Perpetuity is a term that should be familiar for those of you who are well versed in corporate finance. However, for those who are not and are reading this article to gain general knowledge or for educational purposes in hopes of delving deeper into corporate finance, I’m here to ensure that by the time you reach the end you will fully understand perpetuity, growing perpetuity and any topics within the close perimeter of these 2 concepts.

Unfortunately, before explaining to you what perpetuity is, we are going to introduce a new concept and understand it beforehand. This new concept is called ‘annuity’. Now you may be wondering why this new term was suddenly introduced to you, but don’t you worry because this question will be answered in the following paragraphs. Any additional information that is given will be to help you fully grasp the idea of this topic.

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## Annuity

Let’s start with defining annuity. The exact definition of annuities is insurance contracts that guarantee a set amount of money for the rest of a person’s life or for a set period of time. An annuity can be acquired with a single payment or a series of payments, and it can start paying off right away or at a later date.

## Perpetuity

Now that we got that out of the way and understood the main idea behind annuity let’s get into the main topic at hand, perpetuity. Perpetuity is a type of regular annuity with no end, a never-ending stream of cash payments. It’s also known as a perpetual annuity. The notion of perpetuity allows you to evaluate stocks, real estate, and a variety of other investments. Perpetuity is essentially a never-ending stream of cash flows. This means that if we purchase perpetuity right now after paying a certain lump sum, we should expect repayments that last till the end of time.

Dividend discount models, for example, look at the present value of perpetuity to determine the worth of endless dividend payments. To determine how much those annuity payments would be worth today, this model employs future dividend cash flows and a periodic interest rate. One example of perpetuity is common stocks which are practically an investment in the operations of a company. Another example would be real estate because as soon as the purchase price of real estate has been paid, the owner is entitled to receive an infinite stream of rental payments.

## Valuing Perpetuities

The perpetuity formula is the most basic and clear since it excludes the terminal value. It is the fundamental formula for calculating the price of perpetuity. You have to simply divide the cash flows/payments by the discount rate to calculate the Present Value of perpetuity.

PV = C / R

Where:

PV is the present value of a perpetuity

C is the amount of cash flow received every period

R is the required rate of return

## What is growing perpetuity?

A growing perpetuity is a cash flow that is projected to be received indefinitely and grow at the same pace indefinitely. For instance, if your company has a £1,000 investment that you intend to pay out in perpetuity, this investment is regarded as perpetuity. If, on the other hand, you anticipate getting £1,000 in the first year and the investment to increase at a pace of 5% per year for the rest of your life, it would be considered growing perpetuity.

As we’ve seen in previous paragraphs, a perpetuity is a series of future financial flows that never ends. it’s also shown, however, that the value of these financial flows declines over time. Today, $500 may buy us a lot of things, but in 60 years, it will be worth much less. Receiving endless payments is insufficient for this reason. Therefore, Payments are also required. In conclusion, growing perpetuity is based on the concept that payments must also continue to rise at a particular rate. This will ensure that they are not significantly out of step with inflation.

## The formulae for calculating the present value of a Growing perpetuity

The current value of an infinite sequence of cash flows rising at a constant rate, ad infinitum, is known as the present value of a growing perpetuity. The current value of the cash flows is finite, even if the overall amount of the cash flows is limitless. Because of the time value of money, the lower the present value of cash flows the further they are in the future. And therefore, similar to perpetuity, the present value of a growing perpetuity can be calculated using a simple formula shown below:

Present value of a growing perpetuity= (Expected cash flow in period 1)/ (Expected rate of return) – (Rate of growth of perpetuity payments)

To sum up, to calculate the present value of growing perpetuity you must divide the Expected cash flow in period 1 by the expected rate of return subtracted by the rate of growth of perpetuity payments.

However, for this formulae to be correct the Rate of growth of perpetuity payments must always be greater than the expected rate of return. If the Rate of growth of perpetuity payments is less than the expected rate of return or equal to the Expected rate of return, the formula does not hold true. This is because the stream of payments will cease to be an infinitely decreasing series of numbers that have a finite sum.

## Future value of a growing perpetuity

You’ll need a future date to calculate the future value of a growing perpetuity. The growing perpetuity, on the other hand, is essentially transformed into an annuity. As a result, this measure isn’t as useful as a perpetual growth equation. If you wish to calculate the future worth of growing perpetuity, you’ll need to apply the net present value formula, which is shown below.

The net present value formulae used varies from situation to situation, in regular situations, the one below is used,

Net Present Value = Cash flow / (1 + i)t – initial investment

where i = required return or discount rate and t = number of time periods.

If you’re working on a lengthier project with several cash flows, you’ll need to utilize a slightly different net present value formula shown down below,

Net Present Value = Today’s value of the expected cash flows − Today’s value of invested cash

## Examples of a growing perpetuity

In our daily lives, we are continuously environed by examples of growing perpetuities without even realizing it. One of the main growing perpetuities that we see daily is Endowment funds for colleges that must have long-term growth rates. This is because tuition and other expenditures will grow increasingly expensive as time goes on. As a result, endowment funds at colleges must continue to increase in order to satisfy rising scholarship needs. Another important example is stock valuations. For the computation of terminal value, stock valuations usually assume growing perpetuity. It would be difficult to evaluate a company without the idea of a growing perpetuity.

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