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Perpetuity

Updated on May 6, 2024
Article byWallstreetmojo Team
Reviewed byDheeraj Vaidya, CFA, FRM

Perpetuity Meaning

Perpetuity, most commonly used in accounting and finance, means that a business or an individual receives constant cash flows for an indefinite period (like an annuity that pays forever), and according to the formula, its present value is calculated by dividing the amount of the continuous cash payment by the yield or interest rate.

Perpetuity Meaning

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The payment is received at fixed intervals, which do not have any maturity or expiration. In the investment field, it is used to value bonds, stocks or assets where the issuers promise to give perpetual payments to the security holders. They are not very usual situations because most payments are for limited timeframe.

Key Takeaways

  • Perpetuity implies consistent cash flows a company or individual receives indefinitely, akin to an everlasting annuity. The continuous cash payment amount is divided by the yield or interest rate to find its present value.
  • Perpetuity functions as an eternal annuity with indefinite payouts. Its formula aids in predicting investment returns over time.
  • Preferred shareholders hold priority over equity investors and receive fixed preferred dividends. This method enables calculating the present value of these dividends.

Perpetuity Explained

Perpetuity in finance is a kind of financial arrangement which refers to the flow of a fixed amount of money for indefinite time period in future. It is a cash flow stream which does not have any expiry date or maturity period.

It is also called perpetual payment that is received at a fixed interval of time which may be monthly, quarterly or annually. Cash flows are expected to carry on in cases of bonds, stocks, or any other assets. However, in reality, it is not always the case, because every investment usually has an expiration date or a maturity period. This may be due to terms of contract, or market conditions of the security strategy followed by the issuer.

The perpetuity rule is used in the case of investments where the issuer promises to pay the holder a fixed payment at certain intervals.

Formula

The present value of perpetuityPresent Value Of PerpetuityPerpetuity can be defined as the income stream that the individual gets for an infinite time. Its present value is derived by discounting the identical cash flows with the discounting rate. Here the cash flows are endless, but its current value amounts to a limited value.read more can be calculated as follows –

PV of Perpetuity  = D/R
PV of Perpetuity Formula

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Here. PV = Present Value, D = Dividend or Coupon payment or Cash inflow per period, and r = Discount rate

Alternatively, we can also use the following formula –

PV of Perpetuity = ∞∑n=1 D/(1+r)n

Here n = time period

Example

Let us try to understand the concept of perpetuity in finance with the help of some examples.

You can download this Perpetuity Excel Template here – Perpetuity Excel Template

Smith has invested in a bond that pays him coupon payments for an infinite period. This bond pays Smith $100 every year. Assuming that the discount rate is 8%, how much should Smith pay for this bond?

  • First of all, we know that the coupon payment every year is $100 for an infinite amount of time.
  • And the discount rate is 8%.
  • Using the formula, we get PV of Perpetuity = D / r = $100 / 0.08 = $1250.

For a bond that pays $100 every year for an infinite period with a discount rate of 8%, the perpetuity would be $1250.

Interpretation

The very powerful query would be why we should find out the present value of a perpetuity. Every firm has a projected cash flow that may get realized after 2, 5, or 10 years.

For an investor to be interested in the firm, they needs to know the present value of that future cash flow. The perpetuity rule is one sort of annuity that pays forever.

Concept-wise, it may seem illogical, but it happens in the case of bonds issued by the British government. If an investor invests in this particular sort of bond, she will receive infinite cash flows at the end of each period. But it may have a finite present value. So we can use the perpetuity formula to determine what an investor will receive. And we need to know the present valuePresent ValuePresent Value (PV) is the today's value of money you expect to get from future income. It is computed as the sum of future investment returns discounted at a certain rate of return expectation.read more of future cash flows to be accurate.

Calculator

We can use the following calculator to calculate perpetuity.

D
R
PV of Perpetuity Formula =
 

PV of Perpetuity Formula =
D
=
R
0
= 0
0

Perpetuity Calculation in Excel (with excel template)

Let us now do the same and calculate perpetuity in Excel. This is very simple. You need to provide the two inputs of Dividend and Discount Rate. You can easily calculate the ratio in the template provided.

excel example

Uses

 In the case of preferred shareholdersPreferred ShareholdersA preferred share is a share that enjoys priority in receiving dividends compared to common stock. The dividend rate can be fixed or floating depending upon the terms of the issue. Also, preferred stockholders generally do not enjoy voting rights. However, their claims are discharged before the shares of common stockholders at the time of liquidation.read more, they receive preferred dividends before equity shareholders are paid. And preferred dividendsPreferred DividendsPreferred dividends refer to the amount of dividends payable on preferred stock from profits earned by the company, and preferred stockholders have priority in receiving such dividends over common stockholders.read more are fixed. That’s why we can use this perpetuity value formula to find out the present value of these preferred dividends.·     In finance, valuation methodologies are used to determine a business’s valuation. One of these valuation methodologies is the dividend discount model. This formula is also used in the dividend discount model.Dividend Discount Model.The Dividend Discount Model (DDM) is a method of calculating the stock price based on the likely dividends that will be paid and discounting them at the expected yearly rate. In other words, it is used to value stocks based on the future dividends' net present value.read more.

Perpetuity Vs Annuity

Both the above terms are very frequently used in financial situations where the securities involve caontinuous cash flows. However, there are some differences between them, as follows:

  • The former is for indefinite time period whereas the latter refers to a cash flow which is for a fixed time period, meaning, it has a maturity date.
  • The former will have cash flows that are fixed over the entire time, where the latter may have fixed as well as variable cash flows.
  • Perpetuity value is commonly used in finance where the concept is more theoretical and cash flow assumptions are made for simple study purpose, whereas annuity is used in real cases like retirement savings, insurance plans, etc.
  • The valuation method of both of them are completely different having two different formula.

Frequently Asked Questions (FAQs)

1. Is the common stock a perpetuity? 

Common stock doesn’t precisely qualify as a perpetuity. While both involve a continuous flow of payments, common stock dividends can fluctuate and there’s no specific guarantee of everlasting payments. On the other hand, perpetuities offer fixed payments indefinitely, making them more akin to bonds or preferred shares.

2. What is the difference between royalty and perpetuity? 

Royalty and perpetuity share similarities but differ in scope. Royalty denotes a payment based on usage or sales of intellectual property, like books or music. On the other hand, perpetuity refers to a financial concept where fixed payments continue indefinitely, often linked to investments. While both involve ongoing payments, perpetuity pertains more to financial instruments, whereas royalty extends to creative and intellectual property.

3. Can a perpetuity end? 

The concept of a perpetuity implies endless payments, but in reality, circumstances might lead to an end. For instance, payments can stop if the issuer of a perpetuity dissolves or the underlying asset ceases to generate income. Additionally, factors like inflation or changes in interest rates might influence the value or viability of a perpetuity over time, potentially leading to its termination.

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