1. What is a Growing Perpetuity?

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.

2. How Does the Calculator Work?

The calculator uses the growing perpetuity formula:

Where:

• \( PV \) — Present value of the perpetuity
• \( PMT \) — First periodic payment amount
• \( r \) — Discount rate per period (decimal)
• \( g \) — Growth rate per period (decimal)

Explanation: The formula discounts an infinite series of payments that grow at a constant rate. The growth rate must be less than the discount rate for the formula to be valid.

3. Importance of Growth Rate

Details: The growth rate significantly impacts the present value calculation. Even small changes in the growth rate can lead to large differences in valuation, especially when the growth rate approaches the discount rate.

4. Using the Calculator

Tips: Enter the first payment amount in USD, the discount rate and growth rate as decimals (e.g., 5% = 0.05). The growth rate must be less than the discount rate.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between a perpetuity and growing perpetuity?
A: A regular perpetuity has constant payments, while a growing perpetuity's payments increase at a constant rate over time.

Q2: When is this formula used in real life?
A: Common applications include valuing dividend-paying stocks, certain types of bonds, and long-term leases with rent escalations.

Q3: What happens if growth rate equals discount rate?
A: The formula breaks down (denominator becomes zero). In practice, the growth rate must be less than the discount rate.

Q4: How do you choose an appropriate discount rate?
A: The discount rate should reflect the risk of the cash flows, often based on the opportunity cost of capital or required rate of return.

Q5: Can this model be used for declining payments?
A: Yes, by using a negative growth rate. The formula still requires that r > g (the discount rate exceeds the growth rate).