactly be zero. Hence using the formula for sum of an infinite series, the value of a perpetuity can be calculated.

Formula for Valuing Perpetuities

The formula for valuing perpetuities is very simple and straightforward. It is as follows:

PV = C / R

Where:

PV is the present value of perpetuity

C is the amount of cash flow received every period

R is the required rate of return

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