Perpetuity

AKA Perpetual Annuity or Perpetual Bond, represents a distinctive financial instrument characterized by features that distinguish it from its peers.

Author: Kevin Henderson
Kevin Henderson
Kevin Henderson
Private Equity | Corporate Finance

Kevin is currently the Head of Execution and a Vice President at Ion Pacific, a merchant bank and asset manager based Hong Kong that invests in the technology sector globally. Prior to joining Ion Pacific, Kevin was a Vice President at Accordion Partners, a consulting firm that works with management teams at portfolio companies of leading private equity firms.

Previously, he was an Associate in the Power, Energy, and Infrastructure Investment Banking group at Lazard in New York where he completed numerous M&A transactions and advised corporate clients on a range of financial and strategic issues. Kevin began his career in corporate finance roles at Enbridge Inc. in Canada. During his time at Enbridge Kevin worked across the finance function gaining experience in treasury, corporate planning, and investor relations.

Kevin holds an MBA from Harvard Business School, a Bachelor of Commerce Degree from Queen's University and is a CFA Charterholder.

Reviewed By: Manu Lakshmanan
Manu Lakshmanan
Manu Lakshmanan
Management Consulting | Strategy & Operations

Prior to accepting a position as the Director of Operations Strategy at DJO Global, Manu was a management consultant with McKinsey & Company in Houston. He served clients, including presenting directly to C-level executives, in digital, strategy, M&A, and operations projects.

Manu holds a PHD in Biomedical Engineering from Duke University and a BA in Physics from Cornell University.

Last Updated:January 7, 2024

What Is Perpetuity?

Perpetuity, commonly known as a perpetual annuity or perpetual bond, represents a distinctive financial instrument characterized by features that distinguish it from its peers.

Essentially, it embodies a financial commitment to provide an infinite series of periodic payments that persist indefinitely into the future. It is a perpetual financial pledge to deliver continuous payments, setting it apart from other financial instruments.

The term itself underscores the instrument's perpetual nature. Unlike finite-term annuities or bonds, which come with predetermined maturity dates, perpetuities belong to a category of financial instruments with infinite existence. 

In simpler terms, when an issuer offers a perpetuity, they commit to making payments to the holder for an indefinite duration.

This financial concept holds fundamental importance as it enables investors and financial analysts to quantitatively evaluate the worth of financial instruments that produce perpetual cash flows. 

Perpetual annuities assume a central role in diverse financial and economic scenarios, serving as valuable instruments for making well-informed decisions and engaging in long-term financial strategizing.

For investors, perpetuities offer consistent income without a fixed endpoint, making them attractive for those seeking reliable, long-term financial security. 

Understanding the principles of perpetuity is essential for anybody looking to make investment decisions, as it empowers them to make sound financial choices in an ever-evolving world.

Key Takeaways

  • Perpetuities offer endless payments, distinguishing them from finite financial instruments.
  • Perpetuities serve as a risk mitigation tool. Investors and organizations seeking consistent, predictable income streams can use perpetuities to reduce financial uncertainty. 
  • Real-life examples of perpetuities include preferred stocks, historical bonds, real estate, and annuities.
  • Growing perpetuities represent increasing cash flows each period; they find use in various financial contexts.

Understanding Perpetuity

In finance, perpetuity is a unique concept that doesn't always get as much attention as well-known terms like stocks, bonds, and annuities. Yet, beneath its simple appearance, this concept is a fundamental financial tool with unique features. 

Exploring perpetuities reveals a fascinating world where timeless elements intersect with financial complexity.

A perpetuity is a financial instrument that promises an unending stream of payments. Unlike finite financial arrangements with predetermined maturity dates, this financial instrument defies temporal constraints. It represents continuity, with payments lasting as long as the issuer remains solvent.

Some important characteristics of this concept include:

  1. Infinite Life: As the name suggests, its most compelling and defining feature is its perpetual or infinite lifespan. The concept implies that as long as the issuer remains solvent and operational, the payments to the holder will continue.
  2. Fixed Payments: These securities typically offer fixed, unchanging payments throughout their existence. This distinctive feature sets them apart from many instruments that may experience changes in payments due to:
  3. No Maturity Date: Unlike bonds or annuities, perpetuities do not have a maturity date. As a result, they remain a rare exception, promising uninterrupted payments without the looming expiration.

Do Perpetuities Exist In Real Life?

Yes, perpetuities do exist in real life. However, they are rare when compared to other financial instruments with finite terms. Perpetuities frequently form part of particular types of investments and financial arrangements. 

They signify a commitment to delivering continuous payments without a predefined expiration date. Here are a few examples where perpetuities can be observed:

Preferred Stocks

Some preferred stocks come close to being perpetuities. These stocks promise fixed dividend payments to shareholders. As long as the company remains operational, these dividends continue indefinitely. 

The issuer can call preferred stocks back after a certain period. However, certain types of such stock may not have a fixed maturity date. These resemble perpetuities.

Consol Bonds (Historical)

Historically, consol bonds were issued by governments such as Great Britain in the 18th and 19th centuries. These bonds promised fixed annual interest payments to bondholders indefinitely. 

While such bonds are less common today, they demonstrate the concept of perpetual financial commitments.

Real Estate Investments

Property generating perpetual rental income can be seen as perpetuities in the real estate sector. 

Rental income from properties provides a recurring stream of cash flows as long as the property remains operational and tenanted, resembling the unending payments of perpetuities.

Endowment Funds

Some educational institutions and nonprofit organizations receive endowment funds, which are often invested to generate income. The funds generated from endowments can be used to support the organization's activities perpetually.

Certain Annuities

While most annuities have fixed terms, there are cases where annuities might be structured to provide payments for the annuitant's lifetime, effectively behaving like perpetuity as long as the individual is alive.

It's important to note that while these examples reflect the idea of perpetuity, there are often contractual or legal considerations that could affect their perpetual nature. 

In some cases, issuers or organizations might have mechanisms to call back or terminate perpetuity-like arrangements under specific conditions. As such, carefully examining the terms and conditions is essential to fully understand these financial instruments' nature.

Perpetuity Formula

Valuing perpetuity involves determining the present value of an infinite stream of cash flows it promises. The formula, rooted in the concept of present value, plays a pivotal role in this process:

PV = C/ r

Where:

The discount rate ‘r’ carries paramount significance in the valuation. This rate encompasses the opportunity cost of capital. It is influenced by existing interest rates in the market and the level of risk associated with the particular perpetuity.

Examples of Perpetuity

Let's look at some examples to gain a deeper understanding of perpetuity.

Example 1

Imagine inheriting a parcel of land with a natural spring. Your choice is to lease this land to a bottled water company, with their agreement to provide an annual lease payment indefinitely in return for spring access.

The lease contract outlines that you will be granted $5,000 annually, commencing at the end of the initial year. 

This lease payment illustrates how a perpetuity extends indefinitely. 

Now, let's calculate the present value of this. ​

In our example:

  • C = $5,000
  • r is the discount rate

Assuming you seek a 5% annual return on your investments, proceed by inputting the values into the formula.

PV = $5,000/ 5%

PV = $100,000

Therefore, at a 5% discount rate, the current value of the perpetuity stands at $100,000.

Consequently, should you decide to invest $100,000 with an annual return rate of 5%, it would generate a perpetual annual income of $5,000, similar to the lease payment received from the bottled water company.

Example 2

Picture yourself as the lottery winner who guarantees an annual payout of $50,000, beginning in one year and lasting throughout your lifetime. This yearly payout represents a variation of perpetuity, persisting indefinitely without a predetermined end date.

Let's calculate its present value, assuming a 4% discount rate (your required rate of return or interest rate). We'll use the same formula from above:

In this case:

  • C = $50,000 (annual lottery payment)
  • r = 4% (discount rate)

Now, plug these values into the formula:

PV = $50,000/ 4%

PV = $1,250,000

As a result, with a 4% discount rate, the present value will be $1,250,000.

Therefore, if you decided to invest $1,250,000 at an annual return rate of 4%, it would yield a perpetual annual income of $50,000. This income would align with the annual lottery payment you receive.

In this instance, the lottery prize serves as a perpetuity, delivering an uninterrupted stream of cash without a defined end date, with its value contingent on your discount rate.

Growing Perpetuity

A growing perpetuity is a financial concept representing a series of cash flows that continues indefinitely into the future, but unlike a regular perpetuity, these cash flows grow at a constant rate each period. 

It is a common valuation method for assets or investments expected to generate income that increases over time at a steady rate. This model finds applications in various areas, including:

By calculating the present value of these perpetually growing cash flows, investors and analysts can estimate the current worth of future income streams, aiding in decision-making and investment valuation. 

However, ensuring that the growth rate remains below the discount rate to avoid infinite present values is essential.

The formula is as follows:

PV = C/ (r - g)

Where:

  • PV is the present value of the growing perpetuity
  • C is the initial cash flow (the cash flow at the end of the first period)
  • r is the discount rate, representing the required rate of return
  • g is the growth rate of the cash flows per period

The growth rate “g” is essential in determining the increasing nature of the cash flows. 

In order for this equation to be valid, the growth rate must be lower than the discount rate. When cash flows grow at a rate exceeding the discount rate, it results in an infinite present value. This outcome is not practical.

Example of Growing Perpetuity

Picture a scenario where you're contemplating investing in a stock set to provide ongoing dividends without a predetermined end. 

The initial dividend, to be received in a year, amounts to $100, with an anticipated annual growth rate of 5%. Your investment criteria demand a 10% annual return.

Let's calculate the present value of this growing perpetuity:

  • C = $100 (initial dividend in year 1)
  • r = 10% (discount rate)
  • g = 5% (growth rate)

Now, plug these values into the formula:

PV = $100/ (10% - 5%)

PV = $2,000

So, the present value of the growing perpetuity, given a 10% discount rate and a 5% growth rate, is $2,000. This represents the current worth of the perpetually increasing cash flows.

This implies that you would find investing $2,000 in the stock reasonable, provided it aligns with your required rate of return and the anticipated dividend growth rate.

A growing perpetuity represents a series of continuous cash flows, each growing at a constant rate per period. It is a valuable tool for valuing assets or investments with perpetually increasing income streams.

Advantages of Perpetuities

Here are some benefits associated with these perpetual payments:

  1. Stability in Income: Due to their fixed payment structure, these instruments provide investors with a reliable income source. This attribute particularly attracts risk-averse investors seeking consistent, unvarying cash flows.
  2. Predictability for Long-Term Planning: The consistent nature of fixed payments empowers investors to engage in careful long-term financial planning.
  3. Diversification of Investment Portfolios: Including these financial instruments within an investment portfolio adds a layer of diversification. They introduce a source of income that may exhibit less volatility than other investment options.

Drawbacks of Perpetuities

Here are some drawbacks of these perpetual payments:

  1. Vulnerability to Inflation: Fixed payments in perpetuities can be susceptible to the erosive effects of inflation over time. As the cost of living rises, the real value of constant payments may decline.
  2. Sensitivity to Interest Rate Fluctuations: Perpetuities bear a sensitivity to changes in prevailing interest rates. If market interest rates experience an upward surge, the value of existing perpetuities may decline. This makes them less appealing to potential investors.
  3. Issuer Solvency Concerns: Given the nature of these instruments, the issuer's commitment to making payments endures indefinitely. However, if the issuer encounters financial distress, it could potentially lead to disruptions in the regular payment stream to perpetuity holders.

Conclusion

While often overlooked in favor of more mainstream financial instruments like stocks and bonds, perpetuities hold a distinctive place in the financial landscape. 

They promise perpetual payments, providing stability and predictability for those seeking long-term financial security. 

They can be found in various forms, such as certain preferred stocks, historical consol bonds, and even in the context of real estate investments and endowment funds, each demonstrating the concept of perpetual financial commitments.

To assess the value of perpetuities, one must consider the critical factors of the discount rate and, in the case of growing perpetuities, growth rates. 

However, it's important to note that perpetuities can be vulnerable to the erosive effects of inflation and sensitive to fluctuations in prevailing interest rates. Additionally, their value relies on the issuer's financial stability, making issuer solvency a potential concern.

In addition to traditional perpetuities, growing perpetuities offer a model for assets or investments with perpetually increasing income streams, expanding the versatility of perpetuity concepts in financial valuation and decision-making.

In a world where financial planning and investment strategies often focus on the short term, perpetuities offer a unique perspective on long-term financial security and the enduring nature of financial commitments.

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Researched and Authored by Bhavik Govan | LinkedIn

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