Perpetuity

Definition

Perpetuity refers to an infinite or never-ending stream of cash flows or payments. In the context of time value of money and present/future value calculations, perpetuity is a special type of annuity where the payments continue indefinitely without end.

5 Must Know Facts For Your Next Test

1. Perpetuities are a special case of annuities where the payments continue indefinitely, without an end date.
2. The present value of a perpetuity can be calculated as the annual payment divided by the discount rate.
3. Perpetuities are often used to model long-term investments, such as dividends from stocks or rental income from real estate.
4. The future value of a perpetuity cannot be calculated, as the payments continue forever into the future.
5. Perpetuities are an important concept in capital budgeting, valuation, and financial planning.

Review Questions

• Explain how the present value of a perpetuity is calculated and the key factors that influence it.
  • The present value of a perpetuity is calculated as the annual payment divided by the discount rate. The key factors that influence the present value are the size of the annual payment and the discount rate used. A higher annual payment increases the present value, while a higher discount rate decreases the present value. This is because a higher discount rate reduces the present worth of the future payments. The present value formula for a perpetuity is: PV = Annual Payment / Discount Rate.
• Describe the differences between a perpetuity and a finite annuity in terms of present and future value calculations.
  • The key difference between a perpetuity and a finite annuity is the duration of the cash flows. A perpetuity has an infinite stream of payments, while a finite annuity has a fixed number of payments over a specific time period. For a perpetuity, the present value can be calculated using the simple formula of annual payment divided by the discount rate. However, the future value of a perpetuity cannot be determined, as the payments continue indefinitely. In contrast, both the present value and future value of a finite annuity can be calculated using standard time value of money formulas that account for the finite number of payments.
• Analyze how the concept of perpetuity is applied in real-world financial and investment decisions.
  • Perpetuities are commonly used to model long-term, recurring cash flows in various financial and investment contexts. For example, the valuation of dividend-paying stocks often relies on the perpetuity model, where the stock price is calculated as the expected annual dividend divided by the required rate of return. Similarly, the valuation of rental real estate properties may use a perpetuity approach to account for the ongoing rental income. In capital budgeting, perpetuities are used to evaluate the present value of projects with infinite, or very long-term, cash flows. Understanding the concept of perpetuity and how to apply it in present and future value calculations is crucial for making informed financial decisions regarding long-term investments and assets.

Related terms

Annuity:

A series of equal payments made at regular intervals, such as monthly or yearly, for a specific period of time.

Present Value:

The current worth of a future sum of money or stream of cash flows, discounted at an appropriate interest rate.

Future Value:

The value of an asset or cash at a future date, accounting for compound interest or growth.