1. What is a Perpetuity?

A perpetuity is a type of annuity that pays an infinite series of identical cash flows at regular intervals. The present value (PV) of a perpetuity can be calculated using a simple formula when the discount rate is constant.

2. How Does the Calculator Work?

The calculator uses the perpetuity formula:

Where:

• \( PV \) — Present value of the perpetuity (USD)
• \( D \) — Annual dividend or cash flow (USD)
• \( r \) — Discount rate (in decimal form, e.g., 0.05 for 5%)

Explanation: The formula discounts an infinite series of identical cash flows by dividing the annual payment by the discount rate.

3. Importance of PV Calculation

Details: Calculating the present value of perpetuities is essential in finance for valuing assets with infinite cash flows, such as certain types of stocks, endowments, and permanent bonds.

4. Using the Calculator

Tips: Enter the annual dividend in USD and the discount rate as a decimal (e.g., 5% = 0.05). Both values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What are real-world examples of perpetuities?
A: Preferred stocks with fixed dividends, certain government bonds, and endowment funds often behave like perpetuities.

Q2: How does growth affect perpetuity valuation?
A: For growing perpetuities, the formula becomes PV = D/(r-g) where g is the growth rate (must be less than r).

Q3: What discount rate should I use?
A: Typically use the required rate of return or opportunity cost of capital appropriate for the investment's risk level.

Q4: Are perpetuities truly infinite?
A: While nothing lasts forever, perpetuities are useful models for very long-term cash flows where the exact end date is irrelevant.

Q5: How sensitive is PV to discount rate changes?
A: Very sensitive - small changes in r create large PV changes due to the infinite time horizon.