Perpetual growth rate: Meaning, Criticisms & Real-World Uses

What Is Perpetual Growth Rate?

The perpetual growth rate is a fundamental concept within financial modeling and [valuation models) that represents the constant rate at which a company's cash flow or dividends are expected to grow indefinitely into the future. It is a critical input in various financial calculations, particularly in discounted cash flow (DCF) analysis to estimate a company's intrinsic value. The underlying assumption is that, after a period of explicit high growth, a business will eventually mature and its growth will stabilize at a sustainable, long-term rate, often tied to macroeconomic factors. This perpetual growth rate is essential for calculating the terminal value of a company, which represents the present value of all cash flows beyond a defined forecast period.

History and Origin

The concept of a constant, perpetual growth rate in valuation gained prominence with the development of the Gordon Growth Model, also known as the dividend discount model with constant growth. This model was formally introduced by Myron J. Gordon and Eli Shapiro in their 1956 paper, "Capital Equipment Analysis: The Required Rate of Profit," and further referenced by Gordon in 1959. Their work built upon earlier theoretical ideas in financial economics, notably those put forth by John Burr Williams in his 1938 book, The Theory of Investment Value. The Gordon Growth Model posits that the value of a stock is derived from the present value of its future dividends, assuming those dividends grow at a constant rate in perpetuity. This simplified approach made it a widely adopted tool for estimating long-term value in various financial contexts.

Key Takeaways

The perpetual growth rate is the assumed constant rate at which a company's free cash flows or dividends will grow forever.
It is a crucial input for calculating the terminal value in a discounted cash flow (DCF) model.
The rate is typically low, reflecting a sustainable long-term pace, often aligned with the long-run economic growth of an economy.
Small changes in the perpetual growth rate can significantly impact the final valuation.
It implies a company can maintain growth indefinitely, a strong assumption that requires careful justification.

Formula and Calculation

The perpetual growth rate is primarily used within the terminal value calculation of a discounted cash flow (DCF) model or in the dividend discount model (specifically, the Gordon Growth Model).

For the terminal value in a DCF, the formula is:

TV = \frac{FCF_{N+1}}{WACC - g}

Where:

( TV ) = Terminal Value
( FCF_{N+1} ) = Free Cash Flow in the first year after the explicit forecast period (Year N+1)
( WACC ) = Weighted Average Cost of Capital (the discount rate used to bring future cash flows to their present value)
( g ) = Perpetual Growth Rate

For the Gordon Growth Model, the formula for the stock's intrinsic value (( P_0 )) is:

P_0 = \frac{D_1}{r - g}

Where:

( P_0 ) = Current stock price or intrinsic value
( D_1 ) = Expected dividend per share in the next period
( r ) = Required rate of return (cost of equity)
( g ) = Perpetual Growth Rate of dividends

In both formulas, the perpetual growth rate (( g )) must be less than the discount rate (( WACC ) or ( r )). If ( g \ge WACC ) or ( g \ge r ), the formula yields an undefined or negative value, which is illogical for a healthy, going concern.

Interpreting the Perpetual Growth Rate

Interpreting the perpetual growth rate requires a realistic perspective on a company's long-term potential. This rate should generally be set no higher than the long-term expected rate of inflation or the long-run nominal gross domestic product (GDP) growth rate of the economy in which the company operates. For example, if the long-run real GDP growth rate is anticipated to be 2% and inflation is 2%, a nominal perpetual growth rate of 4% might be considered the absolute upper bound.

Using a perpetual growth rate significantly higher than the overall economic conditions implies that the company will eventually grow to become larger than the entire economy, which is not sustainable in the long run. Analysts often use a rate between 0% and 3%, reflecting the view that mature companies cannot grow at exceptionally high rates indefinitely. Consideration of industry analysis and the company's competitive advantages helps in selecting a reasonable rate.

Hypothetical Example

Imagine an analyst is valuing a mature, stable manufacturing company using a discounted cash flow (DCF) model. After forecasting explicit free cash flow for the next five years, they need to estimate the terminal value beyond year five.

Year 5 Free Cash Flow (( FCF_5 )): $100 million
Assumed Perpetual Growth Rate (( g )): 2.5% (This means ( FCF_{N+1} = FCF_5 \times (1+g) = $100 \text{ million} \times (1 + 0.025) = $102.5 \text{ million} )).
Weighted Average Cost of Capital (( WACC )): 8%

Using the terminal value formula:

TV = \frac{FCF_{N+1}}{WACC - g} = \frac{\$102.5 \text{ million}}{0.08 - 0.025} = \frac{\$102.5 \text{ million}}{0.055} = \$1,863.64 \text{ million}

This calculated terminal value of $1,863.64 million would then be discounted back to the present value along with the explicit forecast period cash flows to arrive at the company's total estimated intrinsic value.

Practical Applications

The perpetual growth rate is a cornerstone in various financial valuation scenarios, especially within corporate finance. Its primary application is in the discounted cash flow (DCF) method, where it is used to determine the terminal value—the value of a business beyond the explicit forecast period. This is crucial for:

Equity Valuation: Investment analysts use the perpetual growth rate to estimate the long-term sustainable growth of a company's earnings or dividends, thereby deriving an equity value for potential investment.
Mergers and Acquisitions (M&A): Acquirers employ DCF models, incorporating a perpetual growth rate, to assess the fair value of target companies, helping to determine appropriate offer prices.
Project Evaluation: For long-term projects with indefinite cash flows, the perpetual growth rate can be used to estimate their continuing value.
Portfolio Management: Fund managers might use models incorporating this rate to benchmark current stock prices against their calculated intrinsic values, informing buy/sell decisions within their investment portfolio.

Given its significance, analysts often align the chosen perpetual growth rate with the long-run projections for global or domestic Gross Domestic Product (GDP) growth. For instance, the Federal Reserve's Summary of Economic Projections provides insights into policymakers' assessments of the longer-run growth rate of real GDP for the United States, which often falls within a narrow band (e.g., 1.7%–2.0% as a central tendency for the longer run). Su⁷ch macroeconomic forecasts provide a realistic ceiling for a company's sustainable long-term growth.

Limitations and Criticisms

While widely used, the perpetual growth rate faces significant limitations and criticisms in financial analysis. The most prominent critique is the inherent assumption that a company can grow at a constant rate forever. In reality, very few, if any, businesses can sustain a steady growth trajectory indefinitely due to market saturation, competition, technological disruption, and economic cycles. As the U.S. Securities and Exchange Commission (SEC) has noted regarding financial projections, such forward-looking statements "should not be relied upon as being necessarily indicative of future results, and readers of this prospectus/consent solicitation are cautioned not to place undue reliance on the prospective financial information" due to the "unpredictability of the underlying assumptions and estimates."

An⁶other major drawback is the extreme sensitivity analysis of the terminal value to small changes in the perpetual growth rate. Even a slight increase or decrease in the assumed rate can lead to a disproportionately large change in the calculated terminal value, which often constitutes a substantial portion (sometimes over 50%) of the total valuation. Th⁵is sensitivity means that the perpetual growth rate can become a "plug" figure to achieve a desired valuation, rather than a truly objective estimate.

C⁴ritics also point out the difficulty in accurately forecasting a realistic perpetual growth rate, especially for younger firms or industries undergoing rapid change. Th³e uncertainty of projecting cash flows and growth rates far into the future makes the perpetuity growth rate inherently uncertain. Th²erefore, many analysts supplement DCF models with other valuation methods, such as multiples-based approaches, to provide a more balanced view.

Perpetual Growth Rate vs. Terminal Value

The terms "perpetual growth rate" and "terminal value" are closely related within valuation, but they refer to distinct concepts. The perpetual growth rate is an assumption or input into a valuation model. It is the specific percentage rate at which a company's cash flows or dividends are assumed to grow constantly into the infinite future. It reflects the sustainable long-term growth capacity of a business.

In contrast, terminal value is the output of a calculation. It represents the present value of all future cash flows of a business beyond an explicit forecast period (typically 5-10 years). The perpetual growth rate is a crucial component in calculating this terminal value, as it provides the basis for projecting those indefinite future cash flows. Essentially, the perpetual growth rate is the engine that drives the terminal value calculation, estimating the value of a company's operations that are expected to continue forever at a stable growth rate.

FAQs

What is a reasonable perpetual growth rate to use?

A reasonable perpetual growth rate is typically between 0% and 3%, and generally should not exceed the expected long-run nominal Gross Domestic Product (GDP) growth rate of the economy in which the company operates. It should reflect a sustainable long-term growth rate for a mature company. Higher rates imply unrealistic indefinite expansion beyond macroeconomic growth.

#¹## Why is the perpetual growth rate important in valuation?
The perpetual growth rate is crucial because it allows analysts to calculate the terminal value of a business. In discounted cash flow (DCF) models, the terminal value often accounts for a significant portion of a company's total valuation, as it captures the value generated by the business beyond a typical 5-10 year explicit forecast period. Without it, valuing a company with an indefinite lifespan would be incomplete.

Can the perpetual growth rate be negative?

Theoretically, a perpetual growth rate could be negative, implying a company is expected to shrink indefinitely. However, in most practical valuation scenarios for a "going concern" (a business expected to continue operating), a negative perpetual growth rate is rarely used because it would eventually lead to zero or negative value, suggesting the business would cease to exist. A negative rate might be considered for distressed assets or companies in permanent decline.

How does the perpetual growth rate relate to inflation?

The perpetual growth rate should ideally not exceed the long-term inflation rate plus the long-term real growth rate of the economy. If a company's cash flows grow faster than inflation indefinitely, their real purchasing power would continuously increase, which is unsustainable for a single entity relative to the overall economy. Therefore, the perpetual growth rate is often benchmarked against the expected long-term inflation rate.