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Growing Perpetuity Formula:
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A growing perpetuity is an infinite series of periodic payments that grow at a constant rate. It's commonly used in finance to value assets with perpetual cash flows that increase over time, such as dividend-paying stocks with growing dividends.
The calculator uses the growing perpetuity formula:
Where:
Explanation: The formula discounts an infinite series of cash flows that grow at a constant rate. The discount rate must exceed the growth rate for the formula to be valid.
Details: Calculating present value of growing perpetuities is essential for valuing long-term investments, stocks with growing dividends, pension obligations, and other financial instruments with perpetual, growing cash flows.
Tips: Enter the initial payment in USD, discount rate as a decimal (e.g., 5% = 0.05), and growth rate as a decimal. The discount rate must be greater than the growth rate.
Q1: What happens if growth rate equals discount rate?
A: The formula becomes undefined (division by zero). In practice, the growth rate must be less than the discount rate for the formula to be valid.
Q2: How is this different from a regular perpetuity?
A: A regular perpetuity has constant payments (g=0), while a growing perpetuity has payments that increase at a constant rate.
Q3: What are typical applications of this formula?
A: Valuing dividend-paying stocks with growing dividends, certain types of real estate investments, and endowment funds.
Q4: Can the growth rate be negative?
A: Yes, the formula works for negative growth rates (declining payments), as long as the discount rate exceeds the growth rate.
Q5: How often should the rates be compounded?
A: The rates should match the payment frequency (annual payments use annual rates, monthly payments use monthly rates, etc.).