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 time 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 a 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 often 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 a perpetuity is**

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

- A good example of this is the British bonds known as ‘consols’, which were redeemed in 2015. By making the purchase of a consol, 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 actually not. The manner in which the amount is calculated factors in the time value of the money, and so each installment 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 of the same include scholarships granted from a particular endowment fund, or permanently invested and irredeemable money.
- The basic nature and concept of a perpetuity is 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 the ‘terminal year’ of a business operation or company.

**Advantages of a perpetuity**

- The benefits of a perpetuity can be realized in the near future, and this is one of the major advantages of a perpetuity over annuities or other bonds.
- An assured cash flow (regardless of the amount) allows better investments and a back up financing option for future expenditure 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 payments to charities as it ensures a regular flow of cash in specific intervals.

**Disadvantages of a perpetuity**

- It is difficult to calculate the face value of a 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 a viable choice for the long run since the money cannot be withdrawn from it. Thus, regardless of your financial situation, it will stay tied up in the 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

**Want to save this article for later?** Click the heart in the bottom right corner to save to your own articles box!

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.