Perpetuity growth model

What Is the Perpetuity Growth Model?

The perpetuity growth model is a financial valuation tool used to determine the present value of a series of future cash flows that are expected to grow at a constant rate indefinitely. It is a fundamental concept within the broader field of Valuation and is most commonly applied in Discounted Cash Flow (DCF) analysis to estimate the Terminal Value of a business or asset. This model posits that a business can generate cash flows that continue to grow at a predictable, stable rate into perpetuity, offering a way to quantify value beyond a finite forecast period.

History and Origin

The conceptual underpinning of valuing perpetual streams of income dates back to early financial theory. However, the specific formulation of a constant Growth Rate in a perpetual series gained prominence with the development of the Dividend Discount Model (DDM). The most recognized iteration, often referred to as the Gordon Growth Model, was developed by Myron J. Gordon and Eli Shapiro in the mid-1950s. Their work built upon earlier theoretical frameworks, establishing a widely accepted method for valuing stocks based on the present value of expected future Dividend payments growing at a constant rate. This model extended the basic perpetuity concept to incorporate a sustainable growth component, making it applicable to a wider range of businesses and financial assets.

Key Takeaways

• The perpetuity growth model calculates the present value of cash flows that are assumed to grow at a constant rate forever.
• It is a critical component in discounted cash flow (DCF) valuation, primarily for estimating terminal value.
• The model assumes a stable, sustainable growth rate that typically cannot exceed the long-term growth rate of the overall economy.
• Small changes in the assumed growth rate or discount rate can significantly impact the calculated value.
• It is most suitable for mature companies with predictable cash flow patterns.

Formula and Calculation

The formula for the perpetuity growth model is:

Where:

• (PV) = Present Value (or Terminal Value) of the growing perpetuity
• (CF_1) = The expected Cash Flow in the next period (e.g., Year 1 after the explicit forecast period in a DCF)
• (r) = The discount rate (e.g., Cost of Capital or Cost of Equity), expressed as a decimal
• (g) = The constant growth rate of the cash flows, expressed as a decimal

A crucial condition for this formula is that the discount rate ((r)) must be greater than the growth rate ((g)). If (g) were equal to or greater than (r), the denominator would be zero or negative, leading to an infinite or undefined valuation, which is mathematically unsound.¹²

Interpreting the Perpetuity Growth Model

The perpetuity growth model provides a powerful framework for valuing assets that are expected to generate cash flows indefinitely. In practical applications, the derived value represents the sum of all future cash flows, discounted back to their Present Value. The choice of the perpetual Growth Rate ((g)) is paramount to the model's output. It is generally accepted that the perpetual growth rate should not exceed the long-term nominal growth rate of the economy in which the company operates.¹¹ This is because no single company can realistically grow faster than the overall economy indefinitely. For instance, professor Aswath Damodaran emphasizes this constraint, suggesting that for most companies, the long-term stable growth rate should ideally approximate the Risk-free Rate or the global economic growth rate.¹⁰ The interpretation of the resulting value hinges on the realism of the inputs, particularly the terminal growth assumption and the chosen discount rate.

Hypothetical Example

Consider a mature company, "EverGreen Corp.," that analysts expect to generate a Free Cash Flow to the firm of $10 million in the first year after its explicit forecast period. The company's weighted average cost of capital (WACC) is estimated at 10%, and analysts project a perpetual growth rate for its cash flows of 3% per year, reflecting its stable market position and limited future Investment opportunities.

Using the perpetuity growth model:

• (CF_1) = $10 million
• (r) = 10% (0.10)
• (g) = 3% (0.03)

Based on these assumptions, the terminal value of EverGreen Corp. is approximately $142.86 million. This value would then be discounted back to the present day as part of a larger discounted cash flow valuation.

Practical Applications

The perpetuity growth model is primarily used in financial modeling to calculate the Terminal Value in a Discounted Cash Flow (DCF) valuation. Since it is impractical to forecast individual cash flows infinitely, the terminal value captures the value of all cash flows beyond a specific forecast horizon (typically 5 to 10 years). This component often represents a significant portion, sometimes 50% or more, of a company's total estimated intrinsic value.⁹

Beyond corporate valuation, the perpetuity growth model can be adapted for:

• Real Estate Valuation: Estimating the value of properties that are expected to generate rental income growing at a constant rate indefinitely.
• Infrastructure Projects: Valuing long-lived assets like utilities or toll roads with predictable, steadily increasing cash flows.
• Pension Fund Management: Calculating the present value of long-term liabilities with assumed constant growth in payments.

The assumptions for the long-term growth rate are often benchmarked against broad economic indicators. For example, the International Monetary Fund (IMF) regularly publishes projections for global economic growth, which can serve as a reference point for appropriate long-term growth assumptions in valuations.⁸ In its July 2025 World Economic Outlook update, the IMF projected global growth at 3.0% for 2025 and 3.1% for 2026, with further expectations for 3.1% global growth five years from now.⁶, ⁷

Limitations and Criticisms

Despite its widespread use, the perpetuity growth model faces several limitations and criticisms:

• Sensitivity to Inputs: Even a minor alteration to the perpetual growth rate ((g)) or the discount rate ((r)) can lead to substantial differences in the calculated terminal value. This high sensitivity makes the model prone to significant forecasting errors.⁵
• The "Perpetuity" Assumption: Assuming that a business or its cash flows will grow at a constant rate forever is a strong simplification. In reality, very few, if any, companies can sustain a constant growth rate indefinitely due to competitive pressures, market saturation, and economic cycles.
• Growth Rate Constraint: The critical assumption that (r > g) means the chosen growth rate must be realistically sustainable and below the discount rate. A common practical constraint is that (g) cannot exceed the nominal long-term growth rate of the economy. If a company's Reinvestment Rate is zero, the growth rate would also be zero.⁴
• Determining the "Stable" Point: Deciding when a company's growth transitions from a high-growth phase to a stable, perpetual growth phase is subjective and can heavily influence the valuation. Academic research, such as that by Pablo Fernandez, highlights that while different discounted cash flow valuation methods should theoretically yield the same value, incorrect application of assumptions, especially in perpetuity calculations, can lead to discrepancies.², ³

Perpetuity Growth Model vs. Terminal Value

While closely related, the "perpetuity growth model" and "Terminal Value" are distinct concepts.

Perpetuity Growth Model: This refers to the specific formula or mathematical construct used to calculate the present value of a stream of cash flows that grows at a constant rate forever. It is a valuation method.

Terminal Value: This is the value attributed to a business or asset at the end of a detailed forecast period in a discounted cash flow (DCF) analysis. It represents the present value of all cash flows that are expected to occur beyond the explicit forecast horizon. The perpetuity growth model is one of the primary methods used to estimate this terminal value. Other methods for calculating terminal value include using an exit multiple, where a multiple (e.g., EBITDA multiple) is applied to a financial metric in the terminal year to estimate the business's worth.¹ In essence, the perpetuity growth model is a tool within the broader calculation of terminal value.

FAQs

Q1: Can the perpetuity growth rate be higher than the discount rate?
No, for the formula to yield a sensible and finite value, the discount rate must always be greater than the perpetuity growth rate. If the growth rate equals or exceeds the discount rate, the mathematical result would be infinite or negative, which is illogical for valuation purposes.

Q2: What is a realistic growth rate to use in the perpetuity growth model?
A realistic perpetuity growth rate is typically a stable, low rate that reflects the long-term nominal growth of the overall economy. It should generally not exceed the average annual growth rate of gross domestic product (GDP) for the economy in which the company primarily operates, or global GDP for multinational corporations. This ensures the assumption of perpetual growth remains plausible.

Q3: Is the perpetuity growth model suitable for all companies?
The perpetuity growth model is best suited for mature companies with stable, predictable cash flows and established market positions. It is generally not appropriate for high-growth startups or companies in volatile industries, as their future growth patterns are highly uncertain and unlikely to settle into a constant, perpetual rate in the near term. For such companies, multi-stage discounted cash flow models, which allow for varying growth rates over different periods, may be more suitable.

Q4: How does the perpetuity growth model relate to the dividend discount model?
The Gordon Growth Model, a specific form of the Dividend Discount Model, is a direct application of the perpetuity growth model. It uses the same mathematical structure to value a stock based on the assumption that its dividends will grow at a constant rate indefinitely. In this context, the "cash flow" in the perpetuity formula is the next expected dividend payment.