What is Perpetuity?

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Perpetuity is conventionally referred to in the business world as a security or bond that pays for an infinite amount of time in the future. In an attempt to understand perpetuity, one is first needed to understand annuity because perpetuity is a type of annuity that lasts forever into perpetuity. In finance, perpetuity refers to endless, constant cash flow.

Companies trading in the stock exchange market for both common and preferred stocks tend to use the perpetuity concept to validate and calculate the present value of the company’s cash flow.

A perpetuity formula can be used by financial managers when calculating the present values of the dividends for common and preferred stock. The present value of perpetuity helps to determine the exact value of the company if it were to continue to perform at the same rate.

A practical example of perpetuity is Consols, a type of bond issued by the British government. This type of security guarantees holders continuous annual payments. In this case, through the perpetuity concept, the present value of an infinite series of cash flow can be determined. Because of future uncertainties due to the time value for money, the present value is just a fraction of the last.

When a company is receiving a series of payments going into an unknown future, we say that the company is a going concern. For this reason, the terminal year is a perpetuity, and analysts use the perpetuity formula to find its value. To be more specific, the perpetuity formula finds the number of cash flows in the terminal year of operation.

Perpetuity Formula

There are two different annual perpetual valuations; perpetuity with flat or constant annuity and perpetuity with a growing annuity. These two different types of perpetuity have different formulas, but the basic calculation is dividing annual cash flows by the various discount rates (the interest rate that is paid to the Federal Reserve by the financial institutions to borrow cash). This gives a business the value of its cash flow, an essential slice of data as it aids in determining the firm’s total cash flow in a single year.

Flat Perpetuity

This perpetuity formula is the simplest, and it is straightforward as it doesn’t include terminal value. It is the basic formula for the price of perpetuity. Calculate the PV of flat perpetuity you only need to divide the cash flows/payments by the discount rate.

PV\: of\: Perpetuity = \dfrac{Payment}{Interest\: Rate}

Growing Perpetuity

The present value of growing perpetuity formula factors in long term growth. This version is used to calculate the terminal value in a stream of cash flows for valuation purposes is always more complicated.

PV\: of\: Growing\: Perpetuity = \dfrac{Payment}{Interest\: Rate - Growth\: Rate}

Using a perpetuity formula to compute the present value may look simple and straightforward, but one needs to understand the underlying assumptions for each case keenly. For instance, high growth rates or low discount rates result in too high values. Similarly, low growth rates or high discount rates lead to pessimistic present values.

Perpetuity Example

Example 1

Assuming that Donald holds a perpetual bond that generates an annual payment of $500 each year. He believes that the borrower is creditworthy and that an 8% interest rate will be suitable for this bond. Compute the PV for this perpetuity.

Now let’s break it down and identify the values of different variables in the problem.

  • Payment amount = $500
  • Interest rate or yield = 8% or 0.08

Next, we can plug these variables into our formula:

PV\: of\: Perpetuity = \dfrac{500}{0.08} = \$6{,}250

This tells us that someone could pay you $6250 for your bond and receive an 8% return on their money.

Example 2

Jacob, a businessman, invested in a company that will pay him a dividend of $8,000 per share annually. He expects a 6% growth rate in the annual payments. Given the possible risks, Jacob expects a valuation of a 16% discount rate of 16%. Calculate the value of a share under the above assumptions.

Now let’s take a look at the different variables we’ll need.

  • Payment amount = $8,000
  • Interest rate or yield = 16%
  • Growth Rate = 6%
PV\: of\: Growing\: Perpetuity = \dfrac{8{,}000}{0.16 - 0.06} = \$80{,}000

For this example, the perpetuity amount would be $80,000. With all the assumptions of a 6% growth rate in dividend and 16% discount rate of owning the company, then the shares should trade at $80,000 each. 

Perpetuity Analysis

Perpetuity is a type of annuity that receives an infinite amount of periodic payments. The periodic amount is consistent for a flat perpetual annuity and varies for growing perpetuity. As a result of changes in the discount rate, the value of perpetuity can change over time. Meanwhile, the periodic payments remain the same.

Perpetuity is mostly applied in businesses, real estate, and certain types of bonds that pay bondholders an recurring fixed annual amount. In real estate, for example, perpetuity might come into play if you invested in a rental property. You would expect to have a continuous flow of income for an unknown time in the future.

This concept is also applied in the stock exchange market. Shareholders of preferred stock believe that the company will continue to exist for an unknown time in the market and keep paying dividends.

Perpetuity can also be used if you purchase government bonds. You might earn an ongoing amount of cash flow at the end of each period. So the perpetuity formula is used to gauge the current value of the specific amount a bondholder would receive after every period. As a result of a change in the interest rate, the value of perpetuity might change along the way. However, the payment remains equal.

Perpetuity allows for the payment of money with no end in sight. The amount bondholders receive diminishes gradually due to economic constraints or factors such as inflation. This can eat into the value of any fixed payouts. As a result, certain types of perpetuity will grow instead of decline. This ongoing growth leads to a regular stream of payments that increase steadily.

Perpetuity Conclusion

  • Perpetuity is the sum of a regular series of fixed payments that will never end.
  • The present value of a perpetuity is today’s value of all those payments in the future.
  • There two types of perpetuity: flat and growing perpetuity
  • Perpetuity requires two variables: cash flows and interest rates.
  • The periodic amount is consistent for a flat perpetual annuity and varies for growing perpetuity.
  • The value of perpetuity can change over time while the periodic payments remain the same.

Perpetuity Calculator

You can use the present value of perpetuity calculators below to quickly calculate the present value of a bond/share by entering the required numbers.

PV of Perpetuity

PV of Growing Perpetuity