Perpetuity: Never Ending Financial Concept

A perpetuity is a financial instrument that pays a never-ending series of periodic payments. It is commonly used in the contexts of finance, economics, and legal frameworks such as the rule against perpetuities.

A perpetuity is a type of financial instrument or cash flow that continues indefinitely, paying a consistent periodic payment forever. It is frequently referenced in finance, investments, and sometimes in legal contexts.

Types of Perpetuities

Simple Perpetuity

A simple perpetuity involves consistent payments that are made indefinitely, without any changes in the payment value.

Growing Perpetuity

A growing perpetuity features payments that increase at a constant rate indefinitely. This is commonly used to model scenarios where payments increase due to inflation or expected growth rates.

Special Considerations

Present Value of a Perpetuity

The present value (PV) of a perpetuity can be calculated using the formula:

$$ PV = \frac{C}{r} $$

where \( C \) is the annual payment and \( r \) is the discount rate or the interest rate.

For a growing perpetuity, the present value is calculated as:

$$ PV = \frac{C}{r - g} $$

where \( g \) is the growth rate.

Historical Context and Applicability

Perpetuities have historical significance, especially in the context of annuities and investments. British consols, bonds issued by the British government, are historical examples of perpetuities. These instruments continue to make payments indefinitely.

Rule Against Perpetuities

In legal terms, the Rule Against Perpetuities is a common law principle designed to prevent the tying up of property (usually real estate) for an excessive duration beyond the control of living persons.

Examples

• British Consols: These are bonds issued by the British government that pay interest forever without a maturity date.
• Scholarship Endowments: Universities often create endowments to pay scholarships perpetually.

Comparisons

Perpetuity vs. Annuity

While an annuity provides payments for a fixed period, a perpetuity continues indefinitely. A simple annuity’s present value is typically calculated for the known period of payments, while a perpetuity’s calculation assumes an infinite period.

Related Terms

• Annuity: A series of payments made at fixed intervals for a specified period.
• Discount Rate: The interest rate used to discount future cash flows to their present value.
• Consol: A type of perpetual bond, especially those historically significant in the UK.

FAQs

What is the difference between a perpetuity and a growing perpetuity?

A perpetuity pays a fixed amount indefinitely, while a growing perpetuity pays an amount that increases at a constant rate.

How do you calculate the present value of a perpetuity?

The present value is calculated using the formula \( PV = \frac{C}{r} \).

Why is the Rule Against Perpetuities important?

This rule is important to prevent property from being tied up indefinitely, ensuring that assets can be freely transferred and used by future generations.

References

1. Bodie, Z., Kane, A., & Marcus, A. J. (2014). Investments. McGraw-Hill Education.
2. Brigham, E. F., & Ehrhardt, M. C. (2016). Financial Management: Theory & Practice. Cengage Learning.
3. Merton, R. C. (1973). Theory of Rational Option Pricing. Bell Journal of Economics and Management Science.

Summary

Perpetuities play a significant role in finance and legal contexts by representing instruments that pay indefinite periodic payments. Understanding the calculation of their present value, as well as their applications and legal constraints, is crucial for effective financial management.