The term ‘perpetuity’ means what the word suggests – a never-ending cash flow of a certain amount that goes on for an unspecified or unending period. It is, in essence, a kind of annuity with periodic payments that begin at a certain time and then last perpetually.

The calculation of the present value of perpetuity depends on various factors. The formula used to calculate the current value of a perpetuity is:

P =C _{(1+r)1 }+ C_{(1+r)2} + C_{(1+r)3 }… = C_{r}

Here,** ‘**P’ refers to the present value of the amount, ‘C’ represents the cash flow, and ‘r’ is the discounted rate.

## Key Takeaways

- Perpetuity is a financial concept representing a stream of indefinite cash flows.
- Perpetuities are used in finance to calculate the present value of an asset with infinite cash flows.
- The present value of infinity can be calculated using the formula PV = C / r, where PV is the present value, C is the cash flow per period, and r is the discount rate.

**Understanding what perpetuity is**

The basic concept, as already understood, is security yielding a never-ending cash flow. To comprehend this better, we will look at the components of perpetuity and some examples.

- A good example is the British bonds known as ‘consols’, which were redeemed in 2015. By purchasing a console, a person was entitled to receive regular yearly payments without a specific time limit.
- An opportunity like this seems highly lucrative, but at the same time, it is not. How the amount is calculated factors in the time value of the money, so each instalment can be just a fraction of the previous. The payments may go on forever, but the amount paid never amounts to too much.
- Other common examples include scholarships granted from a particular endowment fund or permanently invested and irredeemable money.
- The basic nature and concept of perpetuity are used in several financial theories. A few instances include calculations of the Dividend Discount Model and valuation of financial assets or real estate finances.
- The perpetuity formula is also commonly used to determine the cash flow in a business’s ‘terminal year’.

**Advantages of a perpetuity**

- The benefits of perpetuity can be realized shortly, which is one of the major advantages of perpetuity over annuities or other bonds.
- An assured cash flow (regardless of the amount) allows better investments and a backup financing option for future expenditures and purchases.
- Risks regarding fluctuations in the capital market may be effectively avoided. Costs and interest rates may become higher in the future, and this serves as a mode of safe investment and regular yields.
- Perpetuities are highly useful for scholarship payments or charities as they ensure a regular cash flow in specific intervals.

**Disadvantages of a perpetuity**

- It isn’t easy to calculate the face value of perpetuity because it goes on indefinitely into the future.
- Since amounts are likely to reduce in the future, it is not a good option for retiring people to rely on.
- Investing in such a bond may not be viable in the long run since the money cannot be withdrawn. Thus, regardless of your financial situation, it will stay tied up in perpetuity even if it is not yielding satisfactory results.

**References**

- https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2755252
- https://www.tandfonline.com/doi/abs/10.1080/03461238.1990.10413872

Last Updated : 11 June, 2023

Chara Yadav holds MBA in Finance. Her goal is to simplify finance-related topics. She has worked in finance for about 25 years. She has held multiple finance and banking classes for business schools and communities. Read more at her bio page.

Rosie80While I appreciate the detailed breakdown, the examples provided were somewhat limited in scope. I’d like to see a more extensive application across various industries next time.

Maria HillI see where you’re coming from, Rosie. Adding more industries would make the explanation more relatable and engaging.

Mohammed StevensThe references provided are well-respected and lend credibility to the article. Thank you for substantiating the content with reputable sources.

Mandy GriffithsThe references were indeed a valuable addition. It’s always good to trace the origins of the information.

Matthew59There’s a dry humor in the tone of this article that I find to be quite entertaining. Who knew perpetuity could be delivered with a comedic touch?

Saunders FionaYeah, that subtle injection of humor was certainly unexpected but appreciated.

Graham SteveGlad to know I wasn’t the only one picking up on the humor!

CthomasThe formulaic explanation of perpetuity was a bit too oversimplified. I expected a more in-depth mathematical breakdown.

QsmithYou might want to explore scholarly articles that go into the mathematical complexities if you’re seeking that level of detail.

Lewis LoganHighly informative discussion about perpetuity. Personally, I find the mention of ‘consols’ particularly interesting. I wonder about the practical impacts they had in their time.

Lisa SmithNever thought I’d find a financial concept to be an enjoyable read. The narrative style of the article is engaging and refreshing.

BmorrisCompletely agree. I did not expect perpetuity to be explained in such an approachable and engaging manner.

KbakerUnderstanding how perpetuity can be advantageous and disadvantageous was very insightful. It made this whole concept more practical and relatable to real-life investment scenarios.

Watson TylerAbsolutely. The discussion of risks and the practical implications of perpetuity was enlightening.

George SimpsonThis article failed to address the historical significance of perpetuity in financial markets or its position in modern economics. An incomplete analysis in my opinion.

Kevin21Perhaps you both could write and publish your own comprehensive analysis if you’re not satisfied with this one.

Chris25Couldn’t agree more, George. It’s a significant oversight on the part of the author.

Wright TomThis is the most comprehensive and illuminating explanation of perpetuity I’ve ever read. The formula is simply explained and broken down, making it very straightforward. The practical application of perpetuity in finance is well illustrated as well. I will definitely refer back to this when studying for my finance exam.

Lucas27I wholeheartedly agree, Tom. It’s very well composed and highly informative.

ShillYou both are sounding like textbook examples yourselves. I was hoping for more humor in this discussion.

Barry53The clear distinction between the advantages and disadvantages was enlightening. It further emphasizes the need for balanced and informed decision-making in the world of finance.

HstewartIndeed, Barry. Knowing the pros and cons makes for smarter investments and strategic financial planning.