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Present Value of a Perpetuity with Growth Calculator

Calculates the present value of an infinite stream of cash flows growing at a constant rate.

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Present Value

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Overview

The Present Value of a Perpetuity with Growth formula, often called the Gordon Growth Model, is a fundamental tool in finance for valuing assets that are expected to generate a stream of cash flows indefinitely, with each cash flow growing at a constant rate. It discounts these future growing cash flows back to their present value, providing a single figure that represents the current worth of that future income stream. This model is particularly useful for valuing stocks, real estate, or businesses that are assumed to have perpetual life and stable growth.

Symbols

Variables

= Cash Flow in Period 1, r = Discount Rate, g = Growth Rate, PV = Present Value

Cash Flow in Period 1
$
Discount Rate
%
Growth Rate
%
PV
Present Value
$

Apply it well

When To Use

When to use: Apply this formula when valuing an asset that is expected to generate cash flows indefinitely, and these cash flows are projected to grow at a constant, stable rate. It's crucial that the discount rate (r) is greater than the growth rate (g) for the formula to yield a meaningful, finite present value. This model is commonly used in equity valuation, particularly for mature companies with predictable growth.

Why it matters: This equation is vital for investors and financial analysts as it provides a theoretical framework for determining the intrinsic value of income-generating assets. It helps in making investment decisions, assessing the fairness of asset prices, and understanding the impact of growth rates and discount rates on valuation. Its application extends to corporate finance for capital budgeting and strategic planning.

Avoid these traps

Common Mistakes

  • Using C0 instead of C1 for the initial cash flow.
  • Applying the formula when r is less than or equal to g.
  • Not converting percentages to decimals for r and g before calculation.

One free problem

Practice Problem

A company is expected to pay a dividend of $100 next year, and these dividends are projected to grow at a constant rate of 5% indefinitely. If the required rate of return for this stock is 10%, what is the present value of this perpetuity?

Cash Flow in Period 1100 $
Discount Rate0.1 %
Growth Rate0.05 %

Solve for: PV

Hint: Ensure the discount rate is greater than the growth rate.

The full worked solution stays in the interactive walkthrough.

References

Sources

  1. Brealey, R. A., Myers, S. C., & Allen, F. (2020). Principles of Corporate Finance (13th ed.). McGraw-Hill Education.
  2. Wikipedia: Gordon growth model
  3. Principles of Corporate Finance by Brealey, Myers, Allen
  4. Investments by Bodie, Kane, Marcus
  5. Gordon growth model (Wikipedia article)
  6. Bodie, Zvi, Alex Kane, and Alan J. Marcus. Investments. McGraw-Hill Education.
  7. Brealey, Richard A., Stewart C. Myers, and Franklin Allen. Principles of Corporate Finance. McGraw-Hill Education.
  8. Ross, Stephen A., Randolph W. Westerfield, and Jeffrey Jaffe. Corporate Finance. McGraw-Hill Education.