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